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Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 1 Scientific Subroutine Package Library Summary List of Modules The Scientific Subroutine Package (SSP) routines are divided into a number of separate libraries based upon the category of program that each module can be placed. The following listing is a listing of each of the libraries and the modules contained in each library. Statistics Library 1 - Data Screening Modules - STATDATA.ARC TALLY - totals, means, standard deviations, minimums, and maximums BOUND - selection of observations within bounds SUBST - subset selection from observation matrix ABSNT - detection of missing data TAB1 - tabulation of data (one variable) TAB2 - tabulation of data (two variables) SUBMX - building of subset matrix Statistics Library 2 - Correlation and Regression - STATCORR.ARC CORRE - means, standard deviations, and correlations MISR - means, standard deviations, third and fourth moments (skew and kurtosis), correlations, simple regression coefficients and their standard errors, considers that data may be missing ORDER - rearrangement of intercorrelations MULTR - multiple linear regression GDATA - data matrix generation for polynomial regression STPRG - stepwise multiple linear regression PROBT - probit analysis CANOR - canonical correlation Statistics Library 3 - Design Analysis - STATDSGN.ARC AVDAT - data storage allocation Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 2 AVCAL - Sigma and Delta operation MEANQ - mean square operation Statistics Library 4 - Discriminant Analysis - STATDSCR.ARC DMATX - means and dispersion matrix DISCR - discriminant functions Statistics Library 5 - Factor Analysis - STATFCTR.ARC TRACE - cumulative percentage of eigenvalues LOAD - factor loading VARMX - varimax rotation Statistics Library 6 - Time Series - STATTMSR.ARC AUTO - autocovariances CORSS - crosscovariances SMO - application of filter coefficients (weights) EXSMO - triple exponential smoothing Statistics Library 7 - Nonparametric Statistics - STATNONP.ARC KOLMO - Kolmogorov-Smirnov one-sample test KOLM2 - Kolmogorov-Smirnov two-sample test SMIRN - Kolmogorov-Smirnov limiting distribution values CHISQ - Chi square test for contingency tables KRANK - Kendall rank correlation MPAIR - Wilcoxin's signed ranks test QTEST - Cochran Q-test RANK - rank observations SIGNT - sign test SRANK - Spearman rank correlation TIE - calculation of ties in ranked observations Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 3 TWOAV - Friedman two-way analysis of variance statistic UTEST - Mann-Whitney U-test WTEST - Kendall coefficient of concordance Statistics Library 8 - Generation of Random Variables and Distribution Functions - STATRAND.ARC RANDU - uniform random deviates GAUSS - normal deviates NTDR - normal distribution function BTDR - beta distribution function CDTR - Chi square distribution function NDTRI - inverse of normal distribution function Statistics Library 9 - Elementary Statistics and Miscellaneous Functions - STATMISC.ARC MOMEN - First four moments TTEST - test on population means BISER - biserial correlation coefficient PHI - phi coefficient POINT - point-biserial correlation coefficient TETRA - tetrachordic correlation coefficient SRATE - survival rates Matrices Library 1 - Storage Functions - MATSTOR.ARC MCPY - matrix copy RCPY - copy row of matrix into vector CCPY - copy column of matrix into vector DCPY - copy diagonal of matrix into vector XCPY - copy submatrix from given matrix MSTR - storage conversion Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 4 LOC - location in compressed-stored matrix CONVT - single precision - double precision conversion ARRAY - vector storage - double dimensioned storage conversion Matrices Library 2 - Operations - MATOPS.ARC GMADD - add two general matrices GMSUB - subtract two general matrices GMPRD - product of two general matrices GMTRA - transpose of a general matrix GTPRD - transpose product of two general matrices MADD - add two matrices MSUB - subtract two matrices MPRD - matrix product (row into column) MTRA - transpose a matrix TPRD - transpose product of two matrices MATA - transpose product of a matrix by itself SADD - add scalar to matrix SSUB - subtract scalar from matrix SMPY - matrix multiplied by a scalar SDIV - matrix divided by a scalar SCLA - matrix clear and add scalar DCLA - replace diagonal with scalar RADD - add row of one matrix to row of another matrix CADD - add column of one matrix to column of another matrix SRMA - scalar multiply row and add to another row SCMA - scalar multiply column and add to another column RINT - interchange two rows CINT - interchange two columns RSUM - sum the rows of a matrix Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 5 CSUM - sum the columns of a matrix RTAB - tabulate the rows of a matrix CTAB - tabulate the columns of a matrix RSRT - sort matrix rows CSRT - sort matrix columns RCUT - partition by row CCUT - partition by column RTIE - adjoin two matrices by row CTIE - adjoin two matrices by column MPRC - permute rows or columns DMPRC - double precision permute of rows or columns MFUN - matrix transformation by a function RECP - reciprocal function for MFUN Matrices Library 3 - Inversion, System of Linear Equations and Related