Numerical Recipes Routines

(Second Edition: C++, C or Fortran)

addint

interpolate and add, used by mglin [19.6]

airy

Airy functions [6.7]

amebsa

simulated annealing in continuous spaces [10.9]

amoeba

minimize in N-dimensions by downhill simplex method [10.4]

amotry

evaluate a trial point, used by amoeba [10.4]

amotsa

evaluate a trial point, used by amebsa [10.9]

anneal

traveling salesman problem by simulated annealing [10.9]

anorm2

utility used by mgfas [19.6]

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 [20.5]

asolve

used by linbcg for preconditioner [2.7]

atimes

used by linbcg for sparse multiplication [2.7]

avevar

calculate mean and variance of a data set [14.2]

badluk

Friday the 13th when the moon is full [1.1]

balanc

balance a nonsymmetric matrix [11.5]

banbks

band diagonal systems, backsubstitution [2.4]

bandec

band diagonal systems, decomposition [2.4]

banmul

multiply vector by band diagonal matrix [2.4]

bcucof

construct two-dimensional bicubic [3.6]

bcuint

two-dimensional bicubic interpolation [3.6]

beschb

Chebyshev expansion used by bessjy [6.7]

bessi0

modified Bessel function I_0 [6.6]

bessi1

modified Bessel function I_1 [6.6]

bessi

modified Bessel function I of integer order [6.6]

bessik

modified Bessel functions of fractional order [6.7]

bessj0

Bessel function J_0 [6.5]

bessj1

Bessel function J_1 [6.5]

bessj

Bessel function J of general integer order [6.5]

bessjy

Bessel functions of fractional order [6.7]

bessk0

modified Bessel function K_0 [6.6]

bessk1

modified Bessel function K_1 [6.6]

bessk

modified Bessel function K of integer order [6.6]

bessy0

Bessel function Y_0 [6.5]

bessy1

Bessel function Y_1 [6.5]

bessy

Bessel function Y of general integer order [6.5]

beta

beta function [6.1]

betacf

continued fraction used by betai [6.4]

betai

incomplete beta function [6.4]

bico

binomial coefficients function [6.1]

bksub

backsubstitution, used by SOLVDE [17.3]

bnldev

binomial distributed random deviates [7.3]

brent

find minimum of a function by Brent's method [10.2]

broydn

secant method for systems of equations [9.7]

bsstep

integrate ODEs, Bulirsch-Stoer step [16.4]

caldat

calendar date from Julian day number [1.1]

chder

derivative of a function already Chebyshev fitted [5.9]

chebev

Chebyshev polynomial evaluation [5.8]

chebft

fit a Chebyshev polynomial to a function [5.8]

chebpc

polynomial coefficients from a Chebyshev fit [5.10]

chint

integrate a function already Chebyshev fitted [5.9]

chixy

used by fitexy to calculate a \chi^2 [15.3]

choldc

Cholesky decomposition [2.9]

cholsl

Cholesky backsubstitution [2.9]

chsone

chi-square test for difference between data and model [14.3]

chstwo

chi-square test for difference between two data sets [14.3]

cisi

cosine and sine integrals Ci and Si [6.9]

cntab1

contingency table analysis using chi-square [14.4]

cntab2

contingency table analysis using entropy measure [14.4]

convlv

convolution or deconvolution of data using FFT [13.1]

copy

utility used by mglin, mgfas [19.6]

correl

correlation or autocorrelation of data using FFT [13.2]

cosft1

fast cosine transform with endpoints [12.3]

cosft2

``staggered'' fast cosine transform [12.3]

covsrt

rearrange covariance matrix, used by lfit [15.4]

crank

replaces array elements by their rank [14.6]

cyclic

solution of cyclic tridiagonal systems [2.7]

daub4

Daubechies 4-coefficient wavelet filter [13.10]

dawson

Dawson's integral [6.10]

dbrent

find minimum of a function using derivative information [10.3]

ddpoly

evaluate a polynomial and its derivatives [5.3]

decchk

decimal check digit calculation or verification [20.3]

