Alphabetical Listing of IMSL Routines

This chapter contains an alphabetical listing of routines included in the IDL Advanced Math and Stats module.

IMSL_AIRY_AI—Evaluates the Airy function.

IMSL_AIRY_BI—Evaluates the Airy function of the second kind.

"IMSL_ALLBEST" on page 630—Selects the best multiple linear regression models.

IMSL_ANOVA1—Analyzes one-way classification model.

IMSL_ANOVABALANCED—Balanced fixed, random, or mixed model.

IMSL_ANOVAFACT—Analyzes a balanced factorial design with fixed effects.

IMSL_ANOVANESTED—Nested random mode.

"IMSL_ARMA" on page 913—Computes method-of-moments or least-squares estimates of parameters for a nonseasonal ARMA model.

"IMSL_AUTOCORRELATION" on page 940—Sample autocorrelation function.

IMSL_BESSI—Evaluates a modified Bessel function of the first kind with real order and real or complex parameters.

IMSL_BESSI_EXP—Evaluates the exponentially scaled modified Bessel function of the first kind of orders zero and one.

IMSL_BESSJ—Evaluates a Bessel function of the first kind with real order and real or complex parameters.

IMSL_BESSK—Evaluates a modified Bessel function of the second kind with real order and real or complex parameters.

IMSL_BESSK_EXP—Evaluates the exponentially scaled modified Bessel function of the third kind of orders zero and one.

IMSL_BESSY—Evaluates a Bessel function of the second kind with real order and real or complex parameters.

IMSL_BETA—Evaluates the real beta function B(x,y).

IMSL_BETACDF—Evaluates the beta probability distribution function.

IMSL_BETAI—Evaluates the real incomplete beta function.

IMSL_BINOMIALCDF—Evaluates the binomial distribution function.

IMSL_BINOMIALCOEF—Evaluate binomial coefficient.

IMSL_BINOMIALPDF—Evaluates the binomial probability function.

IMSL_BINORMALCDF—Evaluates the bivariate normal distribution function.

"IMSL_BOXCOXTRANS" on page 935—Perform Box-Cox transformation

IMSL_BSINTERP—Computes a one- or two-dimensional spline interpolant.

IMSL_BSKNOTS—Computes the knots for a spline interpolant.

IMSL_BSLSQ—Computes a one- or two-dimensional, least-squares spline approximation.

IMSL_CAT_GLM—Generalized linear models.

IMSL_CHFAC—Computes the Cholesky factor, L, of a real or complex symmetric positive definite matrix A, such that A = LL^T.

IMSL_CHISQCDF—Evaluates the chi-squared distribution function. Using a keyword, the inverse of the chi-squared distribution can be evaluated.

IMSL_CHISQCDF—Evaluates the chi-squared distribution function. Using a keyword, the inverse of the chi-squared distribution can be evaluated.

IMSL_CHISQTEST—Performs a chi-squared goodness-of-fit test.

IMSL_CHNNDFAC—Computes the Cholesky factorization of the real matrix A such that A = R^TR = LL^T.

IMSL_CHNNDSOL—Solves a real symmetric nonnegative definite system of linear equations Ax = b. Computes the solution to Ax = b given the Cholesky factor.

IMSL_CHSOL—Solves a symmetric positive definite system of real or complex linear equations Ax = b.

IMSL_COCHRANQ—Cochran's Q test.

IMSL_CONLSQ—Computes a least-squares constrained spline approximation.

IMSL_CONSTANT—Returns the value of various mathematical and physical constants.

IMSL_CONSTRAINED_NLP—Using a sequential equality constrained quadratic programming method.

IMSL_CONT_TABLE—Sets up a table to generate pseudorandom numbers from a general continuous distribution.

IMSL_CONTINGENCY—Performs a chi-squared analysis of a two-way contingency table.

IMSL_CONVOL1D—Computes the discrete convolution of two one dimensional arrays.

IMSL_CORR1D—Compute the discrete correlation of two one-dimensional arrays.

IMSL_COVARIANCES—Computes the sample variance-covariance or correlation matrix.

IMSL_CSINTERP—Computes a cubic spline interpolant, specifying various endpoint conditions. The default interpolant satisfies the not-a-knot condition.

IMSL_CSSHAPE—Computes a shape-preserving cubic spline.

IMSL_CSSMOOTH—Computes a smooth cubic spline approximation to noisy data by using cross-validation to estimate the smoothing parameter or by directly choosing the smoothing parameter.

IMSL_CSTRENDS—Cox and Stuarts' sign test for trends in location and dispersion.

IMSL_DATETODAYS—Computes the number of days from January 1, 1900, to the given date.

