C02 -- Zeros of Polynomials |
| c02aff |
All zeros of complex polynomial, modified Laguerre method |
| c02agf |
All zeros of real polynomial, modified Laguerre method |
C05 -- Roots of One or More Transcendental Equations |
| c05adf |
Zero of continuous function in given interval, Bus and Dekker algorithm |
| c05nbf |
Solution of system of nonlinear equations using function values only (easy-to-use) |
| c05pbf |
Solution of system of nonlinear equations using 1st derivatives (easy-to-use) |
| c05zaf |
Check user's routine for calculating 1st derivatives |
C06 -- Summation of Series |
| c06eaf |
Single 1-D real discrete Fourier transform, no extra workspace |
| c06ebf |
Single 1-D Hermitian discrete Fourier transform, no extra workspace |
| c06ecf |
Single 1-D complex discrete Fourier transform, no extra workspace |
| c06ekf |
Circular convolution or correlation of two real vectors, no extra workspace |
| c06fpf |
Multiple 1-D real discrete Fourier transforms |
| c06fqf |
Multiple 1-D Hermitian discrete Fourier transforms |
| c06frf |
Multiple 1-D complex discrete Fourier transforms |
| c06fuf |
2-D complex discrete Fourier transform |
| c06gbf |
Complex conjugate of Hermitian sequence |
| c06gqf |
Complex conjugate of multiple Hermitian sequences |
| c06gsf |
Convert Hermitian sequences to general complex sequences |
D01 -- Quadrature |
| d01ajf |
1-D quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker,allowing for badly-behaved integrands |
| d01akf |
1-D quadrature, adaptive, finite interval, method suitable for oscillating functions |
| d01alf |
1-D quadrature, adaptive, finite interval, allowing for singularities at user-specifiedbreak-points |
| d01amf |
1-D quadrature, adaptive, infinite or semi-infinite interval |
| d01anf |
1-D quadrature, adaptive, finite interval, weight function cos ( omega x) or sin ( omega x) |
| d01apf |
1-D quadrature, adaptive, finite interval, weight function with end-point singularities ofalgebraico-logarithmic type |
| d01aqf |
1-D quadrature, adaptive, finite interval, weight function 1/(x - c), Cauchy principal value(Hilbert transform) |
| d01asf |
1-D quadrature, adaptive, semi-infinite interval, weight function cos ( omega x) or sin ( omega x) |
| d01bbf |
Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule |
| d01fcf |
Multi-dimensional adaptive quadrature over hyper-rectangle |
| d01gaf |
1-D quadrature, integration of function defined by data values, Gill-Miller method |
| d01gbf |
Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method |
D02 -- Ordinary Differential Equations |
| d02bbf |
ODEs, IVP, Runge-Kutta-Merson method, over a range, intermediate output (simple driver) |
| d02bhf |
ODEs, IVP, Runge-Kutta-Merson method, until function of solution is zero (simple driver) |
| d02cjf |
ODEs, IVP, Adams method, until function of solution is zero, intermediate output (simple driver) |
| d02ejf |
ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output (simple driver) |
| d02gaf |
ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem |
| d02gbf |
ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem |
| d02kef |
2nd order Sturm-Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction,user-specified break-points |
| d02raf |
ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction,continuation facility |
D03 -- Partial Differential Equations |
| d03edf |
Elliptic PDE, solution of finite difference equations by a multigrid technique |
| d03eef | Discretize a 2nd order elliptic PDE on a rectangle |
E01 -- Interpolation |
| e01baf |
Interpolating functions, cubic spline interpolant, one variable |
| e01bef |
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable |
| e01bff |
Interpolated values, interpolant computed by e01bef -, function only, one variable |
| e01bgf | Interpolated values, interpolant computed by e01bef -, function and 1st derivative, one variable |
| e01bhf | Interpolated values, interpolant computed by e01bef -, definite integral, one variable |
| e01daf |
Interpolating functions, fitting bicubic spline, data on rectangular grid |
| e01saf |
Interpolating functions, method of Renka and Cline, two variables |
| e01sbf | Interpolated values, evaluate interpolant computed by e01saf -, two variables |
| e01sef | Interpolating functions, modified Shepard's method, two variables |
| e01sff | Interpolated values, evaluate interpolant computed by e01sef -, two variables |
E02 -- Curve and Surface Fitting |
| e02adf | Least-squares curve fit, by polynomials, arbitrary data points |
| e02aef | Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list) |
| e02agf | Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points, |
| e02ahf | Derivative of fitted polynomial in Chebyshev series form |
