With PV-WAVE Advantage, the power of the IMSL advanced mathematics and statistics packages is at your fingertips. Powerful mathematical routines are available to make your programming more productive and provide you with the utmost in numerical power. The IMSL mathematical libraries provide a full range of capabilities, with subroutines for engineering, the sciences and other areas requiring accurate, reliable mathematical computation. The routines will save implementation time and help guarantee the accuracy of your results because you do not have to rely on implementing your own or public domain algorithms.

A more complete listing of Mathematical and Statistical Functions:

Linear Systems

CHFAC Computes the Cholesky factor L of a real or complex symmetric positive definite matrix A, such that A=LLH.   CHNNDFAC Computes the Cholesky factorization of the real matrix A such that A=RTR=LLT.   CHNNDSOL Solves a real symmetric nonnegative definite system of linear equations Ax=b. Computes the solution to Ax=b given the Cholesky factor.   CHSOL Solves s symmetric positive definite system of real or complex linear equations Ax=b. INV Computes the inverse of a real or complex square matrix.   LUFAC Computes the LU factorization of a real or complex matrix.   LUSOL Solves a general system of real or complex linear equations Ax=b.   QRFAC Computes the QR factorization of a real matrix A.   QRSOL Solves a real linear least-squares problem Ax=b.   SVDCOMP Computes the singular value decomposition (SVD), A=USVT, of a real or complex rectangular matrix A. An estimate of the rank of A also can be computed. Eigensystem Analysis 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.   EIGSYMGEN Computes the generalized eigenexpansion of a system The matrices A and B are real and symmetric, and B is positive definite. Interpolation and Approximation   BSINTERP Computes a one- or two-dimensional spline interpolant.   BSKNOTS Computes the knots for a spline interpolant.   BSLSQ Computes a one- or two-dimensional, least-squares spline approximation.   CONLSQ Computes a least-squares constrained spline approximation.   CSINTERP Computes a cubic spline interpolant, specifying various endpoint conditions. The default interpolant satisfies the "not-a-knot" condition.   CSSHAPE Computes a shape-preserving cubic spline.   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.   FCNLSQ Computes a least-squares fit using user-supplied functions.   RADBE Evaluates a radial-basis fit computed by RADBF.   RADBF Computes an approximation to scattered data in IRn for n>2 using radial-basis functions.   SCAT2DINTERP Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.   SPINTEG Computes the integral of a one- or two-dimensional spline.   SPVALUE Computes values of a spline or values of one of its derivatives.

Quadrature

GQUAD Computes a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule with various classical weight functions.   INTFCN INTFCN Integrates a user-supplied function. Using different combinations of keywords and parameters, one of several types of integration can be performed including the following: Integration of functions based on Gauss-Kronrod rules Integration of functions with singular points given Integration of functions with algebraic-logarithmic singularities Integration of functions over an infinite or semi-infinite interval Integration of functions containing a sine or cosine factor Computation of Fourier sine and cosine transforms Integrals in the Cauchy principle value sense Integration of smooth functions using a nonadaptive rule Computation of two-dimensional iterated integrals   FFTCOMP Computes the discrete Fourier transform of a real or complex sequence. Using keywords, a real-to-complex transform or a two-dimensional complex Fourier transform can be computed.   INTFCNHYPER Integrates a function on a hyper-rectangle as follows:

Differential Equations

Transforms

FFTINIT Computes the parameters for a one-dimensional FFT for optional use with function FFTCOMP.   Nonlinear Equations   ZEROFCN ZEROFCN Finds the real zeros of a real function using Müller's method.   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.   ZEROSYS Solves a system of n nonlinear equations, Fi(x)=0, using a modified Powell hybrid algorithm.

Optimization

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.   FMINV Minimizes a function f(x) of n variables using a quasi-Newton method.   LINPROG Solves a linear programming problem using the revised simplex algorithm.   NLINLSQ Solves a nonlinear least-squares problem using a modified Levenberg-Marquardt algorithm.   NONLINPROG Solves a general nonlinear programming problem using the successive quadratic programming (QP) algorithm.   QUADPROG Solves a quadratic programming (QP) problem subject to linear equality or inequality constraints.

Probability Distribution Functions and Inverses

BETACDF Evaluates the beta probability distribution function.   BINOMIALCDF Evaluates the binomial distribution function.   BINORMALCDF Evaluates the bivariate normal distribution function.   CHISQCDF Evaluates the chi-squared distribution function. Using a keyword, the inverse of the chi-squared distribution can be evaluated.   FCDF Evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.   GAMMACDF Evaluates the gamma distribution function.   HYPERGEOCDF Evaluates the hypergeometric distribution function.   NORMALCDF Evaluates the standard normal (Gaussian) distribution function. Using a keyword, the inverse of the standard normal (Gaussian) distribution can be evaluated.   POISSONCDF Evaluates the Poisson distribution function.   TCDF Evaluates the Student's t distribution function.

