Numerical Recipes in Fortran 77

Computer Programs by Chapter and Section

sect	program	description
1.0	flmoon	calculate phases of the moon by date
1.1	julday	Julian Day number from calendar date
1.1	badluk	Friday the 13th when the moon is full
1.1	caldat	calendar date from Julian day number
2.1	gaussj	Gauss-Jordan matrix inversion and linear equation solution
2.3	ludcmp	linear equation solution, LU decomposition
2.3	lubksb	linear equation solution, backsubstitution
2.4	tridag	solution of tridiagonal systems
2.5	mprove	linear equation solution, iterative improvement
2.6	svbksb	singular value backsubstitution
2.6	svdcmp	singular value decomposition of a matrix
2.8	vander	solve Vandermonde systems
2.8	toeplz	solve Toeplitz systems
3.1	polint	polynomial interpolation
3.2	ratint	rational function interpolation
3.3	spline	construct a cubic spline
3.3	splint	cubic spline interpolation
3.4	locate	search an ordered table by bisection
3.4	hunt	search a table when calls are correlated
3.5	polcoe	polynomial coefficients from table of values
3.5	polcof	polynomial coefficients from table of values
3.6	polin2	two-dimensional polynomial interpolation
3.6	bcucof	construct two-dimensional bicubic
3.6	bcuint	two-dimensional bicubic interpolation
3.6	splie2	construct two-dimensional spline
3.6	splin2	two-dimensional spline interpolation
4.2	trapzd	trapezoidal rule
4.2	qtrap	integrate using trapezoidal rule
4.2	qsimp	integrate using Simpson’s rule
4.3	qromb	integrate using Romberg adaptive method
4.4	midpnt	extended midpoint rule
4.4	qromo	integrate using open Romberg adaptive method
4.4	midinf	integrate a function on a semi-infinite interval
4.5	qgaus	integrate a function by Gaussian quadratures
4.5	gauleg	Gauss-Legendre weights and abscissas
4.6	quad3d	integrate a function over a three-dimensional space
5.1	eulsum	sum a series by Eulervan Wijngaarden algorithm
5.3	ddpoly	evaluate a polynomial and its derivatives
5.3	poldiv	divide one polynomial by another
5.8	chebft	fit a Chebyshev polynomial to a function
5.8	chebev	Chebyshev polynomial evaluation
5.9	chder	derivative of a function already Chebyshev fitted
5.9	chint	integrate a function already Chebyshev fitted
5.10	chebpc	polynomial coefficients from a Chebyshev fit
5.10	pcshft	polynomial coefficients of a shifted polynomial
6.1	gammln	logarithm of gamma function
6.1	factrl	factorial function
6.1	bico	binomial coefficients function
6.1	factln	logarithm of factorial function
6.1	beta	beta function
6.2	gammp	incomplete gamma function
6.2	gammq	complement of incomplete gamma function
6.2	gser	series used by gammp and gammq
6.2	gcf	continued fraction used by gammp and gammq
6.2	erf	error function
6.2	erfc	complementary error function
6.2	erfcc	complementary error function, concise routine
6.4	betai	incomplete beta function
6.4	betacf	continued fraction used by betai
6.5	bessj0	Bessel function J0
6.5	bessy0	Bessel function Y0
6.5	bessj1	Bessel function J1
6.5	bessy1	Bessel function Y1
6.5	bessy	Bessel function Y of general integer order
6.5	bessj	Bessel function J of general integer order
6.6	bessi0	modified Bessel function I0
6.6	bessk0	modified Bessel function K0
6.6	bessi1	modified Bessel function I1
6.6	bessk1	modified Bessel function K1
6.6	bessk	modified Bessel function K of integer order
6.6	bessi	modified Bessel function I of integer order
6.8	plgndr	Legendre polynomials, associated (spherical harmonics)
6.11	sncndn	Jacobian elliptic functions
7.1	ran0	random deviate by Park and Miller minimal standard