| e02ajf | Integral of fitted polynomial in Chebyshev series form |
| e02akf | Evaluation of fitted polynomial in one variable, from Chebyshev series form |
| e02baf | Least-squares curve cubic spline fit (including interpolation) |
| e02bbf | Evaluation of fitted cubic spline, function only |
| e02bcf | Evaluation of fitted cubic spline, function and derivatives |
| e02bdf | Evaluation of fitted cubic spline, definite integral |
| e02bef | Least-squares cubic spline curve fit, automatic knot placement |
| e02daf | Least-squares surface fit, bicubic splines |
| e02dcf | Least-squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid |
| e02ddf | Least-squares surface fit by bicubic splines with automatic knot placement, scattered data |
| e02def | Evaluation of a fitted bicubic spline at a vector of points |
| e02dff | Evaluation of a fitted bicubic spline at a mesh of points |
| e02gaf | 1L -approximation by general linear function |
| e02zaf | Sort 2-D data into panels for fitting bicubic splines |
E04 -- Minimizing or Maximizing a Function |
| e04dgf | Unconstrained minimum, pre-conditioned conjugate gradient algorithm, function of several variables using 1stderivatives (comprehensive) |
| e04dkf | Supply optional parameter values to e04dgf - |
| e04fdf | Unconstrained minimum of a sum of squares, combined Gauss-Newton and modified Newton algorithm usingfunction values only (easy-to-use) |
| e04gcf | Unconstrained minimum of a sum of squares, combined Gauss-Newton and quasi-Newton algorithm, using 1stderivatives (easy-to-use) |
| e04jaf | Minimum, function of several variables, quasi-Newton algorithm, simple bounds,using function values only(easy-to-use) |
| e04mbf | Linear programming problem (easy-to-use) |
| e04naf | Quadratic programming problem (comprehensive) |
| e04ucf | Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values andoptionally 1st derivatives (comprehensive) |
| e04uef | Supply optional parameter values to e04ucf - |
| e04ycf | Covariance matrix for nonlinear least-squares problem |
F01 -- Matrix Factorizations |
| f01brf | LU factorization of real sparse matrix |
| f01bsf | LU factorization of real sparse matrix with known sparsity pattern |
| f01maf | Incomplete Cholesky factorization of real sparse symmetric positive-definite matrix |
| f01mcf | TLDL factorization of real symmetric positive-definite variable-bandwidth matrix |
| f01qcf | QR factorization of real m by n matrix (m >= n) |
| f01qdf | TOperations with orthogonal matrices, compute QB or Q B after factorization by f01qcf - or f01qff - |
| f01qef | Operations with orthogonal matrices, form colspanumns of Q after factorization by f01qcf - or f01qff - |
| f01rcf | QR factorization of complex m by n matrix (m >= n) |
| f01rdf | HOperations with unitary matrices, compute QB or Q B after factorization by f01rcf - |
| f01ref | Operations with unitary matrices, form colspanumns of Q after factorization by f01rcf - |
F02 -- Eigenvalue and Eigenvectors |
| f02aaf | All eigenvalues of real symmetric matrix (Black Box) |
| f02abf | All eigenvalues and eigenvectors of real symmetric matrix (Black Box) |
| f02adf | All eigenvalues of generalized real symmetric-definite eigenproblem (Black Box) |
| f02aef | All eigenvalues and eigenvectors of generalized real symmetric-definite eigenproblem (Black Box) |
| f02aff | All eigenvalues of real matrix (Black Box) |
| f02agf | All eigenvalues and eigenvectors of real matrix (Black Box) |
| f02ajf | All eigenvalues of complex matrix (Black Box) |
| f02akf | All eigenvalues and eigenvectors of complex matrix (Black Box) |
| f02awf | All eigenvalues of complex Hermitian matrix (Black Box) |
| f02axf | All eigenvalues and eigenvectors of complex Hermitian matrix (Black Box) |
| f02bbf | Selected eigenvalues and eigenvectors of real symmetric matrix (Black Box) |
| f02bjf | All eigenvalues and optionally eigenvectors of generalized eigenproblem by QZ algorithm, real matrices (Black Box) |
| f02fjf | Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) |
| f02wef | SVD of real matrix |
| f02xef | SVD of complex matrix |
F04 -- Simultaneous Linear Equations |
| f04adf | Approximate solution of complex simultaneous linear equations with multiple right-hand sides (Black Box) |
| f04arf | Approximate solution of real simultaneous linear equations, one right-hand side (Black Box) |
| f04asf | Accurate solution of real symmetric positive-definite simultaneous linear equations, one right-hand side(Black Box) |
| f04atf | Accurate solution of real simultaneous linear equations, one right-hand side (Black Box) |
| f04axf | Approximate solution of real sparse simultaneous linear equations (coefficient matrix already factorized) |