Topics - MATINSL.ARC MINV - matrix inversion SINV - invert a symmetric positive definite matrix DSINV - invert at double precision symmetric positive definite matrix SIMQ - solution of simultaneous linear algebraic equations GELG - system of general simultaneous linear equations by Gauss elimination DGELG - system of double precision general simultaneous linear equations by Gauss elimination RSLMC - solution of simultaneous linear equations with iterative refinement FACTR - triangular factorization of a nonsingular matrix MFGR - matrix factorization and rank determination DMFGR - double precision matrix factorization and rank determination GELS - system of general simultaneous linear equations with symmetric coefficients Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 6 DGELS - double precision system of general simultaneous linear equations with symmetric coefficients GELB - system of general simultaneous linear equations with band structured coefficients DGELB - double precision system of general simultaneous linear equations with band structured coefficients MTDS - divide a matrix by a triangular matrix DMTDS - double precision division of a matrix by a triangular matrix MLSS - solution of simultaneous linear equations with symmetric positive semidefinite matrix DMLSS - double precision solution of simultaneous linear equations with symmetric positive semidefinite matrix MCHB - triangular factorization of a symmetric positive definite band matrix DMCHB - double precision triangular factorization of a symmetric positive definite band matrix MFSS - triangular factorization and rank determination of a symmetric positive semidefinite matrix DMFSS - double precision triangular factorization and rank determination of a symmetric positive semidefinite matrix MFSD - triangular factorization of a symmetric positive definite matrix DMFSD - double precision triangular factorization of a symmetric positive definite matrix LLSQ - solution of linear least squares problem DLLSQ - double precision solution of linear least squares problem Matrices Library 4 - Eigenanalysis and Related Topics - MATEIGEN.ARC EIGEN - eigenvalues and eigenvectors of a real, symmetric matrix NROOT - eigenvalues and eigenvectors of a special nonsymmetric matrix ATEIG - eigenvalues of a real almost triangular matrix HSBG - reduction of a real matrix to almost triangular form Polynomial Library 1 - Operations - POLYOPS.ARC Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 7 PADD - add two polynomials PSUB - subtract one polynomial from another PMPY - multiply two polynomials PDIV - divide one polynomial by another PCLA - replace one polynomial by another PADDM - multiply polynomial by a constant and add to another polynomial PVAL - value of a polynomial PVSUB - substitute variable of polynomial by another polynomial PILD - evaluate polynomial and its first derivative PDER - derivative of a polynomial PINT - integral of a polynomial PQSD - quadratic synthetic division of a polynomial PCLD - complete synthetic division of a polynomial PGCD - greatest common divisor of two polynomials PNORM - normalize coefficient vector of polynomial PECN - economization of a polynomial for symmetric range DPECN - double precision economization of a polynomial for symmetric range PECS - economization of a polynomial for unsymmetric range DPECS - double precision economization of a polynomial for unsymmetric range Polynomial Library 2 - Roots - POLYROOT.ARC POLRT - real and complex roots of a real polynomial PRQD - roots of a real polynomial by QD algorithm with displacement DPRQD - double precision roots of a real polynomial by QD algorithm with displacement PRBM - roots of a real polynomial by Bairstow's algorithm DPRBM - double precision roots of a real polynomial by Bairstow's algorithm Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 8 PQFB - determine a quadratic factor of a real polynomial DPQFB - double precision determination of a quadratic factor of a real polynomial Polynomial Library 3 - Special Types - POLYSPTP.ARC CNP - value of n-th Chebyshev polynomial DCNP - double precision value of n-th Chebyshev polynomial CNPS - value of series expansion in Chebyshev polynomials DCNPS - double precision value of series expansion in Chebyshev polynomials TCNP - transform series expansion in Chebyshev polynomials to a polynomial DTCNP - double precision transform series expansion in Chebyshev polynomials to a polynomial CSP - value of n-th shifted Chebyshev polynomial DCSP - double precision value of n-th shifted Chebyshev polynomial CSPS - value of series expansion in shifted Chebyshev polynomials DCSPS - double precision value of series expansion in shifted Chebyshev polynomials TCSP - transform series expansion in shifted Chebyshev polynomials to a polynomial DTCSP - double precision transform series expansion in shifted Chebyshev polynomials to a polynomial HEP - value of Hermite polynomial DHEP - double precision value of Hermite polynomial HEPS - value of series expansion in Hermite polynomials DHEPS - double precision value of series expansion in Hermite polynomials THEP - transform series expansion in Hermite polynomials to a polynomial DTHEP - double precision transform series expansion in Hermite polynomials to a polynomial LAP - value of Laguerre polynomial