7.1	ran1	random deviate, minimal standard plus shuffle
7.1	ran2	random deviate by L’Ecuyer long period plus shuffle
7.1	ran3	random deviate by Knuth subtractive method
7.2	expdev	exponential random deviates
7.2	gasdev	normally distributed random deviates
7.3	gamdev	gamma-law distribution random deviates
7.3	poidev	Poisson distributed random deviates
7.3	bnldev	binomial distributed random deviates
7.4	irbit1	random bit sequence
7.4	irbit2	random bit sequence
7.5	ran4	random deviates from DES-like hashing
8.1	piksrt	sort an array by straight insertion
8.1	piksr2	sort two arrays by straight insertion
8.1	shell	sort an array by Shell’s method
8.2	sort	sort an array by quicksort method
8.2	sort2	sort two arrays by quicksort method
8.4	indexx	construct an index for an array
8.4	sort3	sort, use an index to sort 3 or more arrays
8.4	rank	construct a rank table for an array
8.6	eclass	determine equivalence classes from list
8.6	eclazz	determine equivalence classes from procedure
9.0	scrsho	graph a function to search for roots
9.1	zbrac	outward search for brackets on roots
9.1	zbrak	inward search for brackets on roots
9.1	rtbis	find root of a function by bisection
9.2	rtflsp	find root of a function by false-position
9.2	rtsec	find root of a function by secant method
9.3	zbrent	find root of a function by Brent’s method
9.4	rtnewt	find root of a function by Newton-Raphson
9.4	rtsafe	find root of a function by Newton-Raphson and bisection
9.5	laguer	find a root of a polynomial by Laguerre’s method
9.5	zroots	roots of a polynomial by Laguerre’s method with deflation
9.5	qroot	complex or double root of a polynomial, Bairstow
9.6	mnewt	Newton’s method for systems of equations
10.1	mnbrak	bracket the minimum of a function
10.1	golden	find minimum of a function by golden section search
10.2	brent	find minimum of a function by Brent’s method
10.3	dbrent	find minimum of a function using derivative information
10.4	amoeba	minimize in N-dimensions by downhill simplex method
10.4	amotry	evaluate a trial point, used by amoeba
10.5	powell	minimize in N-dimensions by Powell’s method
10.5	linmin	minimum of a function along a ray in N-dimensions
10.5	f1dim	function used by linmin
10.6	frprmn	minimize in N-dimensions by conjugate gradient
10.6	df1dim	alternative function used by linmin
10.7	dfpmin	minimize in N-dimensions by variable metric method
10.8	simplx	linear programming maximization of a linear function
10.8	simp1	linear programming, used by simplx
10.8	simp2	linear programming, used by simplx
10.8	simp3	linear programming, used by simplx
10.9	anneal	traveling salesman problem by simulated annealing
10.9	revcst	cost of a reversal, used by anneal
10.9	revers	do a reversal, used by anneal
10.9	trncst	cost of a transposition, used by anneal
10.9	trnspt	do a transposition, used by anneal
10.9	metrop	Metropolis algorithm, used by anneal
10.9	amebsa	simulated annealing in continuous spaces
10.9	amotsa	evaluate a trial point, used by amebsa
11.1	jacobi	eigenvalues and eigenvectors of a symmetric matrix
11.1	eigsrt	eigenvectors, sorts into order by eigenvalue
11.2	tred2	Householder reduction of a real, symmetric matrix
11.3	tqli	eigensolution of a symmetric tridiagonal matrix
11.5	balanc	balance a nonsymmetric matrix
11.5	elmhes	reduce a general matrix to Hessenberg form
11.6	hqr	eigenvalues of a Hessenberg matrix
12.2	four1	fast Fourier transform (FFT) in one dimension
12.3	twofft	fast Fourier transform of two real functions
12.3	realft	fast Fourier transform of a single real function