| f04faf | Approximate solution of real symmetric positive-definite tridiagonal simultaneous linear equations, oneright-handside (Black Box) |
| f04jgf | Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of m real equations in n unknowns,rank <= n, m >= n |
| f04maf | Real sparse symmetric positive-definite simultaneous linear equations(coefficient matrix already factorized) |
| f04mbf | Real sparse symmetric simultaneous linear equations |
| f04mcf | Approximate solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations(coefficient matrix already factorized) |
| f04qaf | Sparse linear least-squares problem, m real equations in n unknowns |
F07 -- Linear Equations (LAPACK) |
| f07adf | LU factorization of real m by n matrix (SGETRF/DGETRF) |
| f07aef | Solution of real system of linear equations, multiple right-hand sides,matrix already factorized by f07adf -(SGETRS/DGETRS) |
| f07fdf | Cholesky factorization of real symmetric positive-definite matrix (SPOTRF/DPOTRF) |
| f07fef | Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrixalready factorized by |
| f07fdf | - (SPOTRS/DPOTRS) |
G01 -- Simple Calculations and Statistical Data |
| g01aaf | Mean, variance, skewness, kurtosis etc, one variable, from raw data |
| g01adf | Mean, variance, skewness, kurtosis etc, one variable, from frequency table |
| g01aef | Frequency table from raw data |
| g01aff | 2Two-way contingency table analysis, with chi /Fisher's exact test |
| g01alf | Computes a five-point summary (median, hinges and extremes) |
| g01arf | Constructs a stem and leaf plot |
| g01eaf | Computes probabilities for the standard Normal distribution |
| g01ebf | Computes probabilities for Student's t-distribution |
| g01ecf | 2Computes probabilities for chi distribution |
| g01edf | Computes probabilities for F-distribution |
| g01eef | Computes upper and lower tail probabilities and probability density function for the beta distribution |
| g01eff | Computes probabilities for the gamma distribution |
| g01faf | Computes deviates for the standard Normal distribution |
| g01fbf | Computes deviates for Student's t-distribution |
| g01fcf | 2Computes deviates for the chi distribution |
| g01fdf | Computes deviates for the F-distribution |
| g01fef | Computes deviates for the beta distribution |
| g01fff | Computes deviates for the gamma distribution |
| g01haf | Computes probabilities for the bivariate Normal distribution |
G02 -- Correlation and Regression Analysis |
| g02bqf | Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data |
| g02bxf | Computes (optionally weighted) correlation and covariance matrices |
| g02caf | Simple linear regression with constant term, no missing values |
| g02daf | Fits a general (multiple) linear regression model |
| g02dgf | Fits a general linear regression model for new dependent variable |
| g02dnf | Computes estimable function of a general linear regression model and its standard error |
| g02faf | Calculates standardized residuals and influence statistics |
| g02gbf | Fits a generalized linear model with binomial errors |
| g02gcf | Fits a generalized linear model with Poisson errors |
G03 -- Multivariate Methods |
| g03aaf | Performs principal component analysis |
| g03adf | Performs canonical correlation analysis |
| g03baf | Computes orthogonal rotations for loading matrix, generalized orthomax criterion |
G05 -- Random Number Generators |
| g05caf | Pseudo-random real numbers, uniform distribution over (0,1) |
| g05cbf | Initialise random number generating routines to give repeatable sequence |
| g05ccf | Initialise random number generating routines to give non-repeatable sequence |
| g05cff | Save state of random number generating routines |
| g05cgf | Restore state of random number generating routines |
| g05ddf | Pseudo-random real numbers, Normal distribution |
| g05dff | Pseudo-random real numbers, Cauchy distribution |
| g05dpf | Pseudo-random real numbers, Weibull distribution |
| g05dyf | Pseudo-random integer from uniform distribution |
| g05dzf | Pseudo-random logical (boolean) value |
| g05eaf | Set up reference vector for multivariate Normal distribution |
| g05ecf | Set up reference vector for generating pseudo-random integers, Poisson distribution |
| g05edf | Set up reference vector for generating pseudo-random integers, binomial distribution |
| g05ehf | Pseudo-random permutation of an integer vector |
| g05ejf | Pseudo-random sample from an integer vector |
| g05exf | Set up reference vector from supplied cumulative distribution function or probability distribution function |
| g05eyf | Pseudo-random integer from reference vector |
| g05ezf | Pseudo-random multivariate Normal vector from reference vector |
