LSDRaster.cpp

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// LSDRaster
// Land Surface Dynamics Raster
//
// An object within the University
//  of Edinburgh Land Surface Dynamics group topographic toolbox
//  for manipulating
//  and analysing raster data, with a particular focus on topography
//
// Developed by:
//  Simon M. Mudd
//  Martin D. Hurst
//  David T. Milodowski
//  Stuart W.D. Grieve
//  Declan A. Valters
//  Fiona Clubb
//
// Copyright (C) 2013 Simon M. Mudd 2013
//
// Developer can be contacted by simon.m.mudd _at_ ed.ac.uk
//
//    Simon Mudd
//    University of Edinburgh
//    School of GeoSciences
//    Drummond Street
//    Edinburgh, EH8 9XP
//    Scotland
//    United Kingdom
//
// This program is free software;
// you can redistribute it and/or modify it under the terms of the
// GNU General Public License as published by the Free Software Foundation;
// either version 2 of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY;
// without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
// See the GNU General Public License for more details.
//
// You should have received a copy of the
// GNU General Public License along with this program;
// if not, write to:
// Free Software Foundation, Inc.,
// 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301
// USA
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// LSDRaster.cpp
// cpp file for the LSDRaster object
// LSD stands for Land Surface Dynamics
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This object is written by
// Simon M. Mudd, University of Edinburgh
// David T. Milodowski, University of Edinburgh
// Martin D. Hurst, British Geological Survey
// Fiona Clubb, University of Edinburgh
// Stuart Grieve, University of Edinburgh
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Version 1.0.0    16/07/2013
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// change log
// MASSIVE MERGE: Starting version 1.0.0 on 15/07/2013
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//-----------------------------------------------------------------
//DOCUMENTATION URL: http://www.geos.ed.ac.uk/~s0675405/LSD_Docs/
//-----------------------------------------------------------------



#ifndef LSDRaster_CPP
#define LSDRaster_CPP

#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <limits>
#include <string>
#include <queue>
#include <algorithm>
#include <map>
#include <math.h>
#include <string.h>
#include <omp.h>
#include <ctime>
#include <sys/stat.h>
#include <stdint.h>
#include "TNT/tnt.h"
#include "TNT/jama_lu.h"
#include "TNT/jama_eig.h"
#include "LSDRaster.hpp"
#include "LSDStatsTools.hpp"
#include "LSDIndexRaster.hpp"
#include "LSDShapeTools.hpp"
using namespace std;
using namespace TNT;
using namespace JAMA;

#ifdef _WIN32
#ifndef M_PI
double M_PI = 3.14159265358979323846;
#endif
#endif
// Sorting compiling problems with MSVC
// #ifdef _WIN32
// #ifndef(M_PI)
// extern double M_PI;
// #endif
// #endif


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// operators
// SMM, 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster& LSDRaster::operator=(const LSDRaster& rhs)
 {
  if (&rhs != this)
   {
    create(rhs.get_NRows(),rhs.get_NCols(),rhs.get_XMinimum(),rhs.get_YMinimum(),
           rhs.get_DataResolution(),rhs.get_NoDataValue(),rhs.get_RasterData(),
           rhs.get_GeoReferencingStrings());
   }
  return *this;
 }

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// the create function. This is default and throws an error
// SMM 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::create()
{
  //cout << "LSDRaster line 64 Warning you have an empty LSDRaster!" << endl;
  //exit(EXIT_FAILURE);
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this creates a raster using an infile
// SMM 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::create(string filename, string extension)
{
  read_raster(filename,extension);
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this creates a raster filled with no data values
// SMM 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::create(int nrows, int ncols, float xmin, float ymin,
            float cellsize, float ndv, Array2D<float> data)
{
  NRows = nrows;
  NCols = ncols;
  XMinimum = xmin;
  YMinimum = ymin;
  DataResolution = cellsize;
  NoDataValue = ndv;

  RasterData = data.copy();

  if (RasterData.dim1() != NRows)
  {
    cout << "LSDRaster line 89 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }
  if (RasterData.dim2() != NCols)
  {
    cout << "LSDRaster line 94 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this overloaded function creates a raster filled with no data values,
// but the data type is double-precision floating point numbers
// DAV 2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::create(int nrows, int ncols, double xmin, double ymin,
            double cellsize, int ndv, Array2D<double> data)
{
  NRows = nrows;
  NCols = ncols;
  XMinimum = xmin;
  YMinimum = ymin;
  DataResolution = cellsize;   // Implcitly converting double to float?
  NoDataValue = ndv;     // Converting double to int??!

  // Using the <double> data member
  RasterData_dbl = data.copy();

  if (RasterData_dbl.dim1() != NRows)
  {
    cout << "LSDRaster line 89 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }
  if (RasterData_dbl.dim2() != NCols)
  {
    cout << "LSDRaster line 94 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Like the above function, but copies the GeoReferencing
// SMM 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::create(int nrows, int ncols, float xmin, float ymin,
           float cellsize, float ndv, Array2D<float> data, map<string,string> temp_GRS)
{

  //cout << "Hey I am making a new raster using some data you gave me!" << endl;

  NRows = nrows;
  NCols = ncols;
  XMinimum = xmin;
  YMinimum = ymin;
  DataResolution = cellsize;
  NoDataValue = ndv;

  //cout << "Now for the georeferencing strings" << endl;
  GeoReferencingStrings = temp_GRS;
  //cout << "Got them! " << endl;

  //cout << "Set params" << endl;

  RasterData = data.copy();

  //cout << "Set data" << endl;

  if (RasterData.dim1() != NRows)
  {
    cout << "LSDRaster line 89 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }
  if (RasterData.dim2() != NCols)
  {
    cout << "LSDRaster line 94 dimension of data is not the same as stated in NRows!" << endl;
    exit(EXIT_FAILURE);
  }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Creates an LSDRaster from an LSDIndexRaster
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::create(LSDIndexRaster& IntLSDRaster)
{
  NRows = IntLSDRaster.get_NRows();
  NCols = IntLSDRaster.get_NCols();
  XMinimum = IntLSDRaster.get_XMinimum();
  YMinimum = IntLSDRaster.get_YMinimum();
  DataResolution = IntLSDRaster.get_DataResolution();
  NoDataValue = IntLSDRaster.get_NoDataValue();
  GeoReferencingStrings = IntLSDRaster.get_GeoReferencingStrings();
  Array2D<int> RasterDataInt = IntLSDRaster.get_RasterData();
  vector<int> list_unique_values;

  //Declarations
  Array2D<int> RasterDataFloat(NRows,NCols,NoDataValue);

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      RasterDataFloat[i][j] = float(RasterDataInt[i][j]);
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function reads a DEM
// One has to provide both the filename and the extension
// the '.' between the filename and extension is not included
// for example, if the full filename is test.asc
// then
// filename = "test"
// and
// ext = "asc"
// The full filename could also be "test.01.asc"
// so filename would be "test.01"
// and ext would again be "asc"
//
// SMM 2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::read_raster(string filename, string extension)
{
  string string_filename;
  string dot = ".";
  string_filename = filename+dot+extension;
  //cout << "\n\nLoading an LSDRaster, the filename is " << string_filename << endl;

  // First get the size of the file
  int rc = get_file_size(string_filename);
  //cout << "The size of the file is: " << rc << endl;


  if (extension == "asc")
  {
    // open the data file
    ifstream data_in(string_filename.c_str());

    if( data_in.fail() )
    {
      cout << "\nFATAL ERROR: the data file \"" << string_filename
          << "\" doesn't exist" << std::endl;
      exit(EXIT_FAILURE);
    }

    //Read in raster data
    string str;      // a temporary string for discarding text

    // read the georeferencing data and metadata
    data_in >> str >> NCols;
    //cout << "NCols: " << NCols << " str: " << endl;
    data_in >> str >> NRows;
    //cout << "NRows: " << NRows << " str: " << endl;
    data_in >> str >> XMinimum >> str >> YMinimum
          >> str >> DataResolution
          >> str >> NoDataValue;

    //cout << "Loading asc file; NCols: " << NCols << " NRows: " << NRows << endl
    //     << "X minimum: " << XMinimum << " YMinimum: " << YMinimum << endl
    //     << "Data Resolution: " << DataResolution << " and No Data Value: "
    //     << NoDataValue << endl;

    // this is the array into which data is fed
    Array2D<float> data(NRows,NCols,NoDataValue);

    // read the data
    for (int i=0; i<NRows; ++i)
    {
      for (int j=0; j<NCols; ++j)
      {
        data_in >> data[i][j];
      }
    }
    data_in.close();

    // now update the objects raster data
    RasterData = data.copy();
  }
  else if (extension == "flt")
  {
    // float data (a binary format created by ArcMap) has a header file
    // this file must be opened first
    string header_filename;
    string header_extension = "hdr";
    header_filename = filename+dot+header_extension;

    ifstream ifs(header_filename.c_str());
    if( ifs.fail() )
    {
      cout << "\nFATAL ERROR: the header file \"" << header_filename
         << "\" doesn't exist" << std::endl;
      exit(EXIT_FAILURE);
    }
    else
    {
      string str;
      ifs >> str >> NCols;
      //cout << "NCols: " << NCols << " str: " << endl;
      ifs >> str >> NRows;
      //cout << "NRows: " << NRows << " str: " << endl;
      ifs >> str >> XMinimum >> str >> YMinimum
          >> str >> DataResolution
          >> str >> NoDataValue;
    }
    ifs.close();

    //cout << "Loading flt file; NCols: " << NCols << " NRows: " << NRows << endl
    //     << "X minimum: " << XMinimum << " YMinimum: " << YMinimum << endl
    //     << "Data Resolution: " << DataResolution << " and No Data Value: "
    //     << NoDataValue << endl;

    // this is the array into which data is fed
    Array2D<float> data(NRows,NCols,NoDataValue);

    // now read the DEM, using the binary stream option
    ifstream ifs_data(string_filename.c_str(), ios::in | ios::binary);
    if( ifs_data.fail() )
    {
      cout << "\nFATAL ERROR: the data file \"" << string_filename
           << "\" doesn't exist" << endl;
      exit(EXIT_FAILURE);
    }
    else
    {
      float temp;
      for (int i=0; i<NRows; ++i)
      {
        for (int j=0; j<NCols; ++j)
        {
          ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
          data[i][j] = float(temp);
        }
      }
    }
    ifs_data.close();

    // now update the objects raster data
    RasterData = data.copy();
  }
  else if (extension == "bil")
  {
    // float data (a binary format created by ArcMap) has a header file
    // this file must be opened first
    string header_filename;
    string header_extension = "hdr";
    header_filename = filename+dot+header_extension;
    int NoDataExists = 0;
    int DataType = 4;     // default is float data

    ifstream ifs(header_filename.c_str());
    if( ifs.fail() )
    {
      cout << "\nFATAL ERROR: the header file \"" << header_filename
           << "\" doesn't exist" << std::endl;
      exit(EXIT_FAILURE);
    }
    else
    {
      string str;
      ifs >> str;
      if (str != "ENVI")
      {
        cout << "\nFATAL ERROR: this is not an ENVI header file!, first line is: "
             << str << endl;
        exit(EXIT_FAILURE);
      }
      else
      {
        // the the rest of the lines
        int NChars = 5000; // need a big buffer beacause of the projection string
        char* thisline = new char[NChars]; //char thisline[NChars]; MSVC/Clang uniformisation
        vector<string> lines;
        while( ifs.getline(thisline, NChars) )
        {
          lines.push_back(thisline);
        }
        //cout << "Number of lines is: " << lines.size() << endl;
        //for(int i = 0; i< int(lines.size()); i++)
        //{
        //  cout << "Line["<<i<<"]: " << lines[i] << endl;
        //}

        // now loop through and get the number of rows
        int counter = 0;
        int NLines = int(lines.size());
        int this_NRows = 0;
        size_t found;
        string str_find = "lines";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            // get the data using a stringstream
            istringstream iss(lines[counter]);
            iss >> str >> str >> str;
            this_NRows = atoi(str.c_str());
            //cout << "NRows = " << this_NRows << endl;
            NRows = this_NRows;

            // advance to the end so you move on to the new loop
            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }

        // get the number of columns
        counter = 0;
        int this_NCols = 0;
        str_find = "samples";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            // get the data using a stringstream
            istringstream iss(lines[counter]);
            iss >> str >> str >> str;
            this_NCols = atoi(str.c_str());
            //cout << "NCols = " << this_NCols << endl;
            NCols = this_NCols;

            // advance to the end so you move on to the new loop
            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }

        // get data ignore value
        counter = 0;
        float this_NoDataValue = 0;
        str_find = "data ignore value";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            // get the data using a stringstream
            istringstream iss(lines[counter]);
            iss >> str >> str >> str >> str >> str;
            this_NoDataValue = atoi(str.c_str());
            //cout << "NCols = " << this_NCols << endl;
            NoDataValue = this_NoDataValue;

            NoDataExists = 1;   // set this to true

            // advance to the end so you move on to the new loop
            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }

        // get data type
        counter = 0;
        str_find = "data type";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            // get the data using a stringstream
            istringstream iss(lines[counter]);
            iss >> str >> str >> str >> str >> str;
            DataType = atoi(str.c_str());
            //cout << "Data Type = " << DataType << endl;

            // advance to the end so you move on to the new loop
            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }

        // get the map info
        counter = 0;
        string this_map_info = "empty";
        str_find = "map info";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            //cout << "Found map info on line " << counter << '\n';

            // now split the line
            size_t start_pos;
            size_t end_pos;
            string open_curly_bracket = "{";
            string closed_curly_bracket = "}";
            start_pos = lines[counter].find(open_curly_bracket);
            end_pos = lines[counter].find(closed_curly_bracket);
            //cout << "startpos: " << start_pos << " and end pos: " << end_pos << endl;
            string info_str = lines[counter].substr(start_pos+1, end_pos-start_pos-1);
            //cout << "\nThe map info string is:\n" << info_str << endl;
            string mi_key = "ENVI_map_info";
            GeoReferencingStrings[mi_key] = info_str;

            // now parse the string
            vector<string> mapinfo_strings;
            istringstream iss(info_str);
            while( iss.good() )
            {
              string substr;
              getline( iss, substr, ',' );
              mapinfo_strings.push_back( substr );
            }
            XMinimum = atof(mapinfo_strings[3].c_str());
            float YMax = atof(mapinfo_strings[4].c_str());

            DataResolution = atof(mapinfo_strings[5].c_str());

            // get Y minimum
            // IMPORTANT THIS USES CONVENTION THAT THE MINIMUM AND MAXIMUM VALUES
            // ARE AT THE PIXEL EDGES AS IN QGIS!!!
            YMinimum = YMax - (NRows)*DataResolution;

            //using a string comparison as float(X) != float(X) in many cases due to floating point math
            // http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm  - SWDG
            if (mapinfo_strings[5] != mapinfo_strings[6])
            {
              cout << "Warning! Loading ENVI DEM, but X and Y data spacing are different!" << endl;
            }

            //cout << "Xmin: " << XMinimum << " YMin: " << YMinimum << " spacing: "
            //     << DataResolution << endl;

            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }

        // get the projection string
        counter = 0;
        string this_coordinate_system_string = "empty";
        str_find = "coordinate system string";
        while (counter < NLines)
        {
          found = lines[counter].find(str_find);
          if (found!=string::npos)
          {
            //cout << "Found coordinate system string on line " << counter << '\n';

            // now split the line
            size_t start_pos;
            size_t end_pos;
            string open_curly_bracket = "{";
            string closed_curly_bracket = "}";
            start_pos = lines[counter].find(open_curly_bracket);
            end_pos = lines[counter].find(closed_curly_bracket);
            //cout << "startpos: " << start_pos << " and end pos: " << end_pos << endl;
            string csys_str = lines[counter].substr(start_pos+1, end_pos-start_pos-1);
            //cout << "\nThe coordinate system string is:\n" << csys_str << endl;
            string cs_key = "ENVI_coordinate_system";
            GeoReferencingStrings[cs_key] = csys_str;
            counter = lines.size();
          }
          else
          {
            counter++;
          }
        }
      }
    }
    ifs.close();

    // this is the array into which data is fed
    if (NoDataExists == 0)
    {
      NoDataValue = -9999;
    }
    //bool set_NDV = false;
    Array2D<float> data(NRows,NCols,NoDataValue);

    // now read the DEM, using the binary stream option
    ifstream ifs_data(string_filename.c_str(), ios::in | ios::binary);
    if( ifs_data.fail() )
    {
      cout << "\nFATAL ERROR: the data file \"" << string_filename
           << "\" doesn't exist" << endl;
      exit(EXIT_FAILURE);
    }
    else
    {
      if (DataType == 2)
      {
        cout << "Loading raster, recasting data from int to float!" << endl;
        short int temp;
        cout << "Integer size: " << sizeof(temp) << endl;
        for (int i=0; i<NRows; ++i)
        {
          for (int j=0; j<NCols; ++j)
          {
            ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
            //cout << temp << " ";
            data[i][j] = float(temp);
            if (data[i][j]<-1e10)
            {
              data[i][j] = NoDataValue;
            }
          }
          //cout << endl;
        }
      }
      else if (DataType == 4)
      {
        float temp;
        //cout << "Float size: " << sizeof(temp) << endl;
        for (int i=0; i<NRows; ++i)
        {
          for (int j=0; j<NCols; ++j)
          {
            ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));

            data[i][j] = float(temp);
            if (data[i][j]<-1e10)
            {
              data[i][j] = NoDataValue;
            }
          }
        }
      }
      else if (DataType == 5)
      {
        double temp;
        cout << "I am trying to load a double precision raster. Wish me luck!" << endl;
        for (int i=0; i<NRows; ++i)
        {
          for (int j=0; j<NCols; ++j)
          {
            ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));

            data[i][j] = double(temp);
            if (data[i][j]<-1e10)
            {
              data[i][j] = NoDataValue;
            }
          }
        }
      }
      else if (DataType == 13)
      {
        unsigned long int temp;
        cout << "size unsigned long int: " << sizeof(temp) << endl;

        float temp2;
        cout << "size float: " << sizeof(temp2) << endl;

        int temp3;
        cout << "size int: " << sizeof(temp3) << endl;

        // figure out the size of the file
        cout << "the size of the file is: " << rc << endl;

        int data_size = int(sizeof(temp));

        // see if this matches the dimensions of the DEM
        if (NRows*NCols*int(sizeof(temp)) != rc)
        {
          cout << "Something is funny here, I expect a file size of: "
               << NRows*NCols*int(data_size) << endl;
          cout << "changing to the right data size: ";
          data_size = rc/(NRows*NCols);
          cout << data_size << endl;
        }

        //data_size= 8;

        for (int i=0; i<NRows; ++i)
        {
          for (int j=0; j<NCols; ++j)
          {
            ifs_data.read(reinterpret_cast<char*>(&temp3), data_size);

            //if (i%250 == 0 && j%250 == 0)
            //{
            //  cout << "["<<i<<"]["<<j<<"]: " << temp3 << " recast: " << float(temp3) << endl;
            //}

            data[i][j] = float(temp3);

            if (data[i][j]<-1e10)
            {
              data[i][j] = NoDataValue;
            }
          }
        }
      }
      else
      {
        cout << "WARNING loading ENVI raster with unusual data type. " << endl
             << "If you get a crazy DEM go to LINE 625 of LSDRaster.cpp to debug" << endl;

        int DataSize = rc/(NRows*NCols);

        float temp;   // might need to change this
        //cout << "Float size: " << sizeof(temp) << endl;
        for (int i=0; i<NRows; ++i)
        {
          for (int j=0; j<NCols; ++j)
          {


            // Use data type to control the bytes being read for each entry
            ifs_data.read(reinterpret_cast<char*>(&temp), DataSize);

            data[i][j] = float(temp);
            if (data[i][j]<-1e10)
            {
              data[i][j] = NoDataValue;
            }
          }
        }
      }
    }
    ifs_data.close();

    //cout << "Loading ENVI bil file; NCols: " << NCols << " NRows: " << NRows << endl
    //   << "X minimum: " << XMinimum << " YMinimum: " << YMinimum << endl
    //     << "Data Resolution: " << DataResolution << " and No Data Value: "
    //     << NoDataValue << endl;

    // now update the objects raster data
    RasterData = data.copy();
  }
  else
  {
    cout << "You did not enter and appropriate extension!" << endl
          << "You entered: " << extension << " options are .flt, .asc and .bil" << endl;
    exit(EXIT_FAILURE);
  }


}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


// Generic function for reading rasters in ascii format
// This is used by the LSDCatchmentModel.
void LSDRaster::read_ascii_raster(string FILENAME)
//TNT::Array2D<double> LSDRaster::read_ascii_raster(string FILENAME)
{
  //string string_filename;
  //string dot = ".";
  //string_filename = filename+dot+extension;
  std::cout << "\n\nLoading DEM, the filename is " << FILENAME << std::endl;

  // open the data file
  std::ifstream data_in(FILENAME.c_str());

  if( data_in.fail() )
  {
    cout << "\nFATAL ERROR: the data file \"" << FILENAME
        << "\" doesn't exist" << std::endl;
    exit(EXIT_FAILURE);
  }

  //Read in raster data
  std::string str;      // a temporary string for discarding text

  // read the georeferencing data and metadata
  data_in >> str >> NCols;
  std::cout << "NCols: " << NCols << " str: " << std::endl;
  data_in >> str >> NRows;
  std::cout << "NRows: " << NRows << " str: " << std::endl;
  data_in >> str >> XMinimum
          >> str >> YMinimum
          >> str >> DataResolution
          >> str >> NoDataValue;

  std::cout << "Loading asc file; NCols: " << NCols
            << " NRows: " << NRows << std::endl
            << "X minimum: " << XMinimum << " YMinimum: " << YMinimum << std::endl
            << "Data Resolution: " << DataResolution << " and No Data Value: "
            << NoDataValue << std::endl;

  // this is the array into which data is fed
  TNT::Array2D<double> asciidata(NRows,NCols,NoDataValue);

  // read the data
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      data_in >> asciidata[i][j];
    }
  }
  data_in.close();
  RasterData_dbl = asciidata.copy();
  //RasterData_dbl = asciidata.copy();

  // now update the objects raster data
  //RasterData = data.copy();
  //return RasterData_dbl;
}

void LSDRaster::read_ascii_raster_integers(string FILENAME)
{
  // eugh...duplicated code...quick fix
  std::cout << "\n\nLoading DEM, the filename is " << FILENAME << std::endl;

  // open the data file
  std::ifstream data_in(FILENAME.c_str());

  if( data_in.fail() )
  {
    cout << "\nFATAL ERROR: the data file \"" << FILENAME
        << "\" doesn't exist" << std::endl;
    exit(EXIT_FAILURE);
  }

  //Read in raster data
  std::string str;      // a temporary string for discarding text

  // read the georeferencing data and metadata
  data_in >> str >> NCols;
  std::cout << "NCols: " << NCols << " str: " << std::endl;
  data_in >> str >> NRows;
  std::cout << "NRows: " << NRows << " str: " << std::endl;
  data_in >> str >> XMinimum
          >> str >> YMinimum
          >> str >> DataResolution
          >> str >> NoDataValue;

  std::cout << "Loading asc file; NCols: " << NCols
            << " NRows: " << NRows << std::endl
            << "X minimum: " << XMinimum << " YMinimum: " << YMinimum << std::endl
            << "Data Resolution: " << DataResolution << " and No Data Value: "
            << NoDataValue << std::endl;

  // this is the array into which data is fed
  TNT::Array2D<int> asciidata(NRows,NCols,NoDataValue);

  // read the data
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      data_in >> asciidata[i][j];
    }
  }
  data_in.close();
  RasterData_int = asciidata.copy();
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// write_raster
// this function writes a raster. One has to give the filename and extension
// currently the options are for .asc and .flt files
//
// SMM 2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::write_raster(string filename, string extension)
{
  string string_filename;
  string dot = ".";
  string_filename = filename+dot+extension;
  cout << "The filename is " << string_filename << endl;

  // this first bit of logic is for the asc file.
  if (extension == "asc")
  {
    // open the data file
    ofstream data_out(string_filename.c_str());

    if( data_out.fail() )
    {
      cout << "\nFATAL ERROR: unable to write to " << string_filename << endl;
      exit(EXIT_FAILURE);
    }

    data_out <<  "ncols\t" << NCols
       << "\nnrows\t" << NRows
       << "\nxllcorner\t" << setprecision(14) << XMinimum
       << "\nyllcorner\t" << setprecision(14) << YMinimum
       << "\ncellsize\t" << DataResolution
       << "\nNODATA_value\t" << NoDataValue << endl;


    for (int i=0; i<NRows; ++i)
    {
      for (int j=0; j<NCols; ++j)
      {
        data_out << setprecision(6) << RasterData[i][j] << " ";
      }
      if (i != NRows-1) data_out << endl;
    }
    data_out.close();

  }
  else if (extension == "flt")
  {
    // float data (a binary format created by ArcMap) has a header file
    // this file must be opened first
    string header_filename;
    string header_extension = "hdr";
    header_filename = filename+dot+header_extension;

    ofstream header_ofs(header_filename.c_str());
    string str;
    header_ofs <<  "ncols         " << NCols
      << "\nnrows         " << NRows
      << "\nxllcorner     " << setprecision(14) << XMinimum
      << "\nyllcorner     " << setprecision(14) << YMinimum
      << "\ncellsize      " << DataResolution
      << "\nNODATA_value  " << NoDataValue
      << "\nbyteorder     LSBFIRST" << endl;
    header_ofs.close();

    // now do the main data
    ofstream data_ofs(string_filename.c_str(), ios::out | ios::binary);
    float temp;
    for (int i=0; i<NRows; ++i)
    {
      for (int j=0; j<NCols; ++j)
      {
        temp = float(RasterData[i][j]);
        data_ofs.write(reinterpret_cast<char *>(&temp),sizeof(temp));
      }
    }
    data_ofs.close();
  }
  else if (extension == "bil")
  {
    // float data (a binary format created by ArcMap) has a header file
    // this file must be opened first
    string header_filename;
    string header_extension = "hdr";
    header_filename = filename+dot+header_extension;

    // you need to strip the filename
    string frontslash = "/";
    size_t found = string_filename.find_last_of(frontslash);
    //cout << "Found is: " << found << endl;

    int length = int(string_filename.length());
    string this_fname = string_filename.substr(found+1,length-found-1);
    //cout << "fname is: " << this_fname << endl;

    ofstream header_ofs(header_filename.c_str());
    string str;
    header_ofs <<  "ENVI" << endl;
    header_ofs << "description = {" << endl << this_fname << "}" << endl;
    header_ofs <<  "samples = " << NCols << endl;
    header_ofs <<  "lines = " << NRows << endl;
    header_ofs <<  "bands = 1" << endl;
    header_ofs <<  "header offset = 0" << endl;
    header_ofs <<  "file type = ENVI Standard" << endl;
    header_ofs <<  "data type = 4" << endl;
    header_ofs <<  "interleave = bsq" << endl;
    header_ofs <<  "byte order = 0" << endl;

    // now check to see if there are the map info and coordinate system
    map<string,string>::iterator iter;
    string cs_str_key = "ENVI_coordinate_system";
    string mi_str_key = "ENVI_map_info";

    string cs_str;
    string mi_str;
    iter = GeoReferencingStrings.find(mi_str_key);
    if (iter != GeoReferencingStrings.end() )
    {
      mi_str = (*iter).second;
      //cout << "Map info system string exists, it is: " << mi_str << endl;
      header_ofs <<  "map info = {"<<mi_str<<"}" << endl;
    }
    else
    {
      cout << "Warning, writing ENVI file but no map info string" << endl;
    }
    iter = GeoReferencingStrings.find(cs_str_key);
    if (iter != GeoReferencingStrings.end() )
    {
      cs_str = (*iter).second;
      //cout << "Coord, system string exists, it is: " << cs_str << endl;
      header_ofs <<  "coordinate system string = {"<<cs_str<<"}" << endl;
    }
    else
    {
      cout << "Warning, writing ENVI file but no coordinate system string" << endl;
    }
    header_ofs <<  "data ignore value = " << NoDataValue << endl;

    header_ofs.close();

    // now do the main data
    ofstream data_ofs(string_filename.c_str(), ios::out | ios::binary);
    float temp;
    for (int i=0; i<NRows; ++i)
    {
      for (int j=0; j<NCols; ++j)
      {

        temp = float(RasterData[i][j]);
        //if (i%250 == 0 && j%250 == 0)
        //{
        //  cout << "data["<<i<<"]["<<j<<"]: " << temp << endl;
        //}


        data_ofs.write(reinterpret_cast<char *>(&temp),sizeof(temp));
      }
    }
    data_ofs.close();
  }
  else
  {
    cout << "You did not enter and approprate extension!" << endl
    << "You entered: " << extension << " options are flt, bil and asc" << endl;
    exit(EXIT_FAILURE);
   }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// write_double_raster
// this function writes a raster. One has to give the filename and extension
// currently the options are for .asc files only (Sorry!)
//
// DAV 2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::write_double_flt_raster(string filename, string string_filename)
{
  // float data (a binary format created by ArcMap) has a header file
  // this file must be opened first
  string dot = ".";
  string header_filename;
  string header_extension = "hdr";
  header_filename = filename+dot+header_extension;

  ofstream header_ofs(header_filename.c_str());
  string str;
  header_ofs <<  "ncols         " << NCols
    << "\nnrows         " << NRows
    << "\nxllcorner     " << setprecision(14) << XMinimum
    << "\nyllcorner     " << setprecision(14) << YMinimum
    << "\ncellsize      " << DataResolution
    << "\nNODATA_value  " << NoDataValue
    << "\nbyteorder     LSBFIRST" << endl;
  header_ofs.close();

  // now do the main data
  ofstream data_ofs(string_filename.c_str(), ios::out | ios::binary);
  float temp;
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      temp = double(RasterData_dbl[i][j]);
      data_ofs.write(reinterpret_cast<char *>(&temp),sizeof(temp));
    }
  }
  data_ofs.close();
}

void LSDRaster::write_double_bil_raster(string filename, string string_filename)
{
  // float data (a binary format created by ArcMap) has a header file
  // this file must be opened first
  string dot = ".";
  string header_filename;
  string header_extension = "hdr";
  header_filename = filename+dot+header_extension;

  // you need to strip the filename
  string frontslash = "/";
  size_t found = string_filename.find_last_of(frontslash);
  //cout << "Found is: " << found << endl;

  int length = int(string_filename.length());
  string this_fname = string_filename.substr(found+1,length-found-1);
  //cout << "fname is: " << this_fname << endl;

  ofstream header_ofs(header_filename.c_str());
  string str;
  header_ofs <<  "ENVI" << endl;
  header_ofs << "description = {" << endl << this_fname << "}" << endl;
  header_ofs <<  "samples = " << NCols << endl;
  header_ofs <<  "lines = " << NRows << endl;
  header_ofs <<  "bands = 1" << endl;
  header_ofs <<  "header offset = 0" << endl;
  header_ofs <<  "file type = ENVI Standard" << endl;
  header_ofs <<  "data type = 4" << endl;
  header_ofs <<  "interleave = bsq" << endl;
  header_ofs <<  "byte order = 0" << endl;

  // now check to see if there are the map info and coordinate system
  map<string,string>::iterator iter;
  string cs_str_key = "ENVI_coordinate_system";
  string mi_str_key = "ENVI_map_info";

  string cs_str;
  string mi_str;
  iter = GeoReferencingStrings.find(mi_str_key);
  if (iter != GeoReferencingStrings.end() )
  {
    mi_str = (*iter).second;
    //cout << "Map info system string exists, it is: " << mi_str << endl;
    header_ofs <<  "map info = {"<<mi_str<<"}" << endl;
  }
  else
  {
    cout << "Warning, writing ENVI file but no map info string" << endl;
  }
  iter = GeoReferencingStrings.find(cs_str_key);
  if (iter != GeoReferencingStrings.end() )
  {
    cs_str = (*iter).second;
    //cout << "Coord, system string exists, it is: " << cs_str << endl;
    header_ofs <<  "coordinate system string = {"<<cs_str<<"}" << endl;
  }
  else
  {
    cout << "Warning, writing ENVI file but no coordinate system string" << endl;
  }
  header_ofs <<  "data ignore value = " << NoDataValue << endl;

  header_ofs.close();

  // now do the main data
  ofstream data_ofs(string_filename.c_str(), ios::out | ios::binary);
  float temp;
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {

      temp = double(RasterData_dbl[i][j]);

      data_ofs.write(reinterpret_cast<char *>(&temp),sizeof(temp));
    }
  }
  data_ofs.close();
}


void LSDRaster::write_double_asc_raster(string string_filename)
{
  ofstream data_out(string_filename.c_str());

  if( data_out.fail() )
  {
    cout << "\nFATAL ERROR: unable to write to " << string_filename << endl;
    exit(EXIT_FAILURE);
  }

  data_out <<  "ncols\t" << NCols
     << "\nnrows\t" << NRows
     << "\nxllcorner\t" << setprecision(14) << XMinimum
     << "\nyllcorner\t" << setprecision(14) << YMinimum
     << "\ncellsize\t" << DataResolution
     << "\nNODATA_value\t" << NoDataValue << endl;


  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      data_out << setprecision(6) << RasterData_dbl[i][j] << " ";
    }
    if (i != NRows-1) data_out << endl;
  }
  data_out.close();
}


void LSDRaster::write_double_raster(string filename, string extension)
{
  string string_filename;
  string dot = ".";
  string_filename = filename+dot+extension;
  cout << "The filename is " << string_filename << endl;

  // this first bit of logic is for the asc file.
  if (extension == "asc")
  {
    // open the data file and write an ASC
    write_double_asc_raster(string_filename);
  }
  else if (extension == "flt")
  {
    // open the data file and write a FLT
    write_double_flt_raster(filename, string_filename);
  }
  else if (extension == "bil")
  {
    // open the data file and write a BIL
    write_double_bil_raster(filename, string_filename);
  }
  else
  {
    cout << "You did not enter an approprate extension!" << endl
    << "You entered: " << extension << " options are asc, flt, bil (bil might not work yet though...)" << endl;
    exit(EXIT_FAILURE);
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function checks to see if two rasters have the same dimesions
// It DOES NOT check georeferencingand
// Georeferencing
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
bool LSDRaster::does_raster_have_same_dimensions(LSDRaster& Compare_raster)
{

  // me check with bad grammar
  bool is_dimensions_same;

  if (NRows == Compare_raster.get_NRows() &&
      NCols == Compare_raster.get_NCols() &&
      XMinimum == Compare_raster.get_XMinimum() &&
      YMinimum == Compare_raster.get_YMinimum() &&
      DataResolution == Compare_raster.get_DataResolution() &&
      NoDataValue == Compare_raster.get_NoDataValue())
  {
    is_dimensions_same = true;
  }
  else
  {
    is_dimensions_same = false;
  }

  return is_dimensions_same;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function checks to see if two rasters have the same dimesions
// It DOES NOT check georeferencingand
// Georeferencing
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
bool LSDRaster::does_raster_have_same_dimensions(LSDIndexRaster& Compare_raster)
{

  // me check with bad grammar
  bool is_dimensions_same;

  if (NRows == Compare_raster.get_NRows() &&
      NCols == Compare_raster.get_NCols() &&
      XMinimum == Compare_raster.get_XMinimum() &&
      YMinimum == Compare_raster.get_YMinimum() &&
      DataResolution == Compare_raster.get_DataResolution() &&
      NoDataValue == Compare_raster.get_NoDataValue())
  {
    is_dimensions_same = true;
  }
  else
  {
    is_dimensions_same = false;
  }

  return is_dimensions_same;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function checks to see if two rasters have the same dimesions and
// Georeferencing
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
bool LSDRaster::does_raster_have_same_dimensions_and_georeferencing(LSDRaster& Compare_raster)
{
  map<string,string> DRS = Compare_raster.get_GeoReferencingStrings();
  string mi_str_key = "ENVI_map_info";
  string cs_str_key = "ENVI_coordinate_system";

  bool is_georef_and_dimensions_same;

  if (NRows == Compare_raster.get_NRows() &&
      NCols == Compare_raster.get_NCols() &&
      XMinimum == Compare_raster.get_XMinimum() &&
      YMinimum == Compare_raster.get_YMinimum() &&
      DataResolution == Compare_raster.get_DataResolution() &&
      NoDataValue == Compare_raster.get_NoDataValue() &&
      GeoReferencingStrings[mi_str_key] == DRS[mi_str_key] &&
      GeoReferencingStrings[cs_str_key] == DRS[cs_str_key])
  {
    is_georef_and_dimensions_same = true;
  }
  else
  {
    is_georef_and_dimensions_same = false;
  }

  return is_georef_and_dimensions_same;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function checks to see if two rasters have the same dimesions and
// Georeferencing. Uses an index raster to check
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
bool LSDRaster::does_raster_have_same_dimensions_and_georeferencing(LSDIndexRaster& Compare_raster)
{
  map<string,string> DRS = Compare_raster.get_GeoReferencingStrings();
  string mi_str_key = "ENVI_map_info";
  string cs_str_key = "ENVI_coordinate_system";

  bool is_georef_and_dimensions_same;

  if (NRows == Compare_raster.get_NRows() &&
      NCols == Compare_raster.get_NCols() &&
      XMinimum == Compare_raster.get_XMinimum() &&
      YMinimum == Compare_raster.get_YMinimum() &&
      DataResolution == Compare_raster.get_DataResolution() &&
      NoDataValue == Compare_raster.get_NoDataValue() &&
      GeoReferencingStrings[mi_str_key] == DRS[mi_str_key] &&
      GeoReferencingStrings[cs_str_key] == DRS[cs_str_key])
  {
    is_georef_and_dimensions_same = true;
  }
  else
  {
    is_georef_and_dimensions_same = false;
  }

  return is_georef_and_dimensions_same;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Method which takes a new xmin and ymax value and modifys the GeoReferencingStrings
// map_info line to contain these new values. Intended for use in the rastertrimmer
// methods and is called from within these methods.
//
// Modifying georeferencing information by hand is messy and should be avoided if
// at all possible.
//
// Returns an updated GeoReferencingStrings object
//
// SWDG 6/11/14
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
map<string, string> LSDRaster::Update_GeoReferencingStrings(float NewXmin, float NewYmax)
{

  // set up strings and iterators
  map<string,string>::iterator iter;

  //String to get the map_info out of the map
  string cs_key = "ENVI_map_info";

  //check to see if there is already a map info string
  iter = GeoReferencingStrings.find(cs_key);
  if (iter != GeoReferencingStrings.end() )
  {
    // there is a mapinfo string
    // now parse the string
    vector<string> mapinfo_strings;
    istringstream iss(GeoReferencingStrings[cs_key]);
    while( iss.good() )
    {
      string substr;
      getline( iss, substr, ',' );
      mapinfo_strings.push_back( substr );
    }

    //Construct the new string with the updated xmin ymin values
    stringstream CombineMapinfo;

    CombineMapinfo << mapinfo_strings[0] << "," << mapinfo_strings[1] << ","
       << mapinfo_strings[2] << ", " << NewXmin << ", " << NewYmax << ","
       << mapinfo_strings[5] << "," << mapinfo_strings[6] << "," << mapinfo_strings[7]
      << "," << mapinfo_strings[8] << "," << mapinfo_strings[9];

    //Store the new string in the map
    GeoReferencingStrings[cs_key] = CombineMapinfo.str();

  }


  return GeoReferencingStrings;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Similar to above, but in this case the function uses data stored within
// the data members of the raster
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::Update_GeoReferencingStrings()
{


  float YMax =  YMinimum + NRows*DataResolution;
  cout << "YMax is: " << YMax << endl;

  // set up strings and iterators
  map<string,string>::iterator iter;
  string mi_str_key = "ENVI_map_info";

  string info_str;

  //check to see if there is already a map info string
  iter = GeoReferencingStrings.find(mi_str_key);
  if (iter != GeoReferencingStrings.end() )
  {
    // there is a mapinfo string
    info_str = GeoReferencingStrings[mi_str_key];

    // now parse the string
    vector<string> mapinfo_strings;
    istringstream iss(info_str);
    while( iss.good() )
    {
      string substr;
      getline( iss, substr, ',' );
      mapinfo_strings.push_back( substr );
    }

    cout << "The number of strings is: " <<  mapinfo_strings.size() << endl;

    //Construct the new string with the updated xmin ymin values
    stringstream CombineMapinfo;

    CombineMapinfo << mapinfo_strings[0] << "," << mapinfo_strings[1] << ","
       << mapinfo_strings[2] << ", " << XMinimum << ", " << YMax << ","
       << DataResolution << "," << DataResolution;
    for(int i = 7; i< int(mapinfo_strings.size()); i++)
    {
      CombineMapinfo << "," << mapinfo_strings[i];
    }

    //Store the new string in the map
    GeoReferencingStrings[mi_str_key] = CombineMapinfo.str();


    cout << "New string is: " << endl << GeoReferencingStrings[mi_str_key] << endl;
  }
  else
  {
    cout << "Missing the ENVI_map_info key" << endl;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function imposes the mapinfo strings. It assumes UTM
// THIS HAS NOT BEEN TESTED!!!!!!!!!!!!
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::impose_georeferencing_UTM(int zone, string NorS)
{
  string str_NorS;
  string str_NorSlong;
  string cs_string_fnbit;
  if (NorS.find("N") == 0 || NorS.find("n") == 0)
  {
    str_NorS = "N";
    str_NorSlong = "North";
    cs_string_fnbit = "0";
  }
  else if (NorS.find("S") == 0 || NorS.find("s") == 0)
  {
    str_NorS = "S";
    str_NorSlong = "South";
    cs_string_fnbit = "10000000";
  }
  else
  {
    cout << "imposing georeferencing, but I didn't understand N or S, defaulting to North." << endl;
    str_NorS = "N";
    str_NorSlong = "North";
    cs_string_fnbit = "0";
  }

  string delim = ", ";
  string str_UTM = "UTM";
  string str_x  = "1";
  string str_y = "1";
  string xmin = dtoa(XMinimum);
  float YMax =  YMinimum + NRows*DataResolution;
  string ymax = dtoa(YMax);

  string DR = dtoa(DataResolution);
  string str_UTMZ = itoa(zone);
  string str_hemis = str_NorSlong;
  string str_spheroid = "WGS-84";

  string new_string = str_UTM+delim+str_x+delim+str_y+delim+xmin+delim
                       +ymax+delim+DR+delim+DR+delim+str_UTMZ+delim+str_hemis
                       +delim+str_spheroid;
  GeoReferencingStrings["ENVI_map_info"]= new_string;

  string cs_string_firstbit = "PROJCS[\"WGS_1984_UTM_Zone_";
  string cs_string_secondbit = str_UTMZ+str_NorS;
  string cs_string_thirdbit =  "\",GEOGCS[\"GCS_WGS_1984\",DATUM[\"D_WGS_1984\",SPHEROID[\"WGS_1984\",6378137,298.257223563]],PRIMEM[\"Greenwich\",0],UNIT[\"Degree\",0.017453292519943295]],PROJECTION[\"Transverse_Mercator\"],PARAMETER[\"latitude_of_origin\",0],PARAMETER[\"central_meridian\",";
  string cs_string_fifthbit = "],PARAMETER[\"scale_factor\",0.9996],PARAMETER[\"false_easting\",500000],PARAMETER[\"false_northing\",";
  string cs_string_seventhbit = "],UNIT[\"Meter\",1]]";

  int central_meridian = Find_UTM_central_meridian(zone);
  string cs_string_central_merid = itoa(central_meridian);


  string cs_str = cs_string_firstbit+cs_string_secondbit+cs_string_thirdbit
                 +cs_string_central_merid+cs_string_fifthbit+cs_string_fnbit
                 +cs_string_seventhbit;

  GeoReferencingStrings["ENVI_coordinate_system"]= cs_str;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function returns the x and y location of a row and column
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_x_and_y_locations(int row, int col, double& x_loc, double& y_loc)
{

  x_loc = XMinimum + float(col)*DataResolution + 0.5*DataResolution;

  // Slightly different logic for y because the DEM starts from the top corner
  y_loc = YMinimum + float(NRows-row)*DataResolution - 0.5*DataResolution;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function returns the x and y location of a row and column
// Same as above but with floats
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_x_and_y_locations(int row, int col, float& x_loc, float& y_loc)
{

  x_loc = XMinimum + float(col)*DataResolution + 0.5*DataResolution;

  // Slightly different logic for y because the DEM starts from the top corner
  y_loc = YMinimum + float(NRows-row)*DataResolution - 0.5*DataResolution;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Function to convert a node position with a row and column to a lat
// and long coordinate
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_lat_and_long_locations(int row, int col, double& lat,
                   double& longitude, LSDCoordinateConverterLLandUTM Converter)
{
  // get the x and y locations of the node
  double x_loc,y_loc;
  get_x_and_y_locations(row, col, x_loc, y_loc);

  // get the UTM zone of the node
  int UTM_zone;
  bool is_North;
  get_UTM_information(UTM_zone, is_North);
  //cout << endl << endl << "Line 1034, UTM zone is: " << UTM_zone << endl;


  if(UTM_zone == NoDataValue)
  {
    lat = NoDataValue;
    longitude = NoDataValue;
  }
  else
  {
    // set the default ellipsoid to WGS84
    int eId = 22;

    double xld = double(x_loc);
    double yld = double(y_loc);

    // use the converter to convert to lat and long
    double Lat,Long;
    Converter.UTMtoLL(eId, yld, xld, UTM_zone, is_North, Lat, Long);


    lat = Lat;
    longitude = Long;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Gets the x and y vectors (used for interpolation)
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_easting_and_northing_vectors(vector<float>& Eastings, vector<float>& Northings)
{
  vector<float> this_easting;
  vector<float> this_northing;

  for (int row = 0; row < NRows; row++)
  {
    this_northing.push_back(YMinimum + float(NRows-row)*DataResolution - 0.5*DataResolution);
  }
  for (int col = 0; col<NCols; col++)
  {
    this_easting.push_back(XMinimum + float(col)*DataResolution + 0.5*DataResolution);
  }

  Eastings = this_easting;
  Northings = this_northing;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Gets the value of a point in UTM using bilinear interpolation
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<float> LSDRaster::interpolate_points_bilinear(vector<float> UTMEvec, vector<float> UTMNvec)
{
  vector<float> Eastings;
  vector<float> Northings;
  vector<float> New_northings;
  get_easting_and_northing_vectors(Eastings, Northings);

  // we need to reverse the northing vecor
  int n_north = int(Northings.size());
  for (int i = 0; i<n_north; i++)
  {
    New_northings.push_back(Northings[NRows-1-i]);
  }

  // This is quite annoying since the number of rows in the raster is the first dimension
  // and the number of columns is the second dimension.
  // Also the raster is inverted so we need to change the direction of the x vector
  //cout << "The size of the easting is: " << Eastings.size() << " N: " << Northings.size() << endl;
  //cout << "D1: " << RasterData.dim1() << " D2: " << RasterData.dim2() << endl;

  if (RasterData.dim2() != int(Eastings.size()))
  {
    cout << "Something has gone wrong with the dimensions of the x and y data for interpolation" << endl;
    cout << "LSDRaster::interpolate_points_bilinear" << endl;
    exit(EXIT_FAILURE);
  }

  vector<float> interp_data;
  float this_data;

  int n_samples = int(UTMEvec.size());

  if(UTMEvec.size() != UTMNvec.size())
  {
    cout << "LSDRaster::interpolate_points_bilinear you x and y vecs are not the same size, prepare for segmentation." << endl;
  }


  Array2D<float> flipped(NCols,NRows);
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col< NCols; col++)
    {
      flipped[col][row] = RasterData[NRows-1-row][col];
    }
  }



  for(int i = 0; i<n_samples; i++)
  {
    //cout << "Sample is: " << i << " of " << n_samples << endl;
    //cout << "eastings: " << Eastings[0] << " " << Eastings[NRows-1] << endl;
    //cout << "Northings: " << Northings[0] << " " << Northings[NCols-1] << endl;
    //cout << "e: " << UTMEvec[i] << " n: " << UTMNvec[i] << endl;

    // this stupid ordering is due to the fact that the rows are first dimension
    // and the
    this_data = interp2D_bilinear(Eastings, New_northings, flipped,
                                  UTMEvec[i],UTMNvec[i]);
    interp_data.push_back(this_data);
  }

  return interp_data;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Uses precalculated interpolated data to fill a DEM
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::fill_with_interpolated_data(vector<int> node_rows,
                                                 vector<int> node_cols,
                                                 vector<float> interpolated_data)
{

  Array2D<float> NewArray = RasterData.copy();

  int N_nodes = int(node_rows.size());
  for(int i = 0; i<N_nodes; i++)
  {
    NewArray[node_rows[i]][node_cols[i]]= interpolated_data[i];
  }

  //create LSDRaster object
  LSDRaster NewRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, NewArray, GeoReferencingStrings);
  return NewRaster;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Gets the value of a point in UTM
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
float LSDRaster::get_value_of_point(float UTME, float UTMN)
{
  float this_value = NoDataValue;
  int row,col;

  bool is_in_raster = check_if_point_is_in_raster(UTME, UTMN);
  if (is_in_raster)
  {
    get_row_and_col_of_a_point(UTME,UTMN,row, col);
    //cout << "[R][C]: " << row << "," << col << endl;

    if (row == NoDataValue || col == NoDataValue)
    {
      this_value = NoDataValue;
    }
    else
    {
      this_value = RasterData[row][col];
    }
  }

  return this_value;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function gets the UTM zone
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_UTM_information(int& UTM_zone, bool& is_North)
{

  // set up strings and iterators
  map<string,string>::iterator iter;

  //check to see if there is already a map info string
  string mi_key = "ENVI_map_info";
  iter = GeoReferencingStrings.find(mi_key);
  if (iter != GeoReferencingStrings.end() )
  {
    string info_str = GeoReferencingStrings[mi_key] ;

    // now parse the string
    vector<string> mapinfo_strings;
    istringstream iss(info_str);
    while( iss.good() )
    {
      string substr;
      getline( iss, substr, ',' );
      mapinfo_strings.push_back( substr );
    }
    UTM_zone = atoi(mapinfo_strings[7].c_str());
    //cout << "Line 1041, UTM zone: " << UTM_zone << endl;
    //cout << "LINE 1042 LSDRaster, N or S: " << mapinfo_strings[7] << endl;

    // find if the zone is in the north
    string n_str = "n";
    string N_str = "N";
    is_North = false;
    size_t found = mapinfo_strings[8].find(N_str);
    if (found!=std::string::npos)
    {
      is_North = true;
    }
    found = mapinfo_strings[8].find(n_str);
    if (found!=std::string::npos)
    {
      is_North = true;
    }
    //cout << "is_North is: " << is_North << endl;

  }
  else
  {
    UTM_zone = NoDataValue;
    is_North = false;
  }

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This is a utility function to find the central meridian of a UTM zone
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
int LSDRaster::Find_UTM_central_meridian(int UTM_zone)
{
  // initiate the vector
  vector<int> zone(61,NoDataValue);

  // here is the lookuptable
  zone[1]=-177;
  zone[2]=-171;
  zone[3]=-165;
  zone[4]=-159;
  zone[5]=-153;
  zone[6]=-147;
  zone[7]=-141;
  zone[8]=-135;
  zone[9]=-129;
  zone[10]=-123;
  zone[11]=-117;
  zone[12]=-111;
  zone[13]=-105;
  zone[14]=-99;
  zone[15]=-93;
  zone[16]=-87;
  zone[17]=-81;
  zone[18]=-75;
  zone[19]=-69;
  zone[20]=-63;
  zone[21]=-57;
  zone[22]=-51;
  zone[23]=-45;
  zone[24]=-39;
  zone[25]=-33;
  zone[26]=-27;
  zone[27]=-21;
  zone[28]=-15;
  zone[29]=-9;
  zone[30]=-3;
  zone[31]=3;
  zone[32]=9;
  zone[33]=15;
  zone[34]=21;
  zone[35]=27;
  zone[36]=33;
  zone[37]=39;
  zone[38]=45;
  zone[39]=51;
  zone[40]=57;
  zone[41]=63;
  zone[42]=69;
  zone[43]=75;
  zone[44]=81;
  zone[45]=87;
  zone[46]=93;
  zone[47]=99;
  zone[48]=105;
  zone[49]=111;
  zone[50]=117;
  zone[51]=123;
  zone[52]=129;
  zone[53]=135;
  zone[54]=141;
  zone[55]=147;
  zone[56]=153;
  zone[57]=159;
  zone[58]=165;
  zone[59]=171;
  zone[60]=177;

  int central_meridian;

  // now look up the table
  if(UTM_zone <1 || UTM_zone > 60)
  {
    cout << "Trying to assign central meridian but you have chosen an invalid UTM zone" << endl;
    cout << "defaulting to central meridian of 0";
    central_meridian = 0;
  }
  else
  {
    central_meridian = zone[UTM_zone];
  }

  return central_meridian;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Checks to see is a point is in the raster
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
bool LSDRaster::check_if_point_is_in_raster(float X_coordinate,float Y_coordinate)
{
  bool is_in_raster = true;

  // Shift origin to that of dataset
  float X_coordinate_shifted_origin = X_coordinate - XMinimum;
  float Y_coordinate_shifted_origin = Y_coordinate - YMinimum;

  // Get row and column of point
  int col_point = int(X_coordinate_shifted_origin/DataResolution);
  int row_point = (NRows - 1) - int(round(Y_coordinate_shifted_origin/DataResolution));

  if(col_point < 0 || col_point > NCols-1 || row_point < 0 || row_point > NRows -1)
  {
    is_in_raster = false;
  }

  return is_in_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Gets the row and column of a point
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::get_row_and_col_of_a_point(float X_coordinate,float Y_coordinate,int& row, int& col)
{
  int this_row = NoDataValue;
  int this_col = NoDataValue;

  // Shift origin to that of dataset
  float X_coordinate_shifted_origin = X_coordinate - XMinimum;
  float Y_coordinate_shifted_origin = Y_coordinate - YMinimum;

  // Get row and column of point
  int col_point = int(X_coordinate_shifted_origin/DataResolution);
  int row_point = (NRows - 1) - int(round(Y_coordinate_shifted_origin/DataResolution)-0.5);

  //cout << "Getting row and col, " << row_point << " " << col_point << endl;

  if(col_point > 0 && col_point < NCols-1)
  {
    this_col = col_point;
  }
  if(row_point > 0 && row_point < NRows -1)
  {
    this_row = row_point;
  }

  row = this_row;
  col = this_col;
}

void LSDRaster::get_row_and_col_of_a_point(double X_coordinate,double Y_coordinate,int& row, int& col)
{
  int this_row = NoDataValue;
  int this_col = NoDataValue;

  // Shift origin to that of dataset
  double X_coordinate_shifted_origin = X_coordinate - XMinimum;
  double Y_coordinate_shifted_origin = Y_coordinate - YMinimum;

