| 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 _ |
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Numerical Recipes in FORTRAN 77 with files from diskette v1.0 and v1.1
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