IMSL_DAYSTODATE—Gives the date corresponding to the number of days since January 1, 1900.

"IMSL_DIFFERENCE" on page 929—Differences a seasonal or nonseasonal time series.

"IMSL_DISCR_ANALYSIS" on page 992—Perform discriminant function analysis.

IMSL_DISCR_TABLE—Sets or retrieves the current table used in either the shuffled or GFSR random number generator

IMSL_EIG—Computes the eigenexpansion of a real or complex matrix A. If the matrix is known to be symmetric or Hermitian, a keyword can be used to trigger more efficient algorithms.

IMSL_EIGSYMGEN—Computes the generalized eigenexpansion of a system Ax = λBx. The matrices A and B are real and symmetric, and B is positive definite.

IMSL_ELE—Evaluates the complete elliptic integral of the second kind E(x).

IMSL_ELK—Evaluates the complete elliptic integral of the kind K(x).

IMSL_ELRC—Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

IMSL_ELRD—Evaluates Carlson's elliptic integral of the second kind R_D(x, y, z).

IMSL_ELRF—Evaluates Carlson's elliptic integral of the first kind R_F(x, y, z).

IMSL_ELRJ—Evaluates Carlson's elliptic integral of the third kind R_J(x, y, z, r).

IMSL_ERF—Evaluates the real error function erf ( x ). Using a keyword, the inverse error function erf^-1(x) can be evaluated.

IMSL_ERFC—Evaluates the real complementary error function erf(x). Using a keyword, the inverse complementary error function erf^-1(x) can be evaluated.

IMSL_EXACT_ENUM—Exact probabilities in a table; total enumeration.

IMSL_EXACT_NETWORK—Exact probabilities in a table.

"IMSL_FACTOR_ANALYSIS" on page 981—Extracts initial factor-loading estimates in factor analysis.

IMSL_FAURE_INIT—Initializes the structure used for computing a shuffled Faure sequence.

IMSL_FAURE_NEXT_PT—Generates shuffled Faure sequence.

IMSL_FCDF—Evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.

IMSL_FCN_DERIV—Computes the first, second, or third derivative of a user-supplied function.

IMSL_FCNLSQ—Computes a least-squares fit using user-supplied functions.

IMSL_FFTCOMP—Computes discrete Fourier transform of a real or complex sequence. Using keywords, a real-to-complex transform or two-dimensional complex Fourier transform can be computed.

IMSL_FFTINIT—Computes parameters for a one-dimensional FFT to be used in the IMSL_FFTCOMP function with keyword Init_Params.

IMSL_FMIN—Finds the minimum point of a smooth function f (x) of a single variable using function evaluations and, optionally, through both function evaluations and first derivative evaluations.

IMSL_FMINV—Minimizes a function f(x) of n variables using a quasi-Newton method.

IMSL_FREQTABLE—Tallies observations into a one-way frequency table.

IMSL_FRESNEL_COSINE—Evaluates cosine Fresnel integral.

IMSL_FRESNEL_SINE—Evaluates sine Fresnel integral.

IMSL_FRIEDMANS_TEST—Friedman's test.

IMSL_GAMMA_ADV—Evaluate the real gamma function.

IMSL_GAMMACDF—Evaluates the gamma distribution function.

IMSL_GAMMAI—Evaluate incomplete gamma function.

"IMSL_GARCH" on page 952—Compute estimates of the parameters of a GARCH(p,q) model

IMSL_GENEIG—Computes the generalized eigenexpansion of a system Ax = λBx.

IMSL_GQUAD—Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.

IMSL_HYPERGEOCDF—Evaluates the hypergeometric distribution function.

"IMSL_HYPOTH_PARTIAL" on page 675—Constructs an equivalent completely testable multivariate general linear hypothesis HβU = G from a partially testable hypothesis H_pβU = G_p.

"IMSL_HYPOTH_SCPH" on page 681—Computes the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis HβU = G given the regression fit.

"IMSL_HYPOTH_TEST" on page 686—Performs tests for a multivariate general linear hypothesis HβU = G given the hypothesis sums of squares and crossproducts matrix S_H.

IMSL_INTFCN—Integrates a user-supplied function using different combinations of keywords and parameters.

IMSL_INTFCN_QMC—Integrates a function on a hyper-rectangle using a quasi-Monte Carlo method.

IMSL_INTFCNHYPER—Integrates a function on a hyper-rectangle.

IMSL_INV—Computes the inverse of a real or complex, square matrix.

"IMSL_K_MEANS" on page 971—Performs a K-means (centroid) cluster analysis.

"IMSL_KALMAN" on page 957—Performs Kalman filtering and evaluates the likelihood function or the state-space model.