  // Get row and column of point
  int col_point = int(X_coordinate_shifted_origin/DataResolution);
  int row_point = (NRows - 1) - int(round(Y_coordinate_shifted_origin/DataResolution));

  //cout << "Getting row and col, " << row_point << " " << col_point << endl;

  if(col_point > 0 && col_point < NCols-1)
  {
    this_col = col_point;
  }
  if(row_point > 0 && row_point < NRows -1)
  {
    this_row = row_point;
  }

  row = this_row;
  col = this_col;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// rewrite_with_random_values
// This overwrites existing data with random values
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::rewrite_with_random_values(float range)
{
  // set a seed for the random values
  long seed = time(NULL);

  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      RasterData[row][col] = ran3(&seed)*range;
    }
  }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Create a raster of nodata values in the shape of the input
// FJC 07/04/17
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::create_raster_nodata()
{
  Array2D<float> NDV_Array(NRows,NCols,NoDataValue);
  LSDRaster NDV_Raster(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue, NDV_Array, GeoReferencingStrings);
  return NDV_Raster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Simple topographic metrics
// Several simple topographic metrics measuered over a kernal
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Calcualte relief
// This calculates relief over a window.
// Right now it can have a circular window with kernalType == 1 or square otherwise
//
// Written by JAJ 6-6-2014
// Inserted into trunk by SMM 9-6-2014
// Modified to better deal with nodata SMM 15/12/2016
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::calculate_relief(float kernelWidth, int kernelType)
{
  int kr = ((kernelWidth/DataResolution))/2-1;
  float max, min;
  Array2D <float> reliefMap(NRows, NCols, 0.0);
  if (kr < 1)
  {
    kernelWidth = 2.5;
    kr = 1;
  }

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        max = RasterData[i][j];
        min = RasterData[i][j];
        for (int sub_i = i-kr; sub_i<=i+kr; ++sub_i)
        {
          // don't exend past the end of map
          if (sub_i>=0 && sub_i<NRows)
          {
            for (int sub_j = j-kr; sub_j<=j+kr; ++sub_j)
            {
              // don't extend past end of map
              if (sub_j>=0 && sub_j<NCols)
              {
                // make sure the data exists
                if (RasterData[sub_i][sub_j] != NoDataValue)
                {
                  if (kernelType == 1)  //circular
                  {
                    if ((pow(sub_i-i,2) + pow(sub_j-j,2))*DataResolution > kernelWidth/2)
                    {
                      if (RasterData[sub_i][sub_j] > max)
                        max = RasterData[sub_i][sub_j];
                      if (RasterData[sub_i][sub_j] < min)
                        min = RasterData[sub_i][sub_j];
                    }
                  }
                  else
                  {
                    if (RasterData[sub_i][sub_j] > max)
                      max = RasterData[sub_i][sub_j];
                    if (RasterData[sub_i][sub_j] < min)
                      min = RasterData[sub_i][sub_j];
                  }
                }
              }
            }
          }
        }
        reliefMap[i][j] = max-min;
      }
      else
      {
        reliefMap[i][j] = NoDataValue;
      }
    }
  }


  return LSDRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                   NoDataValue, reliefMap, GeoReferencingStrings);
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Return the mean elevation of the raster
// JAJ, sometime in February 2014
// modified SMM to make sure division by float 9/6/2014
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
float LSDRaster::mean_elevation(void)
{
  float sum_elevation = 0;
  int n = 0;
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        sum_elevation += RasterData[i][j];
        ++n;
      }
    }
  }
  return float(sum_elevation/float(n));
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Return the maximum elevation of the raster
// JAJ, sometime in February 2014
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
float LSDRaster::max_elevation( void )
{
  float max_elevation = 0.0;
  bool found=false;
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (found==false)
      {
        if (RasterData[i][j] != NoDataValue)
        {
          max_elevation = RasterData[i][j];
          found = true;
        }
      }
      else if (RasterData[i][j] > max_elevation)
      {
        max_elevation = RasterData[i][j];
      }
    }
  }
  return max_elevation;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Return the mean relief of the raster
// JAJ, sometime in February 2014
// modified SMM to make sure division by float 9/6/2014
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
float LSDRaster::mean_relief(float kernelWidth)
{
  LSDRaster relief = calculate_relief(kernelWidth, 1);
  float relief_val, sum_relief = 0;
  int n = 0;

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      relief_val = relief.get_data_element(i, j);
      if (relief_val != NoDataValue)
      {
        sum_relief += relief_val;
        ++n;
      }
    }
  }
  return float(sum_relief/float(n));
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Return the average difference between two rasters.
// Check to see if the rasters are the correct dimension, but does not
// check georeferencing (since it is used with asc model results, mostly)
// SMM 03/04/2015
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
float LSDRaster::difference_rasters(LSDRaster& compare_raster)
{
  float total_difference = 0;
  int n = 0;
  float raster_val1, raster_val2;

  float average_difference;
  // first, compare the raster dimensions
  if(does_raster_have_same_dimensions(compare_raster))
  {
    for (int i=0; i<NRows; ++i)
    {
      for (int j=0; j<NCols; ++j)
      {
        raster_val1 = RasterData[i][j];
        raster_val2 = compare_raster.get_data_element(i, j);
        if (raster_val1 != NoDataValue && raster_val2 != NoDataValue)
        {
          total_difference += raster_val2-raster_val1;
          ++n;
        }
      }
    }
    average_difference = float(total_difference/float(n));
  }
  else
  {
    average_difference = NoDataValue;
  }

  return average_difference;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This mulitplies each pixel in a raster by a multiplier
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::raster_multiplier(float multiplier)
{
  for(int row = 0; row< NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (RasterData[row][col] != NoDataValue)
      {
        RasterData[row][col] = RasterData[row][col]*multiplier;
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Map algebra functions
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::MapAlgebra_multiply(LSDRaster& M_raster)
{
  // first check if rasters are the same size
  if( does_raster_have_same_dimensions(M_raster) )
  {
    //create an array
    Array2D<float> New_array(NRows,NCols,NoDataValue);

    for(int row = 0; row< NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {
        if (RasterData[row][col] != NoDataValue)
        {
          float this_element = M_raster.get_data_element(row,col);
          if(this_element != NoDataValue)
          {
            New_array[row][col] = RasterData[row][col]*this_element;
          }

        }
      }
    }
    //create LSDRaster object
    LSDRaster NewRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, New_array, GeoReferencingStrings);
    return NewRaster;
  }
  else
  {
    cout << "Warning, these rasters are not the same dimension!" << endl;
    return M_raster;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::MapAlgebra_divide(LSDRaster& M_raster)
{
  // first check if rasters are the same size
  if( does_raster_have_same_dimensions(M_raster) )
  {
    //create an array
    Array2D<float> New_array(NRows,NCols,NoDataValue);

    for(int row = 0; row< NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {
        if (RasterData[row][col] != NoDataValue)
        {
          float this_element = M_raster.get_data_element(row,col);
          if(this_element != NoDataValue && this_element != 0)
          {
            New_array[row][col] = RasterData[row][col]/this_element;
          }
        }
      }
    }
    //create LSDRaster object
    LSDRaster NewRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, New_array, GeoReferencingStrings);
    return NewRaster;
  }
  else
  {
    cout << "Warning, these rasters are not the same dimension!" << endl;
    return M_raster;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::MapAlgebra_add(LSDRaster& M_raster)
{
  // first check if rasters are the same size
  if( does_raster_have_same_dimensions(M_raster) )
  {
    //create an array
    Array2D<float> New_array(NRows,NCols,NoDataValue);

    for(int row = 0; row< NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {
        if (RasterData[row][col] != NoDataValue)
        {
          float this_element = M_raster.get_data_element(row,col);
          if(this_element != NoDataValue)
          {
            New_array[row][col] = RasterData[row][col]+this_element;
          }
        }
      }
    }
    //create LSDRaster object
    LSDRaster NewRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, New_array, GeoReferencingStrings);
    return NewRaster;
  }
  else
  {
    cout << "Warning, these rasters are not the same dimension!" << endl;
    return M_raster;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::MapAlgebra_subtract(LSDRaster& M_raster)
{
  // first check if rasters are the same size
  if( does_raster_have_same_dimensions(M_raster) )
  {
    //create an array
    Array2D<float> New_array(NRows,NCols,NoDataValue);

    for(int row = 0; row< NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {
        if (RasterData[row][col] != NoDataValue)
        {
          float this_element = M_raster.get_data_element(row,col);
          if(this_element != NoDataValue)
          {
            New_array[row][col] = RasterData[row][col]-this_element;
          }
        }
      }
    }
    //create LSDRaster object
    LSDRaster NewRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, New_array, GeoReferencingStrings);
    return NewRaster;
  }
  else
  {
    cout << "Warning, these rasters are not the same dimension!" << endl;
    return M_raster;
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// /\ |  |  DIAMOND SQUARE
// \/ |__|
// Routines for the Diamond Square algorithm
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function allows one to sample across values in the raster while wrapping
// around the sides of the raster
// SMM 9/1/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
float LSDRaster::WrapSample(int row, int col)
{

  int wraprow;
  int wrapcol;

  if(row >=0)
  {
    wraprow = row % NRows;
  }
  else
  {
    wraprow = NRows - (-row % NRows);
  }
  if(col >= 0)
  {
    wrapcol = col % NCols;
  }
  else
  {
    wrapcol = NCols - (-col % NCols);
  }

  //cout << "Nrows: " << NRows << " row: " << row << " wraprow: " << wraprow << endl;
  //cout << "Ncols: " << NCols << " col: " << col << " wrapcol: " << wrapcol << endl;

  return RasterData[wraprow][wrapcol];
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function allows one to set values in the raster while wrapping
// around the sides of the raster
// SMM 9/1/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::SetWrapSample(int row, int col, float value)
{
  int wraprow;
  int wrapcol;

  if(row >=0)
  {
    wraprow = row % NRows;
  }
  else
  {
    wraprow = NRows - (-row % NRows);
  }
  if(col >= 0)
  {
    wrapcol = col % NCols;
  }
  else
  {
    wrapcol = NCols - (-col % NCols);
  }

  RasterData[wraprow][wrapcol] = value;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function start with the corners of the algorithm to make individual 'features'
// note: the scale gives the range, so it should be a random value between -scale*0.5 and scale*0.5
// SMM 9/1/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::DSSetFeatureCorners(int featuresize, float scale)
{
  long seed = time(NULL);
  // the function starts from -featuresize since in the diamond square step
  // of the algorithm it wraps from row and column 0
  for (int row = 0; row < NRows; row+= featuresize)
  {
    for (int col = 0; col<NCols; col+= featuresize)
    {
      float randn = (ran3(&seed)-0.5)*scale;
      //cout << "setting feature corners, row: " << row << " and col: " << col << endl;
      SetWrapSample(row,col,randn);
    }
  }
  //cout << "Set the feature corners" << endl;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function samples on the square:
// a     b
//
//    x
//
// c     d
// The corners are known and the centre is calculated
// SMM 9/1/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::DSSampleSquare(int row,int col, int size, float value)
{
  int hs = size / 2;

  float a = WrapSample(col - hs, row - hs);
  float b = WrapSample(col + hs, row - hs);
  float c = WrapSample(col - hs, row + hs);
  float d = WrapSample(col + hs, row + hs);

  if (a == -9999 || b == -9999 || c == -9999 || d == -9999)
  {
    cout << "got a nodata; row: " << row << " and col: " << col << endl;

    if (a == -9999)
    {
      cout << "col - hs: " << col - hs << " and row - hs: " << row - hs << endl;
    }
    if (b == -9999)
    {
      cout << "col + hs: " << col + hs << " and row - hs: " << row - hs << endl;
    }
    if (c == -9999)
    {
      cout << "col - hs: " << col - hs << " and row + hs: " << row + hs << endl;
    }
    if (d == -9999)
    {
      cout << "col + hs: " << col + hs << " and row + hs: " << row + hs << endl;
    }
  }

  SetWrapSample(row, col, ((a + b + c + d) / 4.0) + value);
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This calculates the diamond step
//   c
//
//a  x  b
//
//   d
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::DSSampleDiamond(int row, int col, int size, float value)
{
    int hs = size / 2;

    double a = WrapSample(col - hs, row);
    double b = WrapSample(col + hs, row);
    double c = WrapSample(col, row - hs);
    double d = WrapSample(col, row + hs);

    if (a == -9999 || b == -9999 || c == -9999 || d == -9999)
    {
      cout << "got a nodata DSSampleDiamond; row: " << row << " and col: " << col << endl;

      if (a == -9999)
      {
        cout << "col - hs: " << col - hs << " and row: " << row << endl;
      }
      if (b == -9999)
      {
        cout << "col + hs: " << col + hs << " and row: " << row << endl;
      }
      if (c == -9999)
      {
        cout << "col: " << col << " and row - hs: " << row - hs << endl;
      }
      if (d == -9999)
      {
        cout << "col: " << col << " and row + hs: " << row + hs << endl;
      }

    }

    SetWrapSample(row, col, ((a + b + c + d) / 4.0) + value);
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this function performs the core of the diamond square algorithm
// the 'features' have got to be of size 2^n+1, so the
// feature order is the 'n'. THis means that, say a feature order of 4
// will make a feature with size of 17
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::DiamondSquare_SampleStep(int stepsize, float scale)
{
    int halfstep = stepsize / 2;
    long seed = time(NULL);

  // first do the square step. This gets the sqare for the node
  // at the half distance between the starting points
  for (int row = -halfstep; row < NRows+halfstep; row += stepsize)
  {
    for (int col = -halfstep; col < NCols + halfstep; col += stepsize)
    {
      //cout << "SS row and col: " << row << " " << col << endl;
      DSSampleSquare(row, col, stepsize, ((ran3(&seed)-0.5) * scale));
    }
  }

  // now the DiamondStep.
  // The first diamond gets the point halfway below the first column
  // Second diamond gets the column halfway past the first row.
  // That means for col 0 and row 0 it will wrap to the other side
  // This means these values will need to be wrapped in the inital
  // set corners stage!
  for (int row = -stepsize; row < NRows; row += stepsize)
  {
    for (int col = -stepsize; col < NCols; col += stepsize)
    {
      //cout << "DS row and col: " << row << " " << col << endl;
      DSSampleDiamond(row + halfstep, col, stepsize, ((ran3(&seed)-0.5) * scale));
      DSSampleDiamond(row, col + halfstep, stepsize, ((ran3(&seed)-0.5) * scale));
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this is the diamond square algorithm
// it creates a resized diamond square pseudo-fractal raster
// it has the same xllcorner and yllcorner as the original raster,
// but is resized so the NRows and NCols are to the closed power of 2
//
// Believe it or not I lifted this algorithm from Notch, the creator of Minecraft,
// who posted it online and then had it modified by Charles Randall
// https://www.bluh.org/code-the-diamond-square-algorithm/
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::DiamondSquare(int feature_order, float scale)
{

    // determine the size of the padded array:
    int PaddedRows = int(pow(2,ceil(log(NRows)/log(2))));
    int PaddedCols = int(pow(2,ceil(log(NCols)/log(2))));

    // now get the maximum feature size. This will be the  minimum
    // power of 2 in the x or y direction
    int max_feature_size;
    if (PaddedRows >= PaddedCols)
    {
      max_feature_size = PaddedCols;
    }
    else
    {
      max_feature_size = PaddedRows;
    }

    cout << "NRows: " << NRows << " and PaddedRows: " << PaddedRows << endl;
    cout << "NCols: " << NCols << " and PaddedCols: " << PaddedCols << endl;
    cout << "max_feature_size: " << max_feature_size << endl;

    //create an array
    Array2D<float> DSRaster_array(PaddedRows,PaddedCols,NoDataValue);

    //create LSDRaster diamond square object
    LSDRaster DSRaster(PaddedRows, PaddedCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, DSRaster_array, GeoReferencingStrings);

    // get the feature size: it must be a power of 2.
    int featuresize = pow(2,feature_order);
    if (featuresize > max_feature_size)
    {
      cout << "Your featuresize is too big for the DEM. Changing to max feature size" << endl;
    }

    cout << "feature size is: " << featuresize << endl;

    // now initialize the raster over some feature scale
    DSRaster.DSSetFeatureCorners(featuresize, scale);

    // now loop through the features, running the diamond square algorithm.
    int samplesize = featuresize;
    scale = scale/2;

    cout << "Starting diamond square algorithm, samplesize is: " << samplesize << endl;

    while (samplesize > 1)
    {
      cout << "Running Diamond square, samplesize: " << samplesize << endl;

      DSRaster.DiamondSquare_SampleStep(samplesize,scale);

      // halve the sample size and scale
      samplesize = samplesize/2;
      scale = scale/2;
    }

    return DSRaster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Make LSDRaster object using a 'template' raster and an Array2D of data.
// SWDG 29/8/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::LSDRasterTemplate(Array2D<float> InputData){

  //do a dimensions check and exit on failure
  if (InputData.dim1() == NRows && InputData.dim2() == NCols){
    LSDRaster OutputRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                           NoDataValue, InputData,GeoReferencingStrings);
    return OutputRaster;
  }
  else
  {
    cout << "Array dimensions do not match template LSDRaster object" << endl;
    exit(EXIT_FAILURE);
  }

}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function generates a hillshade raster using the algorithm outlined in
// Burrough and McDonnell Principles of GIS 1990 and in the ArcMap web help
// http://edndoc.esri.com/arcobjects/9.2/net/shared/geoprocessing/
// spatial_analyst_tools/how_hillshade_works.htm. Does not allow for drop shadows.
//
// Takes 3 floats, representing the altitude of the illumination source in
// degrees, the azimuth of the illumination source in degrees and the z factor.
//
// Default values are altitude = 45, azimuth = 315, z_factor = 1
//
// Outputs an LSDRaster object.
//
// SWDG, February 2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// Default version if no arguments given
// MDH, Feb 2015
//=======================================================================================

LSDRaster LSDRaster::hillshade()
{
  float Zenith = 45;
  float Azimuth = 315;
  float ZFactor = 1;
  LSDRaster Hillshade = this->hillshade(Zenith, Azimuth,ZFactor);
  return Hillshade;
}

LSDRaster LSDRaster::hillshade(float altitude, float azimuth, float z_factor)
{
    //print parameters to screen
    cout << "Hillshading with altitude: " << altitude
    << ", azimuth: " << azimuth << " and z-factor: " << z_factor << endl;

    //create output array
    Array2D<float> hillshade(NRows,NCols,NoDataValue);

    //convert zenith and azimuth into radians for calculation
    float zenith_rad = (90 - altitude) * M_PI / 180.0;
    float azimuth_math = 360-azimuth + 90;
    if (azimuth_math >= 360.0) azimuth_math = azimuth_math - 360;
    float azimuth_rad = azimuth_math * M_PI /180.0;

    //calculate hillshade value for every non nodata value in the input raster
    for (int i = 1; i < NRows-1; ++i){
        for (int j = 1; j < NCols-1; ++j){
            float slope_rad = 0;
            float aspect_rad = 0;
            float dzdx = 0;
            float dzdy = 0;

            if (RasterData[i][j] != NoDataValue){
                dzdx = ((RasterData[i][j+1] + 2*RasterData[i+1][j] + RasterData[i+1][j+1]) -
                       (RasterData[i-1][j-1] + 2*RasterData[i-1][j] + RasterData[i-1][j+1]))
                        / (8 * DataResolution);
                dzdy = ((RasterData[i-1][j+1] + 2*RasterData[i][j+1] + RasterData[i+1][j+1]) -
                       (RasterData[i-1][j-1] + 2*RasterData[i][j-1] + RasterData[i+1][j-1]))
                       / (8 * DataResolution);

                slope_rad = atan(z_factor * sqrt((dzdx*dzdx) + (dzdy*dzdy)));

                if (dzdx != 0){
                    aspect_rad = atan2(dzdy, (dzdx*-1));
                    if (aspect_rad < 0) aspect_rad = 2*M_PI + aspect_rad;
                }
                else{
                    if (dzdy > 0) aspect_rad = M_PI/2;
                    else if (dzdy < 0) aspect_rad = 2 * M_PI - M_PI/2;
                    else aspect_rad = aspect_rad;
                }
                hillshade[i][j] = 255.0 * ((cos(zenith_rad) * cos(slope_rad)) +
                                  (sin(zenith_rad) * sin(slope_rad) *
                                  cos(azimuth_rad - aspect_rad)));

                if (hillshade[i][j] < 0) hillshade[i][j] = 0;
            }
        }
    }
    //create LSDRaster hillshade object
    LSDRaster hillshade_raster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                               NoDataValue, hillshade,GeoReferencingStrings);

    return hillshade_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function generates a hillshade derivative raster using the algorithm outlined in
// Codilean (2006) (excluding cast shadows), identifying areas in shadow as 1 and all
// other values as 0. This is now obselete since we have the CastShadows algorithm.
//
// Is interfaced through LSDRaster::TopoShield and should not be called directly,
// to generate a hillshade use LSDRaster::hillshade instead.
//
// Takes 2 ints, representing theta, the zenith angle of the illumination source in
// degrees and the azimuth angle, phi, of the illumination source in degrees.
//
// Outputs an Array2D of floats.
//
// SWDG, 11/4/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Array2D<float> LSDRaster::Shadow(int theta, int phi)
{
    //create array of input data and an output array of same dimensions
    Array2D<float> data = RasterData;
    Array2D<float> hillshade(NRows,NCols,NoDataValue);

    //convert zenith and azimuth into radians for calculation
    float zenith_rad = (90 - theta) * M_PI / 180.0;
    float azimuth_math = 360-phi + 90;
    if (azimuth_math >= 360.0) azimuth_math = azimuth_math - 360;
    float azimuth_rad = azimuth_math * M_PI /180.0;

    //calculate hillshade value for every non nodata value in the input raster
    for (int i = 1; i < NRows-1; ++i){
        for (int j = 1; j < NCols-1; ++j){
            float slope_rad = 0;
            float aspect_rad = 0;
            float dzdx = 0;
            float dzdy = 0;

            if (data[i][j] != NoDataValue){
                dzdx = ((data[i][j+1] + 2*data[i+1][j] + data[i+1][j+1]) -
                       (data[i-1][j-1] + 2*data[i-1][j] + data[i-1][j+1]))
                        / (8 * DataResolution);
                dzdy = ((data[i-1][j+1] + 2*data[i][j+1] + data[i+1][j+1]) -
                       (data[i-1][j-1] + 2*data[i][j-1] + data[i+1][j-1]))
                       / (8 * DataResolution);

                slope_rad = atan(sqrt((dzdx*dzdx) + (dzdy*dzdy)));

                if (dzdx != 0){
                    aspect_rad = atan2(dzdy, (dzdx*-1));
                    if (aspect_rad < 0) aspect_rad = 2*M_PI + aspect_rad;
                }
                else{
                    if (dzdy > 0) aspect_rad = M_PI/2;
                    else if (dzdy < 0) aspect_rad = 2 * M_PI - M_PI/2;
                    else aspect_rad = aspect_rad;
                }

                hillshade[i][j] = acos(((sin(zenith_rad) * cos(slope_rad)) +
                                  (sin(zenith_rad) * sin(slope_rad) *
                                  cos(azimuth_rad - aspect_rad))))*180/M_PI;

                if (hillshade[i][j] > 90) hillshade[i][j] = 1;
                else hillshade[i][j] = 0;
            }

        }
    }

    //create LSDRaster hillshade object
    //LSDRaster hillshade_raster(NRows, NCols, XMinimum, YMinimum, DataResolution,
    //                           NoDataValue, hillshade);

    return hillshade;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function generates a topographic sheilding raster using the algorithm outlined in
// Codilean (2006), creating a raster of values between 0 and 1 which can be used as a
// scaling factor in Cosmo analysis.
//
// Goes further than the original algorithm allowing a theoretical theta, phi pair of
// 1,1 to be supplied and although this will increase the computatin time significantly,
// it is much faster than the original Avenue and VBScript implementations.
// Default parameters are 5 and 5 if no arguments supplied
//
// Takes 2 ints, representing the Elevation/Zenith Angle, and Azimuth Angle step sizes
// required. Codilean (2006) used 5,5 as the standard values, but in reality values of
//10,15 are often preferred to save processing time. **steps must be a factor of 360**
//
// Outputs an LSDRaster
//
// SWDG, 11/4/13
// Updated and tested MDH, 24/2/2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

LSDRaster LSDRaster::TopographicShielding()
{
  //For default parameters
  printf("LSDRaster::%s: No input argumments provided, defaulting to Azimuth/Zenith stepsize of 5 degrees\n",__func__);
  int AzimuthStep = 5;
  int PhiStep = 5;
  return this->TopographicShielding(AzimuthStep,PhiStep);
}

LSDRaster LSDRaster::TopographicShielding(int AzimuthStep, int ZenithStep)
{
  //Function print to screen
  printf("\nLSDRaster::%s: AzimuthStep: %d, ZenithStep: %d\n",__func__,AzimuthStep,ZenithStep);

  //declare constants
  float m = 2.3;  //shielding constant
  //float I0 = 1.;  //Max intensity (=1 for shielding factors)
  //float MaxFactor = 0;  //Maximum Production Factor
  //float f90 = 90.0;

  //Max Production Factor following Codilean Eq2
  //MaxFactor = (2.*M_PI*I0)/((m+1.));
  //Array2D<float> MaxFactorArray(NRows,NCols,MaxFactor);
  float MaxWeight = 0;

  //Calculate first shadow with theta value of 90 and scale it
  Array2D<float> Empty(NRows,NCols,0.);
  Array2D<float> FinalArray = Empty; // = Shadow(0,90) * Scaler90;

  //loop through all the theta, phi pairs and increment the FinalArray with the scaled values
  //start at ZenithStep and AzimuthStep and continue up to Max

  for (int ZenithAngle = ZenithStep; ZenithAngle <= 90; ZenithAngle += ZenithStep)
  {
    for(int AzimuthAngle = AzimuthStep; AzimuthAngle <= 360; AzimuthAngle += AzimuthStep)
    {
      fflush(stdout);
      printf("\nAzimuth: %d, Zenith: %d - ",AzimuthAngle,ZenithAngle);

      //Find cells in shadow (1s and 0s)
      Array2D<float> ShadowsArray;
      if (ZenithAngle < 90) ShadowsArray = Shadows(AzimuthAngle,ZenithAngle);
      else ShadowsArray = Empty;

      //Calculate Weighting
      float Weighting = (AzimuthStep*(M_PI/180.))*(ZenithStep*(M_PI/180.))*cos(ZenithAngle*(M_PI/180.))*pow(sin(ZenithAngle*(M_PI/180.)),m);
      Array2D<float> WeightsArray(NRows,NCols,Weighting);

      //calculate Weight
      FinalArray += ShadowsArray*WeightsArray;
      MaxWeight += Weighting;
    }
  }

  Array2D<float> ShieldingFactor(NRows,NCols,1);
  Array2D<float> MaxWeightArray(NRows,NCols,MaxWeight);
  ShieldingFactor -= FinalArray/MaxWeightArray;

  //make sure there is no shielding value for NDV cells
  Array2D<float> FinalShieldingFactor(NRows,NCols,NoDataValue);
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (RasterData[i][j] != NoDataValue){
        FinalShieldingFactor[i][j] = ShieldingFactor[i][j];
      }
    }
  }

  //write LSDRaster
  LSDRaster Shielding(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                      FinalShieldingFactor,GeoReferencingStrings);
  return Shielding;
}

//LSDRaster LSDRaster::TopographicShielding(int theta_step, int phi_step)
//{
//  //Print to screen
//  printf("LSDRaster::%s\n",__func__);
//
//  //calculate parameter of scaling calculation
//  int phi_factor = 360/phi_step;

//  float MaxFactor = 0;

//  for(int theta = 10; theta < 90; theta += theta_step){
//    MaxFactor += pow(sin(rad(float(theta))),3.3) * phi_factor;
//  }

//  //calculate maximum scaling factor and write it to an array
//  float f90 = 90.0;
//  MaxFactor += pow(sin(rad(f90)),3.3);
//  Array2D<float> MaxFactorArray(NRows,NCols,MaxFactor);

//  //Calculate first shadow with theta value of 90 and scale it
//  Array2D<float> Scaler90(NRows,NCols, pow(sin(rad(f90)),3.3));
//  Array2D<float> FinalArray = Shadow(0,90) * Scaler90;

//  //loop through all the theta, phi pairs and increment the FinalArray with the scaled values
//  for(int theta = 10; theta < 90; theta += theta_step)
//  {
//    for(int phi = 0; phi < 360; phi += phi_step)
//    {
//      cout << "Theta: " << theta << " and phi: " << phi << endl;
//      Array2D<float> TempArray = this->Shadows(phi,theta);
//      Array2D<float> Scaler(NRows, NCols, pow(sin(rad(float(theta))),3.3));
//      FinalArray += TempArray * Scaler;
//    }
//  }

//  //create array of ones needed in sheilding calculation
//  Array2D<float> Ones(NRows,NCols,1);

//  //Shielding factor calculation
//  Array2D<float> ShFactor = Ones - (FinalArray/MaxFactorArray);

//  //deal with nodata values on border of dem - more efficient than doing it in the hillshade function 10s of times.
//  for (int i = 0; i < NRows; ++i)
//  {
//    for (int j = 0; j < NCols; ++j)
//    {
//      if (RasterData[i][j] == NoDataValue) ShFactor[i][j] = NoDataValue;
//    }
//  }

//  //write LSDRaster
//  LSDRaster Shielding(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
//                      ShFactor,GeoReferencingStrings);
//  return Shielding;
//}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


/*=======================================================================================

  This function generates a shadows raster containing drop shadows using the algorithm outlined
  in Codilean (2006), identifying areas in shadow as 1 and all other values as 0. It includes
  the coordinate transformation in order to look for shadow casting.

  Algorithm works by adjusting the coordiantes of the DEM to be relative to the azimuth and zenith
  i.e. X-coordinates should be equal along the Azimuth direction and the DEM itself is tilted by
  the angle Zenith toward Azimuth.

  Is interfaced through LSDRaster::TopoShield and LSDRaster::Hillshade, and should not
  be called directly,  to generate a hillshade use LSDRaster::Hillshade.

  Takes 2 ints, the zenith angle of the illumination source in degrees from horizontal
  and the azimuth angle, of the illumination source in degrees.

  Outputs an LSDRaster showing areas in the shadow of other topography.

  Martin Hurst
  February 2015

========================================================================================*/
LSDRaster LSDRaster::CastShadows(int Azimuth, int ZenithAngle)
{
  Array2D<float> Shadows = this->Shadows(Azimuth,ZenithAngle);
  return LSDRaster(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue, Shadows,GeoReferencingStrings);
}

Array2D<float> LSDRaster::Shadows(int Azimuth, int ZenithAngle)
{
  printf("LSDRaster::%s: ",__func__);

  //Declare coordinate and transform arrays
  Array2D<float> XCoords(NRows,NCols,NoDataValue);
  Array2D<float> YCoords(NRows,NCols,NoDataValue);
  Array2D<float> XCoords_Transform(NRows,NCols,NoDataValue);
  //Array2D<float> YCoords_Transform(NRows,NCols,NoDataValue);
  Array2D<float> ZCoords_Transform(NRows,NCols,NoDataValue);
  Array2D<float> Shadows(NRows,NCols,0.0);

  //variables for screen printing
  int PrintStep = (int)(NCols*(NRows/100));
  int Print = 0;
  int PrintCounter = 0;

  //parameters for searching along shadow paths
  int NSearch = 2;
  vector<int> as, bs;

  //Convert Azimuth and Zenith to radians
  float ZenithRadians = (M_PI/180.)*(ZenithAngle);
  float AzimuthRadians = (M_PI/180.)*(180.-(Azimuth+90.));
  if (AzimuthRadians<0) AzimuthRadians += 2.*M_PI;

  //Print to screen
  //printf("LSDRaster::%s\n",__func__);

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        YCoords[i][j] = (NRows-i)*DataResolution;
        XCoords[i][j] = j*DataResolution;

        //Modified from Codilean 2006 whose equation 6 appears to be wrong (may be due to differrent origins?)
        XCoords_Transform[i][j] = XCoords[i][j]*sin(AzimuthRadians)-YCoords[i][j]*cos(AzimuthRadians);
        //YCoords_Transform[i][j] = XCoords[i][j]*cos(AzimuthRadians)+YCoords[i][j]*sin(AzimuthRadians);

        //Modified from Codilean 2006 whose equation 8 is missing a + sign and needs rederiving following the new equation 6
        ZCoords_Transform[i][j] = (RasterData[i][j]*cos(ZenithRadians)
                                        - (XCoords[i][j]*cos(AzimuthRadians)
                                  + YCoords[i][j]*sin(AzimuthRadians))*sin(ZenithRadians));
      }
    }
  }

  // Check direction to start looking and generate search indices for looking in each quadrant
  // to determine if cells down the look direction are in shadow
  // Also determine directions to loop across DEM, e.g. if Az = 0-90 start in upper right corner
  int Reversei=0;
  int Reversej=0;
  if (Azimuth >= 0 && Azimuth <= 45)
  {
    as.push_back(1);  as.push_back(1);
    bs.push_back(0);  bs.push_back(-1);
    Reversej=1;
  }
  else if (Azimuth > 45 && Azimuth <= 90)
  {
    as.push_back(1);  as.push_back(0);
    bs.push_back(-1);  bs.push_back(-1);
    Reversej=1;
  }
  else if (Azimuth > 90 && Azimuth <= 135)
  {
    as.push_back(0);  as.push_back(-1);
    bs.push_back(-1);  bs.push_back(-1);
    Reversei=1;
    Reversej=1;
  }
  else if (Azimuth > 135 && Azimuth <= 180)
  {
    as.push_back(-1);  as.push_back(-1);
    bs.push_back(-1);  bs.push_back(0);
    Reversei=1;
    Reversej=1;
  }
  else if (Azimuth > 180 && Azimuth <= 225)
  {
    as.push_back(-1);  as.push_back(-1);
    bs.push_back(0);  bs.push_back(1);
    Reversei=1;
  }
  else if (Azimuth > 225 && Azimuth <= 270)
  {
    as.push_back(-1);  as.push_back(0);
    bs.push_back(1);  bs.push_back(1);
    Reversei=1;
  }
  else if (Azimuth > 270 && Azimuth <= 315)
  {
    as.push_back(0);  as.push_back(1);
    bs.push_back(1);  bs.push_back(1);
  }
  else if (Azimuth > 315 && Azimuth <= 360)
  {
    as.push_back(1);  as.push_back(1);
    bs.push_back(1);  bs.push_back(0);
  }
  else
  {
    //critical error, Azimuth outside range
    printf("LSDRaster:FATAL ERROR: Encountered Azimuth out of range. In %s at line %d\n",__func__,__LINE__);
    exit(EXIT_FAILURE);
  }

  //print to screen
  float Percentage = (100.*PrintCounter/(NRows*NCols));
  fflush(stdout);
  printf("%3.0f %% Complete\b\b\b\b\b\b\b\b\b\b\b\b\b\b",Percentage);

  for (int ii=0; ii < NRows; ++ii)
  {
    //check which direction to loop in
    int i,j;
    if (Reversei==1) i = NRows-ii-1;
    else i=ii;

    for (int jj=0; jj < NCols; ++jj)
    {
      //check which direction to loop in
      if (Reversej==1) j = NCols-jj-1;
      else j=jj;

    //print progress to screen (turn this off if parallel?)
      ++PrintCounter;
      if (PrintCounter > Print)
      {
        float Percentage = (100.*PrintCounter/(NRows*NCols));
        fflush(stdout);
        printf("%3.0f\b\b\b",Percentage);
        Print += PrintStep;
      }

      if (i==0 || i==NRows-1 || j==0 || j==NCols-1) continue;
      else if (RasterData[i][j] == NoDataValue) continue;

      //Parameters declared internally to avoid dependencies in parallel processing

      //pull out vector of indices for searching the line in direction of azimuth
      int a = i;
      int b = j;

      //push indices to vectors for line trace until reaching the edges
      //infinite loop, conditions inside should catch breaks
      int ShadowFlag = 0;
      int NDVFlag = 0;
      float MinX = 2*DataResolution;
      float DiffX, DiffZ;
      int a_temp = 0; //assigned meaningless value to stop compiler warnings, value will always be updated.
      int b_temp = 0;
      int i_temp, j_temp;

      while (true)
      {
        //check the three search cells for a minumum X value in rotated coordinate mode
        MinX = 2*DataResolution;
        bool Initialized = false; //this flag tests if a_temp and b_temp have a real value.
        for (int k=0;k<NSearch;++k)
        {
          //assign temporary indices
          i_temp = a+as[k];
          j_temp = b+bs[k];

          if (RasterData[i_temp][j_temp] == NoDataValue)
          {
            NDVFlag = 1;
            break;
          }

          //minimise Y along X direction
          DiffX = fabs(XCoords_Transform[i_temp][j_temp]-XCoords_Transform[i][j]);
          if (DiffX < MinX)
          {
            MinX = DiffX;
            Initialized = true;
            a_temp = i_temp;
            b_temp = j_temp;
          }
        }

        if (Initialized == true){  //without this condition a and b can be assigned values from unallocated memory, causing crashes.
          //update a and b
          a = a_temp;
          b = b_temp;
        }
        else break;

        //Check if edge of shadow, edge of DEM or NDVs reached
        if (ShadowFlag > 10) break;
        else if (a <= 0 || b == 0 || a == NRows-1 || b == NCols-1 || RasterData[a][b]==NoDataValue) break;
        else if (NDVFlag == true) break;
        else
        {
          //Check if transformed elevation a,b greater than at i,j
          DiffZ = ZCoords_Transform[a][b] - ZCoords_Transform[i][j];
          if (DiffZ < 0) Shadows[a][b] = 1;
          else ShadowFlag += 1;
        }
      }
    }
  }

  //Print completion to screen
  fflush(stdout);
  printf("100 %% Complete\r");

  //write LSDRaster and return
  return Shadows;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// calculate_polyfit_surface_metrics
//
// This routine houses the code to fit a 6 term polynomial (z =ax^2 + by^2 + cxy
// + dx + ey + f) to a surface, and then use the derivatives of this to
// calculate various useful geometric properties such as slope and curvature.
//
// The surface is fitted to all the points that lie within circular
// neighbourhood that is defined by the designated window radius.  The user also
// inputs a binary raster, which tells the program which rasters it wants to
// create (label as "true" to produce them, "false" to ignore them. This has 8
// elements, as listed below:
//        0 -> Elevation (smoothed by surface fitting)
//        1 -> Slope
//        2 -> Aspect
//        3 -> Curvature
//        4 -> Planform Curvature
//        5 -> Profile Curvature
//        6 -> Tangential Curvature
//        7 -> Stationary point classification (1=peak, 2=depression, 3=saddle)
// The program returns a vector of LSDRasters.  For options marked "false" in
// boolean input raster, the returned LSDRaster houses a blank raster, as this
// metric has not been calculated.  The desired LSDRaster can be retrieved from
// the output vector by using the cell reference shown in the list above i.e. it
// is the same as the reference in the input binary vector.
//
// DTM 28/03/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<LSDRaster> LSDRaster::calculate_polyfit_surface_metrics(float window_radius, vector<int> raster_selection)
{
  Array2D<float> void_array(1,1,NoDataValue);
  LSDRaster VOID(1,1,NoDataValue,NoDataValue,NoDataValue,NoDataValue,void_array,GeoReferencingStrings);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius < sqrt(2)*DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution * sqrt(2), i.e. the diagonal of a single grid cell: " <<
    sqrt(2)*DataResolution << ".\nWindow radius has been set to sqrt(2) * data resolution." << endl;
    window_radius = sqrt(2)*DataResolution;
  }
  // this fits a polynomial surface over a kernel window. First, perpare the
  // kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel

  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<float> x_kernel(kw,kw,NoDataValue);
  Array2D<float> y_kernel(kw,kw,NoDataValue);
  Array2D<int> mask(kw,kw,0);

  // reset the a,b,c,d,e and f matrices (the coefficient matrices)
  Array2D<float> temp_coef(NRows,NCols,NoDataValue);
  Array2D<float> elevation_raster, slope_raster, aspect_raster, curvature_raster, planform_curvature_raster,
                  profile_curvature_raster, tangential_curvature_raster, classification_raster,
                  s1_raster, s2_raster, s3_raster;
  // Copy across raster template into the desired array containers
  if(raster_selection[0]==1)  elevation_raster = temp_coef.copy();
  if(raster_selection[1]==1)  slope_raster = temp_coef.copy();
  if(raster_selection[2]==1)  aspect_raster = temp_coef.copy();
  if(raster_selection[3]==1)  curvature_raster = temp_coef.copy();
  if(raster_selection[4]==1)  planform_curvature_raster = temp_coef.copy();
  if(raster_selection[5]==1)  profile_curvature_raster = temp_coef.copy();
  if(raster_selection[6]==1)  tangential_curvature_raster = temp_coef.copy();
  if(raster_selection[7]==1)  classification_raster = temp_coef.copy();

  //float a,b,c,d,e,f;

  // scale kernel window to resolution of DEM, and translate coordinates to be
  // centred on cell of interest (the centre cell)
  float x,y,zeta,radial_dist;
  for(int i=0;i<kw;++i)
  {
    for(int j=0;j<kw;++j)
    {
      x_kernel[i][j]=(i-kr)*DataResolution;
      y_kernel[i][j]=(j-kr)*DataResolution;
      // Build circular mask
      // distance from centre to this point.
      radial_dist = sqrt(y_kernel[i][j]*y_kernel[i][j] + x_kernel[i][j]*x_kernel[i][j]);

      //if (floor(radial_dist) <= window_radius)
      if (radial_dist <= window_radius)
      {
        mask[i][j] = 1;
      }
    }
  }
  // FIT POLYNOMIAL SURFACE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO
  // DETERMINE TOPOGRAPHIC METRICS
  // Have N simultaneous linear equations, and N unknowns.
  // => b = Ax, where x is a 1xN array containing the coefficients we need for
  // surface fitting.
  // A is constructed using different combinations of x and y, thus we only need
  // to compute this once, since the window size does not change.
  // For 2nd order surface fitting, there are 6 coefficients, therefore A is a
  // 6x6 matrix
  Array2D<float> A(6,6,0.0);
  for (int i=0; i<kw; ++i)
  {
    for (int j=0; j<kw; ++j)
    {
      if (mask[i][j] == 1)
      {
        x = x_kernel[i][j];
        y = y_kernel[i][j];

        // Generate matrix A
        A[0][0] += pow(x,4);
        A[0][1] += pow(x,2)*pow(y,2);
        A[0][2] += pow(x,3)*y;
        A[0][3] += pow(x,3);
        A[0][4] += pow(x,2)*y;
        A[0][5] += pow(x,2);
        A[1][0] += pow(x,2)*pow(y,2);
        A[1][1] += pow(y,4);
        A[1][2] += x*pow(y,3);
        A[1][3] += x*pow(y,2);
        A[1][4] += pow(y,3);
        A[1][5] += pow(y,2);
        A[2][0] += pow(x,3)*y;
        A[2][1] += x*pow(y,3);
        A[2][2] += pow(x,2)*pow(y,2);
        A[2][3] += pow(x,2)*y;
        A[2][4] += x*pow(y,2);
        A[2][5] += x*y;
        A[3][0] += pow(x,3);
        A[3][1] += x*pow(y,2);
        A[3][2] += pow(x,2)*y;
        A[3][3] += pow(x,2);
        A[3][4] += x*y;
        A[3][5] += x;
        A[4][0] += pow(x,2)*y;
        A[4][1] += pow(y,3);
        A[4][2] += x*pow(y,2);
        A[4][3] += x*y;
        A[4][4] += pow(y,2);
        A[4][5] += y;
        A[5][0] += pow(x,2);
        A[5][1] += pow(y,2);
        A[5][2] += x*y;
        A[5][3] += x;
        A[5][4] += y;
        A[5][5] += 1;
      }
    }
  }

  // Move window over DEM, fitting 2nd order polynomial surface to the
  // elevations within the window.
  //cout << "\n\tRunning 2nd order polynomial fitting" << endl;
  //cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  int ndv_present = 0;

  for(int i=0;i<NRows;++i)
  {
    //cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        if(raster_selection[0]==1)  elevation_raster[i][j] = NoDataValue;
        if(raster_selection[1]==1)  slope_raster[i][j] = NoDataValue;
        if(raster_selection[2]==1)  aspect_raster[i][j] = NoDataValue;
        if(raster_selection[3]==1)  curvature_raster[i][j] = NoDataValue;
        if(raster_selection[4]==1)  planform_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[5]==1)  profile_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[6]==1)  tangential_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[7]==1)  classification_raster[i][j] = NoDataValue;
      }
      else
      {
      // clip DEM
        //zeta_sampler=zeta.copy();
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            data_kernel[i_kernel][j_kernel] = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(data_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
          }
        }
        // Fit polynomial surface, avoiding nodata values
        // ==================> Could change this,
        // as can fit polynomial surface as long as there are 6 data points.
        if(ndv_present == 0)  // test for nodata values within the selection
        {
          Array1D<float> bb(6,0.0);
          Array1D<float> coeffs(6);
          for (int krow=0; krow<kw; ++krow)
          {
            for (int kcol=0; kcol<kw; ++kcol)
            {
              if (mask[krow][kcol] == 1)
              {
                x = x_kernel[krow][kcol];
                y = y_kernel[krow][kcol];
                zeta = data_kernel[krow][kcol];
                // Generate vector bb
                bb[0] += zeta*x*x;
                bb[1] += zeta*y*y;
                bb[2] += zeta*x*y;
                bb[3] += zeta*x;
                bb[4] += zeta*y;
                bb[5] += zeta;
              }    // end mask
            }      // end kernal column
          }        // end kernal row
          // Solve matrix equations using LU decomposition using the TNT JAMA
          // package:
          // A.coefs = b, where coefs is the coefficients vector.
          LU<float> sol_A(A);  // Create LU object
          coeffs = sol_A.solve(bb);

          float a=coeffs[0];
          float b=coeffs[1];
          float c=coeffs[2];
          float d=coeffs[3];
          float e=coeffs[4];
          float f=coeffs[5];

          // Now calculate the required topographic metrics
          if(raster_selection[0]==1)  elevation_raster[i][j] = f;

          // note that the kernal translates coordinates so the derivative terms
          // containing x or y go to zero because x = 0 and y = 0 in the transformed coordinates.
          if(raster_selection[1]==1)  slope_raster[i][j] = sqrt(d*d+e*e);

          if(raster_selection[2]==1)
          {
            if(d==0 && e==0) aspect_raster[i][j] = NoDataValue;
            else if(d==0 && e>0) aspect_raster[i][j] = 90;
            else if(d==0 && e<0) aspect_raster[i][j] = 270;
            else
            {
              aspect_raster[i][j] = 270. - (180./M_PI)*atan(e/d) + 90.*(d/abs(d));
              if(aspect_raster[i][j] > 360.0) aspect_raster[i][j] -= 360;
            }
          }

          if(raster_selection[3]==1)  curvature_raster[i][j] = 2*a+2*b;

          if(raster_selection[4]==1 || raster_selection[5]==1 || raster_selection[6]==1 || raster_selection[7]==1)
          {
            float fx, fy, fxx, fyy, fxy, p, q;
            fx = d;
            fy = e;
            fxx = 2*a;
            fyy = 2*b;
            fxy = c;
            p = fx*fx + fy*fy;
            q = p + 1;

            if (raster_selection[4]==1)
            {
              if (q > 0)  planform_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(sqrt(q*q*q));
              else        planform_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[5]==1)
            {
              if((q*q*q > 0) && ((p*sqrt(q*q*q)) != 0))    profile_curvature_raster[i][j] = (fxx*fx*fx + 2*fxy*fx*fy + fyy*fy*fy)/(p*sqrt(q*q*q));
              else                                         profile_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[6]==1)
            {
              if( q>0 && (p*sqrt(q))!=0) tangential_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(p*sqrt(q));
              else                       tangential_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[7]==1)
            {
              float slope = sqrt(d*d + e*e);
              if (slope < 0.1)
              {
                if (fxx < 0 && fyy < 0 && fxy*fxy < fxx*fxx)      classification_raster[i][j] = 1;// Conditions for peak
                else if (fxx > 0 && fyy > 0 && fxy*fxy < fxx*fyy) classification_raster[i][j] = 2;// Conditions for a depression
                else if (fxx*fyy < 0 || fxy*fxy > fxx*fyy)        classification_raster[i][j] = 3;// Conditions for a saddle
                else classification_raster[i][j] = 0;
              }
            }
          }
        }         // end if statement for no data value
        ndv_present = 0;
      }
    }
  }
  // Now create LSDRasters and load into output vector
  vector<LSDRaster> output_rasters_temp(8,VOID);
  vector<LSDRaster> raster_output = output_rasters_temp;
  if(raster_selection[0]==1)
  {
    LSDRaster Elevation(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,elevation_raster,GeoReferencingStrings);
    raster_output[0] = Elevation;
  }
  if(raster_selection[1]==1)
  {
    LSDRaster Slope(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,slope_raster,GeoReferencingStrings);
    raster_output[1] = Slope;
  }
  if(raster_selection[2]==1)
  {
    LSDRaster Aspect(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,aspect_raster,GeoReferencingStrings);
    raster_output[2] = Aspect;
  }
  if(raster_selection[3]==1)
  {
    LSDRaster Curvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,curvature_raster,GeoReferencingStrings);
    raster_output[3] = Curvature;
  }
  if(raster_selection[4]==1)
  {
    LSDRaster PlCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,planform_curvature_raster,GeoReferencingStrings);
    raster_output[4] = PlCurvature;
  }
  if(raster_selection[5]==1)
  {
    LSDRaster PrCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,profile_curvature_raster,GeoReferencingStrings);
    raster_output[5] = PrCurvature;
  }
  if(raster_selection[6]==1)
  {
    LSDRaster TanCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,tangential_curvature_raster,GeoReferencingStrings);
    raster_output[6] = TanCurvature;
  }
  if(raster_selection[7]==1)
  {
    LSDRaster Class(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,classification_raster,GeoReferencingStrings);
    raster_output[7] = Class;
  }
  return raster_output;
}






//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// calculate_polyfit_surface_metrics_directional_gradients
//
// This routine houses the code to fit a 6 term polynomial (z =ax^2 + by^2 + cxy
// + dx + ey + f) to a surface, and then use the derivatives of this to
// calculate various useful geometric properties such as slope and curvature.
//
// The surface is fitted to all the points that lie within circular
// neighbourhood that is defined by the designated window radius.  The user also
// inputs a binary raster, which tells the program which rasters it wants to
// create (label as "true" to produce them, "false" to ignore them. This has 8
// elements, as listed below:
//        0 -> Elevation (smoothed by surface fitting)
//        1 -> Slope
//        2 -> Aspect
//        3 -> Curvature
//        4 -> Planform Curvature
//        5 -> Profile Curvature
//        6 -> Tangential Curvature
//        7 -> Stationary point classification (1=peak, 2=depression, 3=saddle)
//        8 -> Dirctional gradients (produces two rasters)
// The program returns a vector of LSDRasters.  For options marked "false" in
// boolean input raster, the returned LSDRaster houses a blank raster, as this
// metric has not been calculated.  The desired LSDRaster can be retrieved from
// the output vector by using the cell reference shown in the list above i.e. it
// is the same as the reference in the input binary vector.
//
// SMM (from DTM's code) 22/06/2018
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<LSDRaster> LSDRaster::calculate_polyfit_surface_metrics_directional_gradients(float window_radius, vector<int> raster_selection)
{
  Array2D<float> void_array(1,1,NoDataValue);
  LSDRaster VOID(1,1,NoDataValue,NoDataValue,NoDataValue,NoDataValue,void_array,GeoReferencingStrings);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius < sqrt(2)*DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution * sqrt(2), i.e. the diagonal of a single grid cell: " <<
    sqrt(2)*DataResolution << ".\nWindow radius has been set to sqrt(2) * data resolution." << endl;
    window_radius = sqrt(2)*DataResolution;
  }
  // this fits a polynomial surface over a kernel window. First, perpare the
  // kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel

  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<float> x_kernel(kw,kw,NoDataValue);
  Array2D<float> y_kernel(kw,kw,NoDataValue);
  Array2D<int> mask(kw,kw,0);

  // reset the a,b,c,d,e and f matrices (the coefficient matrices)
  Array2D<float> temp_coef(NRows,NCols,NoDataValue);
  Array2D<float> elevation_raster, slope_raster, aspect_raster, curvature_raster, planform_curvature_raster,
                  profile_curvature_raster, tangential_curvature_raster, classification_raster,
                  s1_raster, s2_raster, s3_raster, dzdx_raster, dzdy_raster;
  // Copy across raster template into the desired array containers
  if(raster_selection[0]==1)  elevation_raster = temp_coef.copy();
  if(raster_selection[1]==1)  slope_raster = temp_coef.copy();
  if(raster_selection[2]==1)  aspect_raster = temp_coef.copy();
  if(raster_selection[3]==1)  curvature_raster = temp_coef.copy();
  if(raster_selection[4]==1)  planform_curvature_raster = temp_coef.copy();
  if(raster_selection[5]==1)  profile_curvature_raster = temp_coef.copy();
  if(raster_selection[6]==1)  tangential_curvature_raster = temp_coef.copy();
  if(raster_selection[7]==1)  classification_raster = temp_coef.copy();
  if(raster_selection[8]==1)
  {
    dzdx_raster = temp_coef.copy();
    dzdy_raster = temp_coef.copy();
  }
  //float a,b,c,d,e,f;

  // scale kernel window to resolution of DEM, and translate coordinates to be
  // centred on cell of interest (the centre cell)
  float x,y,zeta,radial_dist;
  for(int i=0;i<kw;++i)
  {
    for(int j=0;j<kw;++j)
    {
      x_kernel[i][j]=(i-kr)*DataResolution;
      y_kernel[i][j]=(j-kr)*DataResolution;
      // Build circular mask
      // distance from centre to this point.
      radial_dist = sqrt(y_kernel[i][j]*y_kernel[i][j] + x_kernel[i][j]*x_kernel[i][j]);

      //if (floor(radial_dist) <= window_radius)
      if (radial_dist <= window_radius)
      {
        mask[i][j] = 1;
      }
    }
  }
  // FIT POLYNOMIAL SURFACE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO
  // DETERMINE TOPOGRAPHIC METRICS
  // Have N simultaneous linear equations, and N unknowns.
  // => b = Ax, where x is a 1xN array containing the coefficients we need for
  // surface fitting.
  // A is constructed using different combinations of x and y, thus we only need
  // to compute this once, since the window size does not change.
  // For 2nd order surface fitting, there are 6 coefficients, therefore A is a
  // 6x6 matrix
  Array2D<float> A(6,6,0.0);
  for (int i=0; i<kw; ++i)
  {
    for (int j=0; j<kw; ++j)
    {
      if (mask[i][j] == 1)
      {
        x = x_kernel[i][j];
        y = y_kernel[i][j];

