# SLATEC Common Mathematical Library Ve

## Found at: ftp.icm.edu.pl:70/packages/netlib/slatec/toc

SLATEC Common Mathematical Library

Version 4.1

Table of Contents

This table of contents of the SLATEC Common Mathematical Library (CML) has

three sections.

Section I contains the names and purposes of all user-callable CML routines,

arranged by GAMS category. Those unfamiliar with the GAMS scheme should

consult the document "Guide to the SLATEC Common Mathematical Library". The

current library has routines in the following GAMS major categories:

A. Arithmetic, error analysis

C. Elementary and special functions (search also class L5)

D. Linear Algebra

E. Interpolation

F. Solution of nonlinear equations

G. Optimization (search also classes K, L8)

H. Differentiation, integration

I. Differential and integral equations

J. Integral transforms

K. Approximation (search also class L8)

L. Statistics, probability

N. Data handling (search also class L2)

R. Service routines

Z. Other

The library contains routines which operate on different types of data but

vertically before the purpose. Immediately after each name is a hyphen (-)

and one of the alphabetic characters S, D, C, I, H, L, or A, where

S indicates a single precision routine, D double precision, C complex,

that could not reasonably be converted to some other type.

Section II contains the names and purposes of all subsidiary CML routines,

arranged in alphabetical order. Usually these routines are not referenced

to avoid duplicating names that are used by the CML and for the benefit of

for the library.

Section III is an alphabetical list of every routine in the CML and the

categories to which the routine is assigned. Every user-callable routine

name indicates a subsidiary routine.

SECTION I. User-callable Routines

A. Arithmetic, error analysis

A3. Real

A3D. Extended range

XADD-S To provide single-precision floating-point arithmetic

DXADD-D with an extended exponent range.

XADJ-S To provide single-precision floating-point arithmetic

DXADJ-D with an extended exponent range.

XC210-S To provide single-precision floating-point arithmetic

DXC210-D with an extended exponent range.

XCON-S To provide single-precision floating-point arithmetic

DXCON-D with an extended exponent range.

XRED-S To provide single-precision floating-point arithmetic

DXRED-D with an extended exponent range.

XSET-S To provide single-precision floating-point arithmetic

DXSET-D with an extended exponent range.

A4. Complex

A4A. Single precision

CARG-C Compute the argument of a complex number.

A6. Change of representation

A6B. Base conversion

R9PAK-S Pack a base 2 exponent into a floating point number.

D9PAK-D

R9UPAK-S Unpack a floating point number X so that X = Y*2**N.

D9UPAK-D

C. Elementary and special functions (search also class L5)

FUNDOC-A Documentation for FNLIB, a collection of routines for

evaluating elementary and special functions.

C1. Integer-valued functions (e.g., floor, ceiling, factorial, binomial

coefficient)

BINOM-S Compute the binomial coefficients.

DBINOM-D

FAC-S Compute the factorial function.

DFAC-D

POCH-S Evaluate a generalization of Pochhammer's symbol.

DPOCH-D

POCH1-S Calculate a generalization of Pochhammer's symbol starting

DPOCH1-D from first order.

C2. Powers, roots, reciprocals

CBRT-S Compute the cube root.

DCBRT-D

CCBRT-C

C3. Polynomials

C3A. Orthogonal

C3A2. Chebyshev, Legendre

CSEVL-S Evaluate a Chebyshev series.

DCSEVL-D

INITS-S Determine the number of terms needed in an orthogonal

INITDS-D polynomial series so that it meets a specified accuracy.

QMOMO-S This routine computes modified Chebyshev moments. The K-th

DQMOMO-D modified Chebyshev moment is defined as the integral over

(-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev

polynomial of degree K.

XLEGF-S Compute normalized Legendre polynomials and associated

DXLEGF-D Legendre functions.

XNRMP-S Compute normalized Legendre polynomials.

DXNRMP-D

C4. Elementary transcendental functions

C4A. Trigonometric, inverse trigonometric

CACOS-C Compute the complex arc cosine.

CASIN-C Compute the complex arc sine.

CATAN-C Compute the complex arc tangent.

CATAN2-C Compute the complex arc tangent in the proper quadrant.

COSDG-S Compute the cosine of an argument in degrees.

DCOSDG-D

COT-S Compute the cotangent.

DCOT-D

CCOT-C

CTAN-C Compute the complex tangent.

SINDG-S Compute the sine of an argument in degrees.

DSINDG-D

C4B. Exponential, logarithmic

ALNREL-S Evaluate ln(1+X) accurate in the sense of relative error.