| g05faf | Generates a vector of pseudo-random numbers from a uniform distribution |
| g05fbf | Generates a vector of pseudo-random numbers from a (negative) exponential distribution |
| g05fdf | Generates a vector of pseudo-random numbers from a Normal distribution |
| g05fef | Generates a vector of pseudo-random numbers from a beta distribution |
| g05fff | Generates a vector of pseudo-random numbers from a gamma distribution |
| g05hdf | Generates a realisation of a multivariate time series from a VARMA model |
G08 -- Nonparametric Statistics |
| g08aaf | Sign test on two paired samples |
| g08acf | Median test on two samples of unequal size |
| g08aef | Friedman two-way analysis of variance on k matched samples |
| g08aff | Kruskal-Wallis one-way analysis of variance on k samples of unequal size |
| g08agf | Performs the Wilcoxon one sample (matched pairs) signed rank test |
| g08ahf | Performs the Mann-Whitney U test on two independent samples |
| g08ajf | Computes the exact probabilities for the Mann-Whitney U statistic, no ties in pooled sample |
| g08akf | Computes the exact probabilities for the Mann-Whitney U statistic, ties in pooled sample |
| g08cgf | 2Performs the chi goodness of fit test, for standard continuous distributions |
G13 -- Time Series Analysis |
| g13aaf | Univariate time series, seasonal and non-seasonal differencing |
| g13abf | Univariate time series, sample autocorrelation function |
| g13acf | Univariate time series, partial autocorrelations from autocorrelations |
| g13adf | Univariate time series, preliminary estimation, seasonal ARIMA model |
| g13aff | Univariate time series, estimation, seasonal ARIMA model (easy-to-use) |
| g13agf | Univariate time series, update state set for forecasting |
| g13ahf | Univariate time series, forecasting from state set |
| g13ajf | Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model |
| g13asf | Univariate time series, diagnostic checking of residuals, following g13aef - or g13aff - |
| g13baf | Multivariate time series, filtering (pre-whitening) by an ARIMA model |
| g13bcf | Multivariate time series, cross correlations |
| g13bdf | Multivariate time series, preliminary estimation of transfer function model |
| g13bef | Multivariate time series, estimation of multi-input model |
| g13bjf | Multivariate time series, state set and forecasts from fully specified multi-input model |
| g13cbf | Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency(Daniell) window |
| g13cdf | Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency(Daniell) window |
M01 -- Sorting |
| m01caf | Sort a vector, real numbers |
| m01daf | Rank a vector, real numbers |
| m01def | Rank rows of a matrix, real numbers |
| m01djf | Rank colspanumns of a matrix, real numbers |
| m01eaf | Rearrange a vector according to given ranks, real numbers |
| m01zaf | Invert a permutation |
S -- Approximations of Special Functions |
| s01eaf | zComplex exponential, e |
| s13aaf | Exponential integral E (x) 1 |
| s13acf | Cosine integral Ci(x) |
| s13adf | Sine integral Si(x) |
| s14aaf | Gamma function |
| s14abf | Log Gamma function |
| s14baf | Incomplete gamma functions P(a,x) and Q(a,x) |
| s15adf | Complement of error function erfc x |
| s15aef | Error function erf x |
| s17acf | Bessel function Y (x) 0 |
| s17adf | Bessel function Y (x) 1 |
| s17aef | Bessel function J (x) 0 |
| s17aff | Bessel function J (x) 1 |
| s17agf | Airy function Ai(x) |
| s17ahf | Airy function Bi(x) |
| s17ajf | Airy function Ai' (x) |
| s17akf | Airy function Bi' (x) |
| s17dcf | Bessel functions Y (z), real a >= 0, complex z, nu + anu = 0,1,2,... |
| s17def | Bessel functions J (z), real a >= 0, complex z, nu +anu = 0,1,2,... |
| s17dgf | Airy functions Ai(z) and Ai' (z), complex z |
| s17dhf | Airy functions Bi(z) and Bi' (z), complex z |
| s17dlf | jHankel functions H (z), j = 1,2, real nu + aa >= 0, complex z, nu = 0,1,2,... |
| s18acf | Modified Bessel function K (x) 0 |
| s18adf | Modified Bessel function K (x) 1 |
| s18aef | Modified Bessel function I (x) 0 |
| s18aff | Modified Bessel function I (x) 1 |
| s18dcf | Modified Bessel functions K (z), real a >= 0, nu + acomplex z, nu = 0,1,2,... |
| s18def | Modified Bessel functions I (z), real a >= 0, nu + acomplex z, nu = 0,1,2,... |
| s19aaf | Kelvin function ber x |
| s19abf | Kelvin function bei x |
| s19acf | Kelvin function ker x |
| s19adf | Kelvin function kei x |
| s20acf | Fresnel integral S(x) |
| s20adf | Fresnel integral C(x) |
| s21baf | Degenerate symmetrised elliptic integral of 1st kind R (x,y) C |
| s21bbf | Symmetrised elliptic integral of 1st kind R (x,y,z) F |
| s21bcf | Symmetrised elliptic integral of 2nd kind R (x,y,z) D |
| s21bdf | Symmetrised elliptic integral of 3rd kind R (x,y,z,r) J |