        // Generate matrix A
        A[0][0] += pow(x,4);
        A[0][1] += pow(x,2)*pow(y,2);
        A[0][2] += pow(x,3)*y;
        A[0][3] += pow(x,3);
        A[0][4] += pow(x,2)*y;
        A[0][5] += pow(x,2);
        A[1][0] += pow(x,2)*pow(y,2);
        A[1][1] += pow(y,4);
        A[1][2] += x*pow(y,3);
        A[1][3] += x*pow(y,2);
        A[1][4] += pow(y,3);
        A[1][5] += pow(y,2);
        A[2][0] += pow(x,3)*y;
        A[2][1] += x*pow(y,3);
        A[2][2] += pow(x,2)*pow(y,2);
        A[2][3] += pow(x,2)*y;
        A[2][4] += x*pow(y,2);
        A[2][5] += x*y;
        A[3][0] += pow(x,3);
        A[3][1] += x*pow(y,2);
        A[3][2] += pow(x,2)*y;
        A[3][3] += pow(x,2);
        A[3][4] += x*y;
        A[3][5] += x;
        A[4][0] += pow(x,2)*y;
        A[4][1] += pow(y,3);
        A[4][2] += x*pow(y,2);
        A[4][3] += x*y;
        A[4][4] += pow(y,2);
        A[4][5] += y;
        A[5][0] += pow(x,2);
        A[5][1] += pow(y,2);
        A[5][2] += x*y;
        A[5][3] += x;
        A[5][4] += y;
        A[5][5] += 1;
      }
    }
  }

  // Move window over DEM, fitting 2nd order polynomial surface to the
  // elevations within the window.
  //cout << "\n\tRunning 2nd order polynomial fitting" << endl;
  //cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  int ndv_present = 0;

  for(int i=0;i<NRows;++i)
  {
    //cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        if(raster_selection[0]==1)  elevation_raster[i][j] = NoDataValue;
        if(raster_selection[1]==1)  slope_raster[i][j] = NoDataValue;
        if(raster_selection[2]==1)  aspect_raster[i][j] = NoDataValue;
        if(raster_selection[3]==1)  curvature_raster[i][j] = NoDataValue;
        if(raster_selection[4]==1)  planform_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[5]==1)  profile_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[6]==1)  tangential_curvature_raster[i][j] = NoDataValue;
        if(raster_selection[7]==1)  classification_raster[i][j] = NoDataValue;
        if(raster_selection[8]==1)
        {
          dzdx_raster[i][j] = NoDataValue;
          dzdy_raster[i][j] = NoDataValue;
        }
      }
      else
      {
      // clip DEM
        //zeta_sampler=zeta.copy();
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            data_kernel[i_kernel][j_kernel] = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(data_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
          }
        }
        // Fit polynomial surface, avoiding nodata values
        // ==================> Could change this,
        // as can fit polynomial surface as long as there are 6 data points.
        if(ndv_present == 0)  // test for nodata values within the selection
        {
          Array1D<float> bb(6,0.0);
          Array1D<float> coeffs(6);
          for (int krow=0; krow<kw; ++krow)
          {
            for (int kcol=0; kcol<kw; ++kcol)
            {
              if (mask[krow][kcol] == 1)
              {
                x = x_kernel[krow][kcol];
                y = y_kernel[krow][kcol];
                zeta = data_kernel[krow][kcol];
                // Generate vector bb
                bb[0] += zeta*x*x;
                bb[1] += zeta*y*y;
                bb[2] += zeta*x*y;
                bb[3] += zeta*x;
                bb[4] += zeta*y;
                bb[5] += zeta;
              }    // end mask
            }      // end kernal column
          }        // end kernal row
          // Solve matrix equations using LU decomposition using the TNT JAMA
          // package:
          // A.coefs = b, where coefs is the coefficients vector.
          LU<float> sol_A(A);  // Create LU object
          coeffs = sol_A.solve(bb);

          float a=coeffs[0];
          float b=coeffs[1];
          float c=coeffs[2];
          float d=coeffs[3];
          float e=coeffs[4];
          float f=coeffs[5];

          // Now calculate the required topographic metrics
          if(raster_selection[0]==1)  elevation_raster[i][j] = f;

          if(raster_selection[1]==1)  slope_raster[i][j] = sqrt(d*d+e*e);

          if(raster_selection[8]==1)
          {
            // note that the kernal translates coordinates so the derivative terms
            // containing x or y go to zero because x = 0 and y = 0 in the transformed coordinates.
            // The negative sign on the dz dy raster is because the rows increase in decreasing northing direction
            dzdx_raster[i][j] = e;
            dzdy_raster[i][j] = -d;
          }

          if(raster_selection[2]==1)
          {
            if(d==0 && e==0) aspect_raster[i][j] = NoDataValue;
            else if(d==0 && e>0) aspect_raster[i][j] = 90;
            else if(d==0 && e<0) aspect_raster[i][j] = 270;
            else
            {
              aspect_raster[i][j] = 270. - (180./M_PI)*atan(e/d) + 90.*(d/abs(d));
              if(aspect_raster[i][j] > 360.0) aspect_raster[i][j] -= 360;
            }
          }

          if(raster_selection[3]==1)  curvature_raster[i][j] = 2*a+2*b;

          if(raster_selection[4]==1 || raster_selection[5]==1 || raster_selection[6]==1 || raster_selection[7]==1)
          {
            float fx, fy, fxx, fyy, fxy, p, q;
            fx = d;
            fy = e;
            fxx = 2*a;
            fyy = 2*b;
            fxy = c;
            p = fx*fx + fy*fy;
            q = p + 1;

            if (raster_selection[4]==1)
            {
              if (q > 0)  planform_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(sqrt(q*q*q));
              else        planform_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[5]==1)
            {
              if((q*q*q > 0) && ((p*sqrt(q*q*q)) != 0))    profile_curvature_raster[i][j] = (fxx*fx*fx + 2*fxy*fx*fy + fyy*fy*fy)/(p*sqrt(q*q*q));
            else                                         profile_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[6]==1)
            {
              if( q>0 && (p*sqrt(q))!=0) tangential_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(p*sqrt(q));
              else                       tangential_curvature_raster[i][j] = NoDataValue;
            }
            if(raster_selection[7]==1)
            {
              float slope = sqrt(d*d + e*e);
              if (slope < 0.1)
              {
                if (fxx < 0 && fyy < 0 && fxy*fxy < fxx*fxx)      classification_raster[i][j] = 1;// Conditions for peak
                else if (fxx > 0 && fyy > 0 && fxy*fxy < fxx*fyy) classification_raster[i][j] = 2;// Conditions for a depression
                else if (fxx*fyy < 0 || fxy*fxy > fxx*fyy)        classification_raster[i][j] = 3;// Conditions for a saddle
                else classification_raster[i][j] = 0;
              }
            }
          }
        }         // end if statement for no data value
        ndv_present = 0;
      }
    }
  }
  // Now create LSDRasters and load into output vector
  vector<LSDRaster> output_rasters_temp(10,VOID);
  vector<LSDRaster> raster_output = output_rasters_temp;
  if(raster_selection[0]==1)
  {
    LSDRaster Elevation(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,elevation_raster,GeoReferencingStrings);
    raster_output[0] = Elevation;
  }
  if(raster_selection[1]==1)
  {
    LSDRaster Slope(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,slope_raster,GeoReferencingStrings);
    raster_output[1] = Slope;
  }
  if(raster_selection[2]==1)
  {
    LSDRaster Aspect(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,aspect_raster,GeoReferencingStrings);
    raster_output[2] = Aspect;
  }
  if(raster_selection[3]==1)
  {
    LSDRaster Curvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,curvature_raster,GeoReferencingStrings);
    raster_output[3] = Curvature;
  }
  if(raster_selection[4]==1)
  {
    LSDRaster PlCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,planform_curvature_raster,GeoReferencingStrings);
    raster_output[4] = PlCurvature;
  }
  if(raster_selection[5]==1)
  {
    LSDRaster PrCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,profile_curvature_raster,GeoReferencingStrings);
    raster_output[5] = PrCurvature;
  }
  if(raster_selection[6]==1)
  {
    LSDRaster TanCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,tangential_curvature_raster,GeoReferencingStrings);
    raster_output[6] = TanCurvature;
  }
  if(raster_selection[7]==1)
  {
    LSDRaster Class(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,classification_raster,GeoReferencingStrings);
    raster_output[7] = Class;
  }
  if(raster_selection[8]==1)
  {
    LSDRaster DzDx(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,dzdx_raster,GeoReferencingStrings);
    LSDRaster DzDy(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,dzdy_raster,GeoReferencingStrings);
    raster_output[8] = DzDx;
    raster_output[9] = DzDy;
  }

  return raster_output;
}




//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// calculate_polyfit_roughness_metrics
//
// This routine houses the code to fit a 6 term polynomial (z =ax^2 + by^2 + cxy
// + dx + ey + f) to a surface, and then use the derivatives of this to
// calculate roughness parameters, that quantify the variability of topographic
// surface normal vectors.
//
// The surface is fitted to all the points that lie within circular
// neighbourhood that is defined by the designated window radius.  This surface
// is used to determine the orientation of the surface normal vector at each
// cell.  The algorithm then searches through the grid again, using a second
// search window to look for the local variability in normal vector orientation.
// The user also inputs a binary raster, which tells the program which rasters
// it wants to create (label as "true" to produce them, "false" to ignore them.
// This has 3 elements, as listed below:
//        0 -> s1 -> describes clustering of normals around the major axis
//        1 -> s2 -> describes clustering of normals around semi major axis
//        2 -> s3 -> describes clustering around minor axis
// The program returns a vector of LSDRasters.  For options marked "0" in
// binary input raster, the returned LSDRaster houses a blank raster, as this
// metric has not been calculated.  The desired LSDRaster can be retrieved from
// the output vector by using the same cell reference shown in the list above
// i.e. it is the same as the reference in the input binary vector.
//
// DTM 01/04/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<LSDRaster> LSDRaster::calculate_polyfit_roughness_metrics(float window_radius1, float window_radius2, vector<int> raster_selection)
{
  Array2D<float> void_array(1,1,NoDataValue);
  LSDRaster VOID(1,1,NoDataValue,NoDataValue,NoDataValue,NoDataValue,void_array,GeoReferencingStrings);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius1 < sqrt(2)*DataResolution)
  {
    cout << "Supplied window radius: " << window_radius1 << " is less than sqrt(2) * data resolution: " <<
    sqrt(2)*DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius1 = sqrt(2)*DataResolution;
  }
  if (window_radius2 < sqrt(2)*DataResolution)
  {
    cout << "Supplied window radius: " << sqrt(2)*window_radius2 << " is less than the data resolution: " <<
    sqrt(2)*DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius2 = sqrt(2)*DataResolution;
  }
  // this fits a polynomial surface over a kernel window. First, perpare the
  // kernel
  int kr = int(ceil(window_radius1/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel

  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<float> x_kernel(kw,kw,NoDataValue);
  Array2D<float> y_kernel(kw,kw,NoDataValue);
  Array2D<int> mask(kw,kw,0);

  // reset the a,b,c,d,e and f matrices (the coefficient matrices)
  Array2D<float> temp_coef(NRows,NCols,NoDataValue);
  Array2D<float> pheta, phi, s1_raster, s2_raster, s3_raster;
  // Copy across raster template into the desired array containers
  if(raster_selection[0]==1)  s1_raster = temp_coef.copy();
  if(raster_selection[1]==1)  s2_raster = temp_coef.copy();
  if(raster_selection[2]==1)  s3_raster = temp_coef.copy();
  pheta = temp_coef.copy();
  phi = temp_coef.copy();
  //float a,b,c,d,e,f;
  float d,e;
  // scale kernel window to resolution of DEM, and translate coordinates to be
  // centred on cell of interest (the centre cell)
  float x,y,zeta,radial_dist;
  for(int i=0;i<kw;++i)
  {
    for(int j=0;j<kw;++j)
    {
      x_kernel[i][j]=(i-kr)*DataResolution;
      y_kernel[i][j]=(j-kr)*DataResolution;
      // Build circular mask
      // distance from centre to this point.
      radial_dist = sqrt(y_kernel[i][j]*y_kernel[i][j] + x_kernel[i][j]*x_kernel[i][j]);

      if (radial_dist <= window_radius1)
      {
        mask[i][j] = 1;
      }
    }
  }
  // FIT POLYNOMIAL SURFACE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO
  // DETERMINE TOPOGRAPHIC METRICS
  // Have N simultaneous linear equations, and N unknowns.
  // => b = Ax, where x is a 1xN array containing the coefficients we need for
  // surface fitting.
  // A is constructed using different combinations of x and y, thus we only need
  // to compute this once, since the window size does not change.
  // For 2nd order surface fitting, there are 6 coefficients, therefore A is a
  // 6x6 matrix
  Array2D<float> A(6,6,0.0);
  for (int i=0; i<kw; ++i)
  {
    for (int j=0; j<kw; ++j)
    {
      if (mask[i][j] == 1)
      {
        x = x_kernel[i][j];
        y = y_kernel[i][j];

        // Generate matrix A
        A[0][0] += pow(x,4);
        A[0][1] += pow(x,2)*pow(y,2);
        A[0][2] += pow(x,3)*y;
        A[0][3] += pow(x,3);
        A[0][4] += pow(x,2)*y;
        A[0][5] += pow(x,2);
        A[1][0] += pow(x,2)*pow(y,2);
        A[1][1] += pow(y,4);
        A[1][2] += x*pow(y,3);
        A[1][3] += x*pow(y,2);
        A[1][4] += pow(y,3);
        A[1][5] += pow(y,2);
        A[2][0] += pow(x,3)*y;
        A[2][1] += x*pow(y,3);
        A[2][2] += pow(x,2)*pow(y,2);
        A[2][3] += pow(x,2)*y;
        A[2][4] += x*pow(y,2);
        A[2][5] += x*y;
        A[3][0] += pow(x,3);
        A[3][1] += x*pow(y,2);
        A[3][2] += pow(x,2)*y;
        A[3][3] += pow(x,2);
        A[3][4] += x*y;
        A[3][5] += x;
        A[4][0] += pow(x,2)*y;
        A[4][1] += pow(y,3);
        A[4][2] += x*pow(y,2);
        A[4][3] += x*y;
        A[4][4] += pow(y,2);
        A[4][5] += y;
        A[5][0] += pow(x,2);
        A[5][1] += pow(y,2);
        A[5][2] += x*y;
        A[5][3] += x;
        A[5][4] += y;
        A[5][5] += 1;
      }
    }
  }

  // Move window over DEM, fitting 2nd order polynomial surface to the
  // elevations within the window.
  cout << "\n\tRunning 2nd order polynomial fitting" << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  int ndv_present = 0;

  for(int i=0;i<NRows;++i)
  {
    cout << flush << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        pheta[i][j]=NoDataValue;
        phi[i][j]=NoDataValue;
      }
      else
      {
        // clip DEM
        //zeta_sampler=zeta.copy();
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            data_kernel[i_kernel][j_kernel] =
                  RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(data_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
          }
        }
        // Fit polynomial surface, avoiding nodata values          ==================> Could change this, as can fit polynomial surface as long as there are 6 data points.
        if(ndv_present == 0)  // test for nodata values within the selection
        {
          Array1D<float> bb(6,0.0);
          Array1D<float> coeffs(6);
          for (int krow=0; krow<kw; ++krow)
          {
            for (int kcol=0; kcol<kw; ++kcol)
            {
              if (mask[krow][kcol] == 1)
              {
                x = x_kernel[krow][kcol];
                y = y_kernel[krow][kcol];
                zeta = data_kernel[krow][kcol];
                // Generate vector bb
                bb[0] += zeta*x*x;
                bb[1] += zeta*y*y;
                bb[2] += zeta*x*y;
                bb[3] += zeta*x;
                bb[4] += zeta*y;
                bb[5] += zeta;
              }    // end mask
            }      // end kernal column
          }        // end kernal row
          // Solve matrix equations using LU decomposition using the TNT JAMA
          // package:
          // A.coefs = b, where coefs is the coefficients vector.
          LU<float> sol_A(A);  // Create LU object
          coeffs = sol_A.solve(bb);

          //a=coeffs[0];
          //b=coeffs[1];
          //c=coeffs[2];
          d=coeffs[3];
          e=coeffs[4];
          //f=coeffs[5];

          // COMPUTING SURFACE NORMAL in spherical polar coordinate (ignore
          // radial component)
          pheta[i][j] = atan(sqrt(pow(d,2) + pow(e,2)));
          if(d==0 && e==0) phi[i][j] = NoDataValue;
          else if(d==0 && e>0) phi[i][j] = acos(-1)/2;
          else if(d==0 && e<0) phi[i][j] = 3*acos(-1)/2;
          else phi[i][j]=atan(e/d);
        }        // end if statement for no data value
        ndv_present = 0;
      }
    }
  }
  // 2) DETERMINE ORIENTATION MATRIX AT EACH POINT, AND THEN SOLVE FOR THE
  // EIGENVALUES.
  // Prepare new kernel
  kr=ceil(window_radius2/DataResolution);      // Set radius of kernel as >= specified radius
  kw=2*kr+1;                    // width of kernel
  // Declare kernel arrays
  Array2D<float> pheta_kernel(kw,kw);
  Array2D<float> phi_kernel(kw,kw);
  // Build circular mask
  Array2D<int> mask2(kw,kw,0);
  float x_kernel_ref,y_kernel_ref;
  for(int i=0;i<kw;++i)
  {
    for(int j=0;j<kw;++j)
    {
      x_kernel_ref=(i-kr)*DataResolution;
      y_kernel_ref=(j-kr)*DataResolution;
      radial_dist = sqrt(y_kernel_ref*y_kernel_ref + x_kernel_ref*x_kernel_ref); // distance from centre to this point.

      if (radial_dist <= window_radius2)
      {
        mask2[i][j] = 1;
      }
    }
  }

  // Loop over DEM again, this time looking at variability of surface normals
  cout << "Finding eigenvalues for local surface. Search radius = " << kr << "m" << endl;
  for(int i=0; i<NRows; ++i)
  {
    cout << flush << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0; j<NCols; ++j)
    {
      // Avoid edges and nodata values
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        if(raster_selection[0]==1)  s1_raster[i][j] = NoDataValue;
        if(raster_selection[1]==1)  s2_raster[i][j] = NoDataValue;
        if(raster_selection[2]==1)  s3_raster[i][j] = NoDataValue;
      }
      else
      {
        // build orientation matrix for this point
        Array2D<double> T(3,3,0.0);
        Array2D<double> D(3,3);
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            pheta_kernel[i_kernel][j_kernel]=pheta[i-kr+i_kernel][j-kr+j_kernel];
            phi_kernel[i_kernel][j_kernel]=phi[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(phi_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
          }
        }
        int N=0;
        //         if(ndv_present == 0)  // test for nodata values within the selection

          for(int i_kernel=0;i_kernel<kw;++i_kernel)
          {
            for(int j_kernel=0;j_kernel<kw;++j_kernel)
            {
              if (mask2[i_kernel][j_kernel]==1)
              {
                double li,mi,ni;
                li=0;
                mi=0;
                ni=0;
                if(phi_kernel[i_kernel][j_kernel]!=0 && phi_kernel[i_kernel][j_kernel]!=NoDataValue  && pheta_kernel[i_kernel][j_kernel]!=NoDataValue)
                {
                  li=sin(pheta_kernel[i_kernel][j_kernel])*cos(phi_kernel[i_kernel][j_kernel]);
                  mi=sin(pheta_kernel[i_kernel][j_kernel])*sin(phi_kernel[i_kernel][j_kernel]);
                  ni=cos(pheta_kernel[i_kernel][j_kernel]);
                  T[0][0] += pow(li,2);
                  T[0][1] += li*mi;
                  T[0][2] += li*ni;
                  T[1][0] += mi*li;
                  T[1][1] += pow(mi,2);
                  T[1][2] += mi*ni;
                  T[2][0] += ni*li;
                  T[2][1] += ni*mi;
                  T[2][2] += pow(ni,2);
                  ++N;
                }
              }
            }
          }
          // Find eigenvalues of the orientation matrix
          Eigenvalue<double> eigenvalue_matrix(T);
          eigenvalue_matrix.getD(D);
          //surface_roughness(kw,kw,T,lnS1_S2, S3);
          if(raster_selection[0]==1)  s1_raster[i][j] = D[2][2]/N;
          if(raster_selection[1]==1)  s2_raster[i][j] = D[1][1]/N;
          if(raster_selection[2]==1)  s3_raster[i][j] = D[0][0]/N;
//         }
//       ndv_present = 0;
      }
    }
  }

  // Now create LSDRasters and load into output vector
  vector<LSDRaster> output_rasters_temp(3,VOID);
  vector<LSDRaster> raster_output = output_rasters_temp;
  if(raster_selection[0]==1)
  {
    LSDRaster s1(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s1_raster,GeoReferencingStrings);
    raster_output[0] = s1;
  }
  if(raster_selection[1]==1)
  {
    LSDRaster s2(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s2_raster,GeoReferencingStrings);
    raster_output[1] = s2;
  }
  if(raster_selection[2]==1)
  {
    LSDRaster s3(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s3_raster,GeoReferencingStrings);
    raster_output[2] = s3;
  }
  return raster_output;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// calculate_polyfit_coefficient_matrices
//
// this function calcualtes 6 coefficient matrices that allow the user to
// then calcualte slope, curvature, aspect, a classification for finding saddles and peaks
// and other metrics
//
// The coefficient matrices are overwritten during the running of this member function
//
// DTM
//
// Updated 15/07/2013 to use a circular mask for surface fitting. DTM
// Updated 24/07/2013 to check window_radius size and correct values below data resolution. SWDG
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::calculate_polyfit_coefficient_matrices(float window_radius,
                    Array2D<float>& a, Array2D<float>& b,
                    Array2D<float>& c, Array2D<float>& d,
                    Array2D<float>& e, Array2D<float>& f)
{


  // catch if the supplied window radius is less than the data resolution and set
  // it to equal the data resolution - SWDG
  if (window_radius < DataResolution){
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution: " <<
    DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius = DataResolution;
  }

  // this fits a polynomial surface over a kernel window. First, perpare the kernel
  int kr = int(ceil(window_radius/DataResolution));           // Set radius of kernel
  int kw=2*kr+1;                                // width of kernel

  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<float> x_kernel(kw,kw,NoDataValue);
  Array2D<float> y_kernel(kw,kw,NoDataValue);
  Array2D<int> mask(kw,kw,0);

  // reset the a,b,c,d,e and f matrices (the coefficient matrices)
  Array2D<float> temp_coef(NRows,NCols,0.0);
  a = temp_coef.copy();
  b = temp_coef.copy();
  c = temp_coef.copy();
  d = temp_coef.copy();
  e = temp_coef.copy();
  f = temp_coef.copy();

  // scale kernel window to resolution of DEM, and translate coordinates to be
  // centred on cell of interest (the centre cell)
  float x,y,zeta,radial_dist;
  for(int i=0;i<kw;++i)
  {
      for(int j=0;j<kw;++j)
      {
          x_kernel[i][j]=(i-kr)*DataResolution;
          y_kernel[i][j]=(j-kr)*DataResolution;

      // Build circular mask
      // distance from centre to this point.
      radial_dist = sqrt(y_kernel[i][j]*y_kernel[i][j] + x_kernel[i][j]*x_kernel[i][j]);

          if (floor(radial_dist) <= window_radius)
          {
        mask[i][j] = 1;
      }
        }
  }

  // FIT POLYNOMIAL SURFACE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO
  // DETERMINE TOPOGRAPHIC METRICS

  // Have N simultaneous linear equations, and N unknowns.
  // => b = Ax, where x is a 1xN array containing the coefficients we need for
  // surface fitting.
  // A is constructed using different combinations of x and y, thus we only need
  // to compute this once, since the window size does not change.
  // For 2nd order surface fitting, there are 6 coefficients, therefore A is a
  // 6x6 matrix
  Array2D<float> A(6,6);
  for (int i=0; i<kw; ++i)
  {
    for (int j=0; j<kw; ++j)
    {
      if (mask[i][j] == 1)
          {
            x = x_kernel[i][j];
          y = y_kernel[i][j];

          // Generate matrix A
          A[0][0] += pow(x,4);
          A[0][1] += pow(x,2)*pow(y,2);
          A[0][2] += pow(x,3)*y;
          A[0][3] += pow(x,3);
          A[0][4] += pow(x,2)*y;
          A[0][5] += pow(x,2);
          A[1][0] += pow(x,2)*pow(y,2);
          A[1][1] += pow(y,4);
          A[1][2] += x*pow(y,3);
          A[1][3] += x*pow(y,2);
          A[1][4] += pow(y,3);
          A[1][5] += pow(y,2);
          A[2][0] += pow(x,3)*y;
          A[2][1] += x*pow(y,3);
          A[2][2] += pow(x,2)*pow(y,2);
          A[2][3] += pow(x,2)*y;
          A[2][4] += x*pow(y,2);
          A[2][5] += x*y;
          A[3][0] += pow(x,3);
          A[3][1] += x*pow(y,2);
          A[3][2] += pow(x,2)*y;
          A[3][3] += pow(x,2);
          A[3][4] += x*y;
          A[3][5] += x;
          A[4][0] += pow(x,2)*y;
          A[4][1] += pow(y,3);
          A[4][2] += x*pow(y,2);
          A[4][3] += x*y;
          A[4][4] += pow(y,2);
          A[4][5] += y;
          A[5][0] += pow(x,2);
          A[5][1] += pow(y,2);
          A[5][2] += x*y;
          A[5][3] += x;
          A[5][4] += y;
          A[5][5] += 1;
      }
    }
  }

  // Move window over DEM, fitting 2nd order polynomial surface to the
  // elevations within the window.
  cout << "\n\tRunning 2nd order polynomial fitting" << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  int ndv_present = 0;

  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols))
      {
        a[i][j] = NoDataValue;
        b[i][j] = NoDataValue;
        c[i][j] = NoDataValue;
        d[i][j] = NoDataValue;
        e[i][j] = NoDataValue;
        f[i][j] = NoDataValue;
      }
      // Avoid nodata values
      else if(RasterData[i][j]==NoDataValue)
      {
        a[i][j] = NoDataValue;
        b[i][j] = NoDataValue;
        c[i][j] = NoDataValue;
        d[i][j] = NoDataValue;
        e[i][j] = NoDataValue;
        f[i][j] = NoDataValue;
      }
      else
      {
        // clip DEM
        //zeta_sampler=zeta.copy();
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
            for(int j_kernel=0;j_kernel<kw;++j_kernel)
            {
            data_kernel[i_kernel][j_kernel] =
                  RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(data_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
            }
        }

        // Fit polynomial surface, avoiding nodata values
        if(ndv_present == 0)  // test for nodata values within the selection
        {
          Array1D<float> bb(6,0.0);
          Array1D<float> coeffs(6);
          for (int krow=0; krow<kw; ++krow)
          {
            for (int kcol=0; kcol<kw; ++kcol)
            {
              if (mask[krow][kcol] == 1)
                      {
                        x = x_kernel[krow][kcol];
                    y = y_kernel[krow][kcol];
                    zeta = data_kernel[krow][kcol];
                    // Generate vector bb
                    bb[0] += zeta*x*x;
                    bb[1] += zeta*y*y;
                    bb[2] += zeta*x*y;
                    bb[3] += zeta*x;
                    bb[4] += zeta*y;
                    bb[5] += zeta;
                  }    // end mask
                  }      // end kernal column
          }        // end kernal row
          // Solve matrix equations using LU decomposition using the TNT JAMA package:
          // A.coefs = b, where coefs is the coefficients vector.
          LU<float> sol_A(A);  // Create LU object
          coeffs = sol_A.solve(bb);

            a[i][j]=coeffs[0];
            b[i][j]=coeffs[1];
            c[i][j]=coeffs[2];
            d[i][j]=coeffs[3];
            e[i][j]=coeffs[4];
            f[i][j]=coeffs[5];
        }          // end if statement for no data value
        ndv_present = 0;
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// calculate_polyfit_surface_metrics
//
// This routine houses the code to fit a 6 term polynomial (z =ax^2 + by^2 + cxy
// + dx + ey + f) to a surface, and then use the derivatives of this to
// calculate various useful geometric properties such as slope and curvature.
//
// The surface is fitted to all the points that lie within circular
// neighbourhood that is defined by the designated window radius.  The user also
// inputs a binary raster, which tells the program which rasters it wants to
// create (label as "true" to produce them, "false" to ignore them. This has 8
// elements, as listed below:
//        0 -> Elevation (smoothed by surface fitting)
//        1 -> Slope
//        2 -> Aspect
//        3 -> Curvature
//        4 -> Planform Curvature
//        5 -> Profile Curvature
//        6 -> Tangential Curvature
//        7 -> Stationary point classification (1=peak, 2=depression, 3=saddle)
// The program returns a vector of LSDRasters.  For options marked "false" in
// boolean input raster, the returned LSDRaster houses a blank raster, as this
// metric has not been calculated.  The desired LSDRaster can be retrieved from
// the output vector by using the cell reference shown in the list above i.e. it
// is the same as the reference in the input binary vector.
//
// DTM 28/03/2014
//
// FJC 16/10/17 - Overloaded function to fit a polynomial surface to a specified
// number of pixels rather than using a circular window radius.  User passes in
// a vector of nodes which represent the pixel that you want to fit the surface
// to.
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// vector<LSDRaster> LSDRaster::calculate_polyfit_surface_metrics(vector<int> NodeIndices)
// {
//   Array2D<float> void_array(1,1,NoDataValue);
//   LSDRaster VOID(1,1,NoDataValue,NoDataValue,NoDataValue,NoDataValue,void_array,GeoReferencingStrings);
//
//   // mask the DEM based on the nodes of interest
//   Array2D<int> mask_array(NRows,NCols,0);
//   int row, col;
//   for (int i = 0; i < int(NodeIndices.size(); i++))
//   {
//     this_node = NodeIndices[i];
//     FlowInfo.retrieve_current_row_and_col(this_node, row, col);
//     mask_array[row][col] = 1;
//   }
//
//   // reset the a,b,c,d,e and f matrices (the coefficient matrices)
//   Array2D<float> temp_coef(NRows,NCols,NoDataValue);
//   Array2D<float> elevation_raster, slope_raster, aspect_raster, curvature_raster, planform_curvature_raster,
//                   profile_curvature_raster, tangential_curvature_raster, classification_raster,
//                   s1_raster, s2_raster, s3_raster;
//
//   // Copy across raster template into the desired array containers
//   if(raster_selection[0]==1)  elevation_raster = temp_coef.copy();
//   if(raster_selection[1]==1)  slope_raster = temp_coef.copy();
//   if(raster_selection[2]==1)  aspect_raster = temp_coef.copy();
//   if(raster_selection[3]==1)  curvature_raster = temp_coef.copy();
//   if(raster_selection[4]==1)  planform_curvature_raster = temp_coef.copy();
//   if(raster_selection[5]==1)  profile_curvature_raster = temp_coef.copy();
//   if(raster_selection[6]==1)  tangential_curvature_raster = temp_coef.copy();
//   if(raster_selection[7]==1)  classification_raster = temp_coef.copy();
//
//   // FIT POLYNOMIAL SURFACE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO
//   // DETERMINE TOPOGRAPHIC METRICS
//   // Have N simultaneous linear equations, and N unknowns.
//   // => b = Ax, where x is a 1xN array containing the coefficients we need for
//   // surface fitting.
//   // A is constructed using different combinations of x and y, thus we only need
//   // to compute this once, since the window size does not change.
//   // For 2nd order surface fitting, there are 6 coefficients, therefore A is a
//   // 6x6 matrix
//   Array2D<float> A(6,6,0.0);
//   for (int i=0; i<NRows; ++i)
//   {
//     for (int j=0; j<NCols; ++j)
//     {
//       if (mask[i][j] == 1)
//       {
//         x = x_kernel[i][j];
//         y = y_kernel[i][j];
//
//         // Generate matrix A
//         A[0][0] += pow(x,4);
//         A[0][1] += pow(x,2)*pow(y,2);
//         A[0][2] += pow(x,3)*y;
//         A[0][3] += pow(x,3);
//         A[0][4] += pow(x,2)*y;
//         A[0][5] += pow(x,2);
//         A[1][0] += pow(x,2)*pow(y,2);
//         A[1][1] += pow(y,4);
//         A[1][2] += x*pow(y,3);
//         A[1][3] += x*pow(y,2);
//         A[1][4] += pow(y,3);
//         A[1][5] += pow(y,2);
//         A[2][0] += pow(x,3)*y;
//         A[2][1] += x*pow(y,3);
//         A[2][2] += pow(x,2)*pow(y,2);
//         A[2][3] += pow(x,2)*y;
//         A[2][4] += x*pow(y,2);
//         A[2][5] += x*y;
//         A[3][0] += pow(x,3);
//         A[3][1] += x*pow(y,2);
//         A[3][2] += pow(x,2)*y;
//         A[3][3] += pow(x,2);
//         A[3][4] += x*y;
//         A[3][5] += x;
//         A[4][0] += pow(x,2)*y;
//         A[4][1] += pow(y,3);
//         A[4][2] += x*pow(y,2);
//         A[4][3] += x*y;
//         A[4][4] += pow(y,2);
//         A[4][5] += y;
//         A[5][0] += pow(x,2);
//         A[5][1] += pow(y,2);
//         A[5][2] += x*y;
//         A[5][3] += x;
//         A[5][4] += y;
//         A[5][5] += 1;
//       }
//     }
//   }
//
//   // Move window over DEM, fitting 2nd order polynomial surface to the
//   // elevations within the window.
//   //cout << "\n\tRunning 2nd order polynomial fitting" << endl;
//   //cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
//   int ndv_present = 0;
//
//   for(int i=0;i<NRows;++i)
//   {
//     //cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
//     for(int j=0;j<NCols;++j)
//     {
//       // Avoid edges
//       if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
//       {
//         if(raster_selection[0]==1)  elevation_raster[i][j] = NoDataValue;
//         if(raster_selection[1]==1)  slope_raster[i][j] = NoDataValue;
//         if(raster_selection[2]==1)  aspect_raster[i][j] = NoDataValue;
//         if(raster_selection[3]==1)  curvature_raster[i][j] = NoDataValue;
//         if(raster_selection[4]==1)  planform_curvature_raster[i][j] = NoDataValue;
//         if(raster_selection[5]==1)  profile_curvature_raster[i][j] = NoDataValue;
//         if(raster_selection[6]==1)  tangential_curvature_raster[i][j] = NoDataValue;
//         if(raster_selection[7]==1)  classification_raster[i][j] = NoDataValue;
//       }
//       else
//       {
//       // clip DEM
//         //zeta_sampler=zeta.copy();
//         for(int i_kernel=0;i_kernel<kw;++i_kernel)
//         {
//           for(int j_kernel=0;j_kernel<kw;++j_kernel)
//           {
//             data_kernel[i_kernel][j_kernel] = RasterData[i-kr+i_kernel][j-kr+j_kernel];
//             // check for nodata values nearby
//             if(data_kernel[i_kernel][j_kernel]==NoDataValue)
//             {
//               ndv_present=1;
//             }
//           }
//         }
//         // Fit polynomial surface, avoiding nodata values
//         // ==================> Could change this,
//         // as can fit polynomial surface as long as there are 6 data points.
//         if(ndv_present == 0)  // test for nodata values within the selection
//         {
//           Array1D<float> bb(6,0.0);
//           Array1D<float> coeffs(6);
//           for (int krow=0; krow<kw; ++krow)
//           {
//             for (int kcol=0; kcol<kw; ++kcol)
//             {
//               if (mask[krow][kcol] == 1)
//               {
//                 x = x_kernel[krow][kcol];
//                 y = y_kernel[krow][kcol];
//                 zeta = data_kernel[krow][kcol];
//                 // Generate vector bb
//                 bb[0] += zeta*x*x;
//                 bb[1] += zeta*y*y;
//                 bb[2] += zeta*x*y;
//                 bb[3] += zeta*x;
//                 bb[4] += zeta*y;
//                 bb[5] += zeta;
//               }    // end mask
//             }      // end kernal column
//           }        // end kernal row
//           // Solve matrix equations using LU decomposition using the TNT JAMA
//           // package:
//           // A.coefs = b, where coefs is the coefficients vector.
//           LU<float> sol_A(A);  // Create LU object
//           coeffs = sol_A.solve(bb);
//
//           float a=coeffs[0];
//           float b=coeffs[1];
//           float c=coeffs[2];
//           float d=coeffs[3];
//           float e=coeffs[4];
//           float f=coeffs[5];
//
//           // Now calculate the required topographic metrics
//           if(raster_selection[0]==1)  elevation_raster[i][j] = f;
//
//           if(raster_selection[1]==1)  slope_raster[i][j] = sqrt(d*d+e*e);
//
//           if(raster_selection[2]==1)
//           {
//             if(d==0 && e==0) aspect_raster[i][j] = NoDataValue;
//             else if(d==0 && e>0) aspect_raster[i][j] = 90;
//             else if(d==0 && e<0) aspect_raster[i][j] = 270;
//             else
//             {
//               aspect_raster[i][j] = 270. - (180./M_PI)*atan(e/d) + 90.*(d/abs(d));
//               if(aspect_raster[i][j] > 360.0) aspect_raster[i][j] -= 360;
//             }
//           }
//
//           if(raster_selection[3]==1)  curvature_raster[i][j] = 2*a+2*b;
//
//           if(raster_selection[4]==1 || raster_selection[5]==1 || raster_selection[6]==1 || raster_selection[7]==1)
//           {
//             float fx, fy, fxx, fyy, fxy, p, q;
//             fx = d;
//             fy = e;
//             fxx = 2*a;
//             fyy = 2*b;
//             fxy = c;
//             p = fx*fx + fy*fy;
//             q = p + 1;
//
//             if (raster_selection[4]==1)
//             {
//               if (q > 0)  planform_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(sqrt(q*q*q));
//               else        planform_curvature_raster[i][j] = NoDataValue;
//             }
//             if(raster_selection[5]==1)
//             {
//               if((q*q*q > 0) && ((p*sqrt(q*q*q)) != 0))    profile_curvature_raster[i][j] = (fxx*fx*fx + 2*fxy*fx*fy + fyy*fy*fy)/(p*sqrt(q*q*q));
//             else                                         profile_curvature_raster[i][j] = NoDataValue;
//             }
//             if(raster_selection[6]==1)
//             {
//               if( q>0 && (p*sqrt(q))!=0) tangential_curvature_raster[i][j] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(p*sqrt(q));
//               else                       tangential_curvature_raster[i][j] = NoDataValue;
//             }
//             if(raster_selection[7]==1)
//             {
//               float slope = sqrt(d*d + e*e);
//               if (slope < 0.1)
//               {
//                 if (fxx < 0 && fyy < 0 && fxy*fxy < fxx*fxx)      classification_raster[i][j] = 1;// Conditions for peak
//                 else if (fxx > 0 && fyy > 0 && fxy*fxy < fxx*fyy) classification_raster[i][j] = 2;// Conditions for a depression
//                 else if (fxx*fyy < 0 || fxy*fxy > fxx*fyy)        classification_raster[i][j] = 3;// Conditions for a saddle
//                 else classification_raster[i][j] = 0;
//               }
//             }
//           }
//         }         // end if statement for no data value
//         ndv_present = 0;
//       }
//     }
//   }
//   // Now create LSDRasters and load into output vector
//   vector<LSDRaster> output_rasters_temp(8,VOID);
//   vector<LSDRaster> raster_output = output_rasters_temp;
//   if(raster_selection[0]==1)
//   {
//     LSDRaster Elevation(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,elevation_raster,GeoReferencingStrings);
//     raster_output[0] = Elevation;
//   }
//   if(raster_selection[1]==1)
//   {
//     LSDRaster Slope(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,slope_raster,GeoReferencingStrings);
//     raster_output[1] = Slope;
//   }
//   if(raster_selection[2]==1)
//   {
//     LSDRaster Aspect(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,aspect_raster,GeoReferencingStrings);
//     raster_output[2] = Aspect;
//   }
//   if(raster_selection[3]==1)
//   {
//     LSDRaster Curvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,curvature_raster,GeoReferencingStrings);
//     raster_output[3] = Curvature;
//   }
//   if(raster_selection[4]==1)
//   {
//     LSDRaster PlCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,planform_curvature_raster,GeoReferencingStrings);
//     raster_output[4] = PlCurvature;
//   }
//   if(raster_selection[5]==1)
//   {
//     LSDRaster PrCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,profile_curvature_raster,GeoReferencingStrings);
//     raster_output[5] = PrCurvature;
//   }
//   if(raster_selection[6]==1)
//   {
//     LSDRaster TanCurvature(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,tangential_curvature_raster,GeoReferencingStrings);
//     raster_output[6] = TanCurvature;
//   }
//   if(raster_selection[7]==1)
//   {
//     LSDRaster Class(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,classification_raster,GeoReferencingStrings);
//     raster_output[7] = Class;
//   }
//   return raster_output;
// }

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the elevation based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
//
// added by FC 24/03/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_elevation(Array2D<float>& f)
{
  // create the new elevation raster
  Array2D<float> elevation_data(NRows,NCols,NoDataValue);

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (f[row][col] != NoDataValue)
      {
        elevation_data[row][col] = f[row][col];
      }
    }
  }

  LSDRaster elevation_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                           elevation_data,GeoReferencingStrings);
  return elevation_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the slope based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
//
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_slope(Array2D<float>& d, Array2D<float>& e)
{
  // create the new slope raster
  Array2D<float> slope_data(NRows,NCols,NoDataValue);

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (d[row][col] != NoDataValue)
      {
        slope_data[row][col] = sqrt(d[row][col]*d[row][col]+e[row][col]*e[row][col]);
      }
    }
  }

  LSDRaster slope_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         NoDataValue,slope_data,GeoReferencingStrings);
  return slope_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the aspect based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
// SMM modified from DTM standalone code 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_aspect(Array2D<float>& d, Array2D<float>& e)
{
  // create the new slope raster
  Array2D<float> aspect_data(NRows,NCols,NoDataValue);

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (d[row][col] != NoDataValue)
      {
        if(d[row][col]==0 || e[row][col]==0)
        {
          aspect_data[row][col] = NoDataValue;
        }
        else
        {
          aspect_data[row][col] = 180 - 57.29578*atan(e[row][col]/d[row][col])
                                      + 90*(d[row][col]/abs(d[row][col]));
          if(aspect_data[row][col] < 180.0)
          {
            aspect_data[row][col] = 180.0 - aspect_data[row][col];
          }
          else
          {
            aspect_data[row][col] = 360.0 + (180 - aspect_data[row][col]);
          }
        }
      }
    }
  }

  LSDRaster aspect_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,aspect_data,GeoReferencingStrings);
  return aspect_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the curvature based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
//
// SMM modified from DTM standalone code 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_curvature(Array2D<float>& a, Array2D<float>& b)
{
  // create the new slope raster
  Array2D<float> curvature_data(NRows,NCols,NoDataValue);

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (a[row][col] != NoDataValue)
      {
        curvature_data[row][col] = 2*a[row][col]+2*b[row][col];
      }
    }
  }


  LSDRaster curvature_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,curvature_data,GeoReferencingStrings);
  return curvature_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the planform curvature based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
// Code written by DM and FC 09/10/12
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_planform_curvature(Array2D<float>& a, Array2D<float>& b,
                                                          Array2D<float>& c, Array2D<float>& d,
                                                          Array2D<float>& e)
{
  // create the new planform curvature raster
  Array2D<float> pl_curvature_data(NRows,NCols,NoDataValue);
                            float fx, fy, fxx, fyy, fxy, p, q;

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (a[row][col] != NoDataValue)
      {
        fx = d[row][col];
        fy = e[row][col];
        fxx = 2*a[row][col];
        fyy = 2*b[row][col];
        fxy = c[row][col];
        p = fx*fx + fy*fy;
        q = p + 1;

        if (q > 0)
        {
          pl_curvature_data[row][col] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/(sqrt(q*q*q));
        }
        else
        {
          pl_curvature_data[row][col] = NoDataValue;
        }
      }
    }
  }


  LSDRaster planform_curvature_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,pl_curvature_data,GeoReferencingStrings);
  return planform_curvature_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the profile curvature based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
// Code written by FC 09/10/12
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_profile_curvature(Array2D<float>& a, Array2D<float>& b,
                                                          Array2D<float>& c, Array2D<float>& d,
                                                          Array2D<float>& e)
{
  // create the new profile curvature raster
  Array2D<float> profile_curvature_data(NRows,NCols,NoDataValue);
    float fx, fy, fxx, fyy, fxy, p, q, qqq, denom;

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (a[row][col] != NoDataValue)
      {
          fx = d[row][col];
          fy = e[row][col];
          fxx = 2*a[row][col];
          fyy = 2*b[row][col];
          fxy = c[row][col];
          p = fx*fx + fy*fy;
          q = p + 1;

          qqq = q*q*q;
          if( qqq>0)
          {
          denom = (p*sqrt(qqq));
          if( denom != 0)
          {
            profile_curvature_data[row][col] = (fxx*fx*fx + 2*fxy*fx*fy + fyy*fy*fy)/denom;
          }
          else
          {
            profile_curvature_data[row][col] = NoDataValue;
          }
        }
        else
        {
          profile_curvature_data[row][col] = NoDataValue;
        }



      }
    }
  }


  LSDRaster profile_curvature_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,profile_curvature_data,GeoReferencingStrings);
  return profile_curvature_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// This function calculates the tangential curvature based on a polynomial fit
// the window is determined by the calculate_polyfit_coefficient_matrices
// this function also calculates the a,b,c,d,e and f coefficient matrices
// Code written by DM and FC 09/10/12
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_polyfit_tangential_curvature(Array2D<float>& a, Array2D<float>& b,
                                                          Array2D<float>& c, Array2D<float>& d,
                                                          Array2D<float>& e)
{
  // create the new planform curvature raster
  Array2D<float> ta_curvature_data(NRows,NCols,NoDataValue);
    float fx, fy, fxx, fyy, fxy, p, q, denom;

  for (int row = 0; row<NRows; row++)
  {

    for(int col = 0; col<NCols; col++)
    {

      if (a[row][col] != NoDataValue)
      {
        fx = d[row][col];
          fy = e[row][col];
          fxx = 2*a[row][col];
          fyy = 2*b[row][col];
          fxy = c[row][col];
          p = fx*fx + fy*fy;
          q = p + 1;


          if( q>0)
          {
          denom = (p*sqrt(q));
          if( denom != 0)
          {
            ta_curvature_data[row][col] = (fxx*fy*fy - 2*fxy*fx*fy + fyy*fx*fx)/denom;
          }
          else
          {
            ta_curvature_data[row][col] = NoDataValue;
          }
        }
        else
        {
          ta_curvature_data[row][col] = NoDataValue;
        }

      }
    }
  }


  LSDRaster tangential_curvature_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,ta_curvature_data,GeoReferencingStrings);
  return tangential_curvature_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function identifies approximate position of stationary points within
// discrete surface using a threshold slope. The nature of the stationary point
// is then determined to discriminate peaks, depressions and saddles.
// 0 = Non-stationary
// 1 = Peak
// 2 = Depression
// 3 = Saddle
//
// Added by DTM 17/09/2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDIndexRaster LSDRaster::calculate_polyfit_classification(Array2D<float>& a, Array2D<float>& b, Array2D<float>& c,
                                                           Array2D<float>& d, Array2D<float>& e)
{
  // create the new classification raster
  int intNoDataValue = int(NoDataValue);
  Array2D<int> classification(NRows,NCols,intNoDataValue);
  float d2z_dx2,d2z_dy2,d2z_dxdy,slope;
  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (d[row][col] != NoDataValue)
      {
        slope = sqrt(pow(d[row][col],2) + pow(e[row][col],2));
            if (slope < 0.1) // Threshold for assessing whether point is close to a stationary point
            {
          d2z_dx2 = 2*a[row][col];
                d2z_dy2 = 2*b[row][col];
                d2z_dxdy = c[row][col];
                if (d2z_dx2 < 0 && d2z_dy2 < 0 && d2z_dxdy*d2z_dxdy < d2z_dx2*d2z_dy2)  // Conditions for peak
                {
                  classification[row][col] = 1;
                }
                else if (d2z_dx2 > 0 && d2z_dy2 > 0 && d2z_dxdy*d2z_dxdy < d2z_dx2*d2z_dy2) // Conditions for a depression
                {
                  classification[row][col] = 2;
                }
                else if (d2z_dx2*d2z_dy2 < 0 || d2z_dxdy*d2z_dxdy > d2z_dx2*d2z_dy2)  // Conditions for a saddle
                {
                   classification[row][col] = 3;
                }
                else
                {
                  classification = 0;
                }
        }
      }
    }
  }

  LSDIndexRaster sp_class_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                                  intNoDataValue,classification,GeoReferencingStrings);
  return sp_class_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this function takes the polyfit functions and requires a window radius and a vector telling the
// function which rasters to print to file. The function is data efficient since one does not
// need to recalucalte the polyfit coefficeint matrices
// it also takes a string which is the prename of the data files
// the file codes in the vector are:
// 0 slope
// 1 aspect
// 2 curvature
// 3 planform curvature
// 4 profile curvature
// 5 tangential curvature
// 6 classification
// SMM 18-Dec-2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::calculate_and_print_polyfit_rasters(float window_radius, string file_prefix, vector<int> file_code)
{
  // set up polyfit arrays
  Array2D<float> a;
  Array2D<float> b;
  Array2D<float> c;
  Array2D<float> d;
  Array2D<float> e;
  Array2D<float> f;

  int n_vec_entries = file_code.size();
  if ( n_vec_entries !=7)
  {
    cout << endl << "LSDRaster.calcualte_and_print_polyfit_rasters error" << endl;
    cout << "You have the wrong number of entries in the file code vector; taking no action!!!" << endl << endl;
  }
  else
  {
    int window_int = int(window_radius);
    float decimal = window_radius-float(window_int);
    float decimal_ten = decimal*10;
    int decimal_ten_str = int(decimal_ten);
    string window_number_str = itoa(window_int);
    string remainder_str = itoa(decimal_ten_str);
    string p_str = "p";
    string window_size_str = window_number_str+p_str+remainder_str;
    string DEM_flt_extension = "flt";
    string underscore = "_";


    // calcualte polyfit arrays
    calculate_polyfit_coefficient_matrices(window_radius,a, b,c, d, e, f);

    // now go through vector to see which files you want
    if (file_code[0] == 1)
    {
      LSDRaster PolySlope = calculate_polyfit_slope(d, e);
      string S_name = "_pslope_";
      S_name = file_prefix+S_name+window_size_str;
      PolySlope.write_raster(S_name,DEM_flt_extension);
    }
    if (file_code[1] == 1)
    {
      LSDRaster PolyAspect = calculate_polyfit_aspect(d,e);
      string A_name = "_paspect_";
      A_name = file_prefix+A_name+window_size_str;
      PolyAspect.write_raster(A_name,DEM_flt_extension);
    }
    if (file_code[2] == 1)
    {
      LSDRaster PolyCurv = calculate_polyfit_curvature(a,b);
      string C_name = "_pcurv_";
      C_name = file_prefix+C_name+window_size_str;
      PolyCurv.write_raster(C_name,DEM_flt_extension);
    }
    if (file_code[3] == 1)
    {
      LSDRaster PolyPlCurv = calculate_polyfit_planform_curvature(a,b,c,d,e);
      string CP_name = "_pplcurv_";
      CP_name = file_prefix+CP_name+window_size_str;
      PolyPlCurv.write_raster(CP_name,DEM_flt_extension);
    }
    if (file_code[4] == 1)
    {
      LSDRaster PolyPrCurv = calculate_polyfit_profile_curvature(a,b,c,d,e);
      string CPr_name = "_pprcurv_";
      CPr_name = file_prefix+CPr_name+window_size_str;
      PolyPrCurv.write_raster(CPr_name,DEM_flt_extension);
    }
    if (file_code[5] == 1)
    {
      LSDRaster PolyTaCurv = calculate_polyfit_tangential_curvature(a,b,c,d,e);
      string CTa_name = "_ptacurv_";
      CTa_name = file_prefix+CTa_name+window_size_str;
      PolyTaCurv.write_raster(CTa_name,DEM_flt_extension);
    }
    if (file_code[6] == 1)
    {
      LSDIndexRaster PolyClass = calculate_polyfit_classification(a,b,c,d,e);
      string CCl_name = "_pclass_";
      CCl_name = file_prefix+CCl_name+window_size_str;
      PolyClass.write_raster(CCl_name,DEM_flt_extension);
    }
  }

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// this function combines the polyfit functions and the roughness function in one package that
// is data efficient becasue it only requires one calcualtion of the polyfit matrices.
// it takes the window radius of the polyfit and the window of the roughness calcualtion
// the file codes in the vector are:
// 0 slope
// 1 aspect
// 2 curvature
// 3 planform curvature
// 4 profile curvature
// 5 tangential curvature
// 6 classification
// 7 roughness s1
// 8 roughness s2
// 9 roughness s3
// SMM 19-12-2012 -> adapted by DTM 15/07/2013 since it really makes sense just to kick out
// s1,s2,s3 rather than derivatives for options 7-9
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::calculate_and_print_polyfit_and_roughness_rasters(float window_radius, float roughness_radius,
                    string file_prefix, vector<int> file_code)
{
  // set up polyfit arrays
  Array2D<float> a;
  Array2D<float> b;
  Array2D<float> c;
  Array2D<float> d;
  Array2D<float> e;
  Array2D<float> f;

  int n_vec_entries = file_code.size();
  if ( n_vec_entries !=10)
  {
    cout << endl << "LSDRaster.calcualte_and_print_polyfit_rasters error" << endl;
    cout << "You have the wrong number of entries in the file code vector; taking no action!!!" << endl << endl;
  }
  else
  {
    int window_int = int(window_radius);
    float decimal = window_radius-float(window_int);
    float decimal_ten = decimal*10;
    int decimal_ten_str = int(decimal_ten);
    string window_number_str = itoa(window_int);
    string remainder_str = itoa(decimal_ten_str);
    string p_str = "p";
    string window_size_str = window_number_str+p_str+remainder_str;
    string DEM_flt_extension = "flt";
    string underscore = "_";

    int roughness_int = int(roughness_radius);
    float decimalroughness = roughness_radius-float(roughness_int);
    float decimalroughness_ten = decimalroughness*10;
    int decimalroughness_ten_str = int(decimalroughness_ten);
    string roughness_number_str = itoa(roughness_int);
    string remainderroughness_str = itoa(decimalroughness_ten_str);
    string polystring = "ply";
    string roughstring = "rgh";
    string roughness_size_str = roughness_number_str+p_str+remainderroughness_str;
    roughness_size_str = polystring+window_size_str+underscore+roughstring+roughness_size_str;