IMSL_KELVIN_BEI0—Evaluates the Kelvin function of the first kind, bei, of order zero.

IMSL_KELVIN_BER0—Evaluates the Kelvin function of the first kind, ber, of order zero.

IMSL_KELVIN_KEI0—Evaluates the Kelvin function of the second kind, kei, of order zero.

IMSL_KELVIN_KER0—Evaluates the Kelvin function of the second kind, ker, of order zero.

IMSL_KOLMOGOROV1—One-sample continuos data Kolmogorov-Smirnov.

IMSL_KOLMOGOROV2—Two-sample continuos data Kolmogorov-Smirnov.

IMSL_KTRENDS—K-sample trends test.

IMSL_KW_TEST—Kruskal-Wallis test.

"IMSL_LACK_OF_FIT" on page 948—Lack-of-fit test based on the correlation function

IMSL_LAPLACE_INV—Computes the inverse Laplace transform of a complex function.

IMSL_NLINLSQ—Solves a linear least-squares problem with linear constraints.

IMSL_LINLSQ—Linear constraints

IMSL_LINPROG—Solves a linear programming problem using the revised simplex algorithm.

IMSL_LNBETA—Evaluate the log of the real beta function.

IMSL_LNGAMMA—Evaluate the logarithm of the absolute value of the gamma function.

"IMSL_LNORMREGRESS" on page 703—Fits a multiple linear regression model using criteria other than least squares.

IMSL_LUFAC—Computes the LU factorization of a real or complex matrix.

IMSL_LUSOL—Solves a general system of real or complex linear equations Ax = b.

IMSL_MACHINE—Returns information describing the computer's arithmetic.

IMSL_MATRIX_NORM—Computes various norms of a rectangular matrix, a matrix stored in band format, and a matrix stored in coordinate format.

IMSL_MINCONGEN—Minimizes a general objective function subject to linear equality/inequality constraints.

IMSL_MULTICOMP—Performs Student-Newman-Keuls multiple-comparisons test.

"IMSL_MULTIPREDICT" on page 622—Computes predicted values, confidence intervals, and diagnostics after fitting a regression model.

"IMSL_MULTIREGRESS" on page 607—Fits a multiple linear regression model using least squares and optionally compute summary statistics for the regression model.

IMSL_MVAR_NORMALITY—Mardia's test for multivariate normality.

IMSL_NCTRENDS—Noehter's test for cyclical trend.

IMSL_NLINLSQ—Solves a nonlinear least-squares problem using a modified Levenberg-Marquardt algorithm.

"IMSL_NONLINOPT" on page 694—Fits data to a nonlinear model (possibly with linear constraints) using the successive quadratic programming algorithm (applied to the sum of squared errors, sse = Σ(y_i - f(x_i; θ))2) and either a finite difference gradient or a user-supplied gradient.

"IMSL_NONLINREGRESS" on page 665—Fits a nonlinear regression model.

IMSL_NORM—Computes various norms of a vector or the difference of two vectors.

IMSL_NORMALCDF—Evaluates the standard normal (Gaussian) distribution function. Using a keyword, the inverse of the standard normal (Gaussian) distribution can be evaluated.

IMSL_NORM1SAMP—Computes statistics for mean and variance inferences using a sample from a normal population.

IMSL_NORM2SAMP—Computes statistics for mean and variance inferences using samples from two independently normal populations.

IMSL_NORMALITY—Performs a test for normality.

IMSL_ODE—Adams-Gear or Runge-Kutta method.

"IMSL_PARTIAL_AC" on page 945—Sample partial autocorrelation function

IMSL_PARTIAL_COV—Partial correlations and covariances.

IMSL_PDE_MOL—Solves a system of partial differential equations of the form ut = f(x, t, u, u_x, u_xx) using the method of lines. The solution is represented with cubic Hermite polynomials.

IMSL_POISSON2D—Solves Poisson's or Helmholtz's equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.

IMSL_POISSONCDF—Evaluates the Poisson distribution function.

"IMSL_POLYPREDICT" on page 657—Computes predicted values, confidence intervals, and diagnostics after fitting a polynomial regression model.

"IMSL_POLYREGRESS" on page 649—Performs a polynomial least-squares regression.

IMSL_POOLED_COV—Pooled covariance matrix.

"IMSL_PRINC_COMP" on page 976—Computes principal components.

IMSL_QRFAC—Computes the QR factorization of a real matrix A.

IMSL_QRSOL—Solves a real linear least-squares problem Ax = b.

IMSL_QUADPROG—Solves a quadratic programming (QP) problem subject to linear equality or inequality constraints.

IMSL_RADBE—Evaluates a radial-basis fit computed by IMSL_RADBF.

