vector.md

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vector package

Classes

Class	Description
ComplexMatrix	A dense Matrix of ComplexNumbers, implemented as an ArrayMatrix
ComplexNumber	A number of the form _a + bi_ where _i_ is the imaginary unit.
ComplexNumberOperations	Implements the basic ScalarOperations on ComplexNumbers
ComplexVector	A dense Vector of ComplexNumbers implemented as an ArrayVector
FloatMatrix	A dense matrix of JavaScript number primitives, implemented as a column-major Float64Array
FloatVector	A dense Vector of numbers implemented as a Float64Array
LinearRegressor	A Regressor model which uses an ordinary least squares model with regularization to predict a continuous target. The optimal set of parameters is computed with gradient descent.
LogisticRegressionClassifier	A Classifier model which uses logistic regression to predict a discrete target. The optimal set of parameters is computed with gradient descent.
MatrixBuilder	Provides methods for constructing Matrices of a given type
NumberMatrix	A dense matrix of JavaScript number primitives, implemented as an ArrayMatrix
NumberOperations	Implements the basic ScalarOperations on numbers
NumberVector	A dense Vector of numbers implemented as a ArrayVector
RowOperations	A wrapper for static methods representing the elementary row operations
SparseNumberMatrix	A Matrix implemented as a sparse set of JS number primitives keyed by their indices.
SparseNumberVector	A Vector implemented as a sparse set of JS number primitives keyed by their indices.
SupportVectorMachineClassifier	A Classifier model which uses logistic regression to predict a discrete target. The optimal set of parameters is computed with gradient descent.
VectorBuilder	Provides methods for constructing Vectors of a given type

Abstract Classes

Abstract Class	Description
ArrayMatrix	Implements Matrix with a 2-dimensional array of values.
ArrayVector	Implements Vector with an array of values.
ScalarOperations	A class which encapsulates the basic arithmetic operations for an arbitrary scalar type.
SparseMatrix	Implements Matrix with a map of indices to nonzero values.
SparseVector	Implements Vector as a map of indices to nonzero values.

Enumerations

Enumeration	Description
SolutionType	Types of solution to a linear system.