    // calcualte polyfit arrays
    calculate_polyfit_coefficient_matrices(window_radius,a, b,c, d, e, f);

    // now go through vector to see which files you want
    if (file_code[0] == 1)
    {
      LSDRaster PolySlope = calculate_polyfit_slope(d, e);
      string S_name = "_pslope_";
      S_name = file_prefix+S_name+window_size_str;
      PolySlope.write_raster(S_name,DEM_flt_extension);
    }
    if (file_code[1] == 1)
    {
      LSDRaster PolyAspect = calculate_polyfit_aspect(d,e);
      string A_name = "_paspect_";
      A_name = file_prefix+A_name+window_size_str;
      PolyAspect.write_raster(A_name,DEM_flt_extension);
    }
    if (file_code[2] == 1)
    {
      LSDRaster PolyCurv = calculate_polyfit_curvature(a,b);
      string C_name = "_pcurv_";
      C_name = file_prefix+C_name+window_size_str;
      PolyCurv.write_raster(C_name,DEM_flt_extension);
    }
    if (file_code[3] == 1)
    {
      LSDRaster PolyPlCurv = calculate_polyfit_planform_curvature(a,b,c,d,e);
      string CP_name = "_pplcurv_";
      CP_name = file_prefix+CP_name+window_size_str;
      PolyPlCurv.write_raster(CP_name,DEM_flt_extension);
    }
    if (file_code[4] == 1)
    {
      LSDRaster PolyPrCurv = calculate_polyfit_profile_curvature(a,b,c,d,e);
      string CPr_name = "_pprcurv_";
      CPr_name = file_prefix+CPr_name+window_size_str;
      PolyPrCurv.write_raster(CPr_name,DEM_flt_extension);
    }
    if (file_code[5] == 1)
    {
      LSDRaster PolyTaCurv = calculate_polyfit_tangential_curvature(a,b,c,d,e);
      string CTa_name = "_ptacurv_";
      CTa_name = file_prefix+CTa_name+window_size_str;
      PolyTaCurv.write_raster(CTa_name,DEM_flt_extension);
    }
    if (file_code[6] == 1)
    {
      LSDIndexRaster PolyClass = calculate_polyfit_classification(a,b,c,d,e);
      string CCl_name = "_pclass_";
      CCl_name = file_prefix+CCl_name+window_size_str;
      PolyClass.write_raster(CCl_name,DEM_flt_extension);
    }
    if (file_code[7] == 1|| file_code[8] == 1|| file_code[9] == 1)
    {
      Array2D<float> l;
      Array2D<float> m;
      Array2D<float> n;
      Array2D<float> s1;
      Array2D<float> s2;
      Array2D<float> s3;
      calculate_polyfit_directional_cosines(d, e, l, m, n);
      calculate_orientation_matrix_eigenvalues(roughness_radius,l,m,n,s1,s2,s3);

          if (file_code[7] == 1)
        {
        LSDRaster s1_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s1,GeoReferencingStrings);
            string s1_name = "_s1_";
            s1_name = file_prefix+s1_name+roughness_size_str;
            s1_raster.write_raster(s1_name,DEM_flt_extension);
          }
        if (file_code[8] == 1)
        {
        LSDRaster s2_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s2,GeoReferencingStrings);
            string s2_name = "_s2_";
          s2_name = file_prefix+s2_name+roughness_size_str;
          s2_raster.write_raster(s2_name,DEM_flt_extension);
        }
        if (file_code[9] == 1)
        {
          LSDRaster s3_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,s3,GeoReferencingStrings);
            string s3_name = "_s3_";
          s3_name = file_prefix+s3_name+roughness_size_str;
          s3_raster.write_raster(s3_name,DEM_flt_extension);
        }

    }    // end file codes 7,8,9

  }      // end test for file codes logic

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// GET HILLTOP CURVATURE DTM 30/04/13
// Input rasters: curvature, hilltop network.
// Output raster: hilltop curvature
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::get_hilltop_curvature(LSDRaster& curvature, LSDRaster& Hilltops)
{
  // create the new planform curvature raster
  Array2D<float> hilltop_curvature(NRows,NCols,NoDataValue);

  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (Hilltops.get_data_element(row,col) != NoDataValue)
      {
        hilltop_curvature[row][col] = curvature.get_data_element(row,col);
        }
    }
  }

  LSDRaster hilltop_curvature_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,hilltop_curvature,GeoReferencingStrings);
  return hilltop_curvature_raster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// REMOVE POSITIVE HILLTOP CURVATURE
// This function removes positive hilltop curvature values from the hilltop curvature raster
// (to remove noise)
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::remove_positive_hilltop_curvature(LSDRaster& hilltop_curvature)
{

  Array2D<float> CHT_array(NRows,NCols,NoDataValue);
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      float curvature = hilltop_curvature.get_data_element(row,col);
      if (curvature < 0)
      {
         CHT_array[row][col] = curvature;
      }
    }
  }
  LSDRaster CHT(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue, CHT_array,GeoReferencingStrings);

  return CHT;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// REMOVE POSITIVE VALUES FROM RASTER
// This function removes positive values from a raster, for use with hilltop curvature values
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::remove_positive_values()
{
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      if (RasterData[row][col] >= 0)
      {
        RasterData[row][col] = NoDataValue;
      }
    }
  }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

  //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  //
  // GET THE PERCENTAGE OF RIDGE PIXELS THAT ARE BEDROCK
  // This function gets the percentage of pixels that are bedrock from the hilltop curvature
  // raster
  // FJC 01/04/15
  //
  //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  float LSDRaster::get_percentage_bedrock_ridgetops(LSDRaster&roughness, LSDRaster& hilltop_curvature, float threshold)
  {
    float bedrock_pixels = 0;
    float total_pixels = 0;
    for (int row = 0; row < NRows; row++)
    {
      for (int col = 0; col < NCols; col++)
      {
        float CHT = hilltop_curvature.get_data_element(row, col);
        if (CHT != NoDataValue)
        {
          total_pixels++;
          float rough_value = roughness.get_data_element(row, col);
          if (rough_value > threshold)
          {
            bedrock_pixels++;
          }
        }
      }
    }
    cout << "Bedrock threshold is " << threshold << endl;
    cout << "There are " << bedrock_pixels << " bedrock pixels, out of " << total_pixels << " total" << endl;
    float percentage_bedrock = (bedrock_pixels/total_pixels)*100;

    return percentage_bedrock;
  }
  //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Trigonometry
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// Get slope angles
//
// This only works on a slope raster!!
// SMM
// 13/11/2014
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::calculate_slope_angles()
{
  cout << "I am calculating the slope angles; make sure you are using a slope raster!" << endl;

  Array2D<float> slope_angle(NRows,NCols, NoDataValue);

  for(int row = 1; row < NRows - 1; row++)
  {
    for(int col = 1; col < NCols - 1; col++)
    {
      if(RasterData[row][col] != NoDataValue)
      {
        slope_angle[row][col] = atan(RasterData[row][col]);
      }
    }
  }

  LSDRaster Slope_angle(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                        slope_angle,GeoReferencingStrings);
  return Slope_angle;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function calculates the water supply rate that causes overland flow
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::calculate_water_supply_rate_for_saturation(float soil_thick,
                         float K, LSDRaster& ContributingArea, LSDRaster& SlopeAngle)
{

  Array2D<float> W_for_sat(NRows,NCols, NoDataValue);
  float SA;
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if(RasterData[row][col] != NoDataValue)
      {
        if( ContributingArea.get_data_element(row,col) == 0)
        {
          W_for_sat[row][col] = NoDataValue;
        }
        else
        {
          SA = SlopeAngle.get_data_element(row,col);
          W_for_sat[row][col] = (soil_thick*K*sin(SA)*cos(SA)*DataResolution) /
                                ContributingArea.get_data_element(row,col);
        }

      }
    }
  }

  LSDRaster w_for_sat(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                        W_for_sat,GeoReferencingStrings);
  return w_for_sat;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function calculates the water supply rate that causes overland flow
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::calculate_factor_of_safety_at_saturation(float C_r, float rho_s,
                         float soil_thick, float tan_phi, LSDRaster& SlopeAngle)
{

  Array2D<float> FS_for_sat(NRows,NCols, NoDataValue);
  float SA;
  float cos_SA;
  float sin_SA;
  float g = 9.80;       // gravity
  float rho_w = 1000;   // density of water

  if(rho_s < 700)
  {
    cout << "Calculating factor of Safety. You soil density is really low" << endl
         << "Perhaps you entered it in g/cm^3? It should be in kg/m^3" << endl;
    if(rho_s < 5)
    {
      cout << "Assuming density was given in g/cm^3 so muliplying by 1000" << endl;
      rho_s = rho_s*1000;
    }
  }

  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if(RasterData[row][col] != NoDataValue)
      {
        SA = SlopeAngle.get_data_element(row,col);
        cos_SA = cos(SA);
        sin_SA = sin(SA);

        if (sin_SA == 0)
        {
          FS_for_sat[row][col] = 0;
        }
        else if (cos_SA == 0)
        {
          FS_for_sat[row][col] = NoDataValue;
        }
        else
        {
          FS_for_sat[row][col] = C_r/(g*rho_s*soil_thick*cos_SA*sin_SA) +
                                (rho_s - rho_w)*cos_SA*tan_phi/(rho_s*sin_SA);
        }

      }
    }
  }

  LSDRaster fs_for_sat(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                        FS_for_sat,GeoReferencingStrings);
  return fs_for_sat;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// RRRRR  EEEEEE IIIIII
// RR  RR EE       II
// RRRR   EEEE     II
// RR RR  EE       II
// RR  RR EEEEEE IIIIII
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=
// ROCK EXPOSURE INDEX
// DiBiase et al. (2012) developed the rock eposure index as a proxy for the
// degree of rock exposure within a basin as defined by the proportion of pixels
// with a local slope exceeding a critical value.  They calculate local slope by
// fitting a planar surface to a 9 cell moving window (window radius = 1).
// Algorithm written by DTM, 08/10/2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=
void LSDRaster::calculate_plane_coefficient_matrices(float window_radius,
                    Array2D<float>& a_plane, Array2D<float>& b_plane,
                    Array2D<float>& c_plane)
{
  // this fits a plane over a kernel window. First, perpare the kernel
  int kr = int(ceil(window_radius/DataResolution));           // Set radius of kernel
  int kw=2*kr+1;                                // width of kernel
  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<float> x_kernel(kw,kw,NoDataValue);
  Array2D<float> y_kernel(kw,kw,NoDataValue);
  // reset the a,b,c matrices (the coefficient matrices)
  Array2D<float> temp_coef(NRows,NCols,0.0);
  a_plane = temp_coef.copy();
  b_plane = temp_coef.copy();
  c_plane = temp_coef.copy();
  // scale kernel window to resolution of DEM, and translate coordinates to be
  // centred on cell of interest (the centre cell)
  float x,y,zeta;
  for(int i=0;i<kw;++i)
  {
      for(int j=0;j<kw;++j)
      {
          x_kernel[i][j]=(i-kr)*DataResolution;
          y_kernel[i][j]=(j-kr)*DataResolution;
      }
  }
  // FIT PLANE BY LEAST SQUARES REGRESSION AND USE COEFFICIENTS TO DETERMINE
  // LOCAL SLOPE
  // Have N simultaneous linear equations, and N unknowns.
  // => b = Ax, where x is a 1xN array containing the coefficients we need for
  // surface fitting.
  // A is constructed using different combinations of x and y, thus we only need
  // to compute this once, since the window size does not change.
  // For 1st order surface fitting, there are 3 coefficients, therefore A is a
  // 3x3 matrix
  Array2D<float> A(3,3,0.0);
  for (int i=0; i<kw; ++i)
  {
    for (int j=0; j<kw; ++j)
    {
      x = x_kernel[i][j];
      y = y_kernel[i][j];
      // Generate matrix A
      A[0][0] += pow(x,2);
      A[0][1] += x*y;
      A[0][2] += x;
      A[1][0] += y*x;
      A[1][1] += pow(y,2);
      A[1][2] += y;
      A[2][0] += x;
      A[2][1] += y;
      A[2][2] += 1;
    }
  }
  // Move window over DEM, fitting planar surface to the elevations within the
  // window.
  cout << "\n\tRunning planar surface fitting" << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  int ndv_present = 0;
  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if(i-kr < 0 || i+kr+1 > NRows || j-kr < 0 || j+kr+1 > NCols)
      {
        a_plane[i][j] = NoDataValue;
        b_plane[i][j] = NoDataValue;
        c_plane[i][j] = NoDataValue;
      }
      // Avoid nodata values
      else if(RasterData[i][j]==NoDataValue)
      {
        a_plane[i][j] = NoDataValue;
        b_plane[i][j] = NoDataValue;
        c_plane[i][j] = NoDataValue;
      }
      else
      {
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
            for(int j_kernel=0;j_kernel<kw;++j_kernel)
            {
            data_kernel[i_kernel][j_kernel] =
            RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // check for nodata values nearby
            if(data_kernel[i_kernel][j_kernel]==NoDataValue)
            {
              ndv_present=1;
            }
            }
        }
        // Fit best fitting plane, avoiding nodata values
        if(ndv_present == 0)  // test for nodata values within the selection
        {
          Array1D<float> bb(3,0.0);
          Array1D<float> coeffs(3);
          for (int krow=0; krow<kw; ++krow)
          {

              for (int kcol=0; kcol<kw; ++kcol)
              {
              x = x_kernel[krow][kcol];
                y = y_kernel[krow][kcol];
                zeta = data_kernel[krow][kcol];
                // Generate vector bb
                bb[0] += zeta*x;
                bb[1] += zeta*y;
                bb[2] += zeta;
              }
          }
          // Solve matrix equations using LU decomposition using the TNT JAMA package:
          // A.coefs = b, where coefs is the coefficients vector.
          LU<float> sol_A(A);  // Create LU object
          coeffs = sol_A.solve(bb);

            a_plane[i][j]=coeffs[0];
            b_plane[i][j]=coeffs[1];
            c_plane[i][j]=coeffs[2];
        }
        ndv_present = 0;
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_REI(Array2D<float>& a_plane, Array2D<float>& b_plane, float CriticalSlope)
{
  // create the REI raster
  Array2D<float> REI_data(NRows,NCols,NoDataValue);
    float SlopeOfPlane;
  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (a_plane[row][col] != NoDataValue)
      {
        SlopeOfPlane = sqrt(a_plane[row][col]*a_plane[row][col]+b_plane[row][col]*b_plane[row][col]);
        // Create binary matrix 1 = rock, 0 = no rock
            if (SlopeOfPlane > CriticalSlope)
        {
                REI_data[row][col] = 1;
            }
            else
            {
                REI_data[row][col] = 0;
            }
      }
    }
  }

  LSDRaster REI_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,REI_data,GeoReferencingStrings);
  return REI_raster;
}
// Overloaded function that incorporates the above in a nicer wrapper function
LSDRaster LSDRaster::calculate_REI(float window_radius, float CriticalSlope)
{
  Array2D<float> a,b,c;
  calculate_plane_coefficient_matrices(window_radius,a,b,c);
  LSDRaster REI_raster =  calculate_REI(a, b, CriticalSlope);
  return REI_raster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// RRRRR    OOOO   UU   UU  GGGGG HH   HH NN    NN EEEEEE   SSSS    SSSS
// RR  RR  OO  OO  UU   UU GG     HH   HH NNN   NN EE     SS      SS
// RRRR   OO    OO UU   UU GG GGG HHHHHHH NN NN NN EEEE    SSSS    SSSS
// RR RR   OO  OO  UU   UU GG  GG HH   HH NN   NNN EE         SS      SS
// RR  RR   OOOO    UUUUU   GGGG  HH   HH NN    NN EEEEEE SSSSS   SSSSS
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Algorithm that assesses surface roughness based on a polynomial fit.  Runs a
// moving window across the DEM and assesses the variability of surface normals
// within that window.  Specifically the components of the normals are combined
// into an orientation matrix, which is then solved to find the eigenvalues s1,
// s2, s3 (Woodcock, 1977).
//
// Added by DTM 13/09/2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Get directional cosines
void LSDRaster::calculate_polyfit_directional_cosines(Array2D<float>& d, Array2D<float>& e,
                                    Array2D<float>& l, Array2D<float>& m, Array2D<float>& n)
{
  float pheta, phi;
  // reset the l, m and n matrices (the directional cosines matrices)
  Array2D<float> temp_coef(NRows,NCols,NoDataValue);

  l = temp_coef.copy();
  m = temp_coef.copy();
  n = temp_coef.copy();
  // get surface normals (in form of direction cosines) for each point in DEM
  for (int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (d[row][col] != NoDataValue)
      {
        pheta = atan(sqrt(d[row][col]*d[row][col]+e[row][col]*e[row][col]));
        if (e[row][col] == 0 || d[row][col] == 0)
        {
          phi = NoDataValue;
        }
            else
            {
          phi = atan(e[row][col]/d[row][col]);
        }

            // Directional cosines of normal vectors
            if (pheta != 0)
            { // l and m are undefined if pheta = 0 because phi is undefined for a vertical surface normal
                l[row][col]=sin(pheta)*cos(phi);
                m[row][col]=sin(pheta)*sin(phi);
            }

            // Can define n for vertical surface normal, since pheta is always defined
            n[row][col]=cos(pheta);
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Find eigenvalues for orientation matrix
//
// Added by DTM 13/09/2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::calculate_orientation_matrix_eigenvalues(float window_radius,
                    Array2D<float>& l, Array2D<float>& m,
                    Array2D<float>& n, Array2D<float>& s1,
                              Array2D<float>& s2, Array2D<float>& s3)
{
  // Reset the eigenvalue matrices
  Array2D<float> temp_coef(NRows,NCols,0.0);

  //Array2D<float> temp_coef(NRows,NCols,NoDataValue);
  s1 = temp_coef.copy();
  s2 = temp_coef.copy();
  s3 = temp_coef.copy();

  // this fits a polynomial surface over a kernel window. First, perpare the kernel
  int kr = int(ceil(window_radius/DataResolution));       // Set radius of kernel => suggest = 1 cell
  int kw=2*kr+1;                                // width of kernel
  float li,mi,ni;

  // Declare kernel arrays
  Array2D<float> l_kernel(kw,kw,NoDataValue);
  Array2D<float> m_kernel(kw,kw,NoDataValue);
  Array2D<float> n_kernel(kw,kw,NoDataValue);

  // Build circular mask
    Array2D<int> mask(kw,kw,0);
    float x_kernel,y_kernel, radial_dist;
    for(int i=0;i<kw;++i)
  {
      for(int j=0;j<kw;++j)
      {
      x_kernel=(i-kr)*DataResolution;
          y_kernel=(j-kr)*DataResolution;
          radial_dist = sqrt(y_kernel*y_kernel + x_kernel*x_kernel); // distance from centre to this point.
          if (floor(radial_dist) <= window_radius)
          {
        mask[i][j] = 1;
      }
        }
  }

  // Loop over DEM, extacting the directional cosines for the data kernel
  for(int row=0;row<NRows;++row)
  {
    for(int col=0;col<NCols;++col)
      {
          //Avoid edges
          if(row-kr < 0 || row+kr+1 > NRows || col-kr < 0 || col+kr+1 > NCols)
          {
        s1[row][col]=NoDataValue;
              s2[row][col]=NoDataValue;
              s3[row][col]=NoDataValue;
            }
            else
            {
            //Avoid NoDataValues
            if(l[row][col] != NoDataValue)
            {
                // Construct orientation matrix and solve to retrieve eigenvalues for data window
                // Build orientation matrix
                Array2D<float> T(3,3,0.0);
                Array2D<float> D(3,3);
                int N=1;
                for(int i=0;i<kw;++i)
                {
                  for(int j=0;j<kw;++j)
                  {
              if (mask[i][j]==1)
                      {
                li=l[row-kr+i][col-kr+j];
                          mi=m[row-kr+i][col-kr+j];
                          ni=n[row-kr+i][col-kr+j];
                    T[0][0] += li*li;
                    T[0][1] += li*mi;
                    T[0][2] += li*ni;
                    T[1][0] += mi*li;
                    T[1][1] += mi*mi;
                    T[1][2] += mi*ni;
                    T[2][0] += ni*li;
                    T[2][1] += ni*mi;
                    T[2][2] += ni*ni;
                    ++N;
              }
                  }
                }
                // Find eigenvalues of the orientation matrix
                Eigenvalue<float> eigenvalue_matrix(T);
                eigenvalue_matrix.getD(D);
                // Normalised eigenvalues (with respect to number of normals):
                //cout << T << endl;
                s1[row][col]=D[0][0]/N;
                s2[row][col]=D[1][1]/N;
                s3[row][col]=D[2][2]/N;
            }
          }
      }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function is a wrapper to get the three roughness eigenvalues s1, s2 and
// s3.
//
//DTM 15/07/2013  Updated 14/12/2018 with the more recent roughness raster code
// that has more error checking
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::calculate_roughness_rasters(float window_radius, float roughness_radius,
                    string file_prefix, vector<int> file_code)

{
  // set up polyfit arrays
  Array2D<float> a;
  Array2D<float> b;
  Array2D<float> c;
  Array2D<float> d;
  Array2D<float> e;
  Array2D<float> f;

  int n_vec_entries = file_code.size();
  if ( n_vec_entries !=3)
  {
    cout << endl << "LSDRaster.calcualte_and_print_polyfit_rasters error" << endl;
    cout << "You have the wrong number of entries in the file code vector; taking no action!!!" << endl << endl;
  }
  else
  {
    int window_int = int(window_radius);
    float decimal = window_radius-float(window_int);
    float decimal_ten = decimal*10;
    int decimal_ten_str = int(decimal_ten);
    string window_number_str = itoa(window_int);
    string remainder_str = itoa(decimal_ten_str);
    string p_str = "p";
    string window_size_str = window_number_str+p_str+remainder_str;

    // switch to bil format 09/03/2017
    string DEM_flt_extension = "bil";


    string underscore = "_";

    int roughness_int = int(roughness_radius);
    float decimalroughness = roughness_radius-float(roughness_int);
    float decimalroughness_ten = decimalroughness*10;
    int decimalroughness_ten_str = int(decimalroughness_ten);
    string roughness_number_str = itoa(roughness_int);
    string remainderroughness_str = itoa(decimalroughness_ten_str);
    string polystring = "ply";
    string roughstring = "rgh";
    string roughness_size_str = roughness_number_str+p_str+remainderroughness_str;
    roughness_size_str = polystring+window_size_str+underscore+roughstring+roughness_size_str;

    // calcualte polyfit arrays
    vector<LSDRaster> rough_rasters = calculate_polyfit_roughness_metrics(window_radius, roughness_radius, file_code);

    // now go through vector to see which files you want
    if (file_code[0] == 1)
    {
      string s1_name = "_s1_";
      s1_name = file_prefix+s1_name+roughness_size_str;
      rough_rasters[0].write_raster(s1_name,DEM_flt_extension);
    }
    if (file_code[1] == 1)
    {
      string s2_name = "_s2_";
      s2_name = file_prefix+s2_name+roughness_size_str;
      rough_rasters[1].write_raster(s2_name,DEM_flt_extension);
    }
    if (file_code[2] == 1)
    {
      string s3_name = "_s3_";
      s3_name = file_prefix+s3_name+roughness_size_str;
      rough_rasters[2].write_raster(s3_name,DEM_flt_extension);
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// HH  HH YY   YY DDDD   RRRRR    OOOO   LL       OOOO    GGGGG  YY   YY
// HH  HH  YYYY   DD DD  RR  RR  OO  OO  LL      OO  OO  GG        YYYY
// HHHHHH   YY    DD  DD RRRR   OO    OO LL     OO    OO GG GGG    YY
// HH  HH   YY    DD DD  RR RR   OO  OO  LL      OO  OO  GG  GG    YY
// HH  HH   YY    DDDD   RR  RR   OOOO   LLLLLL   OOOO    GGGGG    YY
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function looks for data with 0 elevation and changes it to nodata
// Seems to be required when GDAL has been used to manipulate coastal tiles
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::remove_seas()
{
  cout << "Removing seas, NoDataValue is: " << NoDataValue << endl;
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if(RasterData[row][col] <= 0)
      {
        RasterData[row][col] = NoDataValue;
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This masks to nodata below a threshold value
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::mask_to_nodata_below_threshold(float threshold)
{
  cout << "masking seas, NoDataValue is: " << NoDataValue << endl;
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if(RasterData[row][col] <= threshold)
      {
        RasterData[row][col] = NoDataValue;
      }
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This masks to nodata below or above a threshold value
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster  LSDRaster::mask_to_nodata_using_threshold(float threshold,bool belowthresholdisnodata)
{

  Array2D<float> NewArray = RasterData.copy();

  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      // only do anything if the value at the raster point is not nodata
      if(NewArray[row][col] != NoDataValue)
      {
        // logic for testing below nodata
        if(belowthresholdisnodata)
        {
          if(NewArray[row][col] <= threshold)
          {
            NewArray[row][col] = NoDataValue;
          }
        }
        else  // this logic is for if you are changing to nodata if above threshold
        {
          if(NewArray[row][col] >= threshold)
          {
            NewArray[row][col] = NoDataValue;
          }
        }
      }
    }
  }

  LSDRaster NDR(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,NewArray,GeoReferencingStrings);
  return NDR;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This masks to nodata below or above a threshold value
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster  LSDRaster::mask_to_nodata_using_threshold_using_other_raster(float threshold,bool belowthresholdisnodata, LSDRaster& MaskingRaster)
{

  Array2D<float> NewArray;
  NewArray = RasterData.copy();

  // first check to see if the rasters are the same size
  int IR_NRows = MaskingRaster.get_NRows();
  int IR_NCols = MaskingRaster.get_NCols();

  float this_mask_value;

  if(IR_NRows == NRows && IR_NCols == NCols)
  {
    for(int row = 0; row<NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {

        // only do anything if the value at the raster point is not nodata
        if(NewArray[row][col] != NoDataValue)
        {
          this_mask_value = MaskingRaster.get_data_element(row,col);
          if(this_mask_value != NoDataValue)
          {

            // logic for testing below nodata
            if(belowthresholdisnodata)
            {
              if(this_mask_value <= threshold)
              {
                NewArray[row][col] = NoDataValue;
              }
            }
            else  // this logic is for if you are changing to nodata if above threshold
            {
              if(this_mask_value >= threshold)
              {
                NewArray[row][col] = NoDataValue;
              }
            }
          }
        }
      }
    }
  }
  else
  {
    cout << "Trying to mask raster but the dimensions of the mask do not match"
         << " the dimensions of the raster" << endl;
  }

  LSDRaster NDR(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,NewArray,GeoReferencingStrings);
  return NDR;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This masks to nodata below a threshold value
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::mask_to_indexraster_using_threshold(float threshold,bool belowthresholdisnodata)
{

  // create the array for the index raster
  Array2D<int> NewIndexArray(NRows,NCols,int(NoDataValue));

  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      // only do anything if the value at the raster point is not nodata
      if(RasterData[row][col] != NoDataValue)
      {
        // logic for testing below nodata
        if(belowthresholdisnodata)
        {
          if(RasterData[row][col] <= threshold)
          {
            NewIndexArray[row][col] = int(NoDataValue);
          }
          else
          {
             NewIndexArray[row][col] = 1;
          }
        }
        else  // this logic is for if you are changing to nodata if above threshold
        {
          if(RasterData[row][col] >= threshold)
          {
            NewIndexArray[row][col] = int(NoDataValue);
          }
          else
          {
             NewIndexArray[row][col] = 1;
          }
        }
      }
    }
  }

  LSDIndexRaster NDR(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,NewIndexArray,GeoReferencingStrings);
  return NDR;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This masks to nodata based on a masking raster
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::mask_to_nodata_with_mask_raster(LSDIndexRaster& Mask_raster, int mask_value)
{

  Array2D<float> new_data_raster;
  new_data_raster = RasterData.copy();

  // first check to see if the rasters are the same size
  int IR_NRows = Mask_raster.get_NRows();
  int IR_NCols = Mask_raster.get_NCols();
  int IR_NDV   = Mask_raster.get_NoDataValue();

  if(IR_NRows == NRows && IR_NCols == NCols)
  {
    for(int row = 0; row<NRows; row++)
    {
      for(int col = 0; col<NCols; col++)
      {

        if(Mask_raster.get_data_element(row,col) == IR_NDV ||
           Mask_raster.get_data_element(row,col) == mask_value)
        {
          //cout << "r: " << row << " c: " << col << " mask: " <<Mask_raster.get_data_element(row,col) << endl;
          new_data_raster[row][col] = NoDataValue;
        }
      }
    }
  }
  else
  {
    cout << "Trying to mask raster but the dimensions of the mask do not match"
         << " the dimensions of the raster" << endl;
  }

  LSDRaster NDR(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,new_data_raster,GeoReferencingStrings);
  return NDR;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Fill
//------------------------------------------------------------------------------
//
//This function fills pits/sinks in a DEM by incrementing elevations for cells with
//no downslope neighbour. The process is repeated adnausium until no cells require
//incrementing.
//
//Inputs required are a DEM file in ascii raster format as created by ARCMap
//and a file name to create a filled DEM grid.
//
//This code was built ontop of code made available by Jon D. Pelletier as part
//of his book:
//
//Pelletier,J.D.,'Quantitative Modelling of Landscapes' Cambridge University Press
//
//---------------------------------------------------------------------------------
//
// v1.3 reduced fill increment to 1mm  to avoid 'overfilling'
//
// Martin Hurst, October 2011
//
//---------------------------------------------------------------------------------
//
// v1.2 modified to read *.flt files
//
// Martin Hurst, November 2010
//
//---------------------------------------------------------------------------------
//
// v1.1 function incorporated to allow the tool to fill adjacent pixels immediately
// after filling a given pixel, should speed things up.
//
// Martin Hurst, October 2010
//
//---------------------------------------------------------------------------------
//
// v1.0 is slow as it requires many iterations through the dem
//
// Martin Hurst, June 2010
//
//---------------------------------------------------------------------------------
LSDRaster LSDRaster::fill()
{

  Array2D<float> FilledRasterData;
  FilledRasterData = RasterData.copy();
  cout << "N_rows is: " << NRows << " " << NCols << endl;
  cout << "Data rows: " << RasterData.dim1() << " cols: " << RasterData.dim2() << endl;
  for (int i=1; i<NRows-1; i++)
  {
    cout << "\rRow = " << i+1 << " / " << NRows << "    ";
    for (int j=1; j<NCols-1; j++)
    {
      //cout << "R: " << i << " C: " << j;
      //cout << " FDR: " << FilledRasterData[i][j];
      if (FilledRasterData[i][j] == NoDataValue || FilledRasterData[i-1][j-1] == NoDataValue
               || FilledRasterData[i-1][j] == NoDataValue || FilledRasterData[i-1][j+1] == NoDataValue
               || FilledRasterData[i][j+1] == NoDataValue || FilledRasterData[i+1][j+1] == NoDataValue
               || FilledRasterData[i+1][j] == NoDataValue || FilledRasterData[i+1][j-1] == NoDataValue
               || FilledRasterData[i][j-1] == NoDataValue)
      { }
      else fill_iterator(FilledRasterData,i,j);

      //if (RasterData[i][j] == NoDataValue || RasterData[i-1][j-1] == NoDataValue
      //         || RasterData[i-1][j] == NoDataValue || RasterData[i-1][j+1] == NoDataValue
      //         || RasterData[i][j+1] == NoDataValue || RasterData[i+1][j+1] == NoDataValue
      //         || RasterData[i+1][j] == NoDataValue || RasterData[i+1][j-1] == NoDataValue
      //         || RasterData[i][j-1] == NoDataValue)
      //{ }
      //else fill_iterator(RasterData,i,j);
      //cout << " itercomplete" << endl;
    }
  }
  cout << endl;

  LSDRaster FilledDEM(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,FilledRasterData,GeoReferencingStrings);
  return FilledDEM;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this is a recursive algorithm that is called by the fill function
//
// MDH, 2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::fill_iterator(Array2D<float>& fill_data, int i, int j)
{
  int a=i;
  int b=j;
  float fill_increment = 0.001;
  float min_zeta;
  float centre_zeta = fill_data[a][b];

  if (a==0 || b==0 || a == NRows-1 || b==NCols-1)
  { }
  else if (fill_data[a][b] == NoDataValue || fill_data[a-1][b-1] == NoDataValue
       || fill_data[a-1][b] == NoDataValue
           || fill_data[a-1][b+1] == NoDataValue || fill_data[a][b+1] == NoDataValue
       || fill_data[a+1][b+1] == NoDataValue || fill_data[a+1][b] == NoDataValue
       || fill_data[a+1][b-1] == NoDataValue || fill_data[a][b-1] == NoDataValue)
  {}
  else
  {
    min_zeta = centre_zeta + 10;
    if (fill_data[a-1][b-1] < min_zeta) min_zeta = fill_data[a-1][b-1];
    if (fill_data[a-1][b] < min_zeta) min_zeta = fill_data[a-1][b];
    if (fill_data[a-1][b+1] < min_zeta) min_zeta = fill_data[a-1][b+1];
    if (fill_data[a][b+1] < min_zeta) min_zeta = fill_data[a][b+1];
    if (fill_data[a+1][b+1] < min_zeta) min_zeta = fill_data[a+1][b+1];
    if (fill_data[a+1][b] < min_zeta) min_zeta = fill_data[a+1][b];
    if (fill_data[a+1][b-1] < min_zeta) min_zeta = fill_data[a+1][b-1];
    if (fill_data[a][b-1] < min_zeta) min_zeta = fill_data[a][b-1];

    //increase elevation of centre cell if it is lower than or
    //equal in elevation compared to all adjacent cells
    if (centre_zeta <= min_zeta)
    {

          // efficiency improvement by Dave Milodowski
          float zeta_diff = min_zeta - centre_zeta;
          fill_data[a][b] = fill_data[a][b] + zeta_diff + fill_increment;
      //fill adjacent pixels too
      fill_iterator(fill_data,a-1,b-1);
      fill_iterator(fill_data,a-1,b);
      fill_iterator(fill_data,a-1,b+1);
      fill_iterator(fill_data,a,b+1);
      fill_iterator(fill_data,a+1,b+1);
      fill_iterator(fill_data,a+1,b);
      fill_iterator(fill_data,a+1,b-1);
      fill_iterator(fill_data,a,b-1);
    }
  }
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


//---------------------------------------------------------------------------------------
//
//  New fill function
//
//  This function fills pits/sinks in a DEM by checking for pits from lowest to highest
//  elevation, starting at the DEM boundary (raster edge or adjacent to NDVs). Utilises
//  a priority queue to progressively populate the stack and pop out the the lowest value
//  before checking that the neighbouring cells that are yet to be visited must be higher
//  in a hydrologically correct DEM. This method is substantially faster on datasets with
//  pits consisting of multiple cells since each cell only needs to be visited once.
//
//  Input argument required -> MinSlope the minimum slope between two Nodes once filled
//  If set to zero will create flats.
//
//  Method taken from Wang and Liu (2006), Int. J. of GIS. 20(2), 193-213
//
//  Martin Hurst, 12/3/13 */
//
//  Declare the node structure
///@brief Used in pit filling to store elevation data and row and colum indexes.
//  Method taken from Wang and Liu (2006), Int. J. of GIS. 20(2), 193-213
//  Method taken from Wang and Liu (2006), Int. J. of GIS. 20(2), 193-213
struct FillNode
{
  /// @brief Elevation data.
  float Zeta;
  /// @brief Row index value.
  int RowIndex;
  /// @brief Column index value.
  int ColIndex;
};

//Overload the less than and greater than operators to consider Zeta data only
//N.B. Fill only needs greater than but less than useful for mdflow routing
//(I've coded this but not yet added to LSDRaster, it's only faster than presorting
//when applied to pretty large datasets).
bool operator>( const FillNode& lhs, const FillNode& rhs )
{
  return lhs.Zeta > rhs.Zeta;
}
bool operator<( const FillNode& lhs, const FillNode& rhs )
{
  return lhs.Zeta < rhs.Zeta;
}

LSDRaster LSDRaster::fill(float& MinSlope)
{
  //cout << "Inside NewFill" << endl;
  //cout << "DataResolution is: " << DataResolution << endl;
  //cout << "Data[200][200]: "  << RasterData[200][200] << endl;

  //declare 1/root(2)
  float one_over_root2 = 0.707106781;

  //Declare the priority Queue with greater than comparison
  priority_queue< FillNode, vector<FillNode>, greater<FillNode> > PriorityQueue;
  //Declare a temporary FillNode structure which we populate before adding to the PQ
  //Declare a central node or node of interest
  FillNode TempFillNode, CentreFillNode;

  //declare vectors for slopes and row and col indices
  vector<float> slopes(8,NoDataValue);
  vector<int> row_kernal(8);
  vector<int> col_kernal(8);

  //Get Dimensions
  //int NRows = Zeta.dim1();
  //int NCols = Zeta.dim2();

  //Index array to track whether nodes are in queue or have been processed
  //-9999 = no_data, 0 = data but not processed or in queue,
  //1 = in queue but not processed, 2 = fully processed and removed from queue
  Array2D<int> FillIndex(NRows,NCols,NoDataValue);
  Array2D<float> FilledZeta;
  FilledZeta = RasterData.copy();

  //Collect boundary cells
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (FilledZeta[i][j] != NoDataValue)
      {
        //If there is data the cell needs to be filled so
        //set fill index to zero (i.e. yet to be filled)
        FillIndex[i][j] = 0;

        //If we're at the edge or next to an NoDataValue then
        //put the cell into the priority queue
        if (i==0 || j==0 || i==NRows-1 || j==NCols-1 ||
          FilledZeta[i-1][j-1]==NoDataValue || FilledZeta[i-1][j]==NoDataValue ||
          FilledZeta[i-1][j+1]==NoDataValue || FilledZeta[i][j-1]==NoDataValue ||
          FilledZeta[i][j+1]==NoDataValue || FilledZeta[i+1][j-1]==NoDataValue ||
          FilledZeta[i+1][j]==NoDataValue || FilledZeta[i+1][j+1]==NoDataValue)
        {
          TempFillNode.Zeta = FilledZeta[i][j];
          TempFillNode.RowIndex = i;
          TempFillNode.ColIndex = j;
          PriorityQueue.push(TempFillNode);
          FillIndex[i][j] = 1;
        }
      }
    }
  }

  //Loop through the priority queue from lowest to highest elevations
  //filling as we go and adding unassessed neighbours to the priority queue
  while (!PriorityQueue.empty())
  {
    //first get the highest priority node and assign it before
    //removing it from the queue and declaring it processed
    CentreFillNode = PriorityQueue.top();
    int row=CentreFillNode.RowIndex, col=CentreFillNode.ColIndex;
    //cout << "Pop from Queue: Zeta = " << CentreFillNode.Zeta << endl;

    PriorityQueue.pop();
    FillIndex[row][col] = 2;

    //get neighbour indices
    //rows
    row_kernal[0] = row-1;
    row_kernal[1] = row-1;
    row_kernal[2] = row;
    row_kernal[3] = row+1;
    row_kernal[4] = row+1;
    row_kernal[5] = row+1;
    row_kernal[6] = row;
    row_kernal[7] = row-1;
    //cols
    col_kernal[0] = col;
    col_kernal[1] = col+1;
    col_kernal[2] = col+1;
    col_kernal[3] = col+1;
    col_kernal[4] = col;
    col_kernal[5] = col-1;
    col_kernal[6] = col-1;
    col_kernal[7] = col-1;

    //check if on array boundary and set kernal to NoDataValues to avoid
    //segmentation fault
    if (row == 0)
    {
      row_kernal[0] = NoDataValue;
      row_kernal[1] = NoDataValue;
      row_kernal[7] = NoDataValue;
    }
    else if (row==NRows-1)
    {
      row_kernal[3] = NoDataValue;
      row_kernal[4] = NoDataValue;
      row_kernal[5] = NoDataValue;
    }
    if (col == 0)
    {
      col_kernal[5] = NoDataValue;
      col_kernal[6] = NoDataValue;
      col_kernal[7] = NoDataValue;
    }
    else if (col == NCols-1)
    {
      col_kernal[1] = NoDataValue;
      col_kernal[2] = NoDataValue;
      col_kernal[3] = NoDataValue;
    }

    //loop through neighbours
    for (int Neighbour = 0; Neighbour<8; ++Neighbour)
    {
      //If the neighbour has data and is not already in the priority queue and has not been processed
      if (  row_kernal[Neighbour] == NoDataValue || col_kernal[Neighbour] == NoDataValue ||
          FillIndex[row_kernal[Neighbour]][col_kernal[Neighbour]] == 1 ||
          FillIndex[row_kernal[Neighbour]][col_kernal[Neighbour]] == 2 ||
          FillIndex[row_kernal[Neighbour]][col_kernal[Neighbour]] == NoDataValue ) {}
      else
      {
        //check if neighbour is equal/lower and therefore needs filling
        if (FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]] <= CentreFillNode.Zeta)
        {
          //Modify neighbour's elevation
          if(Neighbour%2 == 0)
          {
            if (MinSlope > 0)
            {
              FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]] =
                               CentreFillNode.Zeta + MinSlope*DataResolution;
            }
            else
            {
              FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]] = CentreFillNode.Zeta;
            }
          }
          else
          {
            if (MinSlope > 0)
            {
              FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]] = CentreFillNode.Zeta
                                                   + MinSlope*DataResolution*one_over_root2;
            }
            else
            {
              FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]] = CentreFillNode.Zeta;
            }
          }
        }
        //New neighbour needs to be added to the priority queue
        TempFillNode.Zeta = FilledZeta[row_kernal[Neighbour]][col_kernal[Neighbour]];
        TempFillNode.RowIndex = row_kernal[Neighbour];
        TempFillNode.ColIndex = col_kernal[Neighbour];
        PriorityQueue.push(TempFillNode);
        FillIndex[row_kernal[Neighbour]][col_kernal[Neighbour]] = 1;
        FillIndex[row][col] = 2;
      }
    }
  }
  LSDRaster FilledDEM(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,FilledZeta,GeoReferencingStrings);
  return FilledDEM;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=







//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//D-inf modules
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Main function for generating a D-infinity flow area raster after Tarboton (1997).
// Calls the recurisve D_infAccum function to get flow area for each pixel.
// Returns flow area in pixels.
//
// Code is ported and optimised from a Java implementation of the algorithm
// supplied under the GNU GPL licence through WhiteBox GAT:
// http://www.uoguelph.ca/~hydrogeo/Whitebox/ and provides identical results
// to the whitebox tool.
//
// SWDG - 26/07/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::D_inf_FlowArea(Array2D<float> FlowDir_array){

  // Arrays of indexes of neighbour cells wrt target cell and their
  //corresponding ranges of angles
  int dX[] = {1, 1, 1, 0, -1, -1, -1, 0};
  int dY[] = {-1, 0, 1, 1, 1, 0, -1, -1};
  float startFD[] = {180, 225, 270, 315, 0, 45, 90, 135};
  float endFD[] = {270, 315, 360, 45, 90, 135, 180, 225};

  Array2D<float> Flowarea_Raster(NRows,NCols,1);
  Array2D<float> CountGrid(NRows,NCols,NoDataValue); //array to hold no of inflowing neighbours

  int inflow_neighbours; //counter for number of inflowing neighbours
  float flowDir; //temp variable to store the flowdir of a neighbour

  // Calculate the number of inflowing neighbours to each cell.
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      flowDir = FlowDir_array[i][j];
      if (flowDir != NoDataValue){
        inflow_neighbours = 0;

        for (int c = 0; c < 8; ++c){ //loop through the 8 neighbours of the target cell
          flowDir = FlowDir_array[i + dY[c]][j + dX[c]];
          if (flowDir >= 0 && flowDir <= 360){
            if (c != 3){  //handles the issue of 0,360 both pointing to North
              if (flowDir > startFD[c] && flowDir < endFD[c]){
                ++inflow_neighbours;
              }
            }
            else{
              if (flowDir > startFD[c] || flowDir < endFD[c]){
                ++inflow_neighbours;
              }
            }
          }
        }
        CountGrid[i][j] = inflow_neighbours;
      }
      else{
        Flowarea_Raster[i][j] = NoDataValue;
      }
    }
  }

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (CountGrid[i][j] == 0){ //there are no inflowing neighbours
        //call the flowarea function and travel downstream from it
        D_infAccum(i, j, CountGrid, Flowarea_Raster, FlowDir_array);
      }
    }
  }

  LSDRaster FlowArea(NRows, NCols, XMinimum, YMinimum, DataResolution,
                          NoDataValue, Flowarea_Raster,GeoReferencingStrings);

  return FlowArea;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Recursive function to calculate accumulating area for a given pixel. Called
// by the driver for every cell which has no contributing cells - eg the highest
// points on the landscape. Avoids the need to flatten and sort the DEM as
// required in the original Tarboton (1997) implementation. For more detail on the
// recursive algorithm following channels see Mark (1998) "Network Models in
// Geomorphology".
//
// Code is ported and optimised from a Java implementation of the algorithm
// supplied under the GNU GPL licence through WhiteBox GAT:
// http://www.uoguelph.ca/~hydrogeo/Whitebox/ and provides identical results
// to the whitebox tool.
//
// SWDG - 26/07/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::D_infAccum(int i, int j, Array2D<float> CountGrid,
              Array2D<float> Flowarea_Raster, Array2D<float> FlowDir)
{

  float flowAccumVal = Flowarea_Raster[i][j];
  float flowDir = FlowDir[i][j];

  //tables of angles and indexes used to rotate around each neighbour
  float FD_Low[] = {0, 45, 90, 135, 180, 225, 270, 315};
  float FD_High_361[] = {45, 90, 135, 180, 225, 270, 315, 361};  //this array ends with 361 to catch angles up to 360
  float FD_High[] = {45, 90, 135, 180, 225, 270, 315, 360};
  int Di1[] = {-1, -1, 0, 1, 1, 1, 0, -1};
  int Dj1[] = {0, 1, 1, 1, 0, -1, -1, -1};
  int Di2[] = {-1, 0, 1, 1, 1, 0, -1, -1};
  int Dj2[] = {1, 1, 1, 0, -1, -1, -1, 0};

  float proportion1 = 0; //proportion of flow to the lowest neighbour
  float proportion2 = 0; //proportion of flow to the second lowest neighbour

  // indexes to store the coordinates of the neighbours where flow is to be routed
  int a1 = 0;
  int b1 = 0;
  int a2 = 0;
  int b2 = 0;

  CountGrid[i][j] = -1; // flags a visted cell

  if (flowDir >= 0){  //avoids flagged pits

    // find which two cells receive flow and the proportion to each
    for (int q = 0; q < 8; ++q){
      if (flowDir >= FD_Low[q] && flowDir < FD_High_361[q]){
        proportion1 = (FD_High[q] - flowDir) / 45;
        a1 = i + Di1[q];
        b1 = j + Dj1[q];
        proportion2 = (flowDir - FD_Low[q]) / 45;
        a2 = i + Di2[q];
        b2 = j + Dj2[q];
        }
    }

      if (proportion1 > 0 && Flowarea_Raster[a1][b1] != NoDataValue){
        Flowarea_Raster[a1][b1] = Flowarea_Raster[a1][b1] + flowAccumVal * proportion1;
        CountGrid[a1][b1] = CountGrid[a1][b1] - 1;
        if (CountGrid[a1][b1] == 0){
          D_infAccum(a1, b1, CountGrid, Flowarea_Raster, FlowDir); //recursive call
        }
      }
      if (proportion2 > 0 && Flowarea_Raster[a2][b2] != NoDataValue){
        Flowarea_Raster[a2][b2] = Flowarea_Raster[a2][b2] + flowAccumVal * proportion2;
        CountGrid[a2][b2] = CountGrid[a2][b2] - 1;
        if (CountGrid[a2][b2] == 0){
          D_infAccum(a2, b2, CountGrid, Flowarea_Raster, FlowDir); //recursive call
      }
    }
  }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// D-infinity flow direction algorithm after Tarboton (1997).
//
// Algorithm takes a filled DEM and for each cell calculates the steepest descent
// based on 8 triangular facets. Flow direction is assigned as an angle from 0-360
// degrees with -1 used to flag unresolved areas such as pits.
//
// Code is ported and optimised from a Java implementation of the algorithm
// supplied under the GNU GPL licence through WhiteBox GAT:
// http://www.uoguelph.ca/~hydrogeo/Whitebox/ and provides identical results
// to the whitebox tool.
//
// SWDG - 26/07/13
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Array2D<float> LSDRaster::D_inf_FlowDir(){

  Array2D<float> FlowDir_Array(NRows,NCols,NoDataValue);

  float maxSlope; //maxiumum slope
  float flowDir = 0; //temp variable to hold flowdirections while looping thru the 8 facets

  //components of the triangular facets as outlined in Tarboton (1997) fig 3
  //& equations 1-5
  float e0;
  float e1;
  float e2;
  float s1;
  float s2;
  float r;
  float s;

  //Facet elevation factors from Tarboton (1997) Table 1
  int acVals[] = {0, 1, 1, 2, 2, 3, 3, 4};
  int afVals[] = {1, -1, 1, -1, 1, -1, 1, -1};
  int e1Col[] = {1, 0, 0, -1, -1, 0, 0, 1};
  int e1Row[] = {0, -1, -1, 0, 0, 1, 1, 0};
  int e2Col[] = {1, 1, -1, -1, -1, -1, 1, 1};
  int e2Row[] = {-1, -1, -1, -1, 1, 1, 1, 1};

  for (int i = 1; i < NRows - 1; ++i){
    for (int j = 1; j < NCols - 1; ++j){
      e0 = RasterData[i][j];
      if (e0 == NoDataValue){
        FlowDir_Array[i][j] = NoDataValue; //if there is no elevation data we cant have a flowdir
      }
      else{
        maxSlope = -9999999;  //set to a low value that != NDV so any slope will be bigger than it

        for (int a = 0; a < 8; ++a){  //loop through the 8 facets
          e1 = RasterData[i + e1Row[a]][j + e1Col[a]];
          e2 = RasterData[i + e2Row[a]][j + e2Col[a]];
          if (e1 != NoDataValue && e2 != NoDataValue){ //avoid facets lyng in no data
            if (e0 > e1 && e0 > e2){
              //calculate slopes (s1,s2,s) and bearings (r) along edges
              //of the facet when e0 is higher than e1 and e2
              s1 = (e0 - e1) / DataResolution;
              if (s1 == 0){
                s1 = 0.00001;
              }
              s2 = (e1 - e2) / DataResolution;
              r = atan(s2 / s1);
              s = sqrt(s1 * s1 + s2 * s2);

              if (s1 < 0 && s2 < 0){
                s = -1 * s;
              }
              if (s1 < 0 && s2 == 0){
                s = -1 * s;
              }
              if (s1 == 0 && s2 < 0){
                s = -1 * s;
              }
              if (s1 == 0.001 && s2 < 0){
                s = -1 * s;
              }
              if (r < 0 || r > atan(1)){
                if (r < 0){
                  r = 0;
                  s = s1;
                }
                else{
                  r = atan(1);
                  s = (e0 - e2) / (DataResolution * sqrt(2)); //diagonal cell length
                }
              }
              if (s >= maxSlope && s != 0.00001){
                maxSlope = s;
                flowDir = afVals[a] * r + acVals[a] * (M_PI / 2);
              }
            }
            //calculate slope (s) and bearing (r) along edges
            //of the facet when e0 is higher than e1 or e2
            else if (e0 > e1 || e0 > e2){
              if (e0 > e1){
                r = 0;
                s = (e0 - e1) / DataResolution;
              }
              else{
                r = atan(1);
                s = (e0 - e2) / (DataResolution * sqrt(2));
              }
              if (s >= maxSlope && s != 0.00001){
                maxSlope = s;
                flowDir = afVals[a] * r + acVals[a] * (M_PI / 2);
              }
            }
          }
        }

        if (maxSlope <= 0){
          FlowDir_Array[i][j] = -1;  //unresolved - Tarboton uses D8 to fill these pits - we have a better fill algorithm
        }
        else{
          flowDir = round((flowDir * (180 / M_PI)) * 10) / 10;
          flowDir = 360 - flowDir + 90;
          if (flowDir > 360){
            flowDir = flowDir - 360;
          }
          FlowDir_Array[i][j] = flowDir;
        }
      }
    }
  }

  return FlowDir_Array;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//Function to write the D-infinity flow directions to an LSDRaster.
//
//SWDG - 26/7/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::write_dinf_flowdir_to_LSDRaster(Array2D<float> dinflow){

  LSDRaster FlowDirection(NRows, NCols, XMinimum, YMinimum, DataResolution,
                          NoDataValue, dinflow,GeoReferencingStrings);

  return FlowDirection;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//Wrapper Function to create a D-infinity flow area raster with one function call.
//
//SWDG - 26/7/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::D_inf(){

  Array2D<float> Dinf_flow = D_inf_FlowDir();
  LSDRaster Dinf_area = D_inf_FlowArea(Dinf_flow);

  return Dinf_area;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//Wrapper Function to create a D-infinity flow area raster, in spatial units, with one function call.
//
//SWDG - 16/10/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::D_inf_units(){

  Array2D<float> Dinf_flow = D_inf_FlowDir();
  LSDRaster Dinf_area = D_inf_FlowArea(Dinf_flow);

  float cell_area = DataResolution*DataResolution;
  Array2D<float> pixel_area(NRows, NCols, cell_area);

  Array2D<float> Dinf_area_units = Dinf_area.get_RasterData() * pixel_area;
  LSDRaster Dinf_area_units_raster = Dinf_area.LSDRasterTemplate(Dinf_area_units);

  return Dinf_area_units_raster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//Wrapper Function to create a D-infinity flow accumulation and drainage area raster
//BG - 09/01/2018
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
vector<LSDRaster> LSDRaster::D_inf_flowacc_DA()
{
  vector<LSDRaster> output(2);

  Array2D<float> Dinf_flow = D_inf_FlowDir();
  LSDRaster Dinf_area = D_inf_FlowArea(Dinf_flow);

  float cell_area = DataResolution*DataResolution;
  Array2D<float> pixel_area(NRows, NCols, cell_area);

  Array2D<float> Dinf_area_units = Dinf_area.get_RasterData() * pixel_area;
  LSDRaster Dinf_area_units_raster = Dinf_area.LSDRasterTemplate(Dinf_area_units);

  output[0] = Dinf_area;
  output[1] = Dinf_area_units_raster;

  return output;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// Function to multiply D_inf flow accumulation data to drainage area by multiplying through
// by the data resolution. (This could be a duplicate function but I don't have time to check!).
//
// MDH - 27/8/14
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=--=-=-=-=-=--=-