DLNREL-D

CLNREL-C

CLOG10-C Compute the principal value of the complex base 10

logarithm.

EXPREL-S Calculate the relative error exponential (EXP(X)-1)/X.

DEXPRL-D

CEXPRL-C

C4C. Hyperbolic, inverse hyperbolic

ACOSH-S Compute the arc hyperbolic cosine.

DACOSH-D

CACOSH-C

ASINH-S Compute the arc hyperbolic sine.

DASINH-D

CASINH-C

ATANH-S Compute the arc hyperbolic tangent.

DATANH-D

CATANH-C

CCOSH-C Compute the complex hyperbolic cosine.

CSINH-C Compute the complex hyperbolic sine.

CTANH-C Compute the complex hyperbolic tangent.

C5. Exponential and logarithmic integrals

ALI-S Compute the logarithmic integral.

DLI-D

E1-S Compute the exponential integral E1(X).

DE1-D

EI-S Compute the exponential integral Ei(X).

DEI-D

EXINT-S Compute an M member sequence of exponential integrals

DEXINT-D E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

SPENC-S Compute a form of Spence's integral due to K. Mitchell.

DSPENC-D

C7. Gamma

C7A. Gamma, log gamma, reciprocal gamma

ALGAMS-S Compute the logarithm of the absolute value of the Gamma

DLGAMS-D function.

ALNGAM-S Compute the logarithm of the absolute value of the Gamma

DLNGAM-D function.

CLNGAM-C

C0LGMC-C Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative

accuracy.

GAMLIM-S Compute the minimum and maximum bounds for the argument in

DGAMLM-D the Gamma function.

GAMMA-S Compute the complete Gamma function.

DGAMMA-D

CGAMMA-C

GAMR-S Compute the reciprocal of the Gamma function.

DGAMR-D

CGAMR-C

POCH-S Evaluate a generalization of Pochhammer's symbol.

DPOCH-D

POCH1-S Calculate a generalization of Pochhammer's symbol starting

DPOCH1-D from first order.

C7B. Beta, log beta

ALBETA-S Compute the natural logarithm of the complete Beta

DLBETA-D function.

CLBETA-C

BETA-S Compute the complete Beta function.

DBETA-D

CBETA-C

C7C. Psi function

PSI-S Compute the Psi (or Digamma) function.

DPSI-D

CPSI-C

PSIFN-S Compute derivatives of the Psi function.

DPSIFN-D

C7E. Incomplete gamma

GAMI-S Evaluate the incomplete Gamma function.

DGAMI-D

GAMIC-S Calculate the complementary incomplete Gamma function.

DGAMIC-D

GAMIT-S Calculate Tricomi's form of the incomplete Gamma function.

DGAMIT-D

C7F. Incomplete beta

BETAI-S Calculate the incomplete Beta function.

DBETAI-D

C8. Error functions

C8A. Error functions, their inverses, integrals, including the normal

distribution function

ERF-S Compute the error function.

DERF-D

ERFC-S Compute the complementary error function.

DERFC-D

C8C. Dawson's integral

DAWS-S Compute Dawson's function.

DDAWS-D

C9. Legendre functions

XLEGF-S Compute normalized Legendre polynomials and associated

DXLEGF-D Legendre functions.

XNRMP-S Compute normalized Legendre polynomials.

DXNRMP-D

C10. Bessel functions

C10A. J, Y, H-(1), H-(2)

C10A1. Real argument, integer order

BESJ0-S Compute the Bessel function of the first kind of order

DBESJ0-D zero.

BESJ1-S Compute the Bessel function of the first kind of order one.

DBESJ1-D

BESY0-S Compute the Bessel function of the second kind of order

DBESY0-D zero.

BESY1-S Compute the Bessel function of the second kind of order

DBESY1-D one.

C10A3. Real argument, real order

BESJ-S Compute an N member sequence of J Bessel functions

DBESJ-D J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA

and X.

BESY-S Implement forward recursion on the three term recursion

DBESY-D relation for a sequence of non-negative order Bessel

functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive

X and non-negative orders FNU.

C10A4. Complex argument, real order

CBESH-C Compute a sequence of the Hankel functions H(m,a,z)

ZBESH-C for superscript m=1 or 2, real nonnegative orders a=b,

b+1,... where b>0, and nonzero complex argument z. A

scaling option is available to help avoid overflow.