Functions

Function	Description
backwardDifferenceMatrix(binCount)	Builds a matrix that transforms a vector to a vector of backward differences
calculateCholeskyDecomposition(A)	Uses the serial version of the Cholesky algorith to calculate the Cholesky decomposition of a matrix A.
calculateEigenvalues(A, numIterations)	Uses the QR algorithm to compute the eigenvalues of a matrix A
calculateGeneralLeastSquares(dataPoints, functionTemplate, numberOfTerms)	Calculates a regression model for an arbitrary function.
calculateLinearLeastSquares(dataPoints)	Calculates a linear regression model for the provided dataPoints.
calculateLUDecomposition(A)	Uses the Doolittle algorithm to calculate the LU Decomposition of a matrix A.
calculateQRDecomposition(A)	Uses the Graham-Schmidt process to calculate the QR decomposition of the matrix A.
calculateSingularValueDecomposition(A)	Uses the Power Method to calculate the Singular Value Decomposition of a matrix A
center(x)	Returns the vector x, shifted so that its mean is at 0
center(A)	Returns the matrix A with each column shifted so that its mean is at 0
centralDifferenceMatrix(binCount)	Builds a matrix that transforms a vector to a vector of central differences
chainProduct(matrices)	Returns the product of the given array of matrices.
columnSumSupremumNorm(A)	Calculates the 1-Norm of a matrix A
correlation(first, second)	Calculates the correlation coefficient r of two vectors
correlation(A)	Calculates the correlation matrix of a matrix A
covariance(first, second)	Calculates the covariance of two vectors
covariance(A)	Calculates the covariance matrix of a matrix A
crossProduct(first, second)	Calculates the cross-product (vector-product) of two vectors. This is defined only for vectors with three dimensions.
derivative(f, xMin, xMax, binCount)	Uses finite differences to build a vector containing approximate values of the derivative of f.
determinant(matrix)	Uses expansion of minors to calculate the determinant of a matrix. Throws an error if the input is not square.
diag(elements)	Creates a new matrix with the specified entries on the diagonal. See MatrixBuilder.diagonal()
dotProduct(first, second)	Computes the dot/inner/scalar product of two vectors. See Vector.innerProduct().
eig(A, numIterations)	Uses the QR algorithm to compute the eigenvalues and eigenvectors of a matrix A
euclideanNorm(v)	Calculates the Euclidean Norm (or 2-Norm) of a vector v
exp(A, order)	Implements the Pade Approximant to compute the exponential of matrix A
eye(size)	Creates a new identity matrix of size size. See MatrixBuilder.identity()
forwardDifferenceMatrix(binCount)	Builds a matrix that transforms a vector to a vector of forward differences
frobeniusNorm(A)	Calculates the Frobenius Norm of a matrix A
GaussianKernel(sigmaSquared)	Creates a gaussian Kernel for use in a SupportVectorMachineClassifier. The gaussian kernel converts a data Matrix into a similarity Matrix where the value of entry (i,j) expresses the similarity of rows i and j in the original data set.
getEigenvectorForEigenvalue(A, lambda)	Given a matrix A and an eigenvalue lambda of that matrix, returns the eigenvector of A corresponding to lambda
gradientDescent(parameters)	Learns an optimal set of parameters theta using gradient descent
hadamardProduct(first, second)	Computes the hadamard (element-wise) product of two vectors.
hadamardProduct(first, second)	Computes the hadamard (element-wise) product of two matrices.
inverse(matrix)	Uses Gauss-Jordan elimination with pivoting to calculate the inverse of a matrix.
isHermitian(matrix)	Tests if a matrix is Hermitian.
isIdentity(matrix)	Tests if a matrix is an identity matrix
isLowerTriangular(matrix)	Tests if a matrix is lower-triangular.
isOrthogonal(matrix)	Tests if a matrix is orthogonal
isOrthonormal(matrix)	Tests if a matrix is orthonormal
isSquare(matrix)	Tests if a matrix is square.
isSymmetric(matrix)	Tests if a matrix is symmetric.
isUpperTriangular(matrix)	Tests if a matrix is upper-triangular.
kroneckerProduct(first, second)	Computes the Kronecker product (generalized outer product) of two matrices.
LinearKernel(data)	A linear kernel for use in a SupportVectorMachineClassifier. The linear kernel converts a data Matrix into a matrix which has been prepended with a column of all ones, representing the constant term in a linear model, or the bias term in an SVM.
linspace(xMin, xMax, binCount)	Builds a vector of binCount evenly spaced numbers between xMin (inclusive) and xMax (exclusive).
mat(data)	Creates a new Matrix of numbers. See MatrixBuilder.fromArray()
mean(x)	Calculates the mean of the values in the vector x
mean(A)	Calculates the mean vector of the matrix A
normalize(v)	Returns a vector with the same direction as the input v, but with a Euclidean norm of 1
ones(entries)	Creates a new vector of all 1s. See VectorBuilder.ones()
ones(shape)	Creates a new matrix of all 1s. See MatrixBuilder.ones()
pca(A, useCorrelation)	Conducts a principal component analysis of a matrix A, and returns A in a new basis corresponding to the principal components.
pNorm(v, p)	Calculates the P-Norm of a vector v
pow(A, n)	Computes _A^n_ recursively.
prettyPrint(num)	Returns an easy-to-read string representing a number
prettyPrint(vector)	Returns an easy-to-read string representing the contents of a Vector
prettyPrint(matrix)	Returns an easy-to-read string representing the contents of a Matrix
RadialBasisFunction(distanceMetric)	Creates a Kernel for use in a SupportVectorMachineClassifier. The RBF kernel converts a data Matrix into a similarity Matrix where the value of entry (i,j) expresses the similarity of rows i and j in the original data set.
rank(matrix)	Calculates the rank of a matrix
reduceDimensions(A, options)	Reduce the number of dimensions of a data matrix A while losing as little information as possible.
reducedRowEchelonForm(matrix)	Uses Gauss-Jordan elimination with pivoting to convert a matrix to Reduced Row-Echelon Form (RREF)
rowEchelonForm(matrix)	Uses Gauss-Jordan elimination with pivoting to convert a matrix to Row-Echelon Form (REF)
rowSumSupremumNorm(A)	Calculates the Infinity-Norm of a matrix A
solve(A, b)	Solves the matrix equation _Ax=b_ for the vector _x_ using the default implementation. See solveByGaussianElimination()
solveByGaussianElimination(A, b)	Uses Gauss-Jordan elimination with pivoting and backward substitution to solve the linear equation _Ax=b_
solveOverdeterminedSystem(A, b)	Gives an approximate solution to an overdetermined linear system.
standardDeviation(x)	Calculates the standard deviation of a vector
standardDeviation(A)	Calculates the standard deviation of each column of the matrix A
standardize(x)	Returns the vector x shifted and scaled to have a mean of 0 and standard deviation of 1
standardize(A)	Returns the matrix A with each column shifted and scaled to have a mean of 0 and standard deviation of 1
sumNorm(v)	Calculates the Sum Norm (or 1-Norm) of a vector v
supremumNorm(v)	Calculates the Supremum Norm (or Infinity-Norm) of a vector v
tripleProduct(first, second, third)	Calculates the scalar triple-product of three vectors. This is defined only for vectors with three dimensions.
variance(x)	Calculates the variance of a vector
variance(A)	Calculates the variance of each column of the matrix A
vec(data)	Creates a new Vector of numbers. See VectorBuilder.fromArray()
zeros(entries)	Creates a new vector of all 0s. See VectorBuilder.zeros()
zeros(shape)	Creates a new matrix of all 0s. See MatrixBuilder.zeros()