LSDRaster LSDRaster::D_inf_ConvertFlowToArea()
{
  float cell_area = DataResolution*DataResolution;
  Array2D<float> Dinf_area_units = RasterData;
  for (int i=0;i<Dinf_area_units.dim1(); ++i)
  {
    for (int j=0; j<Dinf_area_units.dim2(); ++j)
    {
      if (Dinf_area_units[i][j] != NoDataValue) Dinf_area_units[i][j] = Dinf_area_units[i][j]*cell_area;
    }
  }

  return LSDRaster(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue, Dinf_area_units,GeoReferencingStrings);
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// Function to trace upstream from a pour point and extract watershed associated with
// D_inf flow routing
//
// Uses a priority queue ordered by elevation to collect every pixel that drains to a
// particular pour point and returns the resultant basin as an LSDIndexRaster mask
//
// MDH - 26/8/14
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=--=-=-=-=-=--=-
LSDIndexRaster LSDRaster::D_inf_watershed(LSDRaster D_inf_FlowDir, int PourRow, int PourCol)
{
  //Declare the priority Queue with greater than comparison
  priority_queue< FillNode, vector<FillNode>, greater<FillNode> > PriorityQueue;
  //Declare a temporary FillNode structure which we populate before adding to the PQ
  //Declare a central node or node of interest
  FillNode TempNode, CentreNode;
  //Index array to track whether nodes are in queue or have been processed
  //-9999 = no_data, 0 = data but not processed or in queue,
  //1 = in queue but not processed, 2 = fully processed and removed from queue

  // Arrays of indexes of neighbour cells wrt target cell and their
  //corresponding ranges of angles
  int dX[] = {1, 1, 1, 0, -1, -1, -1, 0};
  int dY[] = {-1, 0, 1, 1, 1, 0, -1, -1};
  float startFD[] = {180, 225, 270, 315, 0, 45, 90, 135};
  float endFD[] = {270, 315, 360, 45, 90, 135, 180, 225};
    float FlowDir;

  //Index array for collecting catchment area
  Array2D<int> WatershedArray(NRows,NCols,NoDataValue);
  //Array2D<int> QueueCode(NRows,NCols,NoDataValue);

  //add outlet to priority queue as starting point
  TempNode.Zeta = RasterData[PourRow][PourCol];
  TempNode.RowIndex = PourRow;
  TempNode.ColIndex = PourCol;
  PriorityQueue.push(TempNode);

  int row, col;

  //Loop through the priority queue from lowest to highest elevations
  //filling as we go and adding unassessed neighbours to the priority queue
  while (!PriorityQueue.empty())
  {
    //first get the highest priority node and assign it before
    //removing it from the queue and declaring it processed
    CentreNode = PriorityQueue.top();
    row=CentreNode.RowIndex;
    col=CentreNode.ColIndex;
    PriorityQueue.pop();

    //loop through the 8 neighbours of the target cell
    for (int c = 0; c < 8; ++c)
    {
        //handle edges here
        if ((row +dY[c] > NRows-1) || (col + dX[c] > NCols-1) || (row+dY[c]<0) || (col+dY[c]<0)) continue;

        FlowDir = D_inf_FlowDir.RasterData[row + dY[c]][col + dX[c]];

         if (FlowDir >= 0)
         {
           //handles the issue of 0,360 both pointing to North
            if (c != 3)
            {
              if ((FlowDir > startFD[c]) && (FlowDir < endFD[c]))
              {
                if (WatershedArray[row+dY[c]][col+dX[c]] != 1)
                {
                  //add contributing node to priority queue
                  TempNode.Zeta = RasterData[row+dY[c]][col+dX[c]];
              TempNode.RowIndex = row+dY[c];
              TempNode.ColIndex = col+dX[c];
              PriorityQueue.push(TempNode);
              WatershedArray[row+dY[c]][col+dX[c]] = 1;
                  }
              }
        }
            else
            {
              if (FlowDir > startFD[c] || FlowDir < endFD[c])
              {
                if (WatershedArray[row+dY[c]][col+dX[c]] != 1)
                {
                  //add contributing node to priority queue
                  TempNode.Zeta = RasterData[row+dY[c]][col+dX[c]];
              TempNode.RowIndex = row+dY[c];
              TempNode.ColIndex = col+dX[c];
              PriorityQueue.push(TempNode);
              WatershedArray[row+dY[c]][col+dX[c]] = 1;
                  }
              }
            }
      }
    }
  }
  LSDIndexRaster Watershed(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,WatershedArray,GeoReferencingStrings);
  return Watershed;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Topographic_Index
// Calculates the topographic index, defined as ln(A/S) (Kirkby, 1975), where A
// is the accumulation area and S is the slope.  This is an indicator of the
// distribution of moisture within the topography.
// DTM 01/04/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::calculate_topographic_index(LSDRaster& AccumulationArea, LSDRaster& Slope)
{
  Array2D<float> TopographicIndexArray(NRows,NCols,NoDataValue);
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j]!=NoDataValue) TopographicIndexArray[i][j] = log(AccumulationArea.get_data_element(i,j)/Slope.get_data_element(i,j));
    }
  }
  LSDRaster TopographicIndex(NRows,NCols,XMinimum,YMinimum,DataResolution,
                             NoDataValue,TopographicIndexArray,GeoReferencingStrings);
  return TopographicIndex;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//end of d-inf modules
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Generate data in three text files to create a boomerang plot as in Roering et al [2007].
// Added spline curves and return of a pair of LH values - 1/11/13 SWDG.
// SWDG 27/8/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
pair<float,float> LSDRaster::Boomerang(LSDRaster& Slope, LSDRaster& Dinf, string RasterFilename, float log_bin_width, int SplineResolution, float bin_threshold){

  Array2D<float> slope = Slope.get_RasterData();
  Array2D<float> area = Dinf.get_RasterData();

  //do some log binning
  vector<float> Mean_x_out;
  vector<float> Mean_y_out;
  vector<float> Midpoints_out;
  vector<float> STDDev_x_out;
  vector<float> STDDev_y_out;
  vector<float> STDErr_x_out;
  vector<float> STDErr_y_out;
  vector<int> number_observations;

  log_bin_data(area, slope, log_bin_width, Mean_x_out, Mean_y_out, Midpoints_out,
          STDDev_x_out, STDDev_y_out, STDErr_x_out, STDErr_y_out,
          number_observations, NoDataValue);

  //remove empty bins
  RemoveSmallBins(Mean_x_out, Mean_y_out, Midpoints_out, STDDev_x_out,
              STDDev_y_out, STDErr_x_out, STDErr_y_out, number_observations, bin_threshold);

  //index value of max slope
  int slope_max_index = distance(Mean_y_out.begin(), max_element(Mean_y_out.begin(), Mean_y_out.end()));

  //hillslope length from the maximum binned values
  float LH = Mean_x_out[slope_max_index]/DataResolution;

  // Fit splines through the binned data to get the LH
  vector<float> Spline_X;
  vector<float> Spline_Y;
  PlotCubicSplines(Mean_x_out, Mean_y_out, SplineResolution, Spline_X, Spline_Y);

  //index value of max spline slope
  int slope_max_index_spline = distance(Spline_Y.begin(), max_element(Spline_Y.begin(), Spline_Y.end()));

  //hillslope length from spline curve - maybe get a range of values about the maximum?

  float LH_spline = Spline_X[slope_max_index_spline]/DataResolution;

  //set up a filestream object to write the binned data
  ofstream file;

  stringstream ss_bin;
  ss_bin << RasterFilename << "_boom_binned.txt";
  file.open(ss_bin.str().c_str());   //needs a null terminated character array, not a string. See pg 181 of accelerated c++

  for(int q = 0; q < int(Mean_x_out.size()); q++){
    file << Mean_x_out[q] << " " << Mean_y_out[q] << " " << STDDev_x_out[q] << " " << STDDev_y_out[q] << " " << STDErr_x_out[q] << " " << STDErr_y_out[q] << endl;
  }
  file.close();

  //set up a filestream object to write the spline data
  ofstream SplineFile;

  stringstream ss_spline;
  ss_spline << RasterFilename << "_boom_spline.txt";
  SplineFile.open(ss_spline.str().c_str());   //needs a null terminated character array, not a string. See pg 181 of accelerated c++

  for(int q = 0; q < int(Spline_X.size()); q++){ //fixed bug here where I looped over the wrong vector - SWDG 7/11/13
    SplineFile << Spline_X[q] << " " << Spline_Y[q] << endl;

  }
  SplineFile.close();

  //set up a filestream object to write the data cloud
  ofstream cloud;

  stringstream ss_cloud;
  ss_cloud << RasterFilename << "_boom_cloud.txt";
  cloud.open(ss_cloud.str().c_str());     //needs a null terminated character array, not a string. See pg 181 of accelerated c++

  for (int i = 1; i < NRows-1; ++i){
    for (int j = 1; j < NCols-1; ++j){
      if(area[i][j] != NoDataValue && slope[i][j] != NoDataValue){
        cloud << area[i][j] << " " << slope[i][j] << endl;
      }
    }
  }
  cloud.close();

  // create a pair containing the two LH values, first is the binned value and second is the spline value
  pair <float,float> LH_Pair;
  LH_Pair = make_pair (LH, LH_spline);

  return LH_Pair;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Punch basins out of an LSDRaster to create DEMs of a single catchment.
//
// Writes files in the user supplied format (flt or asc) and returns a vector
// LSDRasters so they can be loaded into other functions.
// Updated 24/9/13 to return a vector of LSDRasters SWDG
// SWDG 27/8/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<LSDRaster> LSDRaster::BasinPuncher(vector<int> basin_ids, LSDIndexRaster BasinArray)
{

  Array2D<int> BasinRaster = BasinArray.get_RasterData();

  vector<LSDRaster> BasinVector; //vector to contain individual basin LSDRasters

  for(int a = 0; a < int(basin_ids.size()); ++a){

    Array2D<float> BasinDEM(NRows, NCols, NoDataValue);
    bool Flag = false;

    for (int i=0; i<NRows; ++i){
      for (int j=0; j<NCols; ++j){
        if(BasinRaster[i][j] == basin_ids[a]){
          Flag = true;
          BasinDEM[i][j] = RasterData[i][j];
        }
      }
    }

    if (Flag == true){ //only write the raster if there is data to write
      LSDRaster Basin(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                      BasinDEM,GeoReferencingStrings);
      BasinVector.push_back(Basin);
    }
  }
  return BasinVector;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Cookie cut a raster using a smaller raster.
//
// Requires that both rasters share a spatial extent.
// Returns an LSDRaster of the data cut to the other ratser's shape.
//
// SWDG 06/07/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::CookieCutRaster(LSDRaster Cutter)
{

  Array2D<float> CutterData = Cutter.get_RasterData();
  Array2D<float> cookie(NRows, NCols, NoDataValue);

  for (int i=0; i<NRows; ++i){
    for (int j=0; j<NCols; ++j){
      if(CutterData[i][j] != NoDataValue){
        cookie[i][j] = RasterData[i][j];
      }
    }
  }

  LSDRaster Cookie(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                  cookie,GeoReferencingStrings);

  return Cookie;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Collect all basin average metrics into a single file.
//
// File is written with the format:
// "basin_id slope elevation aspect area drainage_density hilltop_curvature hillslope_length mean_slope hilltop_relief hilltop_aspect E* R* LH_bins LH_splines LH_density"
// SWDG 27/8/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::CollectBasinMetrics(LSDIndexRaster& Basins, LSDRaster& Slope, LSDRaster& Elevation, LSDRaster& Aspect,
                              LSDRaster& Area, LSDRaster& DrainageDensity, LSDRaster& Cht, LSDRaster& HillslopeLength,
                              LSDRaster& MeanSlope, LSDRaster& Relief, LSDRaster& MeanAspect, LSDRaster& LH_drainage_density, Array2D<float> LH_Data, float CriticalSlope, string RasterFilename)
{

  Array2D<int> basin_ids = Basins.get_RasterData();

  //vectors to contain output data
  vector<int> BasinIDVector;
  vector<float> SlopeVector;
  vector<float> ElevationVector;
  vector<float> AspectVector;
  vector<float> AreaVector;
  vector<float> DrainageDensityVector;
  vector<float> ChtVector;
  vector<float> HillslopeLengthVector;
  vector<float> MeanSlopeVector;
  vector<float> ReliefVector;
  vector<float> MeanAspectVector;
  vector<float> LHFromDDVector;
  vector<float> EStarVector;
  vector<float> RStarVector;

  //Get vector of unique basin indexes
  vector<int> basin_index = Unique(basin_ids, NoDataValue);

  //loop through each basin
  for (vector<int>::iterator it = basin_index.begin(); it !=  basin_index.end(); ++it){

    int SlopeCounter = 0;
    float SlopeSum = 0;
    float ElevationSum = 0;
    int ElevationCounter = 0;
    float AspectSum = 0;
    int AspectCounter = 0;
    float AreaSum = 0;
    int AreaCounter = 0;
    float DrainageDensitySum = 0;
    int DrainageDensityCounter = 0;
    float ChtSum = 0;
    int ChtCounter = 0;
    float HillslopeLengthSum = 0;
    int HillslopeLengthCounter = 0;
    float MeanSlopeSum = 0;
    int MeanSlopeCounter = 0;
    float ReliefSum = 0;
    int ReliefCounter = 0;
    float MeanAspectSum = 0;
    int MeanAspectCounter = 0;
    float LHFromDD = 0;

    for (int i = 0; i < NRows; ++i){
      for (int j = 0; j < NCols; ++j){

       if (Slope.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         SlopeSum += Slope.get_data_element(i,j);
         ++SlopeCounter;
        }
       if (Elevation.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         ElevationSum += Elevation.get_data_element(i,j);
         ++ElevationCounter;
        }
       if (Aspect.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         AspectSum += Aspect.get_data_element(i,j);
         ++AspectCounter;
        }
       if (Area.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         AreaSum += Area.get_data_element(i,j);
         ++AreaCounter;
        }
       if (DrainageDensity.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         DrainageDensitySum += DrainageDensity.get_data_element(i,j);
         ++DrainageDensityCounter;
        }
       if (Cht.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         ChtSum += Cht.get_data_element(i,j);
         ++ChtCounter;
        }
       if (HillslopeLength.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         HillslopeLengthSum += HillslopeLength.get_data_element(i,j);
         ++HillslopeLengthCounter;
        }
       if (MeanSlope.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         MeanSlopeSum += MeanSlope.get_data_element(i,j);
         ++MeanSlopeCounter;
        }
       if (Relief.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         ReliefSum += Relief.get_data_element(i,j);
         ++ReliefCounter;
        }
       if (MeanAspect.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         MeanAspectSum += MeanAspect.get_data_element(i,j);
         ++MeanAspectCounter;
        }
       if (LH_drainage_density.get_data_element(i,j) != NoDataValue && basin_ids[i][j] == *it ){
         LHFromDD = LH_drainage_density.get_data_element(i,j); //this is already a basin average value
        }
      }
    }

    //calculate means
    float AVGSlope = SlopeSum/SlopeCounter;
    float AVGElevation = ElevationSum/ElevationCounter;
    float AVGAspect = AspectSum/AspectCounter;
    float AVGArea = AreaSum/AreaCounter;
    float AVGDrainageDensity = DrainageDensitySum/DrainageDensityCounter;
    float AVGCht = ChtSum/ChtCounter;
    float AVGHillslopeLength = HillslopeLengthSum/HillslopeLengthCounter;
    float AVGMeanSlope = MeanSlopeSum/MeanSlopeCounter;
    float AVGRelief = ReliefSum/ReliefCounter;
    float AVGMeanAspect = MeanAspectSum/MeanAspectCounter;
    float EStar = (2 * (abs(AVGCht)) * AVGHillslopeLength) / CriticalSlope;
    float RStar = AVGRelief / (AVGHillslopeLength * CriticalSlope);

    //write means to vectors
    BasinIDVector.push_back(*it);
    SlopeVector.push_back(AVGSlope);
    ElevationVector.push_back(AVGElevation);
    AspectVector.push_back(AVGAspect);
    AreaVector.push_back(AVGArea);
    DrainageDensityVector.push_back(AVGDrainageDensity);
    ChtVector.push_back(AVGCht);
    HillslopeLengthVector.push_back(AVGHillslopeLength);
    MeanSlopeVector.push_back(AVGMeanSlope);
    ReliefVector.push_back(AVGRelief);
    MeanAspectVector.push_back(AVGMeanAspect);
    LHFromDDVector.push_back(LHFromDD);
    EStarVector.push_back(EStar);
    RStarVector.push_back(RStar);

  }

  stringstream filename;
  filename << RasterFilename << "_BasinMetrics.txt";
  ofstream file;
  cout << filename.str() << endl;
  file.open(filename.str().c_str());
  file << "basin_id slope elevation aspect area drainage_density hilltop_curvature hillslope_length mean_slope hilltop_relief hilltop_aspect E* R* LH_bins LH_splines LH_density" << endl;


  for(int q = 0; q < int(BasinIDVector.size()); q++){

    float LH_bins = 0.0;
    float LH_splines = 0.0;

    for (int k = 0; k < int(LH_Data.dim1()); ++k){
      if (LH_Data[k][0] == BasinIDVector[q]){ //if we have LH data for this basin id then write it to the variables
        LH_bins = LH_Data[k][1];
        LH_splines = LH_Data[k][2];
      }
    }

    file << BasinIDVector[q] << " " << SlopeVector[q] << " " << ElevationVector[q] << " " << AspectVector[q] << " " << AreaVector[q] << " " << DrainageDensityVector[q] << " " << ChtVector[q] << " " << HillslopeLengthVector[q] << " " << MeanSlopeVector[q] <<  " " << ReliefVector[q] << " " << MeanAspectVector[q] << " " << EStarVector[q] << " " << RStarVector[q] << " " << LH_bins << " " << LH_splines << " " << LHFromDDVector[q] << endl;
  }

  file.close();

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Raster_statistics_by_index
//-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// A generic function for calculating commonly used statistics on a raster that
// has been separated into discrete categories (marked by index raster) that are
// to be considered separately.  An example is to calculate basin metrics
// for a bunch of drainage basins labelled with a unique ID (although there is a
// specific function to carry out this particular analysis, this type of problem
// is sufficiently common to warrant a standalone function).
//
// Takes a raster and a corresponding index raster, and calculates the mean, sd
// and standard error by index.  Returns four vectors: mean, st.dev., st.err and
// Number of points for each category.
// DTM 28/11/2013 (adapting SDWG's DrainageDensity function)
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::raster_statistics_by_index(LSDIndexRaster& IndexRaster,
                   vector<float>& mean_vector, vector<float>& SD_vector,
                   vector<float>& SErr_vector, vector<int>& NPts_vector)
{
  int intNoDataValue = IndexRaster.get_NoDataValue();
  //Declare all the variables needed in this method
  vector<int> IDs;
  vector<int> IDs_sorted;
  vector<size_t> index_map;
  int q = 0;
  //convert Basin Raster to an Array
  Array2D<int> ids = IndexRaster.get_RasterData();
  //Loop over every pixel and record the value and basin ID into two vectors
  for (int i = 0; i < NRows; ++i)
  {
    for (int j = 0; j < NCols; ++j)
    {
      if (ids[i][j] != intNoDataValue)
      {
          IDs.push_back(ids[i][j]);
      }
    }
  }
  int N_IDs = IDs.size();
  vector<float> Values(N_IDs, NoDataValue);
  vector<float> SortedValues;
  int vector_index = 0;
  for (int i = 0; i < NRows; ++i)
  {
    for (int j = 0; j < NCols; ++j)
    {
      if (ids[i][j] != intNoDataValue)
      {
        if(RasterData[i][j] != NoDataValue)
        {
          Values[vector_index]=RasterData[i][j];
        }
        ++vector_index;
      }
    }
  }
  //sort our two vectors based on the Basin IDs: has the effect of grouping each basin together in 1D space
  matlab_int_sort(IDs, IDs_sorted, index_map);
  matlab_float_reorder(Values, index_map, SortedValues);

  // get the ID
  cout << "Now getting stats for values by index" << endl;
  int start_id = IDs_sorted[0];
  vector<float> values_for_this_ID;
  float mean, SD, SErr;
  while (q < int(IDs_sorted.size()))
  {
    //cout << q << "/" << IDs_sorted.size() << endl;
    if (start_id == IDs_sorted[q])
    {
      if (SortedValues[q]!=NoDataValue) values_for_this_ID.push_back(SortedValues[q]);
      ++q;
    }
    else
    {
      // get mean, sd and serr.
      if (values_for_this_ID.empty() == true)
      {
        mean = NoDataValue;
        SD = NoDataValue;
        SErr = NoDataValue;
      }
      else
      {
        mean = get_mean(values_for_this_ID);
        SD = get_standard_deviation(values_for_this_ID, mean);
        SErr = get_standard_error(values_for_this_ID, SD);
      }
      //record the mean, sd and serr into the maps
      mean_vector.push_back(mean);
      SD_vector.push_back(SD);
      SErr_vector.push_back(SErr);
      NPts_vector.push_back(values_for_this_ID.size());

      values_for_this_ID.clear();
      start_id = IDs_sorted[q];
    }
  }
  // Process the final basin once the loop is completed
  if (values_for_this_ID.empty() == true)
  {
    mean = NoDataValue;
    SD = NoDataValue;
    SErr = NoDataValue;
  }
  else
  {
    mean = get_mean(values_for_this_ID);
    SD = get_standard_deviation(values_for_this_ID, mean);
    SErr = get_standard_error(values_for_this_ID, SD);
  }
  cout << "kicking out output vectors ";
  mean_vector.push_back(mean);
  SD_vector.push_back(SD);
  SErr_vector.push_back(SErr);
  NPts_vector.push_back(values_for_this_ID.size());
  cout << "...done" << endl;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Module to sample LSDRaster values running along a ridgetop network. Pass in
// a TNT array of floats that denotes the ridge network. Ridge network is
// generated from LSDJunctionNetwork::ExtractRidges
//
// Returns sampled LSDRaster object
//
// SWDG 04/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::RidgeSample(Array2D<float>& Ridges){

  Array2D<float> Sample_data(NRows,NCols,NoDataValue);

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (RasterData[i][j] != NoDataValue && Ridges[i][j] != NoDataValue ){
        Sample_data[i][j] = RasterData[i][j];
      }
    }
  }

  LSDRaster Sample(NRows,NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                   Sample_data,GeoReferencingStrings);
  return Sample;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Pass a smoothing window over a ridge LSDRaster object to calculate an average
// value running along the ridgetop.
//
// Pass in an optional integer smoothing window radius between 1 and 6.
// Default value is 2
//
// Returns LSDRaster object containing the averaged data.
//
// SWDG 04/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::RidgeSmoother(int WindowRadius){

  //arbitrary upper bound to limit too large a radius
  if (WindowRadius < 1 || WindowRadius > 6){
    WindowRadius = 2; //
  }

  Array2D<float> Smoothed(NRows,NCols,NoDataValue);

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      float sum = 0;
      int counter = 0;
      if (RasterData[i][j] != NoDataValue){
          for (int a = (-1*WindowRadius); a <= WindowRadius; ++a){
              for (int b = (-1*WindowRadius); b <= WindowRadius; ++b){
                if(a >= 0 && a <= NRows){
                  if(b >= 0 && b <= NCols){
                    if (RasterData[i+a][j+b] != NoDataValue){
                        sum += RasterData[i+a][j+b];
                        ++counter;
                    }
                  }
                }
             }
          }
      Smoothed[i][j] = sum/counter;
      }
    }
  }

  LSDRaster Smooth(NRows,NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                   Smoothed,GeoReferencingStrings);
  return Smooth;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Pass a buffer over a ridge LSDRaster object to increase sampling area.
//
// Pass in an optional integer buffer radius between 1 and 6.
// Default value is 2
//
// Returns LSDRaster object denoting the buffered ridge data.
//
// Buffers equally in all directions, so use with care to avoid sampling areas
// away from the axis of the original ridge line.
//
// SWDG 04/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::RidgeBuffer(int BufferRadius){

  Array2D<float> HilltopBuffer(NRows, NCols, NoDataValue);

  //arbitrary upper bound to limit too large a buffer
  if (BufferRadius < 1 || BufferRadius > 6){
    BufferRadius = 2;
  }

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (RasterData[i][j] != NoDataValue){
        for (int a = (-1 * BufferRadius); a <= BufferRadius; ++a){
          for (int b = (-1 * BufferRadius); b <= BufferRadius; ++b){
            if(i + a >= 0 && i + a <= NRows){
              if(j + b >= 0 && j + b <= NCols){
                HilltopBuffer[i + a][j + b] = RasterData[i][j];
              }
            }
          }
        }
      }
    }
  }

  LSDRaster Buffer(NRows, NCols, XMinimum, YMinimum, DataResolution,
                   NoDataValue, HilltopBuffer,GeoReferencingStrings);
  return Buffer;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Module assigns an average CHT (or other input LSDRaster value) to each basin,
// works by searching for every hilltop value that falls within a basin, summing
// these values and writing the final average to every cell identified as the
// basin in question.
//
// Pass in an LSDIndexRaster of Drainage basins, generated using
// ChannelNetwork::ExtractBasinsOrder
//
// Returns LSDRaster of average basin CHT for each identified basin.
//
// Very inefficent at present. Module loops through every cell in LSDRaster
// (2 * number of basins) + 1 times. Beware!
// Bug fixed in assignment of basin IDs - SWDG 2/9/13
// SWDG 04/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::BasinAverager(LSDIndexRaster& Basins){

  Array2D<int> basin_ids = Basins.get_RasterData();
  Array2D<float> Averaged(NRows,NCols,NoDataValue);
  //Get vector of unique basin indexes
  vector<int> basin_index = Unique(basin_ids, NoDataValue);

  //loop through each basin
  for (vector<int>::iterator it = basin_index.begin(); it !=  basin_index.end(); ++it){
    int counter = 0;
    float sum = 0;

    for (int i = 0; i < NRows; ++i){
      for (int j = 0; j < NCols; ++j){

       if (RasterData[i][j] != NoDataValue && basin_ids[i][j] == *it ){
         sum += RasterData[i][j];
         ++counter;
        }
      }
    }

    for (int i = 0; i < NRows; ++i){
      for (int j = 0; j < NCols; ++j){
        if(basin_ids[i][j] == *it){
          Averaged[i][j] = sum/counter;
        }
      }
    }
  }

  LSDRaster Averaged_out(NRows,NCols, XMinimum, YMinimum, DataResolution,
                            NoDataValue, Averaged,GeoReferencingStrings);
  return Averaged_out;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Module calculates an average value to each for a given raster from within a basin.
// Returns a Float of the averaged value.
// SWDG 24/3/2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
float LSDRaster::SingleBasinAverager(LSDIndexRaster& Basin){

  Array2D<int> basin_ids = Basin.get_RasterData();
  Array2D<float> Averaged(NRows,NCols,NoDataValue);

  //Get unique basin index
  vector<int> basin_index = Unique(basin_ids, NoDataValue);
  int single_basin_index = basin_index[0];

  int counter = 0;
  float sum = 0;

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){

      if (RasterData[i][j] != NoDataValue && basin_ids[i][j] == single_basin_index ){
        sum += RasterData[i][j];
        ++counter;

      }
    }
  }

  float Average = sum/counter;

  return Average;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
// Write the area(in spatial units of area) of each basin to the basin's pixels.
// Refactored to follow the drainage density calculations design pattern.
// SWDG 20/11/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::BasinArea(LSDIndexRaster Basins){
  //Declare all the variables needed in this method
  vector<int> IDs;
  vector<int> IDs_sorted;
  vector<size_t> index_map;
  int q = 0;
  float area_sum = 0;
  map <int,float> Basin_Areas; //structure to hold pairs of area values with a basin ID as a key
  Array2D<float> Areas(NRows,NCols,NoDataValue);  //Output raster

  //convert Basin Raster to an Array
  Array2D<int> basin_ids = Basins.get_RasterData();

  //Loop over every pixel and record it's basin ID in a vectors
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (basin_ids[i][j] != NoDataValue){
        IDs.push_back(basin_ids[i][j]);
      }
    }
  }

  //sort our vectors based on the Basin IDs: has the effect of grouping each basin together in 1D space
  // so if we count each pixel and multiply it by the pixel area we get basin area
  matlab_int_sort(IDs, IDs_sorted, index_map);

  // get the first basin ID
  int start_id = IDs_sorted[0];

  while (q < int(IDs_sorted.size())){
    if (start_id == IDs_sorted[q]){
      ++area_sum;
      ++q;
    }
    else{
      //record the area in the map using the Basin ID as a key
      Basin_Areas[start_id] = area_sum * (DataResolution * DataResolution);

      area_sum = 0;
      start_id = IDs_sorted[q];
    }
  }

  // Process the final basin once the loop is completed
  Basin_Areas[start_id] = area_sum * (DataResolution * DataResolution);

  //write data to the output raster
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (basin_ids[i][j] != NoDataValue){
        Areas[i][j] = Basin_Areas[basin_ids[i][j]];
      }
    }
  }

  //write the array to an LSDRaster and return it
  LSDRaster Areas_out(NRows, NCols, XMinimum, YMinimum, DataResolution,
                      NoDataValue, Areas,GeoReferencingStrings);
  return Areas_out;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
// Convert a basin, given by a basin ID, into a chain of xy coordinates for
// fast plotting of vector basin outlines.
//
// Produces a generalised polygon and will not cope well with complex geometries.
//
// Needs to be updated to write data into an esri ascii format so the files can
// be loaded into arc.
// SWDG 21/11/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::GetBasinVector(LSDIndexRaster Basins, int BasinOfInterest){

  //convert Basin Raster to an Array
  Array2D<int> basin_ids = Basins.get_RasterData();

  vector<float> I;
  vector<float> J;

  int NDVCount = 0;

  for (int i = 1; i < NRows-1; ++i){
    for (int j = 1; j < NCols-1; ++j){

      NDVCount = 0;

      if (basin_ids[i][j] == BasinOfInterest){

        //count border cells that are NDV
        if (basin_ids[i-1][j-1] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i][j-1] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i+1][j-1] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i-1][j] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i+1][j] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i-1][j+1] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i][j+1] != BasinOfInterest){ ++NDVCount; }
        if (basin_ids[i+1][j+1] != BasinOfInterest){ ++NDVCount; }

        if (NDVCount >= 4 && NDVCount < 8){  //increase the first value to get a simpler polygon
          //edge pixel
          I.push_back(i);
          J.push_back(j);
        }
      }
    }
  }

  //now have 2 vectors of i and j indexes of every point

  int q = 0;

  vector<float> X; //could prealloc here based on I.size()
  vector<float> Y;

  while (q < int(I.size())){

    //convert I,J into x,y
    X.push_back((J[q] * DataResolution) + XMinimum);
    Y.push_back(((I[q] - NRows) * DataResolution) + YMinimum);
    ++q;
  }

   //get centroid
  float mean_x = get_mean(X);
  float mean_y = get_mean(Y);

  //vector to contain the angles between each point and the centroid
  vector<float> A; //could prealloc here too

  int k = 0;

  float an = 0;

  while (k < int(Y.size())){
    //calculate angle between each point and the centroid
    an = atan2(Y[k] - mean_y, X[k] - mean_x);
    A.push_back(an);
    ++k;
  }

  //sort the data by angle and reorder the coordinates based on the sort
  vector<float> A_sorted;
  vector<size_t> index_map;
  vector<float> Reordered_X;
  vector<float> Reordered_Y;

  matlab_float_sort(A, A_sorted, index_map);
  matlab_float_reorder(X, index_map, Reordered_X);
  matlab_float_reorder(Y, index_map, Reordered_Y);

  //write the data to a file
  ofstream write_chain;

  write_chain.open("chain.txt");

  int w = 0;
  while (w < int(X.size())){
    write_chain << Reordered_X[w] << " " << Reordered_Y[w] << endl;
    ++w;
  }

  //close the chain
  write_chain << Reordered_X[0] << " " << Reordered_Y[0] << endl;
  write_chain.close();

}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
// Calulate drainage density of a set of input basins.
//
// Calculated as flow length/basin area.
//
// Refactored to optimise performance. SWDG - 19/11/13
//
// SWDG 04/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::DrainageDensity(LSDIndexRaster& StreamNetwork, LSDIndexRaster& Basins, Array2D<int> FlowDir){

  //Declare all the variables needed in this method
  float two_times_root2 = 2.828427;
  vector<float> Lengths;
  vector<float> SortedLengths;
  vector<int> IDs;
  vector<int> IDs_sorted;
  vector<size_t> index_map;
  int q = 0;
  float length_sum = 0;
  float area_sum = 0;
  map <int,float> Basin_DD; //structure to hold pairs of DD values with a basin ID as a key
  Array2D<float> Density(NRows,NCols,NoDataValue);  //Output raster

  //convert Basin Raster to an Array
  Array2D<int> basin_ids = Basins.get_RasterData();

  //Loop over every pixel and record it's stream length and basin ID in two vectors
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (basin_ids[i][j] != NoDataValue){
        if (StreamNetwork.get_data_element(i,j) != NoDataValue){
          if ((FlowDir[i][j] % 2) != 0 && (FlowDir[i][j] != -1 )){ //is odd but not -1
            Lengths.push_back(DataResolution * two_times_root2); //diagonal
            IDs.push_back(basin_ids[i][j]);
          }
          else if (FlowDir[i][j] % 2 == 0){  //is even
            Lengths.push_back(DataResolution); //cardinal
            IDs.push_back(basin_ids[i][j]);
          }
        }
        else{
          Lengths.push_back(0.0);
          IDs.push_back(basin_ids[i][j]);
        }
      }
    }
  }

  //sort our two vectors based on the Basin IDs: has the effect of grouping each basin together in 1D space
  matlab_int_sort(IDs, IDs_sorted, index_map);
  matlab_float_reorder(Lengths, index_map, SortedLengths);

  // get the first basin ID
  int start_id = IDs_sorted[0];

  while (q < int(IDs_sorted.size())){
    if (start_id == IDs_sorted[q]){
      length_sum += SortedLengths[q];
      area_sum += (DataResolution * DataResolution);
      ++q;
    }
    else{
      Basin_DD[start_id]=(length_sum/area_sum);   //record the DD density in the map using the Basin ID as a key
      length_sum = 0;
      area_sum = 0;
      start_id = IDs_sorted[q];
    }
  }

  // Process the final basin once the loop is completed
  Basin_DD[start_id]=(length_sum/area_sum);

  //write data to the output raster
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (basin_ids[i][j] != NoDataValue){
        Density[i][j] = Basin_DD[basin_ids[i][j]];
      }
    }
  }

  //write the array to an LSDRaster and return it
  LSDRaster DrainageDensity(NRows, NCols, XMinimum, YMinimum, DataResolution,
                            NoDataValue, Density,GeoReferencingStrings);
  return DrainageDensity;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// this function gets the total drainage density of the DEM.
// FJC 27/03/15
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
float LSDRaster::get_drainage_density_of_raster(LSDIndexRaster& StreamNetwork, Array2D<int> FlowDir)
{
  //Declare all the variables needed in this method
  float two_times_root2 = 2.828427;
  float stream_length = 0.0;

  //Loop over every pixel and record its stream length
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
        if (StreamNetwork.get_data_element(i,j) != NoDataValue){
          if ((FlowDir[i][j] % 2) != 0 && (FlowDir[i][j] != -1 )){ //is odd but not -1
            stream_length = stream_length+(DataResolution * two_times_root2); //diagonal
          }
          else if (FlowDir[i][j] % 2 == 0){  //is even
            stream_length = stream_length + DataResolution; //cardinal
          }
        }
        else{
          stream_length = stream_length + 0.0;
        }
    }
  }

  // Get the drainage density (flow length/area)
  float raster_area = NRows*NCols*DataResolution*DataResolution;
  float drainage_density = stream_length/raster_area;

  return drainage_density;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Simple method to convert a drainage density raster into a hillslope length raster.
// Returns a Raster of basin average hillslope lengths. The LH value is calculated using
// LH = 1/2*DD [Tucker et al 2001].
// SWDG - 7/11/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::HillslopeLengthFromDrainageDensity(LSDIndexRaster& StreamNetwork,
                       LSDIndexRaster& Basins, Array2D<int> FlowDir)
{

  LSDRaster DrainageDensity = LSDRaster::DrainageDensity(StreamNetwork, Basins, FlowDir);
  Array2D<float> HillslopeLength(NRows,NCols,NoDataValue);

  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      if (DrainageDensity.get_data_element(i,j) != NoDataValue){
        HillslopeLength[i][j] = 1 / (2 * DrainageDensity.get_data_element(i,j));
      }
    }
  }

  LSDRaster HillslopeLengthRaster = DrainageDensity.LSDRasterTemplate(HillslopeLength);
  return HillslopeLengthRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function built around original c++ code by Martin Hurst to generate a flowarea
// raster.
//
// Computes the proportion of all downslope flows for each cell in the input
// DEM and routes the flow accordingly. Consequently the dem is sorted and indexed
// using LSDStatsTools.
//
// Can handle DEMs containing flats, but pits must be filled using the new
// LSDRaster fill.
//
// Outputs an LSDRaster
//
// SWDG, 18/4/13
//
// Updated 23/4/13 to allow periodic boundary condtitions - SWDG
// Needs to be able to handle the boundary cond vector and only reflect bondaries when needed.
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::MDFlow(vector<string> BoundaryConditions)
{

  int Row2 = NRows + 2;
  int Col2 = NCols + 2;

  //create output array, populated with nodata
  Array2D<float> area_final(NRows, NCols, NoDataValue);

  Array2D<float> elev_pad(Row2, Col2, NoDataValue);
  Array2D<float> area(Row2, Col2, NoDataValue);

  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;


  //translate the data down and right by one cell to create a border
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
        elev_pad[i+1][j+1] = RasterData[i][j];
    }
  }

  //reflect boundaries
  for (int i = 0; i < Row2; ++i){
    for (int j = 0; j < Col2; ++j){
      if(i==0 && j != 0 && j != Col2-1){
        //top row
        elev_pad[i][j] = elev_pad[Row2-2][j];
      }
      if(i==Row2-1 && j != 0 && j != Col2-1){
        //bottom row
        elev_pad[i][j] = elev_pad[1][j];
      }

      if(j==0 && i != 0 && i != Row2-1){
        //left column
        elev_pad[i][j] = elev_pad[i][Col2-2];
      }

      if(j==Col2-1 && i!=0 && i != Row2-1){
        //right column
        elev_pad[i][j] = elev_pad[i][1];
      }
    }
  }

  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every non ndv cell
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      flat.push_back(elev_pad[i][j]);
      if (elev_pad[i][j] != NoDataValue){
        area[i][j] = DataResolution*DataResolution;
      }
    }
  }

  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);

  for(int q = 0 ;q < int(flat.size()); ++q){

    if (sorted[q] != NoDataValue){

      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;

      //skip edge cells
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1){

        //reset variables on each loop
        float total = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        float slope8 = 0;

        //Get sum of magnitude of downslope flow, total, and store the magnitude of
        //each of the 8 downslope cells as slope1->8 *Avoids NDVs*
        if (elev_pad[i][j] > elev_pad[i-1][j-1] && elev_pad[i-1][j-1] != NoDataValue){
          slope1 = (elev_pad[i][j] - elev_pad[i-1][j-1]) * one_ov_root_2;
          total += slope1;
        }
        if (elev_pad[i][j] > elev_pad[i-1][j] && elev_pad[i-1][j] != NoDataValue){
          slope2 = elev_pad[i][j] - elev_pad[i-1][j];
          total += slope2;
        }
        if (elev_pad[i][j] > elev_pad[i-1][j+1] && elev_pad[i-1][j+1] != NoDataValue){
          slope3 = (elev_pad[i][j] - elev_pad[i-1][j+1]) * one_ov_root_2;
          total += slope3;
        }
        if (elev_pad[i][j] > elev_pad[i][j+1] && elev_pad[i][j+1] != NoDataValue){
          slope4 = elev_pad[i][j] - elev_pad[i][j+1];
          total += slope4;
        }
        if (elev_pad[i][j] > elev_pad[i+1][j+1] && elev_pad[i+1][j+1] != NoDataValue){
          slope5 = (elev_pad[i][j] - elev_pad[i+1][j+1]) * one_ov_root_2;
          total += slope5;
        }
        if (elev_pad[i][j] > elev_pad[i+1][j] && elev_pad[i+1][j] != NoDataValue){
          slope6 = elev_pad[i][j] - elev_pad[i+1][j];
          total += slope6;
        }
        if (elev_pad[i][j] > elev_pad[i+1][j-1] && elev_pad[i+1][j-1] != NoDataValue){
          slope7 = (elev_pad[i][j] - elev_pad[i+1][j-1]) * one_ov_root_2;
          total += slope7;
        }
        if (elev_pad[i][j] > elev_pad[i][j-1] && elev_pad[i][j-1] != NoDataValue){
          slope8 = elev_pad[i][j] - elev_pad[i][j-1];
          total += slope8;
        }

      //if no slope is found (total == 0), pass flow to all equal elevation cells]
      if (total == 0) {
        if(elev_pad[i-1][j-1] == elev_pad[i][j]){
          slope1 = 1;
          total += 1;
        }
        if(elev_pad[i-1][j] == elev_pad[i][j]){
          slope2 = 1;
          total += 1;
        }
        if(elev_pad[i-1][j+1] == elev_pad[i][j]){
          slope3 = 1;
          total += 1;
        }
        if(elev_pad[i][j+1] == elev_pad[i][j]){
          slope4 = 1;
          total += 1;
        }
        if(elev_pad[i+1][j+1] == elev_pad[i][j]){
          slope5 = 1;
          total += 1;
        }
        if(elev_pad[i+1][j] == elev_pad[i][j]){
          slope6 = 1;
          total += 1;
        }
        if(elev_pad[i+1][j-1] == elev_pad[i][j]){
          slope7 = 1;
          total += 1;
        }
        if(elev_pad[i][j-1] == elev_pad[i][j]){
          slope8 = 1;
          total += 1;
        }
      }

      //divide slope by total to get the proportion of flow directed to each cell
      //and increment the downslope cells. If no downslope flow to a node, 0 is
      //added, so no change is seen.
      area[i-1][j-1] += area[i][j] * (slope1/total);
      area[i-1][j] += area[i][j] * (slope2/total);
      area[i-1][j+1] += area[i][j] * (slope3/total);
      area[i][j+1] += area[i][j] * (slope4/total);
      area[i+1][j+1] += area[i][j] * (slope5/total);
      area[i+1][j] += area[i][j] * (slope6/total);
      area[i+1][j-1] += area[i][j] * (slope7/total);
      area[i][j-1] += area[i][j] * (slope8/total);
      }
    }
  }

  //translate the data back
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
        area_final[i][j] = area[i+1][j+1];
    }
  }

  //write output LSDRaster object
  LSDRaster MultiFlow(NRows, NCols, XMinimum, YMinimum, DataResolution,
                      NoDataValue, area_final,GeoReferencingStrings);
  return MultiFlow;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function built around original c++ code by Martin Hurst to generate a flowarea
// raster.
//
// Computes the proportion of all downslope flows for each cell in the input
// DEM, and weights them using the equation from Freeman et al 1991 and routes the
// flow accordingly.
//
// Paper link: http://www.sciencedirect.com/science/article/pii/009830049190048I
//
// Cardinal Weighting = (elevation_drop/total_elevation_drop)^1.1
// Diagonal Weighting = ((elevation_drop/total_elevation_drop)*(1/root(2)))^1.1
//
// Can *NOT* handle DEMs containing flats or pits -  must be filled using the new
// LSDRaster fill.
//
// Outputs an LSDRaster
//
// SWDG, 18/4/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::FreemanMDFlow(){

  //create output array, populated with nodata
  Array2D<float> area(NRows, NCols, NoDataValue);

  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;
  float p = 1.1; //value avoids preferential flow to diagonals

  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every npn ndv cell
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      flat.push_back(RasterData[i][j]);
      if (RasterData[i][j] != NoDataValue){
        area[i][j] = DataResolution*DataResolution;
      }
    }
  }

  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);

  for(int q = 0 ;q < int(flat.size()); ++q){

    if (sorted[q] != NoDataValue){

      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;

      //skip edge cells
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1){

        //reset variables on each loop
        float total = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        float slope8 = 0;

        //Get sum of magnitude of downslope flow, total, and store the magnitude of
        //each of the 8 downslope cells as slope1->8 *Avoids NDVs*
        if (RasterData[i][j] > RasterData[i-1][j-1] && RasterData[i-1][j-1] != NoDataValue){
          slope1 = pow(((RasterData[i][j] - RasterData[i-1][j-1]) * one_ov_root_2),p);
          total += slope1;
        }
        if (RasterData[i][j] > RasterData[i-1][j] && RasterData[i-1][j] != NoDataValue){
          slope2 = pow((RasterData[i][j] - RasterData[i-1][j]),p);
          total += slope2;
        }
        if (RasterData[i][j] > RasterData[i-1][j+1] && RasterData[i-1][j+1] != NoDataValue){
          slope3 = pow(((RasterData[i][j] - RasterData[i-1][j+1]) * one_ov_root_2),p);
          total += slope3;
        }
        if (RasterData[i][j] > RasterData[i][j+1] && RasterData[i][j+1] != NoDataValue){
          slope4 = pow((RasterData[i][j] - RasterData[i][j+1]),p);
          total += slope4;
        }
        if (RasterData[i][j] > RasterData[i+1][j+1] && RasterData[i+1][j+1] != NoDataValue){
          slope5 = pow(((RasterData[i][j] - RasterData[i+1][j+1]) * one_ov_root_2),p);
          total += slope5;
        }
        if (RasterData[i][j] > RasterData[i+1][j] && RasterData[i+1][j] != NoDataValue){
          slope6 = pow((RasterData[i][j] - RasterData[i+1][j]),p);
          total += slope6;
        }
        if (RasterData[i][j] > RasterData[i+1][j-1] && RasterData[i+1][j-1] != NoDataValue){
          slope7 = pow(((RasterData[i][j] - RasterData[i+1][j-1]) * one_ov_root_2),p);
          total += slope7;
        }
        if (RasterData[i][j] > RasterData[i][j-1] && RasterData[i][j-1] != NoDataValue){
          slope8 = pow((RasterData[i][j] - RasterData[i][j-1]),p);
          total += slope8;
        }

      //divide slope by total to get the proportion of flow directed to each cell
      //and increment the downslope cells. If no downslope flow to a node, 0 is
      //added, so no change is seen.
      area[i-1][j-1] += area[i][j] * (slope1/total);
      area[i-1][j] += area[i][j] * (slope2/total);
      area[i-1][j+1] += area[i][j] * (slope3/total);
      area[i][j+1] += area[i][j] * (slope4/total);
      area[i+1][j+1] += area[i][j] * (slope5/total);
      area[i+1][j] += area[i][j] * (slope6/total);
      area[i+1][j-1] += area[i][j] * (slope7/total);
      area[i][j-1] += area[i][j] * (slope8/total);
      }
    }
  }
  //write output LSDRaster object
  LSDRaster FreemanMultiFlow(NRows, NCols, XMinimum, YMinimum, DataResolution,
                             NoDataValue, area,GeoReferencingStrings);
  return FreemanMultiFlow;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Route flow from one source pixel using FreemanMDFlow.  Adapted from SWDG's
// code above.
// DTM 07/11/2013
LSDRaster LSDRaster::FreemanMDFlow_SingleSource(int i_source,int j_source)
{

  //create output array, populated with nodata
  Array2D<float> area(NRows, NCols, NoDataValue);

  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;
  float p = 1.1; //value avoids preferential flow to diagonals

  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every npn ndv cell
  for (int i = 0; i < NRows; ++i)
  {
    for (int j = 0; j < NCols; ++j)
    {
      flat.push_back(RasterData[i][j]);
      if (RasterData[i][j] != NoDataValue)
      {
        area[i][j] = 0;
      }
    }
  }
  area[i_source][j_source] = DataResolution*DataResolution;
  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);
  bool reached_source = false;

  for(int q = 0 ;q < int(flat.size()); ++q)
  {

    if (sorted[q] != NoDataValue)
    {
      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;
      // test to see whether we have reached the source
      if(i==i_source && j==j_source) reached_source=true;
      //skip edge cells and cells above the source pixel
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1 && reached_source == true){

        //reset variables on each loop
        float total = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        float slope8 = 0;

        //Get sum of magnitude of downslope flow, total, and store the magnitude of
        //each of the 8 downslope cells as slope1->8 *Avoids NDVs*
        if (RasterData[i][j] > RasterData[i-1][j-1] && RasterData[i-1][j-1] != NoDataValue){
          slope1 = pow(((RasterData[i][j] - RasterData[i-1][j-1]) * one_ov_root_2),p);
          total += slope1;
        }
        if (RasterData[i][j] > RasterData[i-1][j] && RasterData[i-1][j] != NoDataValue){
          slope2 = pow((RasterData[i][j] - RasterData[i-1][j]),p);
          total += slope2;
        }
        if (RasterData[i][j] > RasterData[i-1][j+1] && RasterData[i-1][j+1] != NoDataValue){
          slope3 = pow(((RasterData[i][j] - RasterData[i-1][j+1]) * one_ov_root_2),p);
          total += slope3;
        }
        if (RasterData[i][j] > RasterData[i][j+1] && RasterData[i][j+1] != NoDataValue){
          slope4 = pow((RasterData[i][j] - RasterData[i][j+1]),p);
          total += slope4;
        }
        if (RasterData[i][j] > RasterData[i+1][j+1] && RasterData[i+1][j+1] != NoDataValue){
          slope5 = pow(((RasterData[i][j] - RasterData[i+1][j+1]) * one_ov_root_2),p);
          total += slope5;
        }
        if (RasterData[i][j] > RasterData[i+1][j] && RasterData[i+1][j] != NoDataValue){
          slope6 = pow((RasterData[i][j] - RasterData[i+1][j]),p);
          total += slope6;
        }
        if (RasterData[i][j] > RasterData[i+1][j-1] && RasterData[i+1][j-1] != NoDataValue){
          slope7 = pow(((RasterData[i][j] - RasterData[i+1][j-1]) * one_ov_root_2),p);
          total += slope7;
        }
        if (RasterData[i][j] > RasterData[i][j-1] && RasterData[i][j-1] != NoDataValue){
          slope8 = pow((RasterData[i][j] - RasterData[i][j-1]),p);
          total += slope8;
        }

      //divide slope by total to get the proportion of flow directed to each cell
      //and increment the downslope cells. If no downslope flow to a node, 0 is
      //added, so no change is seen.
      area[i-1][j-1] += area[i][j] * (slope1/total);
      area[i-1][j] += area[i][j] * (slope2/total);
      area[i-1][j+1] += area[i][j] * (slope3/total);
      area[i][j+1] += area[i][j] * (slope4/total);
      area[i+1][j+1] += area[i][j] * (slope5/total);
      area[i+1][j] += area[i][j] * (slope6/total);
      area[i+1][j-1] += area[i][j] * (slope7/total);
      area[i][j-1] += area[i][j] * (slope8/total);
      }
    }
  }
  //write output LSDRaster object
  LSDRaster FreemanMultiFlowSingleSource(NRows, NCols, XMinimum, YMinimum,
                 DataResolution, NoDataValue, area,GeoReferencingStrings);
  return FreemanMultiFlowSingleSource;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This extracts the valley network from previously idenified channel heads
// using workflow outlined in Pelletier (2013)
// DTM 27/06/2014
LSDRaster LSDRaster::FMDChannelsFromChannelHeads(vector<int>& channel_heads_rows,
                              vector<int>& channel_heads_cols, float R_threshold)
{
  int n_sources = channel_heads_rows.size();
  //create output array, populated with nodata
  Array2D<float> area(NRows, NCols, NoDataValue);
  Array2D<int> upslope_channel_heads(NRows, NCols, int(NoDataValue));
  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;
  float p = 1.1; //value avoids preferential flow to diagonals

  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every npn ndv cell
  for (int i = 0; i < NRows; ++i)
  {
    for (int j = 0; j < NCols; ++j)
    {
      flat.push_back(RasterData[i][j]);
      if (RasterData[i][j] != NoDataValue)
      {
        area[i][j] = 0;
        upslope_channel_heads[i][j] = 0;
      }
    }
  }

  int row,col;
  for(int i = 0; i<n_sources; ++i)
  {
    row = channel_heads_rows[i];
    col = channel_heads_cols[i];
    area[row][col] = DataResolution*DataResolution;
    upslope_channel_heads[row][col] = 1;
  }
  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);
  for(int q = 0 ;q < int(flat.size()); ++q)
  {

    if (sorted[q] != NoDataValue)
    {
      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;

      //skip edge cells and cells above the source pixel
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1){

        //reset variables on each loop
        float total = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        float slope8 = 0;

        //Get sum of magnitude of downslope flow, total, and store the magnitude of
        //each of the 8 downslope cells as slope1->8 *Avoids NDVs*
        if (RasterData[i][j] > RasterData[i-1][j-1] && RasterData[i-1][j-1] != NoDataValue){
          slope1 = pow(((RasterData[i][j] - RasterData[i-1][j-1]) * one_ov_root_2),p);
          total += slope1;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i-1][j-1];
        }
        if (RasterData[i][j] > RasterData[i-1][j] && RasterData[i-1][j] != NoDataValue){
          slope2 = pow((RasterData[i][j] - RasterData[i-1][j]),p);
          total += slope2;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i-1][j];
        }
        if (RasterData[i][j] > RasterData[i-1][j+1] && RasterData[i-1][j+1] != NoDataValue){
          slope3 = pow(((RasterData[i][j] - RasterData[i-1][j+1]) * one_ov_root_2),p);
          total += slope3;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i-1][j+1];
        }
        if (RasterData[i][j] > RasterData[i][j+1] && RasterData[i][j+1] != NoDataValue){
          slope4 = pow((RasterData[i][j] - RasterData[i][j+1]),p);
          total += slope4;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i][j+1];
        }
        if (RasterData[i][j] > RasterData[i+1][j+1] && RasterData[i+1][j+1] != NoDataValue){
          slope5 = pow(((RasterData[i][j] - RasterData[i+1][j+1]) * one_ov_root_2),p);
          total += slope5;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i+1][j+1];
        }
        if (RasterData[i][j] > RasterData[i+1][j] && RasterData[i+1][j] != NoDataValue){
          slope6 = pow((RasterData[i][j] - RasterData[i+1][j]),p);
          total += slope6;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i+1][j];
        }
        if (RasterData[i][j] > RasterData[i+1][j-1] && RasterData[i+1][j-1] != NoDataValue){
          slope7 = pow(((RasterData[i][j] - RasterData[i+1][j-1]) * one_ov_root_2),p);
          total += slope7;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i+1][j-1];
        }
        if (RasterData[i][j] > RasterData[i][j-1] && RasterData[i][j-1] != NoDataValue){
          slope8 = pow((RasterData[i][j] - RasterData[i][j-1]),p);
          total += slope8;
          if(upslope_channel_heads[i][j] >=1) ++upslope_channel_heads[i][j-1];
        }

        //divide slope by total to get the proportion of flow directed to each cell
        //and increment the downslope cells. If no downslope flow to a node, 0 is
        //added, so no change is seen.
        if(total>0)
        {
          area[i-1][j-1] += (area[i][j] * (slope1)/total);
          area[i-1][j] += (area[i][j] * (slope2)/total);
          area[i-1][j+1] += (area[i][j] * (slope3)/total);
          area[i][j+1] += (area[i][j] * (slope4)/total);
          area[i+1][j+1] += (area[i][j] * (slope5)/total);
          area[i+1][j] += (area[i][j] * (slope6)/total);
          area[i+1][j-1] += (area[i][j] * (slope7)/total);
          area[i][j-1] += (area[i][j] * (slope8)/total);
        }
      }
    }
  }
  Array2D<float> MDChannelArray(NRows,NCols,NoDataValue);
  // Now reduce the channel network according to upslope pixels
  float test_value;
  for(int i = 0; i< NRows; ++i)
  {
    for(int j = 0; j<NCols; ++j)
    {
      if(upslope_channel_heads[i][j] >= 1 && RasterData[i][j]!=NoDataValue)
      {
        test_value = area[i][j]/float(upslope_channel_heads[i][j]);
        if(test_value >=R_threshold) MDChannelArray[i][j]=area[i][j];

      }
    }
  }
  //write output LSDRaster object
  LSDRaster ChannelRaster(NRows, NCols, XMinimum, YMinimum, DataResolution,
                       NoDataValue, MDChannelArray,GeoReferencingStrings);
  return ChannelRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function built around original c++ code by Martin Hurst to generate a flowarea
// raster.
//
// Computes the proportion of all downslope flows for each cell in the input
// DEM, and weights them using the equation from Quinn et al 1991 and routes the
// flow accordingly.
//
// Paper link: http://onlinelibrary.wiley.com/doi/10.1002/hyp.3360050106/abstract
//
// Cardinal Weighting = (elevation_drop/total_elevation_drop)*DataResolution/2
// Diagonal Weighting =
//      ((elevation_drop/total_elevation_drop)*(1/root(2)))* DataResolution*0.354
//
// Can *NOT* handle DEMs containing flats or pits -  must be filled using the new
// LSDRaster fill.
//
// Outputs an LSDRaster
//
// SWDG, 18/4/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::QuinnMDFlow(){

  //create output array, populated with nodata
  Array2D<float> area(NRows, NCols, NoDataValue);

  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;
  float Lc = DataResolution/2; //cardinal scaling factor
  float Ld = DataResolution * 0.354; //diagonal scaling factor


  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every npn ndv cell
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      flat.push_back(RasterData[i][j]);
      if (RasterData[i][j] != NoDataValue){
        area[i][j] = DataResolution*DataResolution;
      }
    }
  }

  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);

  for(int q = 0 ;q < int(flat.size()); ++q){

    if (sorted[q] != NoDataValue){

      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;

      //skip edge cells
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1){

        //reset variables on each loop
        float total = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        float slope8 = 0;

        //Get sum of magnitude of downslope flow, total, and store the magnitude of
        //each of the 8 downslope cells as slope1->8 *Avoids NDVs*
        if (RasterData[i][j] > RasterData[i-1][j-1] && RasterData[i-1][j-1] != NoDataValue){
          slope1 = ((RasterData[i][j] - RasterData[i-1][j-1]) * one_ov_root_2) * Ld;
          total += slope1;
        }
        if (RasterData[i][j] > RasterData[i-1][j] && RasterData[i-1][j] != NoDataValue){
          slope2 = (RasterData[i][j] - RasterData[i-1][j]) * Lc;
          total += slope2;
        }
        if (RasterData[i][j] > RasterData[i-1][j+1] && RasterData[i-1][j+1] != NoDataValue){
          slope3 = ((RasterData[i][j] - RasterData[i-1][j+1]) * one_ov_root_2) * Ld;
          total += slope3;
        }
        if (RasterData[i][j] > RasterData[i][j+1] && RasterData[i][j+1] != NoDataValue){
          slope4 = (RasterData[i][j] - RasterData[i][j+1]) * Lc;
          total += slope4;
        }
        if (RasterData[i][j] > RasterData[i+1][j+1] && RasterData[i+1][j+1] != NoDataValue){
          slope5 = ((RasterData[i][j] - RasterData[i+1][j+1]) * one_ov_root_2) * Ld;
          total += slope5;
        }
        if (RasterData[i][j] > RasterData[i+1][j] && RasterData[i+1][j] != NoDataValue){
          slope6 = (RasterData[i][j] - RasterData[i+1][j]) * Lc;
          total += slope6;
        }
        if (RasterData[i][j] > RasterData[i+1][j-1] && RasterData[i+1][j-1] != NoDataValue){
          slope7 = ((RasterData[i][j] - RasterData[i+1][j-1]) * one_ov_root_2) * Ld;
          total += slope7;
        }
        if (RasterData[i][j] > RasterData[i][j-1] && RasterData[i][j-1] != NoDataValue){
          slope8 = (RasterData[i][j] - RasterData[i][j-1]) * Lc;
          total += slope8;
        }

      //divide slope by total to get the proportion of flow directed to each cell
      //and increment the downslope cells. If no downslope flow to a node, 0 is
      //added, so no change is seen.
      area[i-1][j-1] += area[i][j] * (slope1/total);
      area[i-1][j] += area[i][j] * (slope2/total);
      area[i-1][j+1] += area[i][j] * (slope3/total);
      area[i][j+1] += area[i][j] * (slope4/total);
      area[i+1][j+1] += area[i][j] * (slope5/total);
      area[i+1][j] += area[i][j] * (slope6/total);
      area[i+1][j-1] += area[i][j] * (slope7/total);
      area[i][j-1] += area[i][j] * (slope8/total);
      }
    }
  }
  //write output LSDRaster object
  LSDRaster QuinnMultiFlow(NRows, NCols, XMinimum, YMinimum, DataResolution,
                           NoDataValue, area,GeoReferencingStrings);
  return QuinnMultiFlow;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function built around original c++ code by Martin Hurst to generate a flowarea
// raster.
//
// Computes the proportion of all downslope flows for each cell in the input
// DEM. Finds the cell of the steepest descent and then checks the two
// neighbouring cells slopes. If either is also downslope proportion flow
// between the steepest cell and the steepest neighbour. If neither neighbour
// is downslope 100% of flow follows the steepest path.
//
// Can *NOT* handle DEMs containing flats or pits -  must be filled using the new
// LSDRaster fill.
//
// Outputs an LSDRaster
//
// SWDG - 02/08/2013
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::M2DFlow(){

  //create output array, populated with nodata
  Array2D<float> area(NRows, NCols, NoDataValue);

  //declare variables
  vector<float> flat;
  vector<float> sorted;
  vector<size_t> index_map;
  float one_ov_root_2 = 0.707106781187;

  //loop through the dem cells creating a row major 1D vector, flat, and
  //setting the cell area to every npn ndv cell
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){
      flat.push_back(RasterData[i][j]);
      if (RasterData[i][j] != NoDataValue){
        area[i][j] = DataResolution*DataResolution;
      }
    }
  }

  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(flat, sorted, index_map);

  for(int q = 0 ;q < int(flat.size()); ++q){

    if (sorted[q] != NoDataValue){

      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
       int j = index_map[q] % NCols;

      //skip edge cells
      if (i != 0 && j != 0 && i != NRows-1 && j != NCols-1){

        //reset variables on each loop
        float slope0 = 0;
        float slope1 = 0;
        float slope2 = 0;
        float slope3 = 0;
        float slope4 = 0;
        float slope5 = 0;
        float slope6 = 0;
        float slope7 = 0;
        vector<float> slopes;

        float p1 = 0;
        float p2 = 0;
        int second_slope = -1; //initialized using value outside of range.