Special Functions

BESSI Evaluates a modified Bessel function of the first kind with real order and real or complex parameters.   BESSJ Evaluates a Bessel function of the first kind with real order and real or complex parameters.   BESSK Evaluates a modified Bessel function of the second kind with real order and real or complex parameters.   BESSY Evaluates a Bessel function of the second kind with real order and real or complex parameters.   BETA Evaluates the real beta function.   BETAI Evaluates the real incomplete beta function.   ERF Evaluates the real error function. Using a keyword, the inverse error function erf-1(x) can be evaluated.   ERFC Evaluates the real complementary error function erfc(x). Using a keyword, the inverse complementary error function erfc-1(x) can be evaluated   GAMMA Evaluates the real gamma function G(x).   GAMMAI Evaluates the incomplete gamma function g(x).   LNBETA Evaluates the logarithm of the beta function in ß(x,y).   LNGAMMA Evaluates the logarithm of the absolute value of the gamma function in |G(x)|.

Basic Statistics and Random Number Generation

CHISQTEST Performs a chi-squared goodness-of-fit test.   FREQTABLE Tallies observations into a one-way frequency table.   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.   RANDOMOPT Uses keywords to set or retrieve the random number seed or to select the uniform (0,1) multiplicative, congruential pseudorandom-number generator.   RANKS Computes the ranks, normal scores or exponential scores for a vector of observations.

Utilities

CMAST_ERR_TRANS Determines if an Informational Error has occurred.   CONSTANT Returns the value of various mathematical and physical constants.   DATETODAYS Computes the number of days from January 1, 1900, to the given date.   DAYSTODATE Gives the date corresponding to the number of days since January 1, 1900.   MACHINE Returns information describing the computer's arithmetic.   NORM Computes various norms of a vector or the difference of two vectors.

Basic Statistics and Random Number Generation

CHISQTEST Performs a chi-squared goodness-of-fit test.   CONTINGENCY Performs a chi-squared analysis of a two-way contingency table.   FREQTABLE Tallies observations into a one-way frequency table.   NORM1SAMP Computes statistics for mean and variance inferences using a sample from a normal population.   NORM2SAMP Computes statistics for mean and variance inferences using samples from two independently normal populations.   NORMALITY Performs a test for normality.   RADOM Generates pseudorandom numbers. The default distribution is a uniform (0,1) distribution, but many different distributions can be specified through the use of keywords.   RANDOMOPT Uses keywords to set or retrieve the random number seed or to select the uniform (0,1) multiplicative, congruential pseudorandom-number generator.   RANKS Computes the ranks, normal scores or exponential scores for a vector of observations.   SIGNTEST Performs a sign test.   SIMPLESTAT Computes basic univariate statistics.   SORTDATA Sorts observations by specified keys, with option to tally cases into a multiway frequency table.   WILCOXON Performs a Wilcoxon rank sum test.

Correlation and Regression

ALLBEST Selects the best multiple linear regression models.   COVARIANCES Computes the sample variance-covariance of correlation matrix.   MULTIPREDICT Computes predicted values, confidence intervals and diagnostics after fitting regression model.   MULTIREGRESS Fits a nonlinear regression model using least squares and optionally computes summary statistics for the regression model.   NONLINREGRESS Fits a nonlinear regression model.   POLYPREDICT Computes predicted values, confidence intervals and diagnostics after fitting a polynomial.   POLYREGRESS Performs a polynomial least-squares regression.   REGRESSORS Generates regressors for a general linear model.   STEPWISE Builds multiple linear regression models using forward, backward or stepwise selection.

Analysis of Variance

ANOVA1 Analyzes a one-way classification model.   ANOVAFACT Analyzes a balanced factorial design with fixed effects.   MULTICOMP Performs Student-Newman-Keuls multiple-comparisons test.

Time Series and Forecasting

ARMA Computes method-of-moments or least-squares estimates of parameters for a nonseasonal ARMA model.   DIFFERENCE Differences a seasonal or nonseasonal time series.

Multivariate Analysis

FACTOR_ANALYSIS Extracts initial factor-loading estimates in factor analysis.   K_MEANS Performs a K-means (centroid) cluster analysis.   PRINC_COMP Computes principal components. Probability Distribution Functions and Inverses   BETACDF Evaluates the beta probability distribution function.   BINOMIALCDF Evaluates the binomial distribution function.   BINORMALCDF Evaluates the bivariate normal distribution function.   CHISQCDF Evaluates the chi-squared distribution function. Using a keyword, the inverse of the chi-squared distribution can be evaluated.   FCDF Evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.   GAMMACDF Evaluates the gamma distribution function.   HYPERGEOCDF Evaluates the hypergeometric distribution function.   NORMALCDF Evaluates the standard normal (Gaussian) distribution function. Using a keyword, the inverse of the standard normal (Gaussian) distribution can be evaluated.   POISSONCDF Evaluates the Poisson distribution function.   TCDF Evaluates the Student's t distribution function

Utilities

CMAST_ERR_TRANS Determines if an Informational Error has occurred.   MACHINE Returns information describing the computer's arithmetic.   STATDATA Retrieves commonly analyzed data sets.