Interfaces

Interface	Description
CholeskyDecomposition	The result of a Cholesky Decomposition
Classifier	A machine learning model with a continuous numeric target
Cost	The output of a cost function
EigenPair	An eigenvector and its corresponding eigenvalue
LeastSquaresApproximation	The result of a least squares approximation.
LinearTransformation	An abstract linear transformation between vectors of type V and vectors of type U.
LUDecomposition	The result of an LU Decomposition
Matrix	A generalized Matrix - one of the core data types
OverdeterminedSolution	A type representing the lack of solution to a linear system.
PrincipalComponentAnalysis	The result of a principal component analysis.
QRDecomposition	The result of a QR decomposition.
Regressor	A machine learning model with a continuous numeric target
RowOperationResult	The result of a row operation (result), and the matrix that we multiply by the original matrix to yield that result (operator)
SingularValueDecomposition	The result of a Singular Value Decomposition
UnderdeterminedSolution	A particular solution to a linear system with infinitely many solutions.
UniqueSolution	The unique solution to a linear system.
Vector	A generalized Vector - one of the core data types

Type Aliases

Type Alias	Description
ApproximationFunction	A function that takes a vector of inputs and produces an output. This must always be a pure function that is linear in its coefficients.
ApproximationFunctionTemplate	A higher-order function which is used to generate an ApproximationFunction. This must be linear in its coefficients, or the result of the linear regression will not be correct.
CostFunction	A function that evaluates the cost of a set of parameters theta
DimensionReductionOptions	Specify how dimension reduction ought to be done.
GradientDescentParameters	The parameters for gradientDescent()
Kernel	A function which takes a Matrix of data (and optionally another Matrix of data on which the kernel was trained) and returns a new Matrix which will be used to train a machine learning model. Generally intended for use with a SupportVectorMachineClassifier.
LearningAlgorithm	An function which, given an initial value of theta and a CostFunction, will compute the optimal value of theta
LinearRegressorHyperparams	The set of hyperparameters for a LinearRegressor
LinearSolution	A general type representing any type of solution to a linear system.
LogisticRegressionHyperparams	The set of hyperparameters for a LogisticRegressionClassifier
MatrixData	The data stored in a Matrix represented as a 2-D array
MatrixEntryFunction	A function that generates a matrix entry based on an existing entry entry, its row index i, and its column index j
MatrixShape	A tuple representing the shape of a Matrix. The first entry is the number of rows, and the second entry is the number of columns.
Norm	A function that calculates a norm for a vector.
SimilarityMetric	A function which expresses the similarity of two Vectors as a number between 0 (very dissimilar) and 1 (identical).
Solver	A function that solves a linear system _Ax=b_
SparseMatrixData	The data stored in a Matrix represented as a map
SparseVectorData	The data stored in a Vector represented as a map
SupportVectorMachineHyperparams	The set of hyperparameters for a SupportVectorMachineClassifier
VectorData	The data stored in a Vector represented as a map
VectorIndexFunction	A function that generates a vector entry based on its index