derivs

sample derivatives routine for stiff [16.6]

df1dim

alternative function used by linmin [10.6]

dfpmin

minimize in N-dimensions by variable metric method [10.7]

dfridr

numerical derivative by Ridders' method [5.7]

dftcor

compute endpoint corrections for Fourier integrals [13.9]

dftint

high-accuracy Fourier integrals [13.9]

difeq

spheroidal matrix coefficients, used by SFROID [17.4]

eclass

determine equivalence classes from list [8.6]

eclazz

determine equivalence classes from procedure [8.6]

ei

exponential integral Ei [6.3]

eigsrt

eigenvectors, sorts into order by eigenvalue [11.1]

elle

Legendre elliptic integral of the second kind [6.11]

ellf

Legendre elliptic integral of the first kind [6.11]

ellpi

Legendre elliptic integral of the third kind [6.11]

elmhes

reduce a general matrix to Hessenberg form [11.5]

erf

error function [6.2]

erfc

complementary error function [6.2]

erfcc

complementary error function, concise routine [6.2]

eulsum

sum a series by Euler--van Wijngaarden algorithm [5.1]

evlmem

power spectral estimation from MEM coefficients [13.7]

expdev

exponential random deviates [7.2]

expint

exponential integral E_n [6.3]

f1dim

function used by linmin [10.5]

factln

logarithm of factorial function [6.1]

factrl

factorial function [6.1]

fasper

power spectrum of unevenly sampled larger data sets [13.8]

fdjac

finite-difference Jacobian, used by newt [9.7]

fgauss

fit a sum of Gaussians using mrqmin [15.5]

fill0

utility used by mglin [19.6]

fit

least-squares fit data to a straight line [15.2]

fitexy

fit data to a straight line, errors in both x and y [15.3]

fixrts

reflect roots of a polynomial into unit circle [13.6]

fleg

fit a Legendre polynomial using lfit or svdfit [15.4]

flmoon

calculate phases of the moon by date [1.0]

fmin

norm of a vector function, used by newt [9.7]

four1

fast Fourier transform (FFT) in one dimension [12.2]

fourew

rewind and permute files, used by fourfs [12.6]

fourfs

FFT for huge data sets on external media [12.6]

fourn

fast Fourier transform in multidimensions [12.4]

fpoly

fit a polynomial using lfit or svdfit [15.4]

fred2

solve linear Fredholm equations of the second kind [18.1]

fredex

example of solving a singular Fredholm equation [18.3]

fredin

interpolate solutions obtained with fred2 [18.1]

frenel

Fresnel integrals S(x) and C(x) [6.9]

frprmn

minimize in N-dimensions by conjugate gradient [10.6]

ftest

F-test for difference of variances [14.2]

gamdev

gamma-law distribution random deviates [7.3]

gammln

logarithm of gamma function [6.1]

gammp

incomplete gamma function [6.2]

gammq

complement of incomplete gamma function [6.2]

gasdev

normally distributed random deviates [7.2]

gaucof

quadrature weights from orthogonal polynomials [4.5]

gauher

Gauss-Hermite weights and abscissas [4.5]

gaujac

Gauss-Jacobi weights and abscissas [4.5]

gaulag

Gauss-Laguerre weights and abscissas [4.5]

gauleg

Gauss-Legendre weights and abscissas [4.5]

gaussj

Gauss-Jordan matrix inversion and linear equation solution [2.1]

gcf

continued fraction used by gammp and gammq [6.2]

golden

find minimum of a function by golden section search [10.1]

gser

series used by gammp and gammq [6.2]

hpsel

find M largest values, without altering an array [8.5]

hpsort

sort an array by heapsort method [8.3]

hqr

eigenvalues of a Hessenberg matrix [11.6]

hufapp

append bits to a Huffman code, used by hufmak [20.4]

hufdec

use Huffman code to decode and decompress a character [20.4]

hufenc

use Huffman code to encode and compress a character [20.4]

hufmak

construct a Huffman code [20.4]

hunt

search a table when calls are correlated [3.4]