        //Get magnitude of downslope flow slope0->7 *Avoids NDVs*
        if (RasterData[i][j] > RasterData[i-1][j-1] && RasterData[i-1][j-1] != NoDataValue){
          slope0 = ((RasterData[i][j] - RasterData[i-1][j-1]) * one_ov_root_2);
          slopes.push_back(slope0);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i-1][j] && RasterData[i-1][j] != NoDataValue){
          slope1 = (RasterData[i][j] - RasterData[i-1][j]);
          slopes.push_back(slope1);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i-1][j+1] && RasterData[i-1][j+1] != NoDataValue){
          slope2 = ((RasterData[i][j] - RasterData[i-1][j+1]) * one_ov_root_2);
          slopes.push_back(slope2);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i][j+1] && RasterData[i][j+1] != NoDataValue){
          slope3 = (RasterData[i][j] - RasterData[i][j+1]);
          slopes.push_back(slope3);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i+1][j+1] && RasterData[i+1][j+1] != NoDataValue){
          slope4 = ((RasterData[i][j] - RasterData[i+1][j+1]) * one_ov_root_2);
          slopes.push_back(slope4);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i+1][j] && RasterData[i+1][j] != NoDataValue){
          slope5 = (RasterData[i][j] - RasterData[i+1][j]);
          slopes.push_back(slope5);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i+1][j-1] && RasterData[i+1][j-1] != NoDataValue){
          slope6 = ((RasterData[i][j] - RasterData[i+1][j-1]) * one_ov_root_2);
          slopes.push_back(slope6);
        }
        else {
          slopes.push_back(0);
        }

        if (RasterData[i][j] > RasterData[i][j-1] && RasterData[i][j-1] != NoDataValue){
          slope7 = (RasterData[i][j] - RasterData[i][j-1]);
          slopes.push_back(slope7);
        }
        else {
          slopes.push_back(0);
        }

        if (int(slopes.size()) > 0 ){   //catch outlets with no neighbours to drain to

          //find maximum slope & its index location in the slopes vector
          float S_max = *max_element(slopes.begin(), slopes.end());
          int S_max_index = find(slopes.begin(), slopes.end(), S_max) - slopes.begin();

          //find steepest neighbour
          if (S_max_index == 0){
            if (slope7 > 0 && slope1 == 0){
              second_slope = 7;
            }
            if (slope7 == 0 && slope1 > 0){
              second_slope = 1;
            }
            if (slope7 > 0 && slope1 > 0){
              if (slope7 > slope1){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope7 == slope1){
              second_slope = 0;
            }
          }

          if (S_max_index == 1){
            if (slope0 > 0 && slope2 == 0){
              second_slope = 7;
            }
            if (slope0 == 0 && slope2 > 0){
              second_slope = 1;
            }
            if (slope0 > 0 && slope2 > 0){
              if (slope0 > slope2){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope0 == slope2){
              second_slope = 0;
            }
          }

          if (S_max_index == 2){
            if (slope1 > 0 && slope3 == 0){
              second_slope = 7;
            }
            if (slope1 == 0 && slope3 > 0){
              second_slope = 1;
            }
            if (slope1 > 0 && slope3 > 0){
              if (slope1 > slope3){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope1 == slope3){
              second_slope = 0;
            }
          }

          if (S_max_index == 3){
            if (slope2 > 0 && slope4 == 0){
              second_slope = 7;
            }
            if (slope2 == 0 && slope4 > 0){
              second_slope = 1;
            }
            if (slope2 > 0 && slope4 > 0){
              if (slope2 > slope4){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope2 == slope4){
              second_slope = 0;
            }
          }

          if (S_max_index == 4){
            if (slope3 > 0 && slope5 == 0){
              second_slope = 7;
            }
            if (slope3 == 0 && slope5 > 0){
              second_slope = 1;
            }
            if (slope3 > 0 && slope5 > 0){
              if (slope3 > slope5){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope3 == slope5){
              second_slope = 0;
            }
          }

          if (S_max_index == 5){
            if (slope4 > 0 && slope6 == 0){
              second_slope = 7;
            }
            if (slope4 == 0 && slope6 > 0){
              second_slope = 1;
            }
            if (slope4 > 0 && slope6 > 0){
              if (slope4 > slope6){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope4 == slope6){
              second_slope = 0;
            }
          }


          if (S_max_index == 6){
            if (slope5 > 0 && slope7 == 0){
              second_slope = 7;
            }
            if (slope5 == 0 && slope7 > 0){
              second_slope = 1;
            }
            if (slope5 > 0 && slope7 > 0){
              if (slope5 > slope7){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope5 == slope7){
              second_slope = 0;
            }
          }

          if (S_max_index == 7){
            if (slope6 > 0 && slope0 == 0){
              second_slope = 7;
            }
            if (slope6 == 0 && slope0 > 0){
              second_slope = 1;
            }
            if (slope6 > 0 && slope0 > 0){
              if (slope6 > slope0){
                second_slope = 7;
              }
              else{
                second_slope = 1;
              }
            }
            if (slope6 == slope0){
              second_slope = 0;
            }
          }

          //get proportions p1 and p2
          if (second_slope != S_max_index){
            p1 = S_max/(S_max + slopes[second_slope]);
            p2 = slopes[second_slope]/(S_max + slopes[second_slope]);
          }
          else{ //flow only in 1 direction
            p1 = 1;
            p2 = 0;
          }

          //partition flow following the steepest slope and it's steepest neighbour
          if (S_max_index == 0 && area[i-1][j-1] != NoDataValue){
            area[i-1][j-1] += area[i][j] * p1;
            if (second_slope == 1){
              area[i-1][j] += area[i][j] * p2;
            }
            if (second_slope == 7){
              area[i][j-1] += area[i][j] * p2;
            }
          }

          if (S_max_index == 1 && area[i-1][j] != NoDataValue){
            area[i-1][j] += area[i][j] * p1;
            if (second_slope == 2){
              area[i-1][j+1] += area[i][j] * p2;
            }
            if (second_slope == 0){
              area[i-1][j-1] += area[i][j] * p2;
            }
          }

          if (S_max_index == 2 && area[i-1][j+1] != NoDataValue){
            area[i-1][j+1] += area[i][j] * p1;
            if (second_slope == 3){
              area[i][j+1] += area[i][j] * p2;
            }
            if (second_slope == 1){
              area[i-1][j] += area[i][j] * p2;
            }
          }

          if (S_max_index == 3 && area[i][j+1] != NoDataValue){
            area[i][j+1] += area[i][j] * p1;
            if (second_slope == 4){
              area[i+1][j+1] += area[i][j] * p2;
            }
            if (second_slope == 2){
              area[i-1][j+1] += area[i][j] * p2;
            }
          }

          if (S_max_index == 4 && area[i+1][j+1] != NoDataValue){
            area[i+1][j+1] += area[i][j] * p1;
            if (second_slope == 5){
              area[i+1][j] += area[i][j] * p2;
            }
            if (second_slope == 3){
              area[i][j+1] += area[i][j] * p2;
            }
          }

          if (S_max_index == 5 && area[i+1][j] != NoDataValue){
            area[i+1][j] += area[i][j] * p1;
            if (second_slope == 6){
              area[i+1][j-1] += area[i][j] * p2;
            }
            if (second_slope == 4){
              area[i+1][j+1] += area[i][j] * p2;
            }
          }

          if (S_max_index == 6 && area[i+1][j-1] != NoDataValue){
            area[i+1][j-1] += area[i][j] * p1;
            if (second_slope == 7){
              area[i][j-1] += area[i][j] * p2;
            }
            if (second_slope == 5){
              area[i+1][j] += area[i][j] * p2;
            }
          }

          if (S_max_index == 7 && area[i][j-1] != NoDataValue){
            area[i][j-1] += area[i][j] * p1;
            if (second_slope == 0){
              area[i-1][j] += area[i][j] * p2;
            }
            if (second_slope == 6){
              area[i-1][j-1] += area[i][j] * p2;
            }
          }
        }
      }
    }
  }

  //write output LSDRaster object
  LSDRaster Multi2Flow(NRows, NCols, XMinimum, YMinimum, DataResolution,
                       NoDataValue, area,GeoReferencingStrings);
  return Multi2Flow;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// PREDICTING CHANNEL HEADS USING TANGENTIAL CURVATURE
//
// This function is used to predict channel head locations based on the method
// proposed by Pelletier (2013).  It creates a contour curvature map and identifies
// channel heads as pixels greater than a user defined contour curvature threshold
// value, set by default at 0.1.  The threshold curvature can also be defined as a
// multiple of the standard deviation of the curvature.  Before this function is
// called the DEM must be filtered using the wiener filter in the LSDRasterSpectral
// object in order to remove high frequency noise.
//
// Reference: Pelletier (2013) A robust, two-parameter method for the extraction of
// drainage networks from high-resolution digital elevation models (DEMs): Evaluation
// using synthetic and real-world DEMs, Water Resources Research 49: 1-15
//
// added by FC 16/07/13
//
// edited by DTM 07/11/13
// Initial function gave a map of pixels with sufficient tangential curvature to be
// designated as a channel.  This map needed to be reduced to give the source pixels
// only.  This is done by i) sorting all the possible sources by elevation and ii)
// routing flow from each potential source using Freeman MD flow.  Any potential
// sources that are located on ANY down-slope pathway from previously visited source
// pixels are excluded from the final source map.
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// LSDIndexRaster LSDRaster::calculate_pelletier_channel_heads(float tan_curv_threshold, Array2D<float>& tan_curv_array)
// {
//   Array2D<float> curv_array(NRows,NCols,NoDataValue);
//   vector<int> possible_sources_row;
//   vector<int> possible_sources_col;
//   vector<float> possible_sources_elev;
//   // Get all the locations where the tan curvature is greater than the user defined threshold
//   for (int row = 0; row < NRows; row++)
//   {
//     for(int col = 0; col < NCols; col++)
//     {
//       if (tan_curv_array[row][col] > tan_curv_threshold)
//       {
//         possible_sources_row.push_back(row);
//         possible_sources_col.push_back(col);
//         possible_sources_elev.push_back(RasterData[row][col]);
//         curv_array[row][col] = tan_curv_array[row][col];
//       }
//     }
//   }
//   //LSDRaster AboveThreshold(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,curv_array);
//   //AboveThreshold.write_raster("thresh","flt");
//   // Now sort possible sources by elevation, then route flow using d-inf,
//   // excluding potential sources that are on downslope pathway from other
//   // sources
// //   int n_possible_sources = possible_sources_elev.size();
// //   if (n_possible_sources <= 0)
// //   {
// //     cout << "NO SOURCES FOUND" << endl;
// //   }
// //   else
// //   {
// //     cout << "Found " << n_possible_sources << " possible source pixels" << endl;
// //   }
//   vector<size_t> index_map;
//
//   // sort
//   matlab_float_sort_descending(possible_sources_elev, possible_sources_elev, index_map);
//   matlab_int_reorder(possible_sources_row, index_map, possible_sources_row);
//   matlab_int_reorder(possible_sources_col, index_map, possible_sources_col);
//   LSDIndexRaster SourcesRaster = IdentifyFurthestUpstreamSourcesWithFreemanMDFlow(possible_sources_row,possible_sources_col,tan_curv_array);
//
//   return SourcesRaster;
// }

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Calculate the minimum bounding rectangle for an LSDRaster Object and crop out
// all the surrounding NoDataValues to reduce the size and load times of output
// rasters.
//
// Ideal for use with chi analysis tools which output basin and chi m value rasters
// which can be predominantly no data. As an example, a 253 Mb file can be reduced to
// ~5 Mb with no loss or resampling of data.
//
// Modded 6/11/14 to cope with bil files and to catch cases where some or all of the
// edges cannot be trimmed - SWDG
//
// Returns A trimmed LSDRaster object.
//
// SWDG 22/08/13
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::RasterTrimmer(){

  //minimum index value in a column
  int a = 0;
  int min_col = 100000; //a big number

  for (int row = 0; row < NRows; ++row){
    a = 0;
    while (RasterData[row][a] == NoDataValue && a < NCols-1){
      ++a;
    }
    if (min_col > a){
      min_col = a;
    }
  }
  ++min_col;

  //maximum index value in a column
  a = NCols - 1;
  int max_col = 0; //a small number

  for (int row = 0; row < NRows; ++row){
    a = NCols - 1;
    while (RasterData[row][a] == NoDataValue && a > 0){
      --a;
    }
    if (max_col < a){
      max_col = a;
    }
  }
  ++max_col;

  //minimum index value in a row
  a = 0;
  int min_row = 100000; //a big number

  for (int col = 0; col < NCols; ++col){
    a = 0;
    while (RasterData[a][col] == NoDataValue && a < NRows - 1){
      ++a;
    }
    if (min_row > a){
      min_row = a;
    }
  }
  ++min_row;

  //maximum index value in a row
  a = NRows - 1;
  int max_row = 0; //a small number

  for (int col = 0; col < NCols; ++col){
    a = NRows - 1;
    while (RasterData[a][col] == NoDataValue && a > 0){
      --a;
    }
    if (max_row < a){
      max_row = a;
    }
  }
  ++max_row;

  if (min_row == 0 && min_col == 0 && max_row == (NRows - 1) && max_col == (NCols - 1))
  {
    cout << "Raster cannot be trimmed! \nReturning original raster.\n" << endl;

    LSDRaster Output(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                     RasterData, GeoReferencingStrings);

    return Output;
  }

  // create new row and col sizes taking account of zero indexing
  int new_row_dimension = (max_row-min_row) + 1;
  int new_col_dimension = (max_col-min_col) + 1;

  Array2D<float>TrimmedData(new_row_dimension, new_col_dimension, NoDataValue);

  //loop over min bounding rectangle and store it in new array of shape new_row_dimension x new_col_dimension
  int TrimmedRow = 0;
  int TrimmedCol = 0;

  //check if the north or west edges cannot be trimmed and stop an out of bounds error
  if (min_row == 0){ min_row = 1; }
  if (min_col == 0){ min_col = 1; }

  for (int row = min_row - 1; row < max_row; ++row){
    for(int col = min_col - 1; col < max_col; ++col){

      TrimmedData[TrimmedRow][TrimmedCol] = RasterData[row][col];
      ++TrimmedCol;
    }
    ++TrimmedRow;
    TrimmedCol = 0;
  }

  //calculate lower left corner coordinates of new array
  float new_XLL = ((min_col - 1) * DataResolution) + XMinimum;
  float new_YLL = YMinimum + ((NRows - (max_row + 0)) * DataResolution);

  //Check if the file is in *.bil format and if it is update the GeoReferencingStrings
  if (!GeoReferencingStrings.empty()){
    float YMax = new_YLL + (new_row_dimension* DataResolution);
    GeoReferencingStrings = Update_GeoReferencingStrings(new_XLL,YMax);
  }

  LSDRaster TrimmedRaster(new_row_dimension, new_col_dimension, new_XLL,
                          new_YLL, DataResolution, NoDataValue, TrimmedData, GeoReferencingStrings);

  return TrimmedRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Calculate the minimum bounding rectangle for an LSDRaster Object and crop out
// all the surrounding NoDataValues to reduce the size and load times of output
// rasters.
//
// This is like the other raster trimmer but you can put a padding of pixels
// around the trimmed raster. Useful for cosmogenic analysis since the valid
// cosmo point may be a few pixels away from the actual stream
//
// Ideal for use with chi analysis tools which output basin and chi m value rasters
// which can be predominantly no data. As an example, a 253 Mb file can be reduced to
// ~5 Mb with no loss or resampling of data.
//
// Modded 6/11/14 to cope with bil files and to catch cases where some or all of the
// edges cannot be trimmed - SWDG
//
// Returns A trimmed LSDRaster object.
//
// SMM 18/03/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::RasterTrimmerPadded(int padding_pixels)
{

  //minimum index value in a column
  int a = 0;
  int min_col = 100000; //a big number

  for (int row = 0; row < NRows; ++row){
    a = 0;
    while (RasterData[row][a] == NoDataValue && a < NCols-1){
      ++a;
    }
    if (min_col > a){
      min_col = a;
    }
  }

  //maximum index value in a column
  a = NCols - 1;
  int max_col = 0; //a small number

  for (int row = 0; row < NRows; ++row){
    a = NCols - 1;
    while (RasterData[row][a] == NoDataValue && a > 0){
      --a;
    }
    if (max_col < a){
      max_col = a;
    }
  }


  //minimum index value in a row
  a = 0;
  int min_row = 100000; //a big number

  for (int col = 0; col < NCols; ++col){
    a = 0;
    while (RasterData[a][col] == NoDataValue && a < NRows - 1){
      ++a;
    }
    if (min_row > a){
      min_row = a;
    }
  }

  //maximum index value in a row
  a = NRows - 1;
  int max_row = 0; //a small number

  for (int col = 0; col < NCols; ++col){
    a = NRows - 1;
    while (RasterData[a][col] == NoDataValue && a > 0){
      --a;
    }
    if (max_row < a){
      max_row = a;
    }
  }

  // pad the rows and columms
  min_row = min_row-padding_pixels;
  min_col = min_col-padding_pixels;
  max_row = max_row+padding_pixels;
  max_col = max_col+padding_pixels;


  if (min_row == 0 && min_col == 0 && max_row == (NRows - 1) && max_col == (NCols - 1))
  {
    cout << "Raster cannot be trimmed! \nReturning original raster.\n" << endl;

    LSDRaster Output(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                     RasterData, GeoReferencingStrings);

    return Output;
  }

  // create new row and col sizes taking account of zero indexing
  int new_row_dimension = (max_row-min_row) + 1;
  int new_col_dimension = (max_col-min_col) + 1;

  Array2D<float>TrimmedData(new_row_dimension, new_col_dimension, NoDataValue);

  //loop over min bounding rectangle and store it in new array of shape new_row_dimension x new_col_dimension
  int TrimmedRow = 0;
  int TrimmedCol = 0;

  //check if the north or west edges cannot be trimmed and stop an out of bounds error
  if (min_row == 0){ min_row = 1; }
  if (min_col == 0){ min_col = 1; }

  for (int row = min_row - 1; row < max_row; ++row){
    for(int col = min_col - 1; col < max_col; ++col){

      TrimmedData[TrimmedRow][TrimmedCol] = RasterData[row][col];
      ++TrimmedCol;
    }
    ++TrimmedRow;
    TrimmedCol = 0;
  }

  //calculate lower left corner coordinates of new array
  float new_XLL = ((min_col - 1) * DataResolution) + XMinimum;
  float new_YLL = YMinimum + ((NRows - (max_row + 0)) * DataResolution);

  //Check if the file is in *.bil format and if it is update the GeoReferencingStrings
  if (!GeoReferencingStrings.empty())
  {
    float YMax = new_YLL + (new_row_dimension* DataResolution);
    GeoReferencingStrings = Update_GeoReferencingStrings(new_XLL,YMax);
  }

  LSDRaster TrimmedRaster(new_row_dimension, new_col_dimension, new_XLL,
                          new_YLL, DataResolution, NoDataValue, TrimmedData, GeoReferencingStrings);

  return TrimmedRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This is a raster trimmer that gets a rectangular DEM that doesn't have NoData
// around the edges.
// That is, it finds the biggest possible raster from your data that is entirely
// covered in data with no nodata nodes around the edge. 
// This means that it will cut out valid data points if there are nodata
// values sitting in the middle. 
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::RasterTrimmerSpiral()
{
  int North_node = 0;
  int South_node = NRows-1;
  int East_node = NCols-1;
  int West_node = 0;
  int row,col;

  bool found_NDV;

  // mark the borders as not found
  bool found_north_border = false;
  bool found_south_border = false;
  bool found_east_border = false;
  bool found_west_border = false;

  // the border row and columns are set to nodata
  int North_border = NoDataValue;
  int South_border = NoDataValue;
  int West_border = NoDataValue;
  int East_border = NoDataValue;

  bool AllBordersFound = false;

  // enter the spiral routine
  while(North_node < South_node && East_node > West_node && AllBordersFound == false)
  {
    //cout << "Nn: " << North_node << " En: " << East_node << " Sn: " << South_node << " Wn: " << West_node << endl;
    //cout << "Nb: " << North_border << " Eb: " << East_border << " Sb: " << South_border << " Wb: " << West_border << endl;

    // first do north edge
    if(found_north_border == false)
    {
      col = West_node;
      row = North_node;
      found_NDV = false;
      while(col<=East_node && found_NDV == false)
      {
        if( RasterData[row][col] == NoDataValue)
        {
          //cout << "N Found nodata: ["<<row<<"]["<< col << "]"<< endl;
          found_NDV = true;
          North_node++;
        }
        col++;
      }
      if (found_NDV == false)
      {
        cout << "I found the north border!" << endl;
        found_north_border = true;
        North_border = North_node;
      }
    }

    // now do the east edge
    if(found_east_border == false)
    {
      row = North_node;
      col = East_node;
      found_NDV = false;
      while(row<=South_node && found_NDV == false)
      {
        if( RasterData[row][col] == NoDataValue)
        {
          //cout << "E Found nodata: ["<<row<<"]["<< col << "]"<< endl;
          found_NDV = true;
          East_node--;
        }
        row++;
      }
      if (found_NDV == false)
      {
        cout << "I found the east border!" << endl;
        found_east_border = true;
        East_border = East_node;
      }
    }

    // now do the south edge
    if(found_south_border == false)
    {
      row = South_node;
      col = West_node;
      found_NDV = false;
      while(col<=East_node && found_NDV == false)
      {
        if( RasterData[row][col] == NoDataValue)
        {
          //cout << "S Found nodata: ["<<row<<"]["<< col << "]"<< endl;
          found_NDV = true;
          South_node--;
        }
        col++;
      }
      if (found_NDV == false)
      {
        cout << "I found the south border!" << endl;
        found_south_border = true;
        South_border = South_node;
      }
    }

    // now do the west edge
    if(found_west_border == false)
    {
      row = North_node;
      col = West_node;
      found_NDV = false;
      while(row<=South_node && found_NDV == false)
      {
        if( RasterData[row][col] == NoDataValue)
        {
          //cout << "W Found nodata: ["<<row<<"]["<< col << "]"<< endl;
          found_NDV = true;
          West_node++;
        }
        row++;
      }
      if (found_NDV == false)
      {
        cout << "I found the west border!" << endl;
        found_west_border = true;
        West_border = West_node;
      }
    }

    // check to see if all the borders have been found
    if(North_border != NoDataValue && South_border != NoDataValue
         && East_border != NoDataValue && West_border != NoDataValue)
    {
      AllBordersFound = true;
    }
  }

  if (AllBordersFound == false)
  {
    cout << "Couldn't trim your raster, sorry! Returning original raster" << endl;
    LSDRaster Output(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue,
                     RasterData, GeoReferencingStrings);
    return Output;
  }

  else
  {
    cout << endl << endl << "Here are the trimmed borders: " << endl;
    //cout << "Nn: " << North_node << " En: " << East_node << " Sn: " << South_node << " Wn: " << West_node << endl;
    cout << "Nb: " << North_border << " Eb: " << East_border << " Sb: " << South_border << " Wb: " << West_border << endl;
    cout << "If these are very close together it probably means you need to do a better job of clipping your raster with GDAL." << endl;

    int min_row = North_border;
    int max_row = South_border;
    int min_col = West_border;
    int max_col = East_border;

    // create new row and col sizes taking account of zero indexing
    int new_row_dimension = (max_row-min_row) + 1;
    int new_col_dimension = (max_col-min_col) + 1;

    cout << "New dimensions are: rows: " << new_row_dimension << " cols: "
         << new_col_dimension << endl;
    cout << "Min row: " << min_row << " max_row: " << max_row << endl;
    cout << "Min col: " << min_col << " max_col: " << max_col << endl;
    cout << "NRows: " << NRows << " and NCols: " << NCols << endl;

    Array2D<float>TrimmedData(new_row_dimension, new_col_dimension, NoDataValue);

    //loop over min bounding rectangle and store it in new array of shape new_row_dimension x new_col_dimension
    int TrimmedRow = 0;
    int TrimmedCol = 0;
    for (int row = min_row; row < max_row; ++row)
    {
      for(int col = min_col; col < max_col; ++col)
      {
        // some debugging
        if (row >= NRows)
        {
          cout << "Row is too big, prepare for seg fault!" << endl;
        }
        if (col >= NCols)
        {
          cout << "Col is too big, prepare for seg fault!" << endl;
        }

        if(TrimmedRow >= new_row_dimension)
        {
          cout << "TrimmedRow is too big, prepare for seg fault!" << endl;
        }
        if(TrimmedCol >= new_col_dimension)
        {
          cout << "TrimmedCol is too big, prepare for seg fault!" << endl;
        }


        TrimmedData[TrimmedRow][TrimmedCol] = RasterData[row][col];
        ++TrimmedCol;
      }
      ++TrimmedRow;
      TrimmedCol = 0;
    }
    cout << "Got the new data array!" << endl;


    //calculate lower left corner coordinates of new array
    float new_XLL = (min_col * DataResolution) + XMinimum;
    float new_YLL = YMinimum + ((NRows - max_row - 1) * DataResolution);
    cout << "New XLL is: " <<  new_XLL << " old is: " << XMinimum << endl;
    cout << "New YLL is: " <<  new_YLL << " old is: " << YMinimum << endl;

    cout << "Making a new raster, with the following vitalstatistix:" << endl;
    cout << "Nrows: " <<  new_row_dimension << " NCols: " << new_col_dimension << endl;
    cout << "XMinimum: " << new_XLL << " YMinimum: " << new_YLL << endl;
    cout << "DataResolution: " << DataResolution << " NDV: " << NoDataValue << endl;
    //cout << GeoReferencingStrings[0] << endl;
    //cout << GeoReferencingStrings[1] << endl;

    cout << "Size of data, Rows " << TrimmedData.dim1() << " Cols: " << TrimmedData.dim2() << endl;

    LSDRaster TrimmedRaster(new_row_dimension, new_col_dimension, new_XLL,
                        new_YLL, DataResolution, NoDataValue, TrimmedData, GeoReferencingStrings);

    cout << "Made the raster, now for georeferencing strings...";
    TrimmedRaster.Update_GeoReferencingStrings();
    cout << "done!" << endl;

    return TrimmedRaster;
  }

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// Trims the raster array by one pixel around the edge. This was primarily written
// for the LSDCatchmentModel which has a padding of zeros around most of the surface
// data arrays. This removes that padding and reduces the size of the array.
//
// It also modifies the NCols and NRows data members, reducing them by 2 to account
// for the new size. Note that it does *not* alter the xll and yll values, because
// these are not modified during the reading in of the original DEM and padding with zeroes.
//
// DAV 2016
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::strip_raster_padding()
{
  // Get the dimensions of the array to be trimmed

  // Calculate the dimensions of the trimmed array (n-2, since there is 1px either edge)
  int trimmed_array_ncols = NCols - 2;
  int trimmed_array_nrows = NRows - 2;

  Array2D<double> trimmedArray(trimmed_array_nrows, trimmed_array_ncols, 0.0);

  for (int i=0; i<trimmed_array_nrows; ++i)
  {
    for (int j=0; j<trimmed_array_ncols; ++j)
    {
      trimmedArray[i][j] = RasterData_dbl[i+1][j+1];
    }
  }
  NCols -= 2;
  NRows -= 2;

  RasterData_dbl = trimmedArray;
  // Wasn't sure about this simple assignment, thought it might do weird stuff but it seems to be ok?. DAV.
  // Check the TNT Documentation under "Operator=":
  // http://math.nist.gov/tnt/tnt_doxygen/class_TNT__Array2D.html#a8
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Buffers a raster using a circular kernel of a user-defined radius
// User specifies the window radius in metres.
//
// FJC 10/02/17
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::BufferRasterData(float window_radius)
{
  // set the kernel radius
  int kr = ceil(window_radius/DataResolution);
  // set exceptions on kr
  if (kr < 1)
  {
    kr = 1;
  }
  Array2D<float> BufferedData(NRows,NCols,NoDataValue);

  // loop through the DEM and get data in a circular kernel around each point
  for (int i = 0; i < NRows; ++i)
  {
    for (int j = 0; j < NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        for (int sub_i = i-kr; sub_i <= i+kr; ++sub_i)
        {
          //don't extent past end of map
          if (sub_i >=0 && sub_i < NRows)
          {
            for (int sub_j = j-kr; sub_j <= j+kr; ++sub_j)
            {
              //don't extend past end of map
              if (sub_j >=0 && sub_j<NCols)
              {
                //circular kernel
                float radial_dist = sqrt(pow(((sub_i-i)*DataResolution),2) + pow(((sub_j-j)*DataResolution),2));
                if (radial_dist <= window_radius)
                {
                  // only overwrite the data if the value is larger
                  if (BufferedData[sub_i][sub_j] < RasterData[i][j])
                  {
                    // within the kernel, overwrite raster with centre value
                    BufferedData[sub_i][sub_j] = RasterData[i][j];
                  }
                }
              }
            }
          }
        }
      }
    }
  }
  LSDRaster BufferedRaster(NRows,NCols, XMinimum, YMinimum, DataResolution,
                            NoDataValue, BufferedData, GeoReferencingStrings);
  return BufferedRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// THis pads a smaller index raster to the same extent as a bigger raster by adding
// no data values
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::PadSmallerRaster(LSDIndexRaster& smaller_raster)
{
  Array2D<int> NewRasterValues(NRows, NCols, 0);

  // find the x and y min and max of the smaller raster
  float SR_XMinimum = smaller_raster.get_XMinimum();
  float SR_YMinimum = smaller_raster.get_YMinimum();

  float SR_NRows = smaller_raster.get_NRows();
  float SR_NCols = smaller_raster.get_NCols();
  float SR_DataR = smaller_raster.get_DataResolution();

  float SR_XMaximum = SR_XMinimum+(SR_NCols)*SR_DataR;
  float SR_YMaximum = SR_YMinimum+(SR_NRows)*SR_DataR;

  // find the rows and col of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  int XLL_col = int((SR_XMinimum-XMinimum+0.5*DataResolution)/DataResolution);
  int XUL_col = int((SR_XMaximum-XMinimum+0.5*DataResolution)/DataResolution);

  // find the row of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  // Slightly different logic for y because the DEM starts from the top corner
  int YLL_row = NRows - int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution);
  int YUL_row = NRows - int((SR_YMaximum-YMinimum+0.5*DataResolution)/DataResolution);

  // check on the lower row:
  cout << "Checking lower left row." << endl;
  cout << "integer subtraction: " << int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution) << endl;
  cout << "float subtraction: " <<  (SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution << endl;

  // this catches a weird rounding error.
  double int_sub =  double(int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution));
  double flt_sub =  (SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution;

  if ((flt_sub- int_sub) > 0.9975)
  {
    YUL_row = YUL_row+1;
  }


  // check these rows
  if (YLL_row < 0)
  {
    YLL_row = 0;
  }
  if (YUL_row >= NRows)
  {
    YUL_row = NRows-1;
  }

  // check these columns
  if (XLL_col < 0)
  {
    XLL_col = 0;
  }
  if (XUL_col >= NCols)
  {
    XUL_col = NCols-1;
  }

  double x_loc, y_loc;
  int big_i, big_j;
    // get the new number of rows and columns:
  int New_NRows = YLL_row-YUL_row;
  int New_NCols = XUL_col-XLL_col;
  Array2D<int> small_rasterdata = smaller_raster.get_RasterData();
  for (int i = 0; i < New_NRows; i++)
  {
    for (int j = 0; j < New_NCols; j++)
    {
      int this_value = small_rasterdata[i][j];
      if (this_value < 0) { this_value = 0; }
      if (this_value > 1000000) { this_value = 0; }
      smaller_raster.get_x_and_y_locations(i, j, x_loc, y_loc);
      //cout << this_value << " "<< x_loc << " " << y_loc << endl;
      get_row_and_col_of_a_point(x_loc, y_loc, big_i, big_j);
      NewRasterValues[big_i][big_j] = this_value;
    }
  }

  LSDIndexRaster NewRaster(NRows,NCols, XMinimum, YMinimum, DataResolution,
                            NoDataValue, NewRasterValues, GeoReferencingStrings);

  NewRaster.Update_GeoReferencingStrings();

  return NewRaster;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// THis clips to a smaller raster. The smaller raster does not need
// to have the same data resolution as the old raster
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::clip_to_smaller_raster(LSDRaster& smaller_raster)
{
  // Get the MinX, MaxX, MinY, MaxY from the rasters
  //float XMaximum = XMinimum + (NCols * DataResolution -1);
  //float YMaximum = YMinimum + (NRows * DataResolution -1);

  float SR_XMinimum = smaller_raster.get_XMinimum();
  float SR_YMinimum = smaller_raster.get_YMinimum();

  float SR_NRows = smaller_raster.get_NRows();
  float SR_NCols = smaller_raster.get_NCols();
  float SR_DataR = smaller_raster.get_DataResolution();

  float SR_XMaximum = SR_XMinimum+(SR_NCols)*SR_DataR;
  float SR_YMaximum = SR_YMinimum+(SR_NRows)*SR_DataR;

  cout << "Small Xmin: " << SR_XMinimum << " YMin: " << SR_YMinimum << " Xmax: "
       << SR_XMaximum << " YMax: " << SR_YMaximum << endl;

  cout << "This data resolution: " << DataResolution << " and smaller raster data resolution: " << SR_DataR << endl;


  // find the col of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  int XLL_col = int((SR_XMinimum-XMinimum+0.5*DataResolution)/DataResolution);
  int XUL_col = int((SR_XMaximum-XMinimum+0.5*DataResolution)/DataResolution);

  // check these columns
  if (XLL_col < 0)
  {
    XLL_col = 0;
  }
  if (XUL_col >= NCols)
  {
    XUL_col = NCols-1;
  }

  // find the row of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  // Slightly different logic for y because the DEM starts from the top corner
  int YLL_row = NRows - int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution);
  int YUL_row = NRows - int((SR_YMaximum-YMinimum+0.5*DataResolution)/DataResolution);

  // check on the lower row:
  cout << "Checking lower left row." << endl;
  cout << "integer subtraction: " << int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution) << endl;
  cout << "float subtraction: " <<  (SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution << endl;

  // this catches a weird rounding error.
  double int_sub =  double(int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution));
  double flt_sub =  (SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution;

  if ((flt_sub- int_sub) > 0.9975)
  {
    YUL_row = YUL_row+1;
  }


  // check these rows
  if (YLL_row < 0)
  {
    YLL_row = 0;
  }
  if (YUL_row >= NRows)
  {
    YUL_row = NRows-1;
  }

  cout << "Small XLLCol: " << XLL_col << " XLR_col: " << XUL_col << " YLLrow: "
       << YLL_row << " YUL_row: " << YUL_row << endl;


  // get the new number of rows and columns:
  int New_NRows = YLL_row-YUL_row;
  int New_NCols = XUL_col-XLL_col;

  cout << "New NRows: " << New_NRows  << " New_NCols: " << New_NCols << endl;

  // now extract the data for the new raster
  float NewR_XMinimum = XMinimum+float(XLL_col)*DataResolution;
  float NewR_YMinimum = YMinimum + ((NRows - YLL_row ) * DataResolution);


  Array2D<float> NewData(New_NRows,New_NCols, NoDataValue);
  for(int row = 0; row< New_NRows; row++)
  {
    for(int col = 0; col<New_NCols; col++)
    {
       NewData[row][col] = RasterData[row+YUL_row][col+XLL_col];
    }
  }

  LSDRaster TrimmedRaster(New_NRows, New_NCols, NewR_XMinimum,
                          NewR_YMinimum, DataResolution, NoDataValue, NewData,
                          GeoReferencingStrings);

  cout << "Made a new raster" << endl;

  TrimmedRaster.Update_GeoReferencingStrings();

  return TrimmedRaster;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This gets the minimum and maximum values and returns them as a vector
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<float> LSDRaster::get_XY_MinMax()
{

  vector<float> XYMaxMin(4,0);

  XYMaxMin[0] = XMinimum;
  XYMaxMin[1] = YMinimum;
  XYMaxMin[2] = XMinimum+(NCols)*DataResolution;
  XYMaxMin[3] = YMinimum+(NRows)*DataResolution;

  return XYMaxMin;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function gets the raster data into a vector
// FJC 06/11/15
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
vector<float> LSDRaster::get_RasterData_vector()
{
  vector<float> Raster_vector;
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      Raster_vector.push_back(RasterData[row][col]);
    }
  }

  return Raster_vector;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function gets the raster data into a vector, ignoring NDVs
// MDH 06/02/17
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
vector<float> LSDRaster::get_RasterData_vector_No_NDVs()
{
  vector<float> Raster_vector;
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      if (RasterData[row][col] != NoDataValue)
		{
			Raster_vector.push_back(RasterData[row][col]);
		}
    }
  }

  return Raster_vector;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// This function writes the raster data (where != NoDataValue) to a text file
// FJC 30/09/16
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::write_RasterData_to_text_file(string filename)
{
	string string_filename;
  string dot = ".";
	string extension = "txt";
  string_filename = filename+dot+extension;
  cout << "The filename is " << string_filename << endl;

	// open the data file
  ofstream data_out(string_filename.c_str());

	if( data_out.fail() )
	{
		cout << "\nFATAL ERROR: unable to write to " << string_filename << endl;
		exit(EXIT_FAILURE);
	}

	data_out << "row col raster_data" << endl;
	for (int row = 0; row < NRows; row++)
	{
		for (int col =0; col < NCols; col++)
		{
			if (RasterData[row][col] != NoDataValue)
			{
				data_out << row << " " << col << " " << RasterData[row][col] << endl;
			}
		}
	}

	data_out.close();
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// THis clips to a smaller raster. The smaller raster does not need
// to have the same data resolution as the old raster
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::clip_to_smaller_raster(LSDIndexRaster& smaller_raster)
{
  // Get the MinX, MaxX, MinY, MaxY from the rasters
  //float XMaximum = XMinimum + (NCols * DataResolution -1);
  //float YMaximum = YMinimum + (NRows * DataResolution -1);

  float SR_XMinimum = smaller_raster.get_XMinimum();
  float SR_YMinimum = smaller_raster.get_YMinimum();

  float SR_NRows = smaller_raster.get_NRows();
  float SR_NCols = smaller_raster.get_NCols();
  float SR_DataR = smaller_raster.get_DataResolution();

  float SR_XMaximum = SR_XMinimum+(SR_NCols)*SR_DataR;
  float SR_YMaximum = SR_YMinimum+(SR_NRows)*SR_DataR;

  cout << "Small Xmin: " << SR_XMinimum << " YMin: " << SR_YMinimum << " Xmax: "
       << SR_XMaximum << " YMax: " << SR_YMaximum << endl;


  // find the col of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  int XLL_col = int((SR_XMinimum-XMinimum+0.5*DataResolution)/DataResolution);
  int XUL_col = int((SR_XMaximum-XMinimum+0.5*DataResolution)/DataResolution);

  // check these columns
  if (XLL_col < 0)
  {
    XLL_col = 0;
  }
  if (XUL_col >= NCols)
  {
    XUL_col = NCols-1;
  }

  // find the row of old raster that has the same Xlocations as the XLL of smaller raster
  // the 0.5*DataResolution is in case of rounding errors
  // Slightly different logic for y because the DEM starts from the top corner
  int YLL_row = NRows - int((SR_YMinimum-YMinimum+0.5*DataResolution)/DataResolution);
  int YUL_row = NRows - int((SR_YMaximum-YMinimum+0.5*DataResolution)/DataResolution);

  // check these rows
  if (YLL_row < 0)
  {
    YLL_row = 0;
  }
  if (YUL_row >= NRows)
  {
    YUL_row = NRows-1;
  }

  cout << "Small XLLCol: " << XLL_col << " XLR_col: " << XUL_col << " XLLrow: "
       << YLL_row << " YUL_row: " << YUL_row << endl;


  // get the new number of rows and columns:
  int New_NRows = YLL_row-YUL_row;
  int New_NCols = XUL_col-XLL_col;

  cout << "New NRows: " << New_NRows  << " New_NCols: " << New_NCols << endl;

  // now extract the data for the new raster
  float NewR_XMinimum = XMinimum+float(XLL_col)*DataResolution;
  float NewR_YMinimum = YMinimum + ((NRows - YLL_row ) * DataResolution);

  Array2D<float> NewData(New_NRows,New_NCols, NoDataValue);

  //cout << "Writing the array" << endl;

  for(int row = 0; row< New_NRows; row++)
  {
    for(int col = 0; col<New_NCols; col++)
    {
       NewData[row][col] = RasterData[row+YUL_row][col+XLL_col];
    }
  }

  //cout << "Wrote the array" << endl;

  LSDRaster TrimmedRaster(New_NRows, New_NCols, NewR_XMinimum,
                          NewR_YMinimum, DataResolution, NoDataValue, NewData,
                          GeoReferencingStrings);

  cout << "Making the raster" << endl;

  TrimmedRaster.Update_GeoReferencingStrings();

  return TrimmedRaster;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Export input LSDRasters as a vector field which can be plotted in python.
// Data is written in the format "i j Magnitude Direction"
// SWDG 20/1/14
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::GetVectors(LSDRaster Magnitude, LSDRaster Direction, string output_file, int step)
{

  vector<string> OutputData;

  for (int i = 0; i < NRows; i+=step){
    for (int j = 0; j < NCols; j+=step){

      if (Magnitude.get_data_element(i,j) != NoDataValue && Direction.get_data_element(i,j) != NoDataValue){
        stringstream output_line;
        output_line << i << " " << j << " " << Magnitude.get_data_element(i,j) << " " << Direction.get_data_element(i,j);
        OutputData.push_back(output_line.str());
      }

    }
  }

  ofstream WriteData;
  WriteData.open(output_file.c_str());

  WriteData << "i j Magnitude Direction" << endl;

  for (int k = 0; k < int(OutputData.size()); ++k){

    WriteData << OutputData[k] << endl;

  }

  WriteData.close();

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
//     sSSSs MM   MM  oOOo   oOOo  TTTTTT HH  HH IIII NN   NN  gGGGG
//    SS     M M M M oO  Oo oO  Oo   TT   HH  HH  II  NNN  NN GG
//     sSSs  M  M  M OO  OO OO  OO   TT   HHHHHH  II  NN N NN GG GGG
//        SS M     M oO  Oo oO  Oo   TT   HH  HH  II  NN  NNN GG  GG
//    sSSSs  M     M  oOOo   oOOo    TT   HH  HH IIII NN   NN  GGGGG
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
//  Perform Non-local means filtering on a DEM following Baude et al. [2005]
//  Smoothes non-gaussian noise.
//
//  Inputs required:
//    the search window radius,
//    the similarity window radius and
//    the degree of filtering
//
//  Martin Hurst, February, 2012
//  Modified by David Milodowski, May 2012- generates grid of recording filtered noise
//
//  WindowRadius has to be <= SimilarityRadius ?
//
//  Adapted from a matlab script by:
//  Author: Jose Vicente Manjon Herrera & Antoni Buades
//  Date: 09-03-2006
//
//  Implementation of the Non local filter proposed for A. Buades, B. Coll and J.M. Morel in
//  "A non-local algorithm for image denoising"
//
//  Added soft threshold optimal correction - David Milodowski, 05/2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
//  Martin Hurst, February, 2012
//  Modified by David Milodowski, May 2012- generates grid of recording filtered noise
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::NonLocalMeansFilter(int WindowRadius, int SimilarityRadius, int DegreeFiltering, float Sigma)
{

  //Declare Arrays to hold Filtered Data and Noise
  Array2D<float> FilteredRasterData(NRows,NCols);
  //Array2D<float> FilteredNoise(NRows,NCols);

  //Declare Array to hold a padded copy of the raster with padding values taken
  //as reflected values from the edge of RasterData
  Array2D<float> PaddedRasterData(NRows+2*SimilarityRadius, NCols+2*SimilarityRadius,0.0);
  PadRasterSymmetric(PaddedRasterData, SimilarityRadius);

  //initiate the local gaussian kernel and populate
  int KernelDimension = 2*SimilarityRadius+1;
  Array2D<float> Kernel(KernelDimension,KernelDimension,0.0);
  MakeGaussianKernel(Kernel, Sigma, SimilarityRadius);

  //initiate temporary arrays
  Array2D<float> W1(KernelDimension,KernelDimension);
  Array2D<float> W2(KernelDimension,KernelDimension);

  //initiate temp variables
  float w, wmax, average, sweight, d;

  //loop through DEM
  int i1, j1, rowmin, rowmax, colmin, colmax;

  for (int i=0; i<NRows; ++i)
  {
    i1 = i+SimilarityRadius;
    for (int j=0; j<NCols; ++j)
      {
        j1 = j+SimilarityRadius;
        //Get DEM sample  with size SimilarityRadius, centred on cell of interest
        for (int a=0; a<(KernelDimension); ++a)
        {
          for (int b=0; b<(KernelDimension); ++b)
          {
            W1[a][b] = PaddedRasterData[i1-SimilarityRadius+a][j1-SimilarityRadius+b];
          }
        }

        wmax=0;
        average=0;
        sweight=0;

        //get bounding conditions
        rowmin = max(i1-WindowRadius,SimilarityRadius);
        rowmax = min(i1+WindowRadius,NRows+SimilarityRadius-1);
        colmin = max(j1-WindowRadius,SimilarityRadius);
        colmax = min(j1+WindowRadius,NCols+SimilarityRadius-1);

        //loop to calculate weigths for each cell
        for (int row=rowmin; row<rowmax+1; ++row)
        {
          for (int col=colmin; col<colmax+1; ++col)
          {
            d=0;

            //If centre cell do nothing
            if (row!=i1 || col!=j1)
            //Otherwise do the calculations
            {
              //Extract DEM centred around each point in kernel
              for (int a=0; a<(KernelDimension); ++a)
              {
                for (int b=0; b<(KernelDimension); ++b)
                {
                  W2[a][b] = PaddedRasterData[row+a-SimilarityRadius][col+b-SimilarityRadius];
                  d += Kernel[a][b]*(W1[a][b]-W2[a][b])*(W1[a][b]-W2[a][b]);
                }
              }

              w = exp(-d/(DegreeFiltering*DegreeFiltering));
              if (w>wmax) wmax=w;
              sweight += w;
              average += w*PaddedRasterData[row][col];
            }
         }
      }
      average += wmax*PaddedRasterData[i1][j1];
      sweight += wmax;

      if (sweight > 0) FilteredRasterData[i][j] = average/sweight;
      else FilteredRasterData[i][j] = RasterData[i][j];

      // Also extract a record of the noise
      //FilteredNoise[i][j]=RasterData[i][j]-FilteredRasterData[i][j];
    }
  }