12.3	sinft	fast sine transform
12.3	cosft1	fast cosine transform with endpoints
12.3	cosft2	“staggered” fast cosine transform
12.4	fourn	fast Fourier transform in multidimensions
12.5	rlft3	FFT of real data in two or three dimensions
12.6	fourfs	FFT for huge data sets on external media
12.6	fourew	rewind and permute files, used by fourfs
13.1	convlv	convolution or deconvolution of data using FFT
13.2	correl	correlation or autocorrelation of data using FFT
13.4	spctrm	power spectrum estimation using FFT
13.6	memcof	evaluate maximum entropy (MEM) coefficients
13.6	fixrts	reflect roots of a polynomial into unit circle
13.6	predic	linear prediction using MEM coefficients
13.7	evlmem	power spectral estimation from MEM coefficients
13.8	period	power spectrum of unevenly sampled data
13.8	fasper	power spectrum of unevenly sampled larger data sets
13.8	spread	extirpolate value into array, used by fasper
13.9	dftcor	compute endpoint corrections for Fourier integrals
13.9	dftint	high-accuracy Fourier integrals
13.10	wt1	one-dimensional discrete wavelet transform
13.10	daub4	Daubechies 4-coefficient wavelet filter
13.10	pwtset	initialize coefficients for pwt
13.10	pwt	partial wavelet transform
13.10	wtn	multidimensional discrete wavelet transform
14.1	moment	calculate moments of a data set
14.2	ttest	Student’s t-test for difference of means
14.2	avevar	calculate mean and variance of a data set
14.2	tutest	Student’s t-test for means, case of unequal variances
14.2	tptest	Student’s t-test for means, case of paired data
14.2	ftest	F-test for difference of variances
14.3	chsone	chi-square test for difference between data and model
14.3	chstwo	chi-square test for difference between two data sets
14.3	ksone	Kolmogorov-Smirnov test of data against model
14.3	kstwo	Kolmogorov-Smirnov test between two data sets
14.3	probks	Kolmogorov-Smirnov probability function
14.4	cntab1	contingency table analysis using chi-square
14.4	cntab2	contingency table analysis using entropy measure
14.5	pearsn	Pearson’s correlation between two data sets
14.6	spear	Spearman’s rank correlation between two data sets
14.6	crank	replaces array elements by their rank
14.6	kendl1	correlation between two data sets, Kendall’s tau
14.6	kendl2	contingency table analysis using Kendall’s tau
14.7	ks2d1s	KS test in two dimensions, data vs. model
14.7	quadct	count points by quadrants, used by ks2d1s
14.7	quadvl	quadrant probabilities, used by ks2d1s
14.7	ks2d2s	KS test in two dimensions, data vs. data
14.8	savgol	Savitzky-Golay smoothing coefficients
15.2	fit	least-squares fit data to a straight line
15.3	fitexy	fit data to a straight line, errors in both x and y
15.3	chixy	used by fitexy to calculate a _2
15.4	lfit	general linear least-squares fit by normal equations
15.4	covsrt	rearrange covariance matrix, used by lfit
15.4	svdfit	linear least-squares fit by singular value decomposition
15.4	svdvar	variances from singular value decomposition
15.4	fpoly	fit a polynomial using lfit or svdfit
15.4	fleg	fit a Legendre polynomial using lfit or svdfit
15.5	mrqmin	nonlinear least-squares fit, Marquardt’s method
15.5	mrqcof	used by mrqmin to evaluate coefficients
15.5	fgauss	fit a sum of Gaussians using mrqmin
15.7	medfit	fit data to a straight line robustly, least absolute deviation
15.7	rofunc	fit data robustly, used by medfit
16.1	rk4	integrate one step of ODEs, fourth-order Runge-Kutta
16.1	rkdumb	integrate ODEs by fourth-order Runge-Kutta