hypdrv

complex hypergeometric function, derivative of [6.12]

hypgeo

complex hypergeometric function [6.12]

hypser

complex hypergeometric function, series evaluation [6.12]

icrc1

cyclic redundancy checksum, used by icrc [20.3]

icrc

cyclic redundancy checksum [20.3]

igray

Gray code and its inverse [20.2]

indexx

construct an index for an array [8.4]

interp

bilinear prolongation, used by mglin, mgfas [19.6]

irbit1

random bit sequence [7.4]

irbit2

random bit sequence [7.4]

jacobi

eigenvalues and eigenvectors of a symmetric matrix [11.1]

jacobn

sample Jacobian routine for stiff [16.6]

julday

Julian Day number from calendar date [1.1]

kendl1

correlation between two data sets, Kendall's tau [14.6]

kendl2

contingency table analysis using Kendall's tau [14.6]

kermom

sample routine for moments of a singular kernel [18.3]

ks2d1s

K--S test in two dimensions, data vs.\ model [14.7]

ks2d2s

K--S test in two dimensions, data vs.\ data [14.7]

ksone

Kolmogorov-Smirnov test of data against model [14.3]

kstwo

Kolmogorov-Smirnov test between two data sets [14.3]

laguer

find a root of a polynomial by Laguerre's method [9.5]

lfit

general linear least-squares fit by normal equations [15.4]

linbcg

biconjugate gradient solution of sparse systems [2.7]

linmin

minimum of a function along a ray in N-dimensions [10.5]

lnsrch

search along a line, used by newt [9.7]

locate

search an ordered table by bisection [3.4]

lop

applies nonlinear operator, used by mgfas [19.6]

lubksb

linear equation solution, backsubstitution [2.3]

ludcmp

linear equation solution, LU decomposition [2.3]

machar

diagnose computer's floating arithmetic [20.1]

maloc

memory allocation utility used by mglin, mgfas [19.6]

matadd

utility used by mgfas [19.6]

matsub

utility used by mgfas [19.6]

medfit

fit data to a straight line robustly, least absolute deviation [15.7]

memcof

evaluate maximum entropy (MEM) coefficients [13.6]

metrop

Metropolis algorithm, used by anneal [10.9]

mgfas

nonlinear elliptic PDE solved by multigrid method [19.6]

mglin

linear elliptic PDE solved by multigrid method [19.6]

midexp

integrate a function that decreases exponentially [4.4]

midinf

integrate a function on a semi-infinite interval [4.4]

midpnt

extended midpoint rule [4.4]

midsql

integrate a function with lower square-root singularity [4.4]

midsqu

integrate a function with upper square-root singularity [4.4]

miser

recursive multidimensional Monte Carlo integration [7.8]

mmid

integrate ODEs by modified midpoint method [16.3]

mnbrak

bracket the minimum of a function [10.1]

mnewt

Newton's method for systems of equations [9.6]

moment

calculate moments of a data set [14.1]

mp2dfr

multiple precision conversion to decimal base [20.6]

mpdiv

multiple precision divide and remainder [20.6]

mpinv

multiple precision reciprocal [20.6]

mpmul

multiple precision multiply, using FFT methods [20.6]

mpops

multiple precision arithmetic, simpler operations [20.6]

mppi

multiple precision example, compute many digits of \pi [20.6]

mprove

linear equation solution, iterative improvement [2.5]

mpsqrt

multiple precision square root [20.6]

mrqcof

used by mrqmin to evaluate coefficients [15.5]

mrqmin

nonlinear least-squares fit, Marquardt's method [15.5]

newt

globally convergent multi-dimensional Newton's method [9.7]

odeint

integrate ODEs with accuracy monitoring [16.2]

orthog

construct nonclassical orthogonal polynomials [4.5]

pade

Pad\'e approximant from power series coefficients [5.12]

pccheb

inverse of chebpc; use to economize power series [5.11]

pcshft

polynomial coefficients of a shifted polynomial [5.10]

pearsn

Pearson's correlation between two data sets [14.5]