CBESJ-C Compute a sequence of the Bessel functions J(a,z) for

ZBESJ-C complex argument z and real nonnegative orders a=b,b+1,

b+2,... where b>0. A scaling option is available to

help avoid overflow.

CBESY-C Compute a sequence of the Bessel functions Y(a,z) for

ZBESY-C complex argument z and real nonnegative orders a=b,b+1,

b+2,... where b>0. A scaling option is available to

help avoid overflow.

C10B. I, K

C10B1. Real argument, integer order

BESI0-S Compute the hyperbolic Bessel function of the first kind

DBESI0-D of order zero.

BESI0E-S Compute the exponentially scaled modified (hyperbolic)

DBSI0E-D Bessel function of the first kind of order zero.

BESI1-S Compute the modified (hyperbolic) Bessel function of the

DBESI1-D first kind of order one.

BESI1E-S Compute the exponentially scaled modified (hyperbolic)

DBSI1E-D Bessel function of the first kind of order one.

BESK0-S Compute the modified (hyperbolic) Bessel function of the

DBESK0-D third kind of order zero.

BESK0E-S Compute the exponentially scaled modified (hyperbolic)

DBSK0E-D Bessel function of the third kind of order zero.

BESK1-S Compute the modified (hyperbolic) Bessel function of the

DBESK1-D third kind of order one.

BESK1E-S Compute the exponentially scaled modified (hyperbolic)

DBSK1E-D Bessel function of the third kind of order one.

C10B3. Real argument, real order

BESI-S Compute an N member sequence of I Bessel functions

DBESI-D I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions

EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative

ALPHA and X.

BESK-S Implement forward recursion on the three term recursion

DBESK-D relation for a sequence of non-negative order Bessel

functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions

EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive

X and non-negative orders FNU.

BESKES-S Compute a sequence of exponentially scaled modified Bessel

DBSKES-D functions of the third kind of fractional order.

BESKS-S Compute a sequence of modified Bessel functions of the

DBESKS-D third kind of fractional order.

C10B4. Complex argument, real order

CBESI-C Compute a sequence of the Bessel functions I(a,z) for

ZBESI-C complex argument z and real nonnegative orders a=b,b+1,

b+2,... where b>0. A scaling option is available to

help avoid overflow.

CBESK-C Compute a sequence of the Bessel functions K(a,z) for

ZBESK-C complex argument z and real nonnegative orders a=b,b+1,

b+2,... where b>0. A scaling option is available to

help avoid overflow.

C10D. Airy and Scorer functions

AI-S Evaluate the Airy function.

DAI-D

AIE-S Calculate the Airy function for a negative argument and an

DAIE-D exponentially scaled Airy function for a non-negative

argument.

BI-S Evaluate the Bairy function (the Airy function of the

DBI-D second kind).

BIE-S Calculate the Bairy function for a negative argument and an

DBIE-D exponentially scaled Bairy function for a non-negative

argument.

CAIRY-C Compute the Airy function Ai(z) or its derivative dAi/dz

ZAIRY-C for complex argument z. A scaling option is available

to help avoid underflow and overflow.

CBIRY-C Compute the Airy function Bi(z) or its derivative dBi/dz

ZBIRY-C for complex argument z. A scaling option is available

to help avoid overflow.

C10F. Integrals of Bessel functions

BSKIN-S Compute repeated integrals of the K-zero Bessel function.

DBSKIN-D

C11. Confluent hypergeometric functions

CHU-S Compute the logarithmic confluent hypergeometric function.

DCHU-D

C14. Elliptic integrals

RC-S Calculate an approximation to

DRC-D RC(X,Y) = Integral from zero to infinity of

-1/2 -1

(1/2)(t+X) (t+Y) dt,

where X is nonnegative and Y is positive.

RD-S Compute the incomplete or complete elliptic integral of the

DRD-D 2nd kind. For X and Y nonnegative, X+Y and Z positive,

RD(X,Y,Z) = Integral from zero to infinity of

-1/2 -1/2 -3/2

(3/2)(t+X) (t+Y) (t+Z) dt.

If X or Y is zero, the integral is complete.

RF-S Compute the incomplete or complete elliptic integral of the

DRF-D 1st kind. For X, Y, and Z non-negative and at most one of

them zero, RF(X,Y,Z) = Integral from zero to infinity of

-1/2 -1/2 -1/2

(1/2)(t+X) (t+Y) (t+Z) dt.

If X, Y or Z is zero, the integral is complete.