IMSL_RADBF—Computes an approximation to scattered data in Rⁿ for n ≥ 2 using radial-basis functions.

IMSL_RAND_FROM_DATA—Generates pseudorandom numbers from multivariate distribution determined from a given sample.

IMSL_RAND_GEN_CONT—Generates pseudorandom numbers from a general continuous distribution.

IMSL_RAND_GEN_DISCR—Generates pseudorandom numbers from a general discrete distribution using an alias method or optionally a table lookup method.

IMSL_RAND_ORTH_MAT—Generates a pseudorandom orthogonal matrix or a correlation matrix

IMSL_RAND_TABLE_2WAY—Generates a pseudorandom two-way table.

IMSL_RANDOM—Generates pseudorandom numbers. The default distribution is a uniform (0, 1) distribution, but many different distributions can be specified through the use of keywords.

IMSL_RANDOM_ARMA—Generate pseudorandom IMSL_ARMA process numbers

IMSL_RANDOM_NPP—Generates pseudorandom numbers from a nonhomogeneous Poisson process.

IMSL_RANDOM_ORDER—Generates pseudorandom order statistics from a standard normal distribution.

IMSL_RANDOM_SAMPLE—Generates a simple pseudorandom sample from a finite population

IMSL_RANDOM_TABLE—Sets or retrieves the current table used in either the shuffled or GFSR random number generator.

IMSL_RANDOMNESS_TEST—Runs test, Paris-serial test, d2 test or triplets tests.

IMSL_RANDOMOPT—Uses keywords to set or retrieve the random number seed or to select the uniform (0, 1) multiplicative, congruential pseudorandom-number generator.

IMSL_RANKS—Computes the ranks, normal scores, or exponential scores for a vector of observations.

"IMSL_REGRESSORS" on page 600—Generates regressors for a general linear model.

IMSL_ROBUST_COV—Robust estimate of covariance matrix.

IMSL_SCAT2DINTERP—Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.

IMSL_SIGNTEST—Performs a sign test.

IMSL_SIMPLESTAT—Computes basic univariate statistics.

IMSL_SMOOTHDATA1D—Smooth one-dimensional data by error detection.

IMSL_SORTDATA—Sorts observations by specified keys, with option to tally cases into a multiway frequency table.

IMSL_SP_BDFAC—Compute the LU factorization of a matrix stored in band storage mode.

IMSL_SP_BDPDFAC—Compute the R^TR Cholesky factorization of symmetric positive definite matrix, A, in band symmetric storage mode.

IMSL_SP_BDPDSOL—Solve a symmetric positive definite system of linear equations Ax = b in band symmetric storage mode.

IMSL_SP_BDSOL—Solve a general band system of linear equations Ax = b.

IMSL_SP_CG—Solve a real symmetric definite linear system using a conjugate gradient method. Using keywords, a preconditioner can be supplied.

IMSL_SP_GMRES—Solve a linear system Ax = b using the restarted generalized minimum residual (GMRES) method.

IMSL_SP_LUFAC—Compute an LU factorization of a sparse matrix stored in either coordinate format or CSC format.

IMSL_SP_LUSOL—Solve a sparse system of linear equations Ax = b.

IMSL_SP_MVMUL—Compute a matrix-vector product involving sparse matrix and a dense vector.

IMSL_SP_PDFAC—Solve a sparse symmetric positive definite system of linear equations Ax = b.

IMSL_SP_PDSOL—Solve a sparse symmetric positive definite system of linear equations Ax = b.

IMSL_SPINTEG—Computes the integral of a one- or two-dimensional spline.

IMSL_SPVALUE—Computes values of a spline or values of one of its derivatives.

IMSL_STATDATA—Retrieves commonly analyzed data sets.

"IMSL_STEPWISE" on page 639—Builds multiple linear regression models using forward, backward, or stepwise selection.

IMSL_SURVIVAL_GLM—Analyzes survival data using a generalized linear model and estimates using various parametric modes.

IMSL_SVDCOMP—Computes the singular value decomposition (SVD), A=USV^T, of a real or complex rectangular matrix A. An estimate of the rank of A also can be computed.

IMSL_TCDF—Evaluates the Student's t distribution function.

IMSL_TIE_STATS—Tie statistics.

IMSL_WILCOXON—Performs a Wilcoxon rank sum test.

IMSL_ZEROFCN—Finds the real zeros of a real function using Müller's method.

IMSL_ZEROPOLY—Finds the zeros of a polynomial with real or complex coefficients using the companion matrix method or, optionally, the Jenkins-Traub, three-stage algorithm.

IMSL_ZEROSYS—Solves a system of n nonlinear equations using a modified Powell hybrid algorithm.