DLAP - double precision value of Laguerre polynomial Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 9 LAPS - value of series expansion in Laguerre polynomials DLAPS - double precision value of series expansion in Laguerre polynomials TLAP - transform series expansion in Laguerre polynomials to a polynomial DTLAP - double precision transform series expansion in Laguerre polynomials to a polynomial LEP - value of Legendre polynomial DLEP - double precision value of Legendre polynomial LEPS - value of series expansion in Legendre polynomials DLEPS - double precision value of series expansion in Legendre polynomials TLEP - transform a series expansion in Legendre polynomials to a polynomial DTLEP - double precision transform a series expansion in Legendre polynomials to a polynomial Roots of Nonlinear Equations Library - ROOTNLEQ.ARC RTWI - refine estimate of root by Wegstein's iteration DRTWI - double precision refine estimate of root by Wegstein's iteration RTMI - determine root within a range by Mueller's iteration DRTMI - double precision determine root within a range by Mueller's iteration RTNI - refine estimate of root by Newton's iteration DRTNI - double precision refine estimate of root by Newton's iteration Extremum of Functions Library - EXTRMFCT.ARC FMFP - unconstrained minimum of a function of several variables - Davidon method DFMFP - double precision unconstrained minimum of a function of several variables - Davidon method FMCG - unconstrained minimum of a function of several variables - conjugate gradient method Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 10 DFMCG - double precision unconstrained minimum of a function of several variables - conjugate gradient method Permutations Library - PERMUT.ARC PPRCM - composition of permutations PERM - operations with permutations and transpositions Sequences Library - Sums and Limits - SEQUENCE.ARC TEAS - limit of a given sequence DTEAS - double precision limit of a given sequence TEUL - sum of a given function sequence DTEUL - double precision sum of a given function sequence Interpolation, Approximation and Smoothing Library - ITRPAPSM.ARC ALI - Aitken-Lagrange interpolation DALI - double precision Aitken-Legrange interpolation AHI - Aitken-Hermite interpolation DAHI - double precision Aitken-Hermite interpolation ACFI - continued fraction interpolation DACFI - double precision continued fraction interpolation ATSG - table selection out of a general table DATSG - double precision table selection out of a general table ATSM - table selection out of a monotonic table DATSM - double precision table selection out of a monotonic table ATSE - table selection out of an equidistant table DATSE - double precision table selection out of an equidistant table SG13 - local least squares smoothing of tabulated functions DSG13 - double precision local least squares smoothing of tabulated functions SE13 - local least squares smoothing of equidistantly tabulated SE15 functions Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 11 SE35 DSE13 - double precision local least squares smoothing of equidistantly DSE15 tabulated functions DSE35 APFS - solve normal equations for least squares fit DAPFS - double precision solve normal equations for least squares fit APCH - least squares polynomial approximation DAPCH - double precision least squares polynomial approximation ARAT - rational least squares approximation FRAT DARAT - double precision rational least squares approximation DFRAT APLL - linear least squares approximation DAPLL - double precision linear least squares approximation FORIF - Fourier analysis of a given function FORIT - Fourier analysis of a tabulated function HARM - complex three dimensional Fourier analysis DHARM - double precision complex three dimensional Fourier analysis RHARM - real one dimensional Fourier analysis DRHARM - double precision real one dimensional Fourier analysis APMM - linear Chebyshev approximation over a discrete range DAPMM - double precision linear Chebyshev approximation over a discrete range Numerical Quadrature Library 1 - NUMQUAD.ARC QTFG - integration of monotonically tabulated function by trapezoidal rule DQTFG - double precision integration of monotonically tabulated function by trapezoidal rule QTFE - integration of equidistantly tabulated function by trapezoidal rule DQTFE - double precision integration of equidistantly tabulated tabulated function by trapezoidal rule Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 12 QSF - integration of equidistantly tabulated function by Simpson's rule DQSF - double precision integration of equidistantly tabulated function by Simpson's rule QHFG - integration of monotonically tabulated function with first derivative by Hermitian formula of first order DQHFG - double precision integration of monotonically tabulated function with first derivative by Hermitian formula of first order QHFE - integration of equidistantly tabulated function with first derivative by Hermitian formula of first order DQHFE - double precision integration of equidistantly tabulated function with first derivative by Hermitian formula of first order QHSG - integration of monotonically tabulated function with first and second derivatives by Hermitian formula of first order DQHSG - double precision integration of