16.2	rkqs	integrate one step of ODEs with accuracy monitoring
16.2	rkck	Cash-Karp-Runge-Kutta step used by rkqs
16.2	odeint	integrate ODEs with accuracy monitoring
16.3	mmid	integrate ODEs by modified midpoint method
16.4	bsstep	integrate ODEs, Bulirsch-Stoer step
16.4	pzextr	polynomial extrapolation, used by bsstep
16.4	rzextr	rational function extrapolation, used by bsstep
16.5	stoerm	integrate conservative second-order ODEs
16.6	stiff	integrate stiff ODEs by fourth-order Rosenbrock
16.6	jacobn	sample Jacobian routine for stiff
16.6	derivs	sample derivatives routine for stiff
16.6	simpr	integrate stiff ODEs by semi-implicit midpoint rule
16.6	stifbs	integrate stiff ODEs, Bulirsch-Stoer step
17.1	shoot	solve two point boundary value problem by shooting
17.2	shootf	ditto, by shooting to a fitting point
17.3	solvde	two point boundary value problem, solve by relaxation
17.3	bksub	backsubstitution, used by solvde
17.3	pinvs	diagonalize a sub-block, used by solvde
17.3	red	reduce columns of a matrix, used by solvde
17.4	sfroid	spheroidal functions by method of solvde
17.4	difeq	spheroidal matrix coefficients, used by sfroid
17.4	sphoot	spheroidal functions by method of shoot
17.4	sphfpt	spheroidal functions by method of shootf
18.1	fred2	solve linear Fredholm equations of the second kind
18.1	fredin	interpolate solutions obtained with fred2
18.2	voltra	linear Volterra equations of the second kind
18.3	wwghts	quadrature weights for an arbitrarily singular kernel
18.3	kermom	sample routine for moments of a singular kernel
18.3	quadmx	sample routine for a quadrature matrix
18.3	fredex	example of solving a singular Fredholm equation
19.5	sor	elliptic PDE solved by successive overrelaxation method
19.6	mglin	linear elliptic PDE solved by multigrid method
19.6	rstrct	half-weighting restriction, used by mglin, mgfas
19.6	interp	bilinear prolongation, used by mglin, mgfas
19.6	addint	interpolate and add, used by mglin
19.6	slvsml	solve on coarsest grid, used by mglin
19.6	relax	Gauss-Seidel relaxation, used by mglin
19.6	resid	calculate residual, used by mglin
19.6	copy	utility used by mglin, mgfas
19.6	fill0	utility used by mglin
19.6	maloc	memory allocation utility used by mglin, mgfas
19.6	mgfas	nonlinear elliptic PDE solved by multigrid method
19.6	relax2	Gauss-Seidel relaxation, used by mgfas
19.6	slvsm2	solve on coarsest grid, used by mgfas
19.6	lop	applies nonlinear operator, used by mgfas
19.6	matadd	utility used by mgfas
19.6	matsub	utility used by mgfas
19.6	anorm2	utility used by mgfas
20.1	machar	diagnose computer’s floating arithmetic
20.2	igray	Gray code and its inverse
20.3	icrc1	cyclic redundancy checksum, used by icrc
20.3	icrc	cyclic redundancy checksum
20.3	decchk	decimal check digit calculation or verification
20.4	hufmak	construct a Huffman code
20.4	hufapp	append bits to a Huffman code, used by hufmak
20.4	hufenc	use Huffman code to encode and compress a character
20.4	hufdec	use Huffman code to decode and decompress a character
20.5	arcmak	construct an arithmetic code
20.5	arcode	encode or decode a character using arithmetic coding
20.5	arcsum	add integer to byte string, used by arcode
20.6	mpops	multiple precision arithmetic, simpler operations
20.6	mpmul	multiple precision multiply, using FFT methods
20.6	mpinv	multiple precision reciprocal
20.6	mpdiv	multiple precision divide and remainder
20.6	mpsqrt	multiple precision square root
20.6	mp2dfr	multiple precision conversion to decimal base
20.6	mppi	multiple precision example, compute many digits of _