period

power spectrum of unevenly sampled data [13.8]

piksr2

sort two arrays by straight insertion [8.1]

piksrt

sort an array by straight insertion [8.1]

pinvs

diagonalize a sub-block, used by SOLVDE [17.3]

plgndr

Legendre polynomials, associated (spherical harmonics) [6.8]

poidev

Poisson distributed random deviates [7.3]

polcoe

polynomial coefficients from table of values [3.5]

polcof

polynomial coefficients from table of values [3.5]

poldiv

divide one polynomial by another [5.3]

polin2

two-dimensional polynomial interpolation [3.6]

polint

polynomial interpolation [3.1]

powell

minimize in N-dimensions by Powell's method [10.5]

predic

linear prediction using MEM coefficients [13.6]

probks

Kolmogorov-Smirnov probability function [14.3]

psdes

``pseudo-DES'' hashing of 64 bits [7.5]

pwt

partial wavelet transform [13.10]

pwtset

initialize coefficients for pwt [13.10]

pythag

calculate (a^2+b^2)^{1/2} without overflow [2.6]

pzextr

polynomial extrapolation, used by bsstep [16.4]

qgaus

integrate a function by Gaussian quadratures [4.5]

qrdcmp

QR decomposition [2.10]

qromb

integrate using Romberg adaptive method [4.3]

qromo

integrate using open Romberg adaptive method [4.4]

qroot

complex or double root of a polynomial, Bairstow [9.5]

qrsolv

QR backsubstitution [2.10]

qrupdt

update a QR decomposition [2.10]

qsimp

integrate using Simpson's rule [4.2]

qtrap

integrate using trapezoidal rule [4.2]

quad3d

integrate a function over a three-dimensional space [4.6]

quadct

count points by quadrants, used by ks2d1s [14.7]

quadmx

sample routine for a quadrature matrix [18.3]

quadvl

quadrant probabilities, used by ks2d1s [14.7]

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 [7.1]

ran4

random deviates from DES-like hashing [7.5]

rank

construct a rank table for an array [8.4]

ranpt

get random point, used by miser [7.8]

ratint

rational function interpolation [3.2]

ratlsq

rational fit by least-squares method [5.13]

ratval

evaluate a rational function [5.3]

rc

Carlson's degenerate elliptic integral [6.11]

rd

Carlson's elliptic integral of the second kind [6.11]

realft

fast Fourier transform of a single real function [12.3]

rebin

sample rebinning used by vegas [7.8]

red

reduce columns of a matrix, used by SOLVDE [17.3]

relax2

Gauss-Seidel relaxation, used by mgfas [19.6]

relax

Gauss-Seidel relaxation, used by mglin [19.6]

resid

calculate residual, used by mglin [19.6]

revcst

cost of a reversal, used by anneal [10.9]

revers

do a reversal, used by anneal [10.9]

rf

Carlson's elliptic integral of the first kind [6.11]

rj

Carlson's elliptic integral of the third kind [6.11]

rk4

integrate one step of ODEs, fourth-order Runge-Kutta [16.1]

rkck

Cash-Karp-Runge-Kutta step used by rkqs [16.2]

rkdumb

integrate ODEs by fourth-order Runge-Kutta [16.1]

rkqs

integrate one step of ODEs with accuracy monitoring [16.2]

rlft3

FFT of real data in two or three dimensions [12.5]

rotate

Jacobi rotation used by qrupdt [2.10]

rsolv

right triangular backsubstitution [2.10]

rstrct

half-weighting restriction, used by mglin, mgfas [19.6]

rtbis

find root of a function by bisection [9.1]

rtflsp

find root of a function by false-position [9.2]

rtnewt

find root of a function by Newton-Raphson [9.4]

rtsafe

find root of a function by Newton-Raphson and bisection [9.4]

rtsec

find root of a function by secant method [9.2]

rzextr

rational function extrapolation, used by bsstep [16.4]

savgol

Savitzky-Golay smoothing coefficients [14.8]

scrsho

graph a function to search for roots [9.0]