  LSDRaster NLFilteredDEM(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,FilteredRasterData,GeoReferencingStrings);
  //LSDRaster NLFilteredNoise(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,FilteredNoise);
  return NLFilteredDEM; //, NLFilteredNoise;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//  Creates a buffer around an array (of size SimilarityRadius) and gives the new border
//  mirror symmetric values of the original array reflected across the boundary.
//  SimilarityRadius should be the size of the window if filtering
//
//  New array has size nrows + 2*SimilarityRadius by ncols + 2*SimilarityRadius
//
//  Martin Hurst, Feb 2012
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::PadRasterSymmetric(Array2D<float>& PaddedRasterData, int& SimilarityRadius)
{


  int PaddedNRows = NRows + 2*SimilarityRadius;
  int PaddedNCols = NCols + 2*SimilarityRadius;

  int minus_i;
  int minus_j;

  for (int i=0; i<PaddedNRows; ++i)
  {
    for (int j=0; j<PaddedNCols; ++j)
    {
      //reverse of i and j
      minus_i = PaddedNRows-1-i;
      minus_j = PaddedNCols-1-j;

      //north boundary
      if (i<SimilarityRadius) {
        if (j<SimilarityRadius) {
          PaddedRasterData[i][j] = RasterData[SimilarityRadius-i][SimilarityRadius-j];
        }
        else if (j>(NCols-1+SimilarityRadius)) {
          PaddedRasterData[i][j] = RasterData[SimilarityRadius-i][j-SimilarityRadius-2*(SimilarityRadius-minus_j)];

        }
        else {
          PaddedRasterData[i][j] = RasterData[SimilarityRadius-i][j-SimilarityRadius];
        }
      }
      //south boundary
      else if (i>NRows-1+SimilarityRadius) {
        if (j<SimilarityRadius) {
          PaddedRasterData[i][j] = RasterData[i-SimilarityRadius-2*(SimilarityRadius-minus_i)][SimilarityRadius-j];
        }
        else if (j>NCols+SimilarityRadius) {
          PaddedRasterData[i][j] = RasterData[i-SimilarityRadius-2*(SimilarityRadius-minus_i)][j-SimilarityRadius-2*(SimilarityRadius-minus_j)];
        }
        else {
          PaddedRasterData[i][j] = RasterData[i-SimilarityRadius-2*(SimilarityRadius-minus_i)][j-SimilarityRadius];
        }
      }
      //west boundary
      else if (j<SimilarityRadius) {
        PaddedRasterData[i][j] = RasterData[i-SimilarityRadius][SimilarityRadius-j];
      }
      //east boundary
      else if (j>NCols-1+SimilarityRadius) {
        PaddedRasterData[i][j] = RasterData[i-SimilarityRadius][j-SimilarityRadius-2*(SimilarityRadius-minus_j)];
      }
      //copy rest of RasterData
      else {
        PaddedRasterData[i][j] = RasterData[i-SimilarityRadius][j-SimilarityRadius];
      }
    }
  }

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//  Generate gaussian weighted kernel
//  kernel array must be predeclared of size SimilarityRadius and consist of zeros:
//  Array2D<float> Kernel(SimilarityRadius,SimilarityRadius,0.0);
//
//  Kernel generated using:
//  G(x,y) = (1/2*pi*sigma^2) exp ((-x^2+y^2)/(2*sigma^2))
//
//  Martin Hurst, Feb 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::MakeGaussianKernel(Array2D<float>& Kernel, float sigma, int SimilarityRadius)
{
  float left_side = 1/(2*M_PI*sigma*sigma);
  float twosigma2 = 2.0*sigma*sigma;
  float right_side;
  float wgt = 0;
  float value;

  //calculate kernel values
  for (int i=0;i<2*SimilarityRadius+1;++i)
  {
    for (int j=0;j<2*SimilarityRadius+1;++j)
    {
      right_side = -(((j-SimilarityRadius)*(j-SimilarityRadius)
                        + (i-SimilarityRadius)*(i-SimilarityRadius))/twosigma2);
      right_side = exp(right_side);
      value = left_side*right_side;
      Kernel[i][j] = value;
      wgt += value;
    }
  }

  //scale to sum to 1
  for (int i=0;i<2*SimilarityRadius+1;++i)
  {
    for (int j=0;j<2*SimilarityRadius+1;++j)
    {
      Kernel[i][j] = Kernel[i][j]/wgt;
    }
  }
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//  Gaussian Filtering
//  Filters the raster using a square 2D Gaussian filter.  The filter is applied
//  using a moving kernel of gaussian weights with a radius of 3*sigma
//
//  Equivalent lenghtscale of smoothing (from Lashermes et al., 2007)
//  original data -> 4*sigma
//  1st derivative -> 2*pi*sigma
//  2nd derivative -> sqrt(2)*pi*sigma
//  David Milodowski, Feb 2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

LSDRaster LSDRaster::GaussianFilter(float sigma, int kr)
{
  // This is the default setting
  if(kr==0) kr = int(ceil(3*sigma/DataResolution));  // Set radius of kernel (default if not specified)
  int kw=2*kr+1;                                     // width of kernel
  Array2D<float> filtered = RasterData.copy();
  Array2D<float> gaussian_kernel_weights(kw,kw,0.0);

  // gemerate kernel
  float x,y;
  for(int i=0;i<kw;++i)
  {
    for(int j=0;j<kw;++j)
    {
      x = (j-kr)*DataResolution;
      y = (i-kr)*DataResolution;
//       gaussian_kernel_weights[i][j]= (1/(2*M_PI*sigma*sigma)) * exp(-(x*x+y*y)/(2*sigma*sigma));
      gaussian_kernel_weights[i][j]= exp(-(x*x+y*y)/(2*sigma*sigma));
    }
  }
  //  Now loop through dem filtering using the gaussian kernel
  for(int i=0;i<NRows;++i)
  {
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
//       if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      if(RasterData[i][j]==NoDataValue)
      {
        filtered[i][j] = NoDataValue;
      }
      else
      {
        float summed_weights = 0;
        float summed_values = 0;

        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            if(i-kr+i_kernel>=0 && i-kr+i_kernel<NRows && j-kr+j_kernel>=0 && j-kr+j_kernel<NCols)
            {
              if(RasterData[i-kr+i_kernel][j-kr+j_kernel]!=NoDataValue)                   // at edges, this takes the one sided gaussian
              {
                summed_weights += gaussian_kernel_weights[i_kernel][j_kernel];
                summed_values += RasterData[i-kr+i_kernel][j-kr+j_kernel]*gaussian_kernel_weights[i_kernel][j_kernel];
              }
            }
          }
        }
        // Get filtered value, ensuring that weights are normalised
        filtered[i][j] = summed_values/summed_weights;
      }
    }
  }
  LSDRaster FilteredRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,filtered);
//   FilteredRaster.write_raster("test_gauss","flt");
  return FilteredRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//  Perona Malik Filtering
//  Filters the raster using the nonlineaer Perona-Malik filter.
//  This follows the algorithm descibed in Passalacqua et al. (2010), A
//  geometric framework for channel network extraction from lidar: Nonlinear
//  diffusion and geodesic paths, J. Geophys. Res., 115(F1), F01002,
// doi:10.1029/2009JF001254.
//  See also  Catte et al. (1992), Image Selective
//  Smoothing and Edge Detection by Nonlinear Diffusion, SIAM J. Numer. Anal.,
//  29(1), 182-193, doi:10.1137/0729012.
//
//  David Milodowski, Feb 2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

LSDRaster LSDRaster::PeronaMalikFilter(int timesteps, float percentile_for_lambda, float dt)
{
  float sigma = 0.05;
  // Calculating lambda
  float lambda = 1;
  vector<float> finite_difference_slopes;
  float slope_NS,slope_EW;
  for (int i=0; i<NRows;++i)
  {
    for (int j=0; j<NCols;++j)
    {
      if(i-1>=0 && i+1<NRows && j-1>=0 && j+1<NCols)
      {
        if(RasterData[i][j]!=NoDataValue && RasterData[i+1][j]!=NoDataValue && RasterData[i-1][j]!=NoDataValue && RasterData[i][j+1]!=NoDataValue && RasterData[i][j-1]!=NoDataValue)
        {
          slope_NS = (RasterData[i+1][j]-RasterData[i-1][j])/(2*DataResolution);
          slope_EW = (RasterData[i][j+1]-RasterData[i][j-1])/(2*DataResolution);
          finite_difference_slopes.push_back(sqrt(slope_NS*slope_NS + slope_EW*slope_EW));
        }
      }
    }
  }
  int N_slopes = finite_difference_slopes.size();
  if(N_slopes>0)
  {
    vector<size_t> index_map;
    matlab_float_sort(finite_difference_slopes,finite_difference_slopes,index_map);
    lambda =  get_percentile(finite_difference_slopes, percentile_for_lambda);
  }
//   lambda = 0.9;
  cout << "lambda " << lambda << endl;
  // Now do the nonlinear filtering
  Array2D<float> Topography = get_RasterData();
  LSDRaster PM_FilteredTopo(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Topography.copy(),GeoReferencingStrings);

  for(int t = 0; t<timesteps; ++t)
  {
    cout << flush << "\t\t\t Perona-Malik Filter; timestep " << t+1 << " of " << timesteps << "\r";
    // Gaussian filter
    int kr = 2;
    LSDRaster GaussianFilteredTopo = PM_FilteredTopo.GaussianFilter(sqrt(sigma),kr);

    // Now get slopes and diffusion coefficients
    float p_n, p_s, p_e, p_w;
    float dh;
    //float slope_n, slope_s, slope_e, slope_w;
    float slope_n_g, slope_s_g, slope_e_g, slope_w_g;
    int count = 0;
    int bad_count=0;
    for (int i=0; i<NRows;++i)
    {
      for (int j=0; j<NCols;++j)
      {
        if(i-1>=0 && i+1<NRows && j-1>=0 && j+1<NCols)
        {
          if(PM_FilteredTopo.get_data_element(i,j)==NoDataValue || PM_FilteredTopo.get_data_element(i+1,j)==NoDataValue
           || PM_FilteredTopo.get_data_element(i-1,j)==NoDataValue || PM_FilteredTopo.get_data_element(i,j+1)==NoDataValue
           || PM_FilteredTopo.get_data_element(i,j-1)==NoDataValue)
          {
            Topography[i][j] = NoDataValue;
            ++bad_count;
          }
          else
          {
            ++count;
            // Calculate the diffusion coefficient
            slope_n_g = (GaussianFilteredTopo.get_data_element(i-1,j)-GaussianFilteredTopo.get_data_element(i,j))/DataResolution;
            slope_s_g = (GaussianFilteredTopo.get_data_element(i+1,j)-GaussianFilteredTopo.get_data_element(i,j))/DataResolution;
            slope_e_g = (GaussianFilteredTopo.get_data_element(i,j+1)-GaussianFilteredTopo.get_data_element(i,j))/DataResolution;
            slope_w_g = (GaussianFilteredTopo.get_data_element(i,j-1)-GaussianFilteredTopo.get_data_element(i,j))/DataResolution;

            p_n = 1/( 1 + ( abs(slope_n_g)/lambda )*( abs(slope_n_g)/lambda ) );
            p_s = 1/( 1 + ( abs(slope_s_g)/lambda )*( abs(slope_s_g)/lambda ) );
            p_e = 1/( 1 + ( abs(slope_e_g)/lambda )*( abs(slope_e_g)/lambda ) );
            p_w = 1/( 1 + ( abs(slope_w_g)/lambda )*( abs(slope_w_g)/lambda ) );
//             p_n = exp(-((abs(slope_n_g)/lambda )*(abs(slope_n_g)/lambda)));
//             p_s = exp(-((abs(slope_s_g)/lambda )*(abs(slope_s_g)/lambda)));
//             p_e = exp(-((abs(slope_e_g)/lambda )*(abs(slope_e_g)/lambda)));
//             p_w = exp(-((abs(slope_w_g)/lambda )*(abs(slope_w_g)/lambda)));

            //slope_n = (PM_FilteredTopo.get_data_element(i-1,j)-PM_FilteredTopo.get_data_element(i,j))/DataResolution;
            //slope_s = (PM_FilteredTopo.get_data_element(i+1,j)-PM_FilteredTopo.get_data_element(i,j))/DataResolution;
            //slope_e = (PM_FilteredTopo.get_data_element(i,j+1)-PM_FilteredTopo.get_data_element(i,j))/DataResolution;
            //slope_w = (PM_FilteredTopo.get_data_element(i,j-1)-PM_FilteredTopo.get_data_element(i,j))/DataResolution;

            dh = dt*(p_n*slope_n_g + p_s*slope_s_g + p_e*slope_e_g + p_w*slope_w_g);
            Topography[i][j]+=dh;

          }
        }
        else Topography[i][j] = NoDataValue;
      }
    }

    // Now update the LSDRaster
    PM_FilteredTopo = PM_FilteredTopo.LSDRasterTemplate(Topography.copy());
  }
  cout << endl;
  return PM_FilteredTopo;
}



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to turn a point shapefile into an LSDIndexRaster.
//
// Can be used to turn a shapefile of channel heads into a sources raster. Does not do
// any bounds checking or shapefile type checking.
//
// SWDG 13/3/14
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDIndexRaster LSDRaster::PointShapefileToRaster(string FileName){

  PointData Points = LoadShapefile(FileName);

  Array2D<int> Output(NRows, NCols, NoDataValue);

  int i;
  int j;
  float YMax = YMinimum + (DataResolution * (NRows));

  for (int q = 0; q < int(Points.X.size()); ++q){

    j = (Points.X[q] - XMinimum)/DataResolution;
    i = (YMax - Points.Y[q])/DataResolution;

    Output[i][j] = 1;

  }

  LSDIndexRaster OutputRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                                     NoDataValue,Output,GeoReferencingStrings);
  return OutputRaster;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to turn a polyline shapefile into an LSDIndexRaster.
//
// Can be used to turn a shapefile of a river network into a raster. Does not do
// any bounds checking or shapefile type checking.
//
// Works by calculating points along each line spaced by less than the data resolution.
// This has the effect of flagging every raster cell along a polyline.
//
// SWDG 21/3/14
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDIndexRaster LSDRaster::PolylineShapefileToRaster(string FileName){

  vector<PointData> Polylines = LoadPolyline(FileName);   //load the coordinates of the shapefile
  Array2D<int> Output(NRows, NCols, NoDataValue);   //output array

  float i;
  float j;
  float k;
  float Xm;
  float Ym;
  float length;
  float fraction;
  int i_new;
  int j_new;

  float YMax = YMinimum + (DataResolution * (NRows));

  for (int w = 0; w < int(Polylines.size()); ++w){
    for (int q = 0; q < int(Polylines[w].X.size())-1; ++q){

      length = sqrt( ((Polylines[w].X[q+1] - Polylines[w].X[q]) * (Polylines[w].X[q+1] - Polylines[w].X[q])) + ((Polylines[w].Y[q+1] - Polylines[w].Y[q]) * (Polylines[w].Y[q+1] - Polylines[w].Y[q])) );
      fraction = length/DataResolution;

      for (int n = 0; n <= fraction; ++n){

        k = n/fraction;  //calculate the next step along the line to get the coordinates of

        Xm = Polylines[w].X[q] + (k*(Polylines[w].X[q+1] - Polylines[w].X[q]));      //get the next point along the line
        Ym = Polylines[w].Y[q] + (k*(Polylines[w].Y[q+1] - Polylines[w].Y[q]));

        j = (Xm - XMinimum)/DataResolution;     //convert the x,y coordinates into raster coords
        i = (YMax - Ym)/DataResolution;

        i_new = trunc(i);           //convert the floating point raster coordinates into integers
        j_new = ceil(j)-1;

        Output[i_new][j_new] = 1;

      }
    }
  }

  LSDIndexRaster OutputRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,
     NoDataValue,Output,GeoReferencingStrings);
  return OutputRaster;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to resample an LSDRaster to a lower resolution.
// OutputResolution is the resolution in spatial units to be resampled to.
// Returns an LSDRaster resampled to the OutputResolution.
// SWDG 17/3/14
// BG Edited on the 18th of February 2019 around 3PM: I am attempting to sort the georefering which happens to dislike the resampling
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::Resample(float OutputResolution){

  if (OutputResolution < DataResolution){
    cout << "Your resample resolution of " << OutputResolution << " is lower that the current data resolution " << DataResolution << endl;
    exit(EXIT_FAILURE);
  }

  int NewNRows = (NRows*DataResolution/OutputResolution);
  int NewNCols = (NCols*DataResolution/OutputResolution);

  Array2D<float> Resampled(NewNRows, NewNCols, NoDataValue);

  int centre_i;
  int centre_j;

  float ResolutionRatio = OutputResolution/DataResolution;

  for (int i = 0; i < NewNRows; ++i){
    for (int j = 0; j < NewNCols; ++j){

      //find the centre of the new grid in the old grid units
      centre_i = (i*ResolutionRatio) + (ResolutionRatio/2);
      centre_j = (j*ResolutionRatio) + (ResolutionRatio/2);

      Resampled[i][j] = RasterData[centre_i][centre_j];
    }
  }

  LSDRaster OutputRaster(NewNRows,NewNCols,XMinimum,YMinimum,OutputResolution,
                      NoDataValue,Resampled,GeoReferencingStrings);

  // this should do the trick bg
  OutputRaster.Update_GeoReferencingStrings();

  return OutputRaster;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// BASIC TOOLS
//---------------------------------------------------------------------------------------
// Basic functions e.g. spatial averaging, which may be useful for loads of stuff
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Creates a mask for neighbourhood functions.   Uses a neighbourhood switch to select
// circular (1) vs square window (0).  Default is a square window.
// DTM 19/06/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Array2D<int> LSDRaster::create_mask(float window_radius, int neighbourhood_switch)
{
  if((neighbourhood_switch != 1) && (neighbourhood_switch != 0))
  {
    neighbourhood_switch = 0;
    cout << "\t\t incorrect specification of neighbourhood type, so set to square (default).\n"
         << " Note that correct neighbourhood_switch values are: 0 = square, 1 = circular" << endl;
  }
  int kernel_radius = int(ceil(window_radius/DataResolution));
  int kernel_width = 2*kernel_radius + 1;
  Array2D<int> mask(kernel_width,kernel_width,0);
  float x,y,radial_dist;
  for(int i=0;i<kernel_width;++i)
  {
    for(int j=0;j<kernel_width;++j)
    {
      x=(i-kernel_radius)*DataResolution;
      y=(j-kernel_radius)*DataResolution;
      // Build circular mask
      // distance from centre to this point.
      if(neighbourhood_switch == 0) mask[i][j] = 1;
      else if(neighbourhood_switch == 1)
      {
        radial_dist = sqrt(y*y + x*x);
        if (floor(radial_dist) <= window_radius)
        {
          mask[i][j] = 1;
    }
      }
      else mask[i][j] = 1;
    }
  }
  return mask;
}
//---------------------------------------------------------------------------------------


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// spatial_average
// Calculates a spatial average using a specified moving window.  Uses a neighbourhood
// switch to select circular (1) vs square window (0)
// DTM 19/06/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::neighbourhood_statistics_spatial_average(float window_radius, int neighbourhood_switch)
{
  Array2D<float> SpatialAverageArray(NRows,NCols,NoDataValue);
//   Array2D<float> StandardDeviationArray(NRows,NCols,NoDataValue);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius < DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution: " <<
    DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius = DataResolution;
  }

  // Prepare kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel
  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<int> mask = create_mask(window_radius, neighbourhood_switch);

  // Move window over DEM and extract neighbourhood pixels
  cout << "\n\tRunning neighbourhood statistics..." << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  float mean, value;
  vector<float> data;
  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        SpatialAverageArray[i][j] = NoDataValue;
      }
      else
      {
        // Sample DEM
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            value = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            if(value!=NoDataValue && mask[i_kernel][j_kernel]==1) data.push_back(value);
          }
        }
        // Get stats
        mean = get_mean(data);
        SpatialAverageArray[i][j] = mean;
        // StandardDeviationArray[i][j] = get_standard_deviation(data,mean);
        data.clear();
      }
    }
  }

  LSDRaster SpatialAverage(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,SpatialAverageArray,GeoReferencingStrings);
  return SpatialAverage;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// overloaded function to kick out 2 rasters -> local standard deviation & average
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<LSDRaster> LSDRaster::neighbourhood_statistics_spatial_average_and_SD(float window_radius, int neighbourhood_switch)
{
  Array2D<float> SpatialAverageArray(NRows,NCols,NoDataValue);
  Array2D<float> StandardDeviationArray(NRows,NCols,NoDataValue);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius < DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution: " <<
    DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius = DataResolution;
  }
  // Prepare kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel
  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<int> mask = create_mask(window_radius, neighbourhood_switch);

  // Move window over DEM and extract neighbourhood pixels
  cout << "\n\tRunning spatial statistics module..." << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  float mean, value;
  vector<float> data;
  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols)
                    || RasterData[i][j]==NoDataValue)
      {
        SpatialAverageArray[i][j] = NoDataValue;
      }
      else
      {
        // Sample DEM
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            value = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            if(value!=NoDataValue && mask[i_kernel][j_kernel]==1) data.push_back(value);
          }
        }

        // Get stats
        mean = get_mean(data);
        SpatialAverageArray[i][j] = mean;
        StandardDeviationArray[i][j] = get_standard_deviation(data,mean);
        data.clear();
      }
    }
  }

  LSDRaster SpatialAverage(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         NoDataValue,SpatialAverageArray,GeoReferencingStrings);
  LSDRaster SpatialSD(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,
                          StandardDeviationArray,GeoReferencingStrings);
  vector<LSDRaster> output_rasters;
  output_rasters.push_back(SpatialAverage);
  output_rasters.push_back(SpatialSD);
  return output_rasters;
}
//------------------------------------------------------------------------------


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// local relief
// Calculates relief using a specified moving window.  Uses a neighbourhood
// switch to select circular (1) vs square window (0)
// SMM 15/11/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::neighbourhood_statistics_local_relief(float window_radius, int neighbourhood_switch)
{
  Array2D<float> SpatialReliefArray(NRows,NCols,NoDataValue);
//   Array2D<float> StandardDeviationArray(NRows,NCols,NoDataValue);

  // catch if the supplied window radius is less than the data resolution and
  // set it to equal the data resolution - SWDG
  if (window_radius < DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution: " <<
    DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius = DataResolution;
  }

  // Prepare kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel
  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<int> mask = create_mask(window_radius, neighbourhood_switch);

  // Move window over DEM and extract neighbourhood pixels
  cout << "\n\tRunning neighbourhood statistics..." << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;

  float min_in_window;
  float max_in_window;
  float value;
  float relief;

  bool max_set, min_set;     // switches to state whether max and min have been set
  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols) || RasterData[i][j]==NoDataValue)
      {
        SpatialReliefArray[i][j] = NoDataValue;
      }
      else
      {
        // reset max and min values
        min_in_window = 100000;      // set to a large value to make sure it is reset lower
        max_in_window = -100000;     // set to a small value

        // Sample DEM
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            value = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            // make sure it is in the mask and not nodata
            if(value!=NoDataValue && mask[i_kernel][j_kernel]==1)
            {

              // set min and max values
              if (value > max_in_window)
              {
                max_in_window = value;
                max_set = true;
              }
              if (value < min_in_window)
              {
                min_in_window = value;
                min_set = true;
              }

            }
          }
        }
        // Get relief
        if(min_set && max_set)
        {
          relief = max_in_window-min_in_window;
        }
        SpatialReliefArray[i][j] = relief;

      }
    }
  }

  LSDRaster SpatialRelief(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,SpatialReliefArray,GeoReferencingStrings);
  return SpatialRelief;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// neighbourhood_statistics_fraction_condition
// A function that determines the fraction of cells in a circular neighbourhood that
// satisfy a given condition
// options
// 0 ==
// 1 !=
// 2 >
// 3 >=
// 4 <
// 5 <=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::neighbourhood_statistics_fraction_condition(float window_radius,
            int neighbourhood_switch, int condition_switch, float test_value)
{
  Array2D<float> FractionTrueArray(NRows,NCols,NoDataValue);

  if (window_radius < DataResolution)
  {
    cout << "Supplied window radius: " << window_radius << " is less than the data resolution: " <<
    DataResolution << ".\nWindow radius has been set to data resolution." << endl;
    window_radius = DataResolution;
  }

  // Prepare kernel
  int kr = int(ceil(window_radius/DataResolution));  // Set radius of kernel
  int kw=2*kr+1;                                     // width of kernel
  Array2D<float> data_kernel(kw,kw,NoDataValue);
  Array2D<int> mask = create_mask(window_radius, neighbourhood_switch);

  // Move window over DEM and extract neighbourhood pixels
  cout << "\n\tRunning neighbourhood statistics..." << endl;
  cout << "\t\tDEM size = " << NRows << " x " << NCols << endl;
  float value;
  float count = 0;
  vector<float> data;

  for(int i=0;i<NRows;++i)
  {
    cout << "\tRow = " << i+1 << " / " << NRows << "    \r";
    for(int j=0;j<NCols;++j)
    {
      // Avoid edges
      if((i-kr < 0) || (i+kr+1 > NRows) || (j-kr < 0) || (j+kr+1 > NCols)
                    || RasterData[i][j]==NoDataValue)
      {
        FractionTrueArray[i][j] = NoDataValue;
      }
      else
      {
        // Sample DEM
        for(int i_kernel=0;i_kernel<kw;++i_kernel)
        {
          for(int j_kernel=0;j_kernel<kw;++j_kernel)
          {
            value = RasterData[i-kr+i_kernel][j-kr+j_kernel];
            if(value!=NoDataValue && mask[i_kernel][j_kernel]==1)
            {
              count = count + 1;
              if(condition_switch == 0 && value == test_value) data.push_back(value);
              if(condition_switch == 1 && value != test_value) data.push_back(value);
              if(condition_switch == 2 && value > test_value) data.push_back(value);
              if(condition_switch == 3 && value >= test_value) data.push_back(value);
              if(condition_switch == 4 && value < test_value) data.push_back(value);
              if(condition_switch == 5 && value <= test_value) data.push_back(value);
            }
          }
        }
        // Get stats
        FractionTrueArray[i][j] = float(data.size())/count;
        count = 0;
        data.clear();
      }
    }
  }
  LSDRaster FractionTrue(NRows,NCols,XMinimum,YMinimum,DataResolution,
                        NoDataValue,FractionTrueArray,GeoReferencingStrings);
  return FractionTrue;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Border with nodata values
// This function replaces the border pixels of a raster with nodatavalues.  This
// is particularly useful when dealing with output from functions that have edge
// effects (e.g. spectral filtering)
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::border_with_nodata(int border_width, int irregular_switch)
{
  Array2D<float> Data = RasterData.copy();
  // kernel dimensions
  int kr = border_width;
  int kw = 2*kr + 1;
  float value;
  for(int i = 0; i<NRows; ++i)
  {
    for(int j = 0; j< NCols; ++j)
    {
      if( i<border_width || i>NRows-border_width-1 || j<border_width || j>NCols-border_width-1)
      {
        Data[i][j]=NoDataValue;
        //cout << i << "/" << NRows << " " << j << "/" << NCols << endl;
      }
      else
      {
        if(irregular_switch == 1)
        {
          // Sample DEM
          for(int i_kernel=0;i_kernel<kw;++i_kernel)
          {
            for(int j_kernel=0;j_kernel<kw;++j_kernel)
            {
              value = RasterData[i-kr+i_kernel][j-kr+j_kernel];
              if(value == NoDataValue)
              {
                i_kernel = kw;    // as soon as NoDataValue found, skip to next cell
                j_kernel = kw;
                Data[i][j]=NoDataValue;
              }
            }
          }
        }
      }
    }
  }

  LSDRaster bordered_DEM(NRows,NCols,XMinimum,YMinimum,DataResolution,
                      NoDataValue,Data,GeoReferencingStrings);
  return bordered_DEM;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Create mask based on threshold value and condition
// This function generates an index raster comprising a mask where values of an LSDRaster
// have met a specified condition (e.g. where all values exceed a threshold slope)
//
// MDH, 27/8/14
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::Create_Mask(string Condition, float TestValue)
{
  //declare mask array
  Array2D<int> Mask(NRows,NCols,NoDataValue);

  //cout << "Creating Mask: Condition is " << Condition << endl;
  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (Condition == "<") {
        if (RasterData[i][j] < TestValue) Mask[i][j] = 1;
      }
      else if (Condition == ">") {
        if (RasterData[i][j] > TestValue) Mask[i][j] = 1;
      }
      else if (Condition == "==") {
        if (RasterData[i][j] == TestValue) Mask[i][j] = 1;
      }
      else
      {
        cout << "Condition is " << Condition << endl;
        cout << "Condition not recognised" << endl;
        exit(EXIT_FAILURE);
      }
    }
  }
  LSDIndexRaster MaskRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Mask,GeoReferencingStrings);
  return MaskRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Extract values by mask
// This function generates a masked raster from an LSDIndexRaster masks, retaining
// values where the Mask == 1
//
// MDH, 27/8/14
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

LSDRaster LSDRaster::ExtractByMask(LSDIndexRaster Mask)
{
  // declare new array
  Array2D<float> MaskedArray(NRows,NCols,NoDataValue);
  Array2D<int> MaskArray = Mask.get_RasterData();

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (MaskArray[i][j] > 0)
      {
        MaskedArray[i][j] = RasterData[i][j];
      }
    }
  }
  LSDRaster MaskedRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,MaskedArray,GeoReferencingStrings);
  return MaskedRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Extract values by mask and update existing LSDRaster object
//
// MDH, 26/7/17
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

void LSDRaster::MaskRaster(LSDIndexRaster Mask)
{
  // declare new array
  Array2D<float> MaskedArray(NRows,NCols,NoDataValue);
  Array2D<int> MaskArray = Mask.get_RasterData();
  int NDV = Mask.get_NoDataValue();

  for (int i=0; i<NRows; ++i)
  {
    for (int j=0; j<NCols; ++j)
    {
      if (MaskArray[i][j] == NDV)
      {
        RasterData[i][j] = NoDataValue;
      }
    }
  }
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this function creates an LSDIndexRaster
// that has values of 0 for nodes that are not on edge or are borderd
// by nodata, and 1 for those that are on the edge and bordered by nodata
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::find_cells_bordered_by_nodata()
{
  // this is the array that holds the mask
  Array2D<int> Mask(NRows,NCols,0);

  // first, get the edges:
  for(int row = 0; row<NRows; row++)
  {
    Mask[row][0] = 1;
    Mask[row][NCols-1] = 1;
  }
  for(int col = 0; col<NCols; col++)
  {
    Mask[0][col] = 1;
    Mask[NRows-1][col] = 1;
  }

  // now loop through the rest of the data.
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if(RasterData[row][col] == NoDataValue)
      {
        // you need to mask all the surrounding nodes
        Mask[row][col] = 1;

        // these are a bunch of tedious if statments to make sure you
        // don't try and access data out of the array bounds
        if(row !=0)
        {
          Mask[row-1][col] = 1;

          if(col != 0)
          {
            Mask[row-1][col-1] = 1;
          }
          if(col != NCols-1)
          {
            Mask[row-1][col+1] = 1;
          }
        }
        if(row !=NRows-1)
        {
          Mask[row+1][col] = 1;

          if(col != 0)
          {
            Mask[row+1][col-1] = 1;
          }
          if(col != NCols-1)
          {
            Mask[row+1][col+1] = 1;
          }
        }
        if(col != 0)
        {
          Mask[row][col-1] = 1;
        }
        if(col != NCols-1)
        {
          Mask[row][col+1] = 1;
        }
      }
    }
  }

  LSDIndexRaster Mask_Raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         int(NoDataValue),Mask,GeoReferencingStrings);
  return Mask_Raster;

}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this looks for isolated instances of nodata and fills them
//
// Not sure about author, I think MDH (SMM comment) 2012
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::check_isolated_nodata()
{
  for (int row=0; row<NRows; ++row)
  {
    for(int col=0; col<NCols; ++col)
    {
      if(RasterData[row][col] < 0)
      {
        cout << "LSDRaster::check_isolated_nodata stargine data point: row: "
             << row << " col: " << col << " data: " << RasterData[row][col];
        RasterData[row][col] = NoDataValue;
      }

      if(RasterData[row][col] == NoDataValue)
      {
        cout << "LSDRaster::check_isolated_nodata found nodata: row: "
             << row << " col: " << col << " data: " << RasterData[row][col];
      }

    }
  }
  cout << "Done!" << endl;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This is a rudimentary NoData filling algorithm
// you should run the raster trimmer before invoking this
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::rudimentary_nodata_fill()
{
  int local_row, local_col;
  float local_average;

  // loop through all interior nodes. Nodes on the edge should not have nodata
  // after the trimming process
  for (int row=1; row<NRows-1; ++row)
  {
    for(int col=1; col<NCols-1; ++col)
    {
      float total = 0;
      int n_cells = 0;
      if(RasterData[row][col] == NoDataValue)
      {
        for(int i = -1; i<=1; i++)
        {
          for(int j = -1; j<=1; j++)
          {
            local_row = row+i;
            local_col = col+j;
            if(RasterData[local_row][local_col] != NoDataValue)
            {
              total+= RasterData[local_row][local_col];
              n_cells++;
            }
          }
        }
      }
      if(n_cells<0)
      {
        local_average = total/float(n_cells);
        RasterData[row][col] = local_average;
      }
    }
  }
  cout << "Done!" << endl;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This is a slightly more complex nodata filler
// you should run the raster trimmer before invoking this
// SMM
// 09/12/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::alternating_direction_nodata_fill(int window_width)
{


  // check argument
  if(window_width <1)
  {
    cout << "You need a positive window width, defaulting to 1" << endl;
    window_width = 1;
  }

  cout << "Sweeping nodata, window width is: " << window_width << endl;

  // This function loops in alternating directions until there is no more nodata
  int NNoData = 0;
  float this_window_sum;
  float local_average;
  int this_window_ndata;
  int window_row, window_col;

  // set up data to be
  Array2D<float> this_sweep_data = RasterData.copy();;
  Array2D<float> updated_raster;

  // set the sweep number to 0
  int nsweep = 0;

  do
  {
    // reset the number of nodata points in this sweep to zero
    NNoData = 0;

    cout << "LINE 8268, Sweep number: " << nsweep << endl;
    cout << "Line 8275, switch is: " << nsweep%4 << endl;

    // copy over the updated raster
    updated_raster = this_sweep_data.copy();

    int begin_ndv = 0;
    for(int row = 0; row<NRows; row++)
    {
      for(int col = 0; col <NCols; col++)
      {
        if( updated_raster[row][col] == NoDataValue)
        {
          begin_ndv++;
        }
      }
    }
    cout << "Line 8285, the updated raster has " << begin_ndv << " no data nodes " << endl;

    // now run a sweep
    switch(nsweep%4)
    {
      case(0):
      {

        // sweep 0
        for (int row=0; row<NRows; ++row)
        {
          for(int col=0; col<NCols; ++col)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              NNoData++;
              this_window_sum = 0;
              this_window_ndata = 0;

              //cout << "Row: " << row << " col: " << col << endl;
              for(int r = -window_width; r<=window_width; r++)
              {
                for(int c = -window_width; c<=window_width; c++)
                {
                  window_row = r+row;
                  window_col = c+col;


                  if(window_row > 0 && window_row < NRows-1
                     && window_col > 0 && window_col < NCols-1)
                  {
                    //cout << "wr: " << window_row << " wc: " << window_col << " data: " << updated_raster[window_row][window_col] << endl;
                    if(updated_raster[window_row][window_col] != NoDataValue)
                    {
                      this_window_sum += updated_raster[window_row][window_col];
                      this_window_ndata += 1;
                    }
                  }
                }
              }

              // now get the average
              if(this_window_ndata>0)
              {
                //cout << "Found a nodata replacement" << endl;
                local_average = this_window_sum/float(this_window_ndata );
                this_sweep_data[row][col] = local_average;
              }
            }
          }
        }
        break;
      }
      case(1):
      {
        // sweep 1
        for (int col=0; col<NCols; ++col)
        {
          for(int row=0; row<NRows; ++row)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              NNoData++;
              this_window_sum = 0;
              this_window_ndata = 0;
              for(int r = -window_width; r<=window_width; r++)
              {
                for(int c = -window_width; c<=window_width; c++)
                {
                  window_row = r+row;
                  window_col = c+col;

                  if(window_row > 0 && window_row < NRows-1 && window_col > 0 && window_col < NCols-1)
                  {
                    if(updated_raster[window_row][window_col] != NoDataValue)
                    {
                      this_window_sum += updated_raster[window_row][window_col];
                      this_window_ndata += 1;
                    }
                  }
                }
              }

              // now get the average
              if(this_window_ndata>0)
              {
                local_average = this_window_sum/float(this_window_ndata );
                this_sweep_data[row][col] = local_average;
              }
            }
          }
        }
        break;
      }
      case(2):
      {
        // sweep 2
        for (int row=0; row<NRows; ++row)
        {
          for(int col=NCols-1; col>0; --col)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              NNoData++;
              this_window_sum = 0;
              this_window_ndata = 0;
              for(int r = -window_width; r<=window_width; r++)
              {
                for(int c = -window_width; c<=window_width; c++)
                {
                  window_row = r+row;
                  window_col = c+col;

                  if(window_row > 0 && window_row < NRows-1 && window_col > 0 && window_col < NCols-1)
                  {
                    if(updated_raster[window_row][window_col] != NoDataValue)
                    {
                      this_window_sum += updated_raster[window_row][window_col];
                      this_window_ndata += 1;
                    }
                  }
                }
              }

              // now get the average
              if(this_window_ndata>0)
              {
                local_average = this_window_sum/float(this_window_ndata );
                this_sweep_data[row][col] = local_average;
              }
            }
          }
        }
        break;
      }
      case(3):
      {
        // sweep 3
        for (int col=0; col<NCols; ++col)
        {
          for(int row=NRows-1; row>0; --row)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              NNoData++;
              this_window_sum = 0;
              this_window_ndata = 0;
              for(int r = -window_width; r<=window_width; r++)
              {
                for(int c = -window_width; c<=window_width; c++)
                {
                  window_row = r+row;
                  window_col = c+col;

                  if(window_row > 0 && window_row < NRows-1 && window_col > 0 && window_col < NCols-1)
                  {
                    if(updated_raster[window_row][window_col] != NoDataValue)
                    {
                      this_window_sum += updated_raster[window_row][window_col];
                      this_window_ndata += 1;
                    }
                  }
                }
              }

              // now get the average
              if(this_window_ndata>0)
              {
                local_average = this_window_sum/float(this_window_ndata );
                this_sweep_data[row][col] = local_average;
              }
            }
          }
        }
      }
      break;
    }

    int test_ndv = 0;
    for(int row = 0; row<NRows; row++)
    {
      for(int col = 0; col <NCols; col++)
      {
        if( this_sweep_data[row][col] == NoDataValue)
        {
          test_ndv++;
        }
      }
    }

    cout << "Line 8452, testing ndv = " << test_ndv<< endl;
    cout << "Line 8445, number of nodata nodes: " << NNoData << endl;
    // increment the sweep number
    nsweep++;

  } while(NNoData > 0);

  LSDRaster Hole_filled_Raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         int(NoDataValue),this_sweep_data,GeoReferencingStrings);
  return Hole_filled_Raster;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Same as above but trims the data
// SMM
// 09/12/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::alternating_direction_nodata_fill_with_trimmer(int window_width)
{
  cout << "Starting nodata filling by trimming the raster" << endl;

  // first remove the seas
  remove_seas();

  // now trim the raster << endl;
  LSDRaster Trimmed_raster = RasterTrimmerSpiral();
  cout << "I've trimmed the raster" << endl;
  LSDRaster nodata_filled = Trimmed_raster.alternating_direction_nodata_fill(window_width);
  cout << "Trimmed raster dimensions are rows: " << nodata_filled.get_NRows()
       << " and cols: " << nodata_filled.get_NCols() << endl;
  return nodata_filled;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Same as above but trims the data
// SMM
// 09/12/2014
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::create_binary_isdata_raster()
{
  Array2D<int> IsDataArray(NRows,NCols,int(NoDataValue));
  for(int row = 0; row<NRows; row++)
  {
    for(int col = 0; col<NCols; col++)
    {
      if (RasterData[row][col] != NoDataValue)
      {
        IsDataArray[row][col] = 1;
      }
    }
  }

  LSDIndexRaster IsDataRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         int(NoDataValue),IsDataArray,GeoReferencingStrings);
  return IsDataRaster;

}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Fill no data in an irregular raster
// No data values must have all neighbours within the window radius != NDV.  Local
// mean of all pixels in the window radius.
// FJC 04/11/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::nodata_fill_irregular_raster(int window_radius)
{
  int pixel_radius = int(window_radius/DataResolution);
  if (window_radius < DataResolution) window_radius = DataResolution;
  Array2D<float> RasterArray = RasterData;

  Array2D<float> FilledRaster(NRows, NCols, NoDataValue);
  //search the neighbours of each pixel for 0 values within the window radius
  for (int row = 0; row < NRows; row ++)
  {
    for (int col = 0; col < NCols; col++)
    {
      if (RasterArray[row][col] != NoDataValue) FilledRaster[row][col] = RasterArray[row][col];
      if (RasterArray[row][col] == NoDataValue)
      {
        vector<int> counts(8,0);
				float total_elev = 0;
				int n_obs = 0;
        for (int i = 1; i <= pixel_radius; i++)
        {
          //set exceptions for first or last row
          int min_row = row-i;
          int max_row = row+i;
          if (min_row < 0) min_row = 0;
          if (max_row >= NRows) max_row = NRows-1;

          //set exceptions for first or last col
          int min_col = col-i;
          int max_col = col+i;
          if (min_col < 0) min_col = 0;
          if (max_col >= NCols) max_col = NCols-1;

          //check whether surrounding pixels in all directions are equal to 0
          if (RasterArray[min_row][min_col]  != NoDataValue) {
						counts.at(0) = 1;
						total_elev += RasterArray[min_row][min_col];
						n_obs++;
					}
          if (RasterArray[row][min_col]  != NoDataValue) {
						counts.at(1) = 1;
						total_elev += RasterArray[row][min_col];
						n_obs++;
					}
          if (RasterArray[max_row][min_col]  != NoDataValue) {
						counts.at(2) = 1;
						total_elev += RasterArray[max_row][min_col];
						n_obs++;
					}
          if (RasterArray[min_row][col]  != NoDataValue) {
						counts.at(3) = 1;
						total_elev += RasterArray[min_row][col];
						n_obs++;
					}
          if (RasterArray[min_row][max_col]  != NoDataValue) {
						counts.at(4) = 1;
						total_elev += RasterArray[min_row][max_col];
						n_obs++;
					}
          if (RasterArray[row][max_col]  != NoDataValue) {
						counts.at(5) = 1;
						total_elev += RasterArray[row][max_col];
						n_obs++;
					}
          if (RasterArray[max_row][max_col]  != NoDataValue) {
						counts.at(6) = 1;
						total_elev += RasterArray[max_row][max_col];
						n_obs++;
					}
          if (RasterArray[max_row][col] != NoDataValue) {
						counts.at(7) = 1;
						total_elev += RasterArray[max_row][col];
						n_obs++;
					}

          // if 1s surround the pixel, then fill in the pixel
          if (counts.at(0) > 0 && counts.at(1) > 0 && counts.at(2) > 0 && counts.at(3) > 0 && counts.at(4) > 0 && counts.at(5) > 0 && counts.at(6) > 0 && counts.at(7) > 0)
          {
						FilledRaster[row][col] = total_elev/n_obs;
            i = pixel_radius+1;
          }
        }
      }
    }
  }

  //create new LSDIndexRaster with the filled patches
  LSDRaster FilledDEM(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,FilledRaster,GeoReferencingStrings);
  return FilledDEM;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This is a slightly more complex nodata filler
// you should run the raster trimmer before invoking this
// SMM
// 09/12/2014
//
// UPDATE - modification of original function to only fill internal no data voids
// This is because the raster trimmer won't work on irregular rasters. Holes are only filled if they are surrounded in all directions by pixels with a valid elevation value within the given window width.
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDRaster LSDRaster::alternating_direction_nodata_fill_irregular_raster(int window_width)
{

  // check argument
  if(window_width <1)
  {
    cout << "You need a positive window width, defaulting to 1" << endl;
    window_width = 1;
  }

  cout << "Sweeping nodata, window width is: " << window_width << endl;

  // This function loops in alternating directions until there is no more nodata
  float total_elev;
  int n_obs;

  // set up data to be
  Array2D<float> this_sweep_data = RasterData.copy();;
  Array2D<float> updated_raster;

  // set the sweep number to 0
  int nsweep = 0;

  do
  {
    cout << "LINE 8268, Sweep number: " << nsweep << endl;
    cout << "Line 8275, switch is: " << nsweep%4 << endl;

    // copy over the updated raster
    updated_raster = this_sweep_data.copy();

    // now run a sweep
    switch(nsweep%4)
    {
      case(0):
      {
        // sweep 0
        for (int row=0; row<NRows; ++row)
        {
          for(int col=0; col<NCols; ++col)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              total_elev = 0;
              n_obs = 0;
							vector<int> counts(8,0);

							for (int i = 1; i < window_width; i++)
							{
								//set exceptions for first or last row
								int min_row = row-i;
								int max_row = row+i;
								if (min_row < 0) min_row = 0;
								if (max_row >= NRows) max_row = NRows-1;

								//set exceptions for first or last col
								int min_col = col-i;
								int max_col = col+i;
								if (min_col < 0) min_col = 0;
								if (max_col >= NCols) max_col = NCols-1;

								//check whether surrounding pixels in all directions are equal to 0
								if (updated_raster[min_row][min_col]  != NoDataValue) {
									if (counts.at(0) == 0) {
										total_elev += updated_raster[min_row][min_col];
										n_obs++;
										counts.at(0) = 1;
									}
								}
								if (updated_raster[row][min_col]  != NoDataValue) {
									if (counts.at(1) == 0) {
										total_elev += updated_raster[row][min_col];
										n_obs++;
										counts.at(1) = 1;
									}
								}
								if (updated_raster[max_row][min_col]  != NoDataValue) {
									if (counts.at(2) == 0) {
										total_elev += updated_raster[max_row][min_col];
										n_obs++;
										counts.at(2) = 1;
									}
								}
								if (updated_raster[min_row][col]  != NoDataValue) {
									if (counts.at(3) == 0) {
										total_elev += updated_raster[min_row][col];
										n_obs++;
										counts.at(3) = 1;
									}
								}
								if (updated_raster[min_row][max_col]  != NoDataValue) {
									if (counts.at(4) == 0) {
										total_elev += updated_raster[min_row][max_col];
										n_obs++;
										counts.at(4) = 1;
									}
								}
								if (updated_raster[row][max_col]  != NoDataValue) {
									if (counts.at(5) == 0) {
										total_elev += updated_raster[row][max_col];
										n_obs++;
										counts.at(5) = 1;
									}
								}
								if (updated_raster[max_row][max_col]  != NoDataValue) {
									if (counts.at(6) == 0) {
										total_elev += updated_raster[max_row][max_col];
										n_obs++;
										counts.at(6) = 1;
									}
								}
								if (updated_raster[max_row][col] != NoDataValue) {
									if (counts.at(7) == 0) {
										total_elev += updated_raster[max_row][col];
										n_obs++;
										counts.at(7) = 1;
									}
								}

								// if 1s surround the pixel, then fill in the pixel
								if (counts.at(0) > 0 && counts.at(1) > 0 && counts.at(2) > 0 && counts.at(3) > 0 && counts.at(4) > 0 && counts.at(5) > 0 && counts.at(6) > 0 && counts.at(7) > 0)
								{
									//cout << "total elev: " << total_elev << " N obs: " << n_obs << endl;
									this_sweep_data[row][col] = total_elev/float(n_obs);
									i = window_width+1;
								}
							}
						}
					}
	 		 	}
        break;
      }
      case(1):
      {
        // sweep 1
        for (int col=0; col<NCols; ++col)
        {
          for(int row=0; row<NRows; ++row)
          {
            // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              total_elev = 0;
              n_obs = 0;
							vector<int> counts(8,0);

							for (int i = 1; i < window_width; i++)
							{
								//set exceptions for first or last row
								int min_row = row-i;
								int max_row = row+i;
								if (min_row < 0) min_row = 0;
								if (max_row >= NRows) max_row = NRows-1;

								//set exceptions for first or last col
								int min_col = col-i;
								int max_col = col+i;
								if (min_col < 0) min_col = 0;
								if (max_col >= NCols) max_col = NCols-1;

									//check whether surrounding pixels in all directions are equal to 0
								if (updated_raster[min_row][min_col]  != NoDataValue) {
									if (counts.at(0) == 0) {
										total_elev += updated_raster[min_row][min_col];
										n_obs++;
										counts.at(0) = 1;
									}
								}
								if (updated_raster[row][min_col]  != NoDataValue) {
									if (counts.at(1) == 0) {
										total_elev += updated_raster[row][min_col];
										n_obs++;
										counts.at(1) = 1;
									}
								}
								if (updated_raster[max_row][min_col]  != NoDataValue) {
									if (counts.at(2) == 0) {
										total_elev += updated_raster[max_row][min_col];
										n_obs++;
										counts.at(2) = 1;
									}
								}
								if (updated_raster[min_row][col]  != NoDataValue) {
									if (counts.at(3) == 0) {
										total_elev += updated_raster[min_row][col];
										n_obs++;
										counts.at(3) = 1;
									}
								}
								if (updated_raster[min_row][max_col]  != NoDataValue) {
									if (counts.at(4) == 0) {
										total_elev += updated_raster[min_row][max_col];
										n_obs++;
										counts.at(4) = 1;
									}
								}
								if (updated_raster[row][max_col]  != NoDataValue) {
									if (counts.at(5) == 0) {
										total_elev += updated_raster[row][max_col];
										n_obs++;
										counts.at(5) = 1;
									}
								}
								if (updated_raster[max_row][max_col]  != NoDataValue) {
									if (counts.at(6) == 0) {
										total_elev += updated_raster[max_row][max_col];
										n_obs++;
										counts.at(6) = 1;
									}
								}
								if (updated_raster[max_row][col] != NoDataValue) {
									if (counts.at(7) == 0) {
										total_elev += updated_raster[max_row][col];
										n_obs++;
										counts.at(7) = 1;
									}
								}

								// if 1s surround the pixel, then fill in the pixel
								if (counts.at(0) > 0 && counts.at(1) > 0 && counts.at(2) > 0 && counts.at(3) > 0 && counts.at(4) > 0 && counts.at(5) > 0 && counts.at(6) > 0 && counts.at(7) > 0)
								{
									this_sweep_data[row][col] = total_elev/float(n_obs);
									i = window_width+1;
								}
							}
						}
					}
	 		 	}
        break;
      }
      case(2):
      {
        // sweep 2
        for (int row=0; row<NRows; ++row)
        {
          for(int col=NCols-1; col>0; --col)
          {
           // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              total_elev = 0;
              n_obs = 0;
							vector<int> counts(8,0);

							for (int i = 1; i < window_width; i++)
							{
								//set exceptions for first or last row
								int min_row = row-i;
								int max_row = row+i;
								if (min_row < 0) min_row = 0;
								if (max_row >= NRows) max_row = NRows-1;

								//set exceptions for first or last col
								int min_col = col-i;
								int max_col = col+i;
								if (min_col < 0) min_col = 0;
								if (max_col >= NCols) max_col = NCols-1;

									//check whether surrounding pixels in all directions are equal to 0
								if (updated_raster[min_row][min_col]  != NoDataValue) {
									if (counts.at(0) == 0) {
										total_elev += updated_raster[min_row][min_col];
										n_obs++;
										counts.at(0) = 1;
									}
								}
								if (updated_raster[row][min_col]  != NoDataValue) {
									if (counts.at(1) == 0) {
										total_elev += updated_raster[row][min_col];
										n_obs++;
										counts.at(1) = 1;
									}
								}
								if (updated_raster[max_row][min_col]  != NoDataValue) {
									if (counts.at(2) == 0) {
										total_elev += updated_raster[max_row][min_col];
										n_obs++;
										counts.at(2) = 1;
									}
								}
								if (updated_raster[min_row][col]  != NoDataValue) {
									if (counts.at(3) == 0) {
										total_elev += updated_raster[min_row][col];
										n_obs++;
										counts.at(3) = 1;
									}
								}
								if (updated_raster[min_row][max_col]  != NoDataValue) {
									if (counts.at(4) == 0) {
										total_elev += updated_raster[min_row][max_col];
										n_obs++;
										counts.at(4) = 1;
									}
								}
								if (updated_raster[row][max_col]  != NoDataValue) {
									if (counts.at(5) == 0) {
										total_elev += updated_raster[row][max_col];
										n_obs++;
										counts.at(5) = 1;
									}
								}
								if (updated_raster[max_row][max_col]  != NoDataValue) {
									if (counts.at(6) == 0) {
										total_elev += updated_raster[max_row][max_col];
										n_obs++;
										counts.at(6) = 1;
									}
								}
								if (updated_raster[max_row][col] != NoDataValue) {
									if (counts.at(7) == 0) {
										total_elev += updated_raster[max_row][col];
										n_obs++;
										counts.at(7) = 1;
									}
								}
								// if 1s surround the pixel, then fill in the pixel
								if (counts.at(0) > 0 && counts.at(1) > 0 && counts.at(2) > 0 && counts.at(3) > 0 && counts.at(4) > 0 && counts.at(5) > 0 && counts.at(6) > 0 && counts.at(7) > 0)
								{
									this_sweep_data[row][col] = total_elev/float(n_obs);
									i = window_width+1;
								}
							}
						}
					}
	 		 	}
        break;
      }
      case(3):
      {
        // sweep 3
        for (int col=0; col<NCols; ++col)
        {
          for(int row=NRows-1; row>0; --row)
          {
            // if the node contains nodata, search the surrounding nodes
           // if the node contains nodata, search the surrounding nodes
            if(updated_raster[row][col] == NoDataValue)
            {
              total_elev = 0;
              n_obs = 0;
							vector<int> counts(8,0);

							for (int i = 1; i < window_width; i++)
							{
								//set exceptions for first or last row
								int min_row = row-i;
								int max_row = row+i;
								if (min_row < 0) min_row = 0;
								if (max_row >= NRows) max_row = NRows-1;

								//set exceptions for first or last col
								int min_col = col-i;
								int max_col = col+i;
								if (min_col < 0) min_col = 0;
								if (max_col >= NCols) max_col = NCols-1;

