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







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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







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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








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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







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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







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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








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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








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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







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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







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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







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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








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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







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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







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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








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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







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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