| 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 _ |