										//check whether surrounding pixels in all directions are equal to 0
								if (updated_raster[min_row][min_col]  != NoDataValue) {
									if (counts.at(0) == 0) {
										total_elev += updated_raster[min_row][min_col];
										n_obs++;
										counts.at(0) = 1;
									}
								}
								if (updated_raster[row][min_col]  != NoDataValue) {
									if (counts.at(1) == 0) {
										total_elev += updated_raster[row][min_col];
										n_obs++;
										counts.at(1) = 1;
									}
								}
								if (updated_raster[max_row][min_col]  != NoDataValue) {
									if (counts.at(2) == 0) {
										total_elev += updated_raster[max_row][min_col];
										n_obs++;
										counts.at(2) = 1;
									}
								}
								if (updated_raster[min_row][col]  != NoDataValue) {
									if (counts.at(3) == 0) {
										total_elev += updated_raster[min_row][col];
										n_obs++;
										counts.at(3) = 1;
									}
								}
								if (updated_raster[min_row][max_col]  != NoDataValue) {
									if (counts.at(4) == 0) {
										total_elev += updated_raster[min_row][max_col];
										n_obs++;
										counts.at(4) = 1;
									}
								}
								if (updated_raster[row][max_col]  != NoDataValue) {
									if (counts.at(5) == 0) {
										total_elev += updated_raster[row][max_col];
										n_obs++;
										counts.at(5) = 1;
									}
								}
								if (updated_raster[max_row][max_col]  != NoDataValue) {
									if (counts.at(6) == 0) {
										total_elev += updated_raster[max_row][max_col];
										n_obs++;
										counts.at(6) = 1;
									}
								}
								if (updated_raster[max_row][col] != NoDataValue) {
									if (counts.at(7) == 0) {
										total_elev += updated_raster[max_row][col];
										n_obs++;
										counts.at(7) = 1;
									}
								}
								// if 1s surround the pixel, then fill in the pixel
								if (counts.at(0) > 0 && counts.at(1) > 0 && counts.at(2) > 0 && counts.at(3) > 0 && counts.at(4) > 0 && counts.at(5) > 0 && counts.at(6) > 0 && counts.at(7) > 0)
								{
									this_sweep_data[row][col] = total_elev/float(n_obs);
									i = window_width+1;
								}
							}
						}
					}
	 		 	}
        break;
    	}
		}

		// increment the sweep number
    nsweep++;

  } while(nsweep < 4);

  LSDRaster Hole_filled_Raster(NRows,NCols,XMinimum,YMinimum,DataResolution,
                         int(NoDataValue),this_sweep_data,GeoReferencingStrings);
  return Hole_filled_Raster;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Isolate channelised portions of the landscape using the method proposed by Lashermes et
// al. (2007) Lashermes, B., E. Foufoula-Georgiou, and W. E. Dietrich (2007), Channel
// network extraction from high resolution topography using wavelets, Geophys. Res. Lett.,
// 34, L23S04, doi:10.1029/2007GL031140.
// This function (i) filters the DEM using a Gaussian filter; (ii) calculates the
// curvature and/or aspect; (iii) uses quantile quantile analysis to define a curvature
// threshold for channel initiation.
// DTM 06/02/2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::IsolateChannelsLashermesCurvature(float sigma, string q_q_filename)
{
  cout << "\t Isolation of channelised pixels using curvature" << endl;
  // filter
  cout << "\t\t Gaussian filter" << endl;
  LSDRaster FilteredTopo = GaussianFilter(sigma);
  // calculate curvature
  vector<LSDRaster> output_rasters;
  float window_radius = 1;
  vector<int> raster_selection(8,0.0);
  raster_selection[3]=1;
  cout << "\t\t Calculate curvature" << endl;
  output_rasters = FilteredTopo.calculate_polyfit_surface_metrics(window_radius, raster_selection);
  LSDRaster curvature = output_rasters[3];
  // use q-q plot to isolate the channels
  cout << "\t\t Finding threshold using q-q plot" << endl;
  LSDIndexRaster channels = curvature.IsolateChannelsQuantileQuantile(q_q_filename);
  return channels;
}
LSDIndexRaster LSDRaster::IsolateChannelsLashermesAspect(float sigma, string q_q_filename)
{
  // filter
  LSDRaster FilteredTopo = GaussianFilter(sigma);
  // calculate curvature
  vector<LSDRaster> output_rasters;
  float window_radius = 1;
  vector<int> raster_selection(8,0.0);
  raster_selection[2]=1;
  output_rasters = FilteredTopo.calculate_polyfit_surface_metrics(window_radius, raster_selection);
  LSDRaster aspect = output_rasters[2];
  // aspect is not a continuous function, so need to repeat with aspect origin rotate by 180 degrees.
  Array2D<float> aspect_temp = aspect.get_RasterData();
  for(int i = 0; i<NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if (aspect_temp[i][j]!=NoDataValue)
      {
         if(aspect_temp[i][j]<180) aspect_temp[i][j]+=180;
         else aspect_temp[i][j]-=180;
      }
    }
  }

  // calculate variability of slope direction d(pheta) = sqrt(d(pheta)/dy^2 + d(pheta)/dx^2)
  Array2D<float> d_pheta(NRows,NCols,NoDataValue);
  float d_pheta_dx,d_pheta_dy,d_pheta1,d_pheta2;
  for(int i = 1; i<NRows-1; ++i)
  {
    for(int j = 1; j < NCols-1; ++j)
    {
      if (aspect.get_data_element(i,j)!=NoDataValue && aspect.get_data_element(i-1,j)!=NoDataValue
       && aspect.get_data_element(i+1,j)!=NoDataValue && aspect.get_data_element(i,j+1)!=NoDataValue
       && aspect.get_data_element(i,j-1)!= NoDataValue)
      {
         d_pheta_dx = (aspect.get_data_element(i,j+1)-aspect.get_data_element(i,j-1))/(2*DataResolution);
         d_pheta_dy = (aspect.get_data_element(i+1,j)-aspect.get_data_element(i-1,j))/(2*DataResolution);
         d_pheta1=sqrt(d_pheta_dx*d_pheta_dx+d_pheta_dy*d_pheta_dy);
         // and for transformed aspects
         d_pheta_dx = (aspect_temp[i][j+1]-aspect_temp[i][j-1])/(2*DataResolution);
         d_pheta_dy = (aspect_temp[i+1][j]-aspect_temp[i-1][j])/(2*DataResolution);
         d_pheta2=sqrt(d_pheta_dx*d_pheta_dx+d_pheta_dy*d_pheta_dy);
         if(d_pheta2<d_pheta1) d_pheta[i][j] = d_pheta2;
         else d_pheta[i][j] = d_pheta1;
      }
    }
  }
  LSDRaster dpheta(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,d_pheta);
  // use q-q plot to isolate the channels
  LSDIndexRaster channels = dpheta.IsolateChannelsQuantileQuantile(q_q_filename);
  return channels;
}
LSDIndexRaster LSDRaster::IsolateChannelsLashermesFull(float sigma, string q_q_filename_prefix)
{
  string q_q_filename_aspect = q_q_filename_prefix + "_aspect.txt";
  string q_q_filename_curvature = q_q_filename_prefix + "_curvature.txt";
  LSDIndexRaster Channels1 = IsolateChannelsLashermesAspect(sigma, q_q_filename_aspect);
  LSDIndexRaster Channels2 = IsolateChannelsLashermesCurvature(sigma, q_q_filename_curvature);
  Array2D<int> binary_array(NRows,NCols,int(NoDataValue));
  for(int i = 1; i<NRows-1; ++i)
  {
    for(int j = 1; j < NCols-1; ++j)
    {
      if(Channels1.get_data_element(i,j)==1 && Channels2.get_data_element(i,j)==1) binary_array[i][j] = 1;
      else if(Channels1.get_data_element(i,j)==0 || Channels2.get_data_element(i,j)==0) binary_array[i][j] = 0;
    }
  }

  LSDIndexRaster channels(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary_array,GeoReferencingStrings);
  return channels;
}
// This version uses curvature and an upstream contributing area threshold
LSDIndexRaster LSDRaster::IsolateChannelsLashermesCurvatureArea(float sigma, float area_threshold, string q_q_filename)
{
  cout << "\t Isolation of channelised pixels using curvature" << endl;
  // filter
  cout << "\t\t Gaussian filter" << endl;
  LSDRaster FilteredTopo = GaussianFilter(sigma);
  // calculate curvature
  vector<LSDRaster> output_rasters;
  float window_radius = 1;
  vector<int> raster_selection(8,0.0);
  raster_selection[3]=1;
  cout << "\t\t Calculate curvature" << endl;
  output_rasters = FilteredTopo.calculate_polyfit_surface_metrics(window_radius, raster_selection);
  LSDRaster curvature = output_rasters[3];
  // use q-q plot to isolate the channels
  cout << "\t\t Finding threshold using q-q plot" << endl;
  LSDIndexRaster channels_init = curvature.IsolateChannelsQuantileQuantile(q_q_filename);
  // Calculate D_inf
  cout << "\t\t D_inf flow routing" << endl;
  LSDRaster Area = FilteredTopo.D_inf();
  // Reclassification of channel mask based on imposed threshold
  Array2D<int> binary_array = channels_init.get_RasterData();
  for(int i = 0; i<NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(channels_init.get_data_element(i,j)!=channels_init.get_NoDataValue())
      {
        if(Area.get_data_element(i,j)<=area_threshold) binary_array[i][j] = 0;
      }
    }
  }

  LSDIndexRaster channels(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary_array,GeoReferencingStrings);
  return channels;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Isolate channelised portions of the landscape using the method proposed by Passalacqua
// et al. (2010) A geometric framework for channel network extraction from lidar: Nonlinear
// diffusion and geodesic paths, J. Geophys. Res., 115(F1), F01002, doi:10.1029/2009JF001254.
//
// This function (i) filters the DEM using a Perona Malik filter; (ii) calculates the
// curvature; (iii) uses quantile quantile analysis to define a curvature threshold
// for channel initiation.
//
// DTM 21/04/2015
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=
LSDIndexRaster LSDRaster::IsolateChannelsGeonet(float timesteps, float area_threshold, float window_radius, string q_q_filename)
{
  cout << "\t Isolation of channelised pixels using curvature" << endl;
  // filter
  cout << "\t\t Perona Malik filter" << endl;
  float slope_percentile = 90;
  float dt = 0.1;
  LSDRaster FilteredTopo = PeronaMalikFilter(timesteps,slope_percentile,dt);
  // calculate curvature
  vector<LSDRaster> output_rasters;
//  float window_radius = 1;
  vector<int> raster_selection(8,0.0);
  raster_selection[3]=1;
  cout << "\t\t Calculate curvature" << endl;
  output_rasters = FilteredTopo.calculate_polyfit_surface_metrics(window_radius, raster_selection);
  LSDRaster curvature = output_rasters[3];
  // use q-q plot to isolate the channels
  cout << "\t\t Finding threshold using q-q plot" << endl;
  LSDIndexRaster channels_init = curvature.IsolateChannelsQuantileQuantile(q_q_filename);
  // Calculate D_inf
  cout << "\t\t D_inf flow routing" << endl;
  LSDRaster Area = FilteredTopo.D_inf();
  // Reclassification of channel mask based on imposed threshold
  Array2D<int> binary_array = channels_init.get_RasterData();
  for(int i = 0; i<NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(channels_init.get_data_element(i,j)!=channels_init.get_NoDataValue())
      {
        if(Area.get_data_element(i,j)<=area_threshold) binary_array[i][j] = 0;
      }
    }
  }

  LSDIndexRaster channels(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary_array,GeoReferencingStrings);
  return channels;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function does part (iii) of the above
LSDIndexRaster LSDRaster::IsolateChannelsQuantileQuantile(string q_q_filename)
{

  vector<float> values;
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j] != NoDataValue)
      {
        values.push_back(RasterData[i][j]);
      }
    }
  }

  vector<float> quantile_values,normal_variates,mn_values;
  int N_points = 10000;//values.size();
  quantile_quantile_analysis(values, quantile_values, normal_variates, mn_values, N_points);
  ofstream ofs;
  ofs.open(q_q_filename.c_str());

  if(ofs.fail())
  {
    cout << "\nFATAL ERROR: unable to write output_file" << endl;
    exit(EXIT_FAILURE);
  }
  ofs << "normal_variate value\n";
  int n_values = quantile_values.size();
  for(int i = 0; i<n_values;++i)
  {
    ofs << normal_variates[i] << " " << quantile_values[i] << " " << mn_values[i] << "\n";
  }
  ofs.close();

  // Find q-q threshold
  cout << "\t finding deviation from Gaussian distribution to define q-q threshold" << endl;
  vector<int> indices;
  int flag = 0;
  float threshold_condition=0.99;
  float curvature_threshold = 0.1;
  int threshold_index=0;
  for(int i = 0; i<n_values; ++i)
  {
    if(normal_variates[i] >= 0)
    {
      if(mn_values[i]<threshold_condition*quantile_values[i])
      {
        if (flag==0)
        {
          flag = 1;
//           curvature_threshold = quantile_values[i];
          threshold_index = i;
        }
      }
      else flag = 0;
    }
  }
  float mean_curvature = get_mean(values);
  float sd_curvature = get_standard_deviation(values,mean_curvature);
  curvature_threshold = mean_curvature+normal_variates[threshold_index]*sd_curvature;
  cout << "\t Creating channel raster based on curvature threshold (threshold = " << curvature_threshold << ")" << endl;
  Array2D<int> binary_raster(NRows,NCols,NoDataValue);
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j] != NoDataValue)
      {
        if(RasterData[i][j] >= curvature_threshold) binary_raster[i][j]=1;
        else binary_raster[i][j]=0;
      }
    }
  }
  cout << "DONE" << endl;
  LSDIndexRaster ChannelMask(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary_raster,GeoReferencingStrings);
  return ChannelMask;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
LSDIndexRaster LSDRaster::IsolateChannelsQuantileQuantileAdaptive(int half_width)
{
  cout << "Calculating adaptive curvature threshold" << endl;
  Array2D<float> curvature_threshold_array(NRows,NCols,NoDataValue);
  for(int i = 0; i < NRows; ++i)
  {
    cout << flush << "processing row " << i+1 << " of " << NRows << "\r" ;
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j]!=NoDataValue)
      {
        vector<float> values;
        for(int i_kernel = i-half_width; i_kernel < i+half_width; ++i_kernel)
        {
          for(int j_kernel = j-half_width; j_kernel < j+half_width; ++j_kernel)
          {
            if(i_kernel>=0 && i_kernel<NRows && j_kernel>=0 && j_kernel<NCols)
            {
              if(RasterData[i_kernel][j_kernel] != NoDataValue)
              {
                values.push_back(RasterData[i_kernel][j_kernel]);
              }
            }
          }
        }

        vector<float> quantile_values,normal_variates,mn_values;
        int N_points = 10000;//values.size();
        if(int(values.size())<10000) N_points = values.size();
        quantile_quantile_analysis(values, quantile_values, normal_variates, mn_values, N_points);

        // Find q-q threshold
        //cout << "\t finding deviation from Gaussian distribution to define q-q threshold" << endl;
        vector<int> indices;
        int flag = 0;
        float threshold_condition=0.99;
        float curvature_threshold = 0.1;
        int threshold_index=0;
        int n_values = quantile_values.size();
        for(int i_val = 0; i_val<n_values; ++i_val)
        {
          if(normal_variates[i_val] >= 0)
          {
            if(mn_values[i_val]<threshold_condition*quantile_values[i_val])
            {
              if (flag==0)
              {
                flag = 1;
//               curvature_threshold = quantile_values[i];
                threshold_index = i_val;
              }
            }
            else flag = 0;
          }
        }
        float mean_curvature = get_mean(values);
        float sd_curvature = get_standard_deviation(values,mean_curvature);
        curvature_threshold = mean_curvature+normal_variates[threshold_index]*sd_curvature;
        curvature_threshold_array[i][j] = curvature_threshold;
  // cout << "\t Creating channel raster based on curvature threshold (threshold = " << curvature_threshold << ")" << endl;
      }
    }
  }
  Array2D<int> binary_raster(NRows,NCols,NoDataValue);
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j] != NoDataValue)
      {
        if(RasterData[i][j] >= curvature_threshold_array[i][j]) binary_raster[i][j]=1;
        else binary_raster[i][j]=0;
      }
    }
  }
  cout << "DONE" << endl;
  LSDIndexRaster ChannelMask(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary_raster,GeoReferencingStrings);
  return ChannelMask;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function calculates the standard deviation of curvature values which
// varies across the landscape due to varying relief, slope, etc.
// The standard deviation of the curvature is used as the curvature threshold to
// find valleys to use in the DrEICH method.
//
// adapted from IsolateChannelsQuantileQuantileAdaptive to just use the
// standard deviation of the curvature rather than the qq plot
// FJC
// 20/07/15
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Array2D<float> LSDRaster::CalculateAdaptiveCurvatureThresholdSD(int half_width)
{
  cout << "Calculating adaptive curvature threshold" << endl;
  Array2D<float> curvature_threshold_array(NRows,NCols,NoDataValue);
  for(int i = 0; i < NRows; ++i)
  {
    cout << flush << "processing row " << i+1 << " of " << NRows << "\r" ;
    for(int j = 0; j < NCols; ++j)
    {
      if(RasterData[i][j]!=NoDataValue)
      {
        vector<float> values;
        for(int i_kernel = i-half_width; i_kernel < i+half_width; ++i_kernel)
        {
          for(int j_kernel = j-half_width; j_kernel < j+half_width; ++j_kernel)
          {
            if(i_kernel>=0 && i_kernel<NRows && j_kernel>=0 && j_kernel<NCols)
            {
              if(RasterData[i_kernel][j_kernel] != NoDataValue)
              {
                values.push_back(RasterData[i_kernel][j_kernel]);
              }
            }
          }
        }

        float mean_curvature = get_mean(values);
        float sd_curvature = get_standard_deviation(values,mean_curvature);
        curvature_threshold_array[i][j] = (2*sd_curvature);
        //cout << "Threshold: " << curvature_threshold_array[i][j] << endl;
  // cout << "\t Creating channel raster based on curvature threshold (threshold = " << curvature_threshold << ")" << endl;
      }
    }
  }
  return curvature_threshold_array;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Simple method to flatten an LSDRaster and place the non NDV values in a file.
// Each value is placed on its own line, so that it can be read more quickly in python etc.
// SWDG 9/2/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::FlattenToFile(string FileName){

  //open a file to write
  ofstream WriteData;
  WriteData.open(FileName.c_str());

  //loop over each cell and if there is a value, write it to the file
  for(int i = 0; i < NRows; ++i){
    for(int j = 0; j < NCols; ++j){
      if (RasterData[i][j] != NoDataValue){
        WriteData << RasterData[i][j] << endl;
      }
    }
  }

  WriteData.close();

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Method to flatten an LSDRaster and place the non NDV values in a csv file.
// Each value is placed on its own line, so that it can be read more quickly in python etc.
// It includes the x and y locations so it can be read by GIS software
// SMM 29/6/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::FlattenToCSV(string FileName_prefix)
{

  // append csv to the filename
  string FileName = FileName_prefix+".csv";

  //open a file to write
  ofstream WriteData;
  WriteData.open(FileName.c_str());

  WriteData.precision(8);
  WriteData << "x,y,value,latitude,longitude" << endl;

  // the x and y locations
  double x_loc, y_loc;
  double latitude,longitude;

  // this is for latitude and longitude
  LSDCoordinateConverterLLandUTM Converter;

  //loop over each cell and if there is a value, write it to the file
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        get_x_and_y_locations(i,j,x_loc,y_loc);
        get_lat_and_long_locations(i, j, latitude, longitude, Converter);

        WriteData << x_loc << "," << y_loc << "," << RasterData[i][j] << "," << latitude << "," << longitude << endl;
      }
    }
  }

  WriteData.close();

}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Method to flatten an LSDRaster and place the non NDV values in a csv file.
// Each value is placed on its own line, so that it can be read more quickly in python etc.
// It includes only lat long in WGS1984 so it can be read by GIS software
// SMM 12/11/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDRaster::FlattenToWGS84CSV(string FileName_prefix)
{

  // append csv to the filename
  string FileName = FileName_prefix+".csv";

  //open a file to write
  ofstream WriteData;
  WriteData.open(FileName.c_str());

  WriteData.precision(8);
  WriteData << "latitude,longitude,value" << endl;

  // the x and y locations
  double latitude,longitude;

  // this is for latitude and longitude
  LSDCoordinateConverterLLandUTM Converter;

  //loop over each cell and if there is a value, write it to the file
  for(int i = 0; i < NRows; ++i)
  {
    for(int j = 0; j < NCols; ++j)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        get_lat_and_long_locations(i, j, latitude, longitude, Converter);

        WriteData << latitude << "," << longitude << "," << RasterData[i][j] << endl;
      }
    }
  }

  WriteData.close();

}



//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to convert an LSDRaster hilltop file into a series of contiguous hilltop patches.
//
//Connects all contiguous patches of hilltop via a unique ID, allowing hilltop patches
//to be generated in a manner similar to the methodology employed by Hurst et al. (2012) and (2013)
//to spatially average data for E*R* calculations. Currently has no method to limit the maximum size
//of segments.
//Requires an integer minimum_patch_size, the minimum number of pixels required for a patch to be created
//SWDG
//5/6/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

LSDIndexRaster LSDRaster::CreateHilltopPatchesNEW(int minimum_patch_size){

  Array2D<int> hilltops(NRows,NCols,int(NoDataValue));
  for(int i = 1; i<NRows-1; ++i){
    for(int j = 1; j<NCols-1; ++j){
      if(RasterData[i][j]!=NoDataValue) hilltops[i][j] = 1;
    }
  }
  LSDIndexRaster HilltopPatches(NRows,NCols,XMinimum,YMinimum,DataResolution,int(NoDataValue),hilltops);
  HilltopPatches = HilltopPatches.filter_by_connected_components(minimum_patch_size);
  HilltopPatches = HilltopPatches.ConnectedComponents();
  return HilltopPatches;
}

LSDIndexRaster LSDRaster::CreateHilltopPatches(int minimum_patch_size){

  //create array to hold patch IDs
  Array2D<int> PatchIDs(NRows,NCols,NoDataValue);

  //define some variables we will use
  bool Neighbours = true;
  int ID = 0;
  int a;
  int b;
  bool clashes = false;
  int center_value;
  int value_to_replace;

  cout << "\n\tAssigning Unique Patch IDs to all hilltop pixels." << endl;

  //cycle over every cell and find connected patches, giving each patch a unique ID
  for(int i = 1; i < NRows-1; ++i){
    for(int j = 1; j < NCols-1; ++j){

      //if the pixel has data it is a hilltop and if it has not been assigned a patchID we must visit it
      if (RasterData[i][j] != NoDataValue && PatchIDs[i][j] == NoDataValue){

        //increment the ID value, to make sure each patch has a unique ID
        ++ID;

        //we have our first px
        a = i;
        b = j;

        //need this set to true to start the loop, does not matter if the initial cell has no
        //neighbours, this will be caught on the first iteration of the loop
        Neighbours = true;

        // edge checking now in every initial neighbour search.
        // if the index is not changing eg i-1,j do we need to check if j is at an edge?

        //now use a while loop to scan thru it's neighbours
        while (Neighbours == true && PatchIDs[a][b] == NoDataValue){
          PatchIDs[a][b] = ID;
          //perform check to find neighbours clockwise from NW
          if (RasterData[a-1][b-1] != NoDataValue && PatchIDs[a-1][b-1] == NoDataValue && (((a-1) != (NRows-1) || (a-1) != 0) || (b-1) != (NCols-1) || (b-1) != 0)){
            --a;
            --b;
          }
          else if (RasterData[a][b-1] != NoDataValue && PatchIDs[a][b-1] == NoDataValue && (((a) != (NRows-1) || (a) != 0) || (b-1) != (NCols-1) || (b-1) != 0)){
            --b;
          }
          else if (RasterData[a+1][b-1] != NoDataValue && PatchIDs[a+1][b-1] == NoDataValue && (((a+1) != (NRows-1) || (i+1) != 0) || (b-1) != (NCols-1) || (b-1) != 0)){
            ++a;
            --b;
          }
          else if (RasterData[a+1][b] != NoDataValue && PatchIDs[a+1][b] == NoDataValue && (((a+1) != (NRows-1) || (a+1) != 0) || (b) != (NCols-1) || (b) != 0)){
            ++a;
          }
          else if (RasterData[a+1][b+1] != NoDataValue && PatchIDs[a+1][b+1] == NoDataValue && (((a+1) != (NRows-1) || (a+1) != 0) || (b+1) != (NCols-1) || (b+1) != 0)){
            ++a;
            ++b;
          }
          else if (RasterData[a][b+1] != NoDataValue && PatchIDs[a][b+1] == NoDataValue && (((a) != (NRows-1) || (a) != 0) || (b+1) != (NCols-1) || (b+1) != 0)){
            ++b;
          }
          else if (RasterData[a-1][b+1] != NoDataValue && PatchIDs[a-1][b+1] == NoDataValue && (((a-1) != (NRows-1) || (a-1) != 0) || (b+1) != (NCols-1) || (b+1) != 0)){
            --a;
            ++b;
          }
          else if (RasterData[a-1][b] != NoDataValue && PatchIDs[a-1][b] == NoDataValue && (((a-1) != (NRows-1) || (a-1) != 0) || (b) != (NCols-1) || (b) != 0)){
            --a;
          }
          else{
          //no neighbours
          Neighbours = false; //ends while loop
          }
        }
      }
    }
  }

  //first pass over dem is complete, now need to merge any patches which have
  //different IDs but are spatially contiguous, "Clashes"

  cout << "\tLooking for contiguous patches that do not share an ID." << endl;
  cout << "\t\tThis may take several minutes in complex terrain..." << endl;

  //start scanning PatchIDs array to find clashes
  for(int i = 1; i < NRows-1; ++i){
    for(int j = 1; j < NCols-1; ++j){
      if (PatchIDs[i][j] != NoDataValue){

        center_value = PatchIDs[i][j];

        //again cycle from NW clockwise round neighbours
        //edge detection is very explicit. Will rewrite to make more implicit
        //but this will have little impact on peformance as I think this will
        //already be optimised at compile time.

        //check all neighbour's values to see if they match the central cell
        if (PatchIDs[i-1][j-1] != center_value && PatchIDs[i-1][j-1] != NoDataValue && (((i-1) != (NRows-1) || (i-1) != 0) || (j-1) != (NCols-1) || (j-1) != 0)){
         value_to_replace = PatchIDs[i-1][j-1];
         clashes = true;
        }
        else if (PatchIDs[i][j-1] != center_value && PatchIDs[i][j-1] != NoDataValue && (((i) != (NRows-1) || (i) != 0) || (j-1) != (NCols-1) || (j-1) != 0)){
         value_to_replace = PatchIDs[i][j-1];
         clashes = true;
        }
        else if (PatchIDs[i+1][j-1] != center_value && PatchIDs[i+1][j-1] != NoDataValue && (((i+1) != (NRows-1) || (i+1) != 0) || (j-1) != (NCols-1) || (j-1) != 0)){
         value_to_replace = PatchIDs[i+1][j-1];
         clashes = true;
        }
        else if (PatchIDs[i+1][j] != center_value && PatchIDs[i+1][j] != NoDataValue && (((i+1) != (NRows-1) || (i+1) != 0) || (j) != (NCols-1) || (j) != 0)){
         value_to_replace = PatchIDs[i+1][j];
         clashes = true;
        }
        else if (PatchIDs[i+1][j+1] != center_value && PatchIDs[i+1][j+1] != NoDataValue && (((i+1) != (NRows-1) || (i+1) != 0) || (j+1) != (NCols-1) || (j+1) != 0)){
         value_to_replace = PatchIDs[i+1][j+1];
         clashes = true;
        }
        else if (PatchIDs[i][j+1] != center_value && PatchIDs[i][j+1] != NoDataValue && (((i) != (NRows-1) || (i) != 0) || (j+1) != (NCols-1) || (j+1) != 0)){
         value_to_replace = PatchIDs[i][j+1];
         clashes = true;
        }
        else if (PatchIDs[i-1][j+1] != center_value && PatchIDs[i-1][j+1] != NoDataValue && (((i-1) != (NRows-1) || (i-1) != 0) || (j+1) != (NCols-1) || (j+1) != 0)){
         value_to_replace = PatchIDs[i-1][j+1];
         clashes = true;
        }
        else if (PatchIDs[i-1][j] != center_value && PatchIDs[i-1][j] != NoDataValue && (((i-1) != (NRows-1) || (i-1) != 0) || (j) != (NCols-1) || (j) != 0)){
         value_to_replace = PatchIDs[i-1][j];
         clashes = true;
        }
        else{
         //no clashes!
         clashes = false;
        }

        //if clashes are present, loop over PatchIDs and fix the clash by updataing the
        //IDs of the clashing patches to match.
        if (clashes == true){

          for(int q = 1; q < NRows-1; ++q){
            for(int w = 1; w < NCols-1; ++w){

              if (PatchIDs[q][w] == value_to_replace){
                PatchIDs[q][w] = center_value;
              }
            }
          }

        //reset initial scan through DEM until it makes it through clean with no clashes
        i = 0;
        j = 0;

        }
      }
    }
  }

  //Strip out any values that only occur below the minimum_segment_size param value
  cout << "\tRemoving patches that have an area smaller than " << minimum_patch_size << " pixels." << endl;

  //flatten the array to make the counting easier
  vector<int> Flat_Patches = Flatten_Without_Nodata(PatchIDs, NoDataValue);

  //get unique patch IDs
  vector<int> Unique_Patches = Unique(PatchIDs, NoDataValue);

  //get number of instances of each value in the vector as a map
  map<int,int> Counts;
  Count_Instances(Flat_Patches,Unique_Patches,Counts);

  //loop over map, get vector of keys where value < user defined limit and store patchIDs to be removed as vector
  vector<int> PatchesToRemove;
  vector<int> PatchesToShorten;

  for (int w = 0; w< int(Unique_Patches.size());++w){

    if (Counts[Unique_Patches[w]] < minimum_patch_size){
      PatchesToRemove.push_back(Unique_Patches[w]);
    }
  }

  //need to handle a vector of zero length (eg all patches are long enough)
  if (!PatchesToRemove.empty()){

    //loop over PatchIDs, checking each value for membership in the vector of values to be removed, and if true, set cell value to NDV
    for(int i = 1; i < NRows-1; ++i){
      for(int j = 1; j < NCols-1; ++j){

        if (PatchIDs[i][j] != NoDataValue){

          if (find(PatchesToRemove.begin(), PatchesToRemove.end(), PatchIDs[i][j]) != PatchesToRemove.end()){
            //the PatchID has been marked for removal, so change it to NDV
            PatchIDs[i][j] = NoDataValue;
          }
        }
      }
    }


  }
  else{
    cout << "\t\tNo patches below the threshold." << endl;
  }

  //create the final LSDIndexRaster and return it
  LSDIndexRaster Patches(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,PatchIDs,GeoReferencingStrings);
  return Patches;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Simple method to remove any values below a user supplied value from an LSDRaster.
//
// Value is a float of the threshold below which values will be removed.
// SWDG 22/6/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::RemoveBelow(float Value){

  Array2D<float> Data = RasterData.copy();

    for(int i = 1; i < NRows-1; ++i){
      for(int j = 1; j < NCols-1; ++j){

        if (Data[i][j] != NoDataValue && Data[i][j] < Value){

          Data[i][j] = NoDataValue;

        }
      }
    }

  LSDRaster Removed(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Data,GeoReferencingStrings);
  return Removed;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Simple method to remove any values above a user supplied value from an LSDRaster.
//
// Value is a float of the threshold above which values will be removed.
// SWDG 25/11/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::RemoveAbove(float Value){

  Array2D<float> Data = RasterData.copy();

    for(int i = 1; i < NRows-1; ++i){
      for(int j = 1; j < NCols-1; ++j){

        if (Data[i][j] != NoDataValue && Data[i][j] > Value){

          Data[i][j] = NoDataValue;

        }
      }
    }

  LSDRaster Removed(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Data,GeoReferencingStrings);
  return Removed;

}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// Apply a mask to an LSDRaster.  Mask designated by LSDIndexRaster containing 1
// values for the pixels that need to be converted to nodata
// DTM 25/08/2015
LSDRaster LSDRaster::apply_mask(LSDIndexRaster& mask){
  Array2D<float> masked_data = RasterData.copy();
  for(int i=0; i<NRows; ++i){
    for(int j=0; j<NCols; ++j){
  if(mask.get_data_element(i,j)==1) masked_data[i][j]=NoDataValue;
    }
  }
  LSDRaster masked_raster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,masked_data,GeoReferencingStrings);
  return masked_raster;
}


//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to convert all values in an LSDIndexRaster to a single value
// SWDG 24/7/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDIndexRaster LSDRaster::ConvertToBinary(int Value, int ndv){

  Array2D<int> binary(NRows,NCols,NoDataValue);

  for(int i = 0; i < NRows; ++i){
    for(int j = 0; j < NCols; ++j){
      if (RasterData[i][j] != NoDataValue && RasterData[i][j] != ndv){
        binary[i][j] = Value;
      }
    }
  }

  LSDIndexRaster binmask(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,binary,GeoReferencingStrings);
  return binmask;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to merge data from two LSDRasters WITH SAME EXTENT together.  The data from the
// raster specified as an argument will be added (will overwrite the original raster if there
// is a conflict).
// FJC 30/09/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::MergeRasters(LSDRaster& RasterToAdd)
{
	Array2D<float> SecondRasterData = RasterToAdd.get_RasterData();
	Array2D<float> NewRasterData(NRows,NCols,NoDataValue);

	for (int row = 0; row < NRows; row++)
	{
		for (int col = 0; col < NCols; col++)
		{
			// no data in first raster, data in second raster
			if (RasterData[row][col] == NoDataValue && SecondRasterData[row][col] != NoDataValue)
			{
				NewRasterData[row][col] = SecondRasterData[row][col];
			}
			// data in first raster, no data in second raster
			else if (RasterData[row][col] != NoDataValue && SecondRasterData[row][col] == NoDataValue)
			{
				NewRasterData[row][col] = RasterData[row][col];
			}
			// data in both rasters - select data from the second raster
			else if (RasterData[row][col] != NoDataValue && SecondRasterData[row][col] != NoDataValue)
			{
				NewRasterData[row][col] = SecondRasterData[row][col];
			}
		}
	}

	LSDRaster NewRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,NewRasterData,GeoReferencingStrings);
	return NewRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Method to merge data from two LSDRasters WITH SAME EXTENT together.  The data from the
// raster specified as an argument will be added (will overwrite the original raster if there
// is a conflict).
// Overloaded function that overwrites the raster rather than creating a new one.
// FJC 07/04/17
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::OverwriteRaster(LSDRaster& RasterToAdd)
{
	Array2D<float> SecondRasterData = RasterToAdd.get_RasterData();

	for (int row = 0; row < NRows; row++)
	{
		for (int col = 0; col < NCols; col++)
		{
			// no data in first raster, data in second raster
			if (SecondRasterData[row][col] != NoDataValue)
			{
				RasterData[row][col] = SecondRasterData[row][col];
			}
		}
	}
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function to get potential floodplain patches using a slope and relief threshold
// FJC 20/10/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDIndexRaster LSDRaster::get_potential_floodplain_patches(LSDRaster& Relief, LSDRaster& Slope, float relief_threshold, float slope_threshold)
{
  Array2D<int> FloodplainArray(NRows,NCols,0);

  //loop through every row and col and get the slope and relief values
  for (int i =0; i < NRows; i++)
  {
    for (int j = 0; j < NCols; j++)
    {
      if (Relief.get_data_element(i,j) != NoDataValue && Slope.get_data_element(i,j) != NoDataValue)
      {
        float slope = Slope.get_data_element(i,j);
        float relief = Relief.get_data_element(i,j);
        if (relief < relief_threshold && slope < slope_threshold)        //floodplain points must be lower than both the relief
        {                                                                //and the slope threshold.
          FloodplainArray[i][j] = 1;
        }
      }
    }
  }

  LSDIndexRaster FloodplainRaster(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,FloodplainArray,GeoReferencingStrings);
  return FloodplainRaster;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function to set the threshold value to use in floodplain extraction
// FJC 16/11/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
float LSDRaster::get_threshold_for_floodplain(float bin_width, float peak_threshold, int peak_distance)
{
  //get vector of raster data
  vector<float> raster_vector;
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      if(RasterData[row][col] >= 0) raster_vector.push_back(RasterData[row][col]);
    }
  }

  //get histogram of the raster values
  vector<float> Midpoints;
  vector<float> LLims;
  vector<float> ULims;
  vector<int> Count;
  vector<float> ProbabilityDensity;
  calculate_histogram(raster_vector, bin_width, Midpoints, LLims, ULims, Count, ProbabilityDensity);

  //get peaks from histogram
  vector<int> peak_indices;
  get_peak_indices(ProbabilityDensity, peak_threshold, peak_distance, peak_indices);

  //using second peak as the floodplain: get the midpoint of the bin with the peak
  float threshold = Midpoints[peak_indices[1]];
  cout << "Threshold value: " << threshold << endl;

  return threshold;
}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Function to set the threshold value to use in floodplain extraction using QQ plots
// FJC 16/11/15
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
float LSDRaster::get_threshold_for_floodplain_QQ(string q_q_filename, float threshold_condition, int lower_percentile, int upper_percentile)
{
  //get vector of raster data
  vector<float> raster_vector;
  for (int row = 0; row < NRows; row++)
  {
    for (int col = 0; col < NCols; col++)
    {
      if(RasterData[row][col] >= 0) raster_vector.push_back(RasterData[row][col]);
    }
  }

  vector<float> quantile_values,normal_variates,mn_values;
  int N_points = 10000;//values.size();
  quantile_quantile_analysis_defined_percentiles(raster_vector, quantile_values, normal_variates, mn_values, N_points, lower_percentile, upper_percentile);
  ofstream ofs;
  ofs.open(q_q_filename.c_str());

  if(ofs.fail())
  {
    cout << "\nFATAL ERROR: unable to write output_file" << endl;
    exit(EXIT_FAILURE);
  }
  ofs << "normal_variate value\n";
  int n_values = quantile_values.size();
  for(int i = 0; i<n_values;++i)
  {
    ofs << normal_variates[i] << " " << quantile_values[i] << " " << mn_values[i] << "\n";
  }
  ofs.close();

  //get range of values - used to get the threshold value
  float range = get_range_from_vector(quantile_values, NoDataValue);
  cout << "Range: " << range << endl;

  // Find q-q threshold
  cout << "\t finding deviation from Gaussian distribution to define q-q threshold" << endl;
  int flag = 0;
  float threshold=0;
  float min_length=200;

  for (int i =0; i < n_values; i++)
  {
    //if (normal_variates[i] <= 0)
    //{
      // get difference between real and normal distributions
		float diff = abs(quantile_values[i] - mn_values[i]);
		// express as fraction of the range of data
		float frac_diff = diff/range;
		if (frac_diff < threshold_condition)
		{
			// first time the condition is fulfilled
			if (flag == 0)
			{
				flag = 1;
				int count = 0;
				//search next points to check if they also fulfil the condition
				for (int j = 1; j <= min_length; j++)
				{
					float next_diff = abs(quantile_values[i+j] - mn_values[i+j]);
					float next_frac = next_diff/range;
					if (next_frac < threshold_condition) count++;
				}
				//cout << "Count is: " << count << endl;
				if (count == min_length)
				{
					threshold = quantile_values[i];
					cout << "Quantile value at threshold: " << quantile_values[i] << " Normal variate: " <<  normal_variates[i] << endl;
				}
				else flag = 0;
			}
      }
   // }
  }

  return threshold;
}

// Get the lengths in spatial units of each part of the channel network, divided by strahler order.
// Returns a string containing the comma separated lengths
// SWDG 17/1/16
string LSDRaster::ChannelLengthByOrder(LSDIndexRaster& StreamNetwork, Array2D<int> FlowDir){

  //Declare all the variables needed in this method
  float two_times_root2 = 2.828427;
  vector<float> Lengths;
  vector<float> SortedLengths;
  vector<int> IDs;
  vector<int> IDs_sorted;
  vector<size_t> index_map;
  int q = 0;
  float length_sum = 0;
  map <int,float> Order_Length; //structure to hold pairs of length values with a basin ID as a key

  //Loop over every pixel and record it's stream length and order in two vectors
  for (int i = 0; i < NRows; ++i){
    for (int j = 0; j < NCols; ++j){

      if (StreamNetwork.get_data_element(i,j) != NoDataValue){
        if ((FlowDir[i][j] % 2) != 0 && (FlowDir[i][j] != -1 )){ //is odd but not -1
          Lengths.push_back(DataResolution * two_times_root2); //diagonal
          IDs.push_back(StreamNetwork.get_data_element(i,j));
        }
        else if (FlowDir[i][j] % 2 == 0){  //is even
          Lengths.push_back(DataResolution); //cardinal
          IDs.push_back(StreamNetwork.get_data_element(i,j));
        }
      }
    }
  }

  //sort our two vectors based on the Basin IDs: has the effect of grouping each order together in 1D space
  matlab_int_sort(IDs, IDs_sorted, index_map);
  matlab_float_reorder(Lengths, index_map, SortedLengths);

  // get the first order
  int start_id = IDs_sorted[0];

  while (q < int(IDs_sorted.size())){
    if (start_id == IDs_sorted[q]){
      length_sum += SortedLengths[q];
      ++q;
    }
    else{
      Order_Length[start_id]=(length_sum);   //record the total length the order as a key
      length_sum = 0;
      start_id = IDs_sorted[q];
    }
  }

  // Process the final order once the loop is completed
  Order_Length[start_id]=(length_sum);


  // set up iterator to cycle through the map
  map<int, float>::iterator it;

  stringstream Output;

  for (it = Order_Length.begin(); it != Order_Length.end(); it++){
    Output << it->second << ",";
  }

  return Output.str();

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
/// Populate a raster with random noise drawn from a gaussian distribution of given mean and minimum values.
/// SWDG 9/6/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::PoupulateRasterGaussian(float minimum, float mean){

  bool allowNegative = false;
  Array2D<float> Gauss(NRows, NCols, NoDataValue);

  for (int i = 1; i < NRows - 1; ++i){
    for (int j = 1; j < NCols - 1; ++j){

      if (RasterData[i][j] != NoDataValue){
        Gauss[i][j] = getGaussianRandom(minimum, mean, allowNegative);
      }
    }
  }

  LSDRaster output(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Gauss,GeoReferencingStrings);
  return output;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
/// Populate a raster with a given value.
/// SWDG 9/6/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
LSDRaster LSDRaster::PoupulateRasterSingleValue(float value){

  Array2D<float> Single(NRows, NCols, NoDataValue);

  for (int i = 1; i < NRows - 1; ++i){
    for (int j = 1; j < NCols - 1; ++j){

      if (RasterData[i][j] != NoDataValue){
        Single[i][j] = value;
      }
    }
  }

  LSDRaster output(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,Single,GeoReferencingStrings);
  return output;

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Write CHT and hilltop gradient data to a *.csv file, coded by UTM coordinates as well
// as lat/long.
// SWDG 2/11/16
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
void LSDRaster::HilltopsToCSV(LSDRaster& CHT, LSDRaster& CHT_gradient, LSDRaster& gradient, int UTMZone, bool isNorth, int eId, string filename){

  vector<float> CHT_1D = Flatten(CHT.get_RasterData());
  vector<float> sorted;
  vector<size_t> index_map;
  vector<string> Data;

  //sort the 1D elevation vector and produce an index
  matlab_float_sort_descending(CHT_1D, sorted, index_map);

  int q = 0;

  //Tests if the sorted vector has NDV at the front or back. We need them at the end.
  //This can fail if you have  strange NDV value that is not a low or high number.
  if (sorted[q] == NoDataValue){
    matlab_float_sort(CHT_1D, sorted, index_map);
  }

  while (sorted[q] != NoDataValue){

    int gradient_flag = 1; //0 == above threshold, 1 == below threshold
    double Lat;
    double Long;

    //use row major ordering to reconstruct each cell's i,j coordinates
    int i = index_map[q] / NCols;
    int j = index_map[q] % NCols;

    //reconstruct UTM
    double UTMe = XMinimum + float(j)*DataResolution + 0.5*DataResolution;
    double UTMn = YMinimum + float(NRows-i)*DataResolution - 0.5*DataResolution;

    //reconstruct lat long
    LSDCoordinateConverterLLandUTM Converter;
    Converter.UTMtoLL(eId, UTMn, UTMe, UTMZone, isNorth, Lat, Long);

    if (CHT_gradient.get_data_element(i, j) == NoDataValue){
      gradient_flag = 0;
    }

    //Build a csv string containing the results
    stringstream ss;
    ss << setiosflags(ios::fixed) << setprecision(7) << q << "," << UTMe << "," << UTMn << "," << Lat << "," << Long << "," << CHT.get_data_element(i, j) << "," << gradient_flag << "," << gradient.get_data_element(i, j);

    Data.push_back(ss.str());
    ++q;

  }

  ofstream WriteData;
  WriteData.open(filename.c_str());

  WriteData << "_ID,Easting,Northing,Lat,Long,CHT,gradient_flag,gradient" << endl;

  for (int w = 0; w < int(Data.size());++w){
    WriteData << Data[w] << endl;
  }

  WriteData.close();

}

//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// Sample the values of 3 input rasters that intersect with the point a,b within
// the area defined by threshold
// SWDG 23/1/17
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
vector< vector<float> > LSDRaster::Sample_Along_Ridge(LSDRaster& Raster1, LSDRaster& Raster2, LSDRaster& Raster3, int a, int b, int threshold){

  vector<int> sorted;
  vector<size_t> index_map;
  vector<size_t> index_map_2;
  vector<int> sub_map;
  vector<float> dists;
  vector<float> sorted_dists;

  LSDIndexRaster BinaryHilltops = Raster1.ConvertToBinary(1, NoDataValue);
  LSDIndexRaster HilltopPatches = BinaryHilltops.ConnectedComponents();

  int ID = HilltopPatches.get_data_element(a, b);

  vector<int> Flat = Flatten(HilltopPatches.get_RasterData());

  //sort the 1D elevation vector and produce an index
  matlab_int_sort(Flat, sorted, index_map);


  for(int q = 0; q < int(Flat.size()); ++q){ //switch to while sorted[q] <= ID

    if (sorted[q] == ID){

      //use row major ordering to reconstruct each cell's i,j coordinates
      int i = index_map[q] / NCols;
      int j = index_map[q] % NCols;

      dists.push_back(distbetween(a,b,i,j));
      sub_map.push_back(int(index_map[q]));
    }
  }

  matlab_float_sort(dists, sorted_dists, index_map_2);

  vector<float> Sample1;
  vector<float> Sample2;
  vector<float> Sample3;
  vector< vector<float> > Vector_of_Samples;
  Vector_of_Samples.reserve(3); //pre-allocate memory for this vector

  if (int(dists.size()) < threshold){
    threshold = int(dists.size());
    cout << "Threshold is larger than the number of pixels in the hilltop segment" << endl;
  }

  for(int w = 0; w < threshold; ++w){

    int tmp_i = sub_map[index_map_2[w]] / NCols;
    int tmp_j = sub_map[index_map_2[w]] % NCols;

    Sample1.push_back(Raster1.get_data_element(tmp_i, tmp_j));
    Sample2.push_back(Raster2.get_data_element(tmp_i, tmp_j));
    Sample3.push_back(Raster3.get_data_element(tmp_i, tmp_j));
  }

  Vector_of_Samples.push_back(Sample1);
  Vector_of_Samples.push_back(Sample2);
  Vector_of_Samples.push_back(Sample3);

  return Vector_of_Samples;
}

//-----------------------------------------------------------------------------//
// Function for converting elevation values in a raster from feet to metres for
// stupid US imperial measurements
// WHY WOULD YOU USE FEET?!
// FJC 16/10/17
//-----------------------------------------------------------------------------//
LSDRaster LSDRaster::convert_from_feet_to_metres()
{
  Array2D<float> elev_in_metres(NRows,NCols,NoDataValue);
  double conversion = 0.3048006096012192;

  for (int i = 0; i < NRows; i++)
  {
    for (int j = 0; j < NCols; j++)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        elev_in_metres[i][j] = RasterData[i][j] * conversion;
      }
    }
  }

  LSDRaster output(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,elev_in_metres,GeoReferencingStrings);
  return output;

}

//-----------------------------------------------------------------------------//
// Function for converting elevation values in a raster from centimetres to metres.
// This is possibly even more stupid than using feet.
// FJC 18/10/17
//-----------------------------------------------------------------------------//
LSDRaster LSDRaster::convert_from_centimetres_to_metres()
{
  Array2D<float> elev_in_metres(NRows,NCols,NoDataValue);

  for (int i = 0; i < NRows; i++)
  {
    for (int j = 0; j < NCols; j++)
    {
      if (RasterData[i][j] != NoDataValue)
      {
        elev_in_metres[i][j] = RasterData[i][j]/100;
      }
    }
  }

  LSDRaster output(NRows,NCols,XMinimum,YMinimum,DataResolution,NoDataValue,elev_in_metres,GeoReferencingStrings);
  return output;

}


//-----------------------------------------------------------------------------//
// Attempt to port the breaching algorithm from RichDEM without getting the entire package
// Probably still experimental
// Original method from Lindsay et al., 2016 DOI:https://doi.org/10.1002/hyp.10648
// BG 2018
//-----------------------------------------------------------------------------//
LSDRaster LSDRaster::Breaching_Lindsay2016()
{
  cout << "I am going to carve/breach your depressions in order to force flow paths." << endl;
  cout << "I am using an algorithm from Lindsay et al., 2016 DOI:https://doi.org/10.1002/hyp.10648" << endl;
  cout << "Implementation adapted from RichDEM: https://github.com/r-barnes/richdem" << endl;
  cout << "Not widely tested yet, It may break..." << endl;

  const uint32_t NO_BACK_LINK = std::numeric_limits<uint32_t>::max();

  Array2D<float> tRasterData = RasterData.copy();

  LSDIndexRaster izEDj = find_cells_bordered_by_nodata();

  // This raster is a bit obscur to me so far
  Array2D<uint32_t> backlinks(NRows,NCols, NO_BACK_LINK);
  // Visited represent the stage of all cells
  // 0-> Unprocessed
  // 1-> EDGE 
  Array2D<uint8_t> visited(NRows,NCols);
  Array2D<uint8_t> pits(NRows,NCols);
  // cout << "1" << endl;
  for(int i=0;i<NRows;i++)
  for(int j=0;j<NCols;j++)
  {
    visited[i][j] = 0;
    pits[i][j] = 0;
  }
  // cout << "2" << endl;

  vector<uint32_t> flood_array;
  priority_queue< FillNode, vector<FillNode>, greater<FillNode> > pq;
  uint32_t total_pits = 0;

  // visited.setAll(LindsayCellType::UNVISITED);

  // cout << "3" << endl;

  //Seed the priority queue
  // RDLOG_PROGRESS<<"Identifying pits and edge cells...";
  for(int y=0;y<NRows;y++)
  for(int x=0;x<NCols;x++)
  {
    // cout << "5" << endl;

    if(tRasterData[y][x]==NoDataValue)             //Don't evaluate NoData cells
    {
      continue;
    }
      FillNode guest;
      guest.RowIndex = y;
      guest.ColIndex = x;
      guest.Zeta = tRasterData[y][x];

    if(izEDj.get_data_element(y,x)==1)
    {
      //Valid edge cells go on priority-queue
      pq.push(guest);
      visited[y][x] = 1;
      continue;
    }
    // cout << "6" << endl;

    //Determine if this is an edge cell, gather information used to determine if
    //it is a pit cell
    float lowest_neighbour = std::numeric_limits<float>::max();    
    for(int n=-1;n<=1;n++)
    for(int n2=-1;n2<=1;n2++)
    {
      if(n==0 && n2==0)
        continue;

      //const int nx = x+n;
      //const int ny = y+n2;
      
      //No need for an inGrid check here because edge cells are filtered above
      // TOCHECK -> BG

      //Cells which can drain into NoData go on priority-queue as edge cells
      if(tRasterData[y][x]==NoDataValue){        
        pq.push(guest);
        visited[y][x] = 1;
        goto nextcell;                //VELOCIRAPTOR
      }

      //Used for identifying the lowest neighbour
      lowest_neighbour = std::min(tRasterData[y][x],lowest_neighbour);
    }
    // cout << "7" << endl;

    //This is a pit cell if it is lower than any of its neighbours. In this
    //case: raise the cell to be just lower than its lowest neighbour. This
    //makes the breaching/tunneling procedures work better. Since depressions
    //might have flat bottoms, we treat flats as pits. Mark flat/pits as such
    //now.
    if(tRasterData[y][x]<=lowest_neighbour){
      tRasterData[y][x] = lowest_neighbour;
      pits[y][x] = 1;
      total_pits++; //TODO: May not need this
    }

    nextcell:;
  }
    // cout << "8" << endl;

  //The Priority-Flood operation assures that we reach pit cells by passing into
  //depressions over the outlet of minimal elevation on their edge.
  // RDLOG_PROGRESS<<"Breaching...";
  while(!pq.empty())
  {

    const FillNode c = pq.top();
    pq.pop();
    // cout << "9" << endl;

    //This cell is a pit: let's consider doing some breaching
    if(pits[c.RowIndex][c.ColIndex]!=0){
      //Locate a cell that is lower than the pit cell, or an edge cell
      int cc = c.ColIndex +  c.RowIndex * NCols;               //Current cell on the path
      float target_height = tRasterData[c.RowIndex][c.ColIndex];                     //Depth to which the cell currently being considered should be carved

      //Trace path back to a cell low enough for the path to drain into it, or
      //to an edge of the DEM
      size_t ti = c.RowIndex, tj = c.ColIndex;
      while(cc!=int(NO_BACK_LINK) && tRasterData[ti][tj]>=target_height)
      {

        tRasterData[ti][tj] = target_height;
        cc      = backlinks[ti][tj]; //Follow path back
        tj = cc % NCols;
        ti = size_t(cc/NCols);

      }

      --total_pits;
      if(total_pits==0)
        break;
    }
    // cout << "10" << endl;

    //Looks for neighbours which are either unvisited or pits
    for(int n=-1;n<=1;n++)
    for(int n2=-1;n2<=1;n2++)    
    {
      if(n==0 && n2==0)
        continue;
      // cout << "10.1" << endl;

      const int nx = c.ColIndex+n;
      const int ny = c.RowIndex+n2;

      if(nx<0 || nx>=NCols || ny<0 || ny>=NRows)
        continue;
      // cout << "10.2" << endl;
      // cout << nx <<" || " << ny << endl;

      if(tRasterData[ny][nx] == NoDataValue)
        continue;
      // cout << "10.3" << endl;

      if(visited[ny][nx]!=0)
        continue;
      // cout << "10.4" << endl;

      const float my_e = tRasterData[ny][nx];
      // cout << "11" << endl;

      //The neighbour is unvisited. Add it to the queue
      FillNode tg;
      tg.RowIndex = ny;
      tg.ColIndex = nx;
      tg.Zeta = my_e;
      pq.push(tg);
      visited[ny][nx]   = 2;
      backlinks[ny][nx] = c.ColIndex +  c.RowIndex * NCols;
      // cout << "12" << endl;
    }
  }

  LSDRaster carved(NRows, NCols, XMinimum, YMinimum, DataResolution, NoDataValue, tRasterData, GeoReferencingStrings);

  return carved;

}

#endif