select

find the Nth largest in an array [8.5]

selip

find the Nth largest, without altering an array [8.5]

sfroid

spheroidal functions by method of SOLVDE [17.4]

shell

sort an array by Shell's method [8.1]

shoot

solve two point boundary value problem by shooting [17.1]

shootf

ditto, by shooting to a fitting point [17.2]

simp1

linear programming, used by simplx [10.8]

simp2

linear programming, used by simplx [10.8]

simp3

linear programming, used by simplx [10.8]

simplx

linear programming maximization of a linear function [10.8]

simpr

integrate stiff ODEs by semi-implicit midpoint rule [16.6]

sinft

fast sine transform [12.3]

slvsm2

solve on coarsest grid, used by mgfas [19.6]

slvsml

solve on coarsest grid, used by mglin [19.6]

sncndn

Jacobian elliptic functions [6.11]

snrm

used by linbcg for vector norm [2.7]

sobseq

Sobol's quasi-random sequence [7.7]

solvde

two point boundary value problem, solve by relaxation [17.3]

sor

elliptic PDE solved by successive overrelaxation method [19.5]

sort2

sort two arrays by quicksort method [8.2]

sort3

sort, use an index to sort 3 or more arrays [8.4]

sort

sort an array by quicksort method [8.2]

spctrm

power spectrum estimation using FFT [13.4]

spear

Spearman's rank correlation between two data sets [14.6]

sphbes

spherical Bessel functions j_n and y_n [6.7]

sphfpt

spheroidal functions by method of shootf [17.4]

sphoot

spheroidal functions by method of shoot [17.4]

splie2

construct two-dimensional spline [3.6]

splin2

two-dimensional spline interpolation [3.6]

spline

construct a cubic spline [3.3]

splint

cubic spline interpolation [3.3]

spread

extirpolate value into array, used by fasper [13.8]

sprsax

product of sparse matrix and vector [2.7]

sprsin

convert matrix to sparse format [2.7]

sprspm

pattern multiply two sparse matrices [2.7]

sprstm

threshold multiply two sparse matrices [2.7]

sprstp

transpose of sparse matrix [2.7]

sprstx

product of transpose sparse matrix and vector [2.7]

stifbs

integrate stiff ODEs, Bulirsch-Stoer step [16.6]

stiff

integrate stiff ODEs by fourth-order Rosenbrock [16.6]

stoerm

integrate conservative second-order ODEs [16.5]

svbksb

singular value backsubstitution [2.6]

svdcmp

singular value decomposition of a matrix [2.6]

svdfit

linear least-squares fit by singular value decomposition [15.4]

svdvar

variances from singular value decomposition [15.4]

toeplz

solve Toeplitz systems [2.8]

tptest

Student's t-test for means, case of paired data [14.2]

tqli

eigensolution of a symmetric tridiagonal matrix [11.3]

trapzd

trapezoidal rule [4.2]

tred2

Householder reduction of a real, symmetric matrix [11.2]

tridag

solution of tridiagonal systems [2.4]

trncst

cost of a transposition, used by anneal [10.9]

trnspt

do a transposition, used by anneal [10.9]

ttest

Student's t-test for difference of means [14.2]

tutest

Student's t-test for means, case of unequal variances [14.2]

twofft

fast Fourier transform of two real functions [12.3]

vander

solve Vandermonde systems [2.8]

vegas

adaptive multidimensional Monte Carlo integration [7.8]

voltra

linear Volterra equations of the second kind [18.2]

wt1

one-dimensional discrete wavelet transform [13.10]

wtn

multidimensional discrete wavelet transform [13.10]

wwghts

quadrature weights for an arbitrarily singular kernel [18.3]

zbrac

outward search for brackets on roots [9.1]

zbrak

inward search for brackets on roots [9.1]

zbrent

find root of a function by Brent's method [9.3]

zrhqr

roots of a polynomial by eigenvalue methods [9.5]

zriddr

find root of a function by Ridders' method [9.2]

zroots

roots of a polynomial by Laguerre's method with deflation [9.5]