monotonically tabulated function with first and second derivatives by Hermitian formula of first order QHSE - integration of equidistantly tabulated function with first and second derivatives by Hermitian formula of second order DQHSE - double precision integration of equidistantly tabulated function with first and second derivatives by Hermitian formula of second order QATR - integration of a given function by trapezoidal rule together with Romberg's extrapolation method DQATR - double precision integration of a given function by trapezoidal rule together with Romberg's extrapolation method Numerical Quadrature Library 2 - Gaussian Quadrature - GAUQUAD.ARC QG2 - integration of a given function by Gaussian quadrature QG3 formulas (2-point, 3-point, ... , 10-point) QG4 QG5 QG6 QG7 QG8 QG9 QG10 DQG4 - double precision integration of a given function by Gaussian Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 13 DQG8 quadrature formulas (4-point, 8-point, ... , 32-point) DQG12 DQG16 DQG24 DQG32 Numerical Quadrature Library 3 - Gauss-Laguerre Quadrature - GLGRQUAD.ARC GL2 - integration of a given function by Gaussian-Leguerre GL3 quadrature formulas (2-point, 3-point, ... , 10-point) GL4 GL5 GL6 GL7 GL8 GL9 GL10 DGL4 - double precision integration of a given function by DGL8 Gaussian-Leguerre quadrature formulas DGL12 (4-point, 8-point, ... , 32-point) DGL16 DGL24 DGL32 Numerical Quadrature Library 4 - Gauss-Hermite Quadrature - GHRMQUAD.ARC GH2 - integration of a given function by Gaussian-Hermite GH3 quadrature formulas (2-point, 3-point, 10-point) GH4 GH5 GH6 GH7 GH8 GH9 GH10 DGH8 - double precision integration of a given function by DGH16 Gaussian Hermite quadrature formulas DGH24 (8-point, 16-point, ... , 64-point) DGH32 DGH48 DGH64 Numerical Quadrature Library 5 - Associated Gauss-Laguerre Quadrature - AGLGQUAD.ARC QA2 - integration of a given function by associated Gaussian- QA3 Laguerre quadrature formulas QA4 (2-point, 3-point, ... , 10-point) QA5 QA6 QA7 Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 14 QA8 QA9 QA10 DQA4 - double precision integration of a given function by DQA8 associated Gaussian-Laguerre quadrature formulas DQA12 (4-point, 8-point, ... , 32-point) DQA16 DQA24 DQA32 Numerical Differentiation Library - NUMDIFF.ARC DGT3 - differentiation of a tabulated function by parabolic interpolation DDGT3 - double precision differentiation of a tabulated function by parabolic interpolation DET3 - differentiation of an equidistantly tabulated function DET5 DDET3 - double precision differentiation of an equidistantly DDET5 tabulated function DCAR - derivative of a function at the center of an interval DDCAR - double precision derivative of a function at the center of an interval DBAR - derivative of a function at the border of an interval DDBAR - double precision derivative of a function at the border of an interval Ordinary Differential Equations Library - ORDDIFEQ.ARC RK1 - solution of first order differential equation by Runge-Kutta method RK2 - tabulated solution of first order differential equation by Runge-Kutta method RKGS - solution of system of first order differential equations with given initial values by Runge-Kutta method DRKGS - double precision solution of system of first order differential equations with given initial values by Runge-Kutta method HPCG - solution of general system of first order ordinary differential equations with given initial values by Hamming's modified predictor-corrector method Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 15 DHPCG - double precision solution of general system of first order ordinary differential equations with given initial values by Hamming's modified predictor-corrector method HPCL - solution of linear system of first order ordinary differential equations with given initial values by Hamming's modified predictor-corrector method DHPCL - double precision solution of linear system of first order ordinary differential equations with given initial values by Hamming's modified predictor-corrector method LBVP - solution of system of linear first order ordinary differential equations with linear boundary conditions by method of adjoint equations DLBVP - double precision solution of system of linear first order ordinary differential equations with linear boundary conditions by method of adjoint equations Special Functions Library - SPCLFNCT.ARC GMMMA - gamma function DLGAM - log of gamma function BESJ - J Bessel function BESY - Y Bessel function I0 - I Bessel function, I-o INUE - I-n Bessel function BESK - K Bessel function EXPI - Exponential integral SICI - sine cosine integral CS - Fresnel integrals CEL1 - complete elliptic integral of the first kind DCEL1 - double precision complete elliptic integral of the first kind CLE2 - complete elliptic integral of the second kind DCEL2 - double precision complete elliptic integral of the second kind ELI1 - generalized elliptic integral of the first kind DELI1 - double precision generalized elliptic integral of Dec 3 18:16 1987 Scientific Subroutine Package - Module Listing Page 16 the second kind ELI2 - generalized elliptic integral of the second kind DELI2 - double precision generalized elliptic integral of the second kind JELF - Jacobian elliptic function DJELF - double precision Jacobian elliptic function i