RJ-S Compute the incomplete or complete (X or Y or Z is zero)

DRJ-D elliptic integral of the 3rd kind. For X, Y, and Z non-

negative, at most one of them zero, and P positive,

RJ(X,Y,Z,P) = Integral from zero to infinity of

-1/2 -1/2 -1/2 -1

(3/2)(t+X) (t+Y) (t+Z) (t+P) dt.

C19. Other special functions

RC3JJ-S Evaluate the 3j symbol f(L1) = ( L1 L2 L3)

DRC3JJ-D (-M2-M3 M2 M3)

for all allowed values of L1, the other parameters

being held fixed.

RC3JM-S Evaluate the 3j symbol g(M2) = (L1 L2 L3 )

DRC3JM-D (M1 M2 -M1-M2)

for all allowed values of M2, the other parameters

being held fixed.

RC6J-S Evaluate the 6j symbol h(L1) = {L1 L2 L3}

DRC6J-D {L4 L5 L6}

for all allowed values of L1, the other parameters

being held fixed.

D. Linear Algebra

D1. Elementary vector and matrix operations

D1A. Elementary vector operations

D1A2. Minimum and maximum components

ISAMAX-S Find the smallest index of that component of a vector

IDAMAX-D having the maximum magnitude.

ICAMAX-C

D1A3. Norm

D1A3A. L-1 (sum of magnitudes)

SASUM-S Compute the sum of the magnitudes of the elements of a

DASUM-D vector.

SCASUM-C

D1A3B. L-2 (Euclidean norm)

SNRM2-S Compute the Euclidean length (L2 norm) of a vector.

DNRM2-D

SCNRM2-C

D1A4. Dot product (inner product)

CDOTC-C Dot product of two complex vectors using the complex

conjugate of the first vector.

DQDOTA-D Compute the inner product of two vectors with extended

precision accumulation and result.

DQDOTI-D Compute the inner product of two vectors with extended

precision accumulation and result.

DSDOT-D Compute the inner product of two vectors with extended

DCDOT-C precision accumulation and result.

SDOT-S Compute the inner product of two vectors.

DDOT-D

CDOTU-C

SDSDOT-S Compute the inner product of two vectors with extended

CDCDOT-C precision accumulation.

D1A5. Copy or exchange (swap)

ICOPY-S Copy a vector.

DCOPY-D

CCOPY-C

ICOPY-I

SCOPY-S Copy a vector.

DCOPY-D

CCOPY-C

ICOPY-I

SCOPYM-S Copy the negative of a vector to a vector.

DCOPYM-D

SSWAP-S Interchange two vectors.

DSWAP-D

CSWAP-C

ISWAP-I

D1A6. Multiplication by scalar

CSSCAL-C Scale a complex vector.

SSCAL-S Multiply a vector by a constant.

DSCAL-D

CSCAL-C

D1A7. Triad (a*x+y for vectors x,y and scalar a)

SAXPY-S Compute a constant times a vector plus a vector.

DAXPY-D

CAXPY-C

D1A8. Elementary rotation (Givens transformation)

SROT-S Apply a plane Givens rotation.

DROT-D

CSROT-C

SROTM-S Apply a modified Givens transformation.

DROTM-D

D1B. Elementary matrix operations

D1B4. Multiplication by vector

CHPR-C Perform the hermitian rank 1 operation.

DGER-D Perform the rank 1 operation.

DSPR-D Perform the symmetric rank 1 operation.

DSYR-D Perform the symmetric rank 1 operation.

SGBMV-S Multiply a real vector by a real general band matrix.

DGBMV-D

CGBMV-C

SGEMV-S Multiply a real vector by a real general matrix.

DGEMV-D

CGEMV-C

SGER-S Perform rank 1 update of a real general matrix.

CGERC-C Perform conjugated rank 1 update of a complex general

SGERC-S matrix.

DGERC-D

CGERU-C Perform unconjugated rank 1 update of a complex general

SGERU-S matrix.

DGERU-D

CHBMV-C Multiply a complex vector by a complex Hermitian band

SHBMV-S matrix.

DHBMV-D

CHEMV-C Multiply a complex vector by a complex Hermitian matrix.

SHEMV-S

DHEMV-D

CHER-C Perform Hermitian rank 1 update of a complex Hermitian

SHER-S matrix.

DHER-D

CHER2-C Perform Hermitian rank 2 update of a complex Hermitian

SHER2-S matrix.

DHER2-D

CHPMV-C Perform the matrix-vector operation.

SHPMV-S

DHPMV-D

CHPR2-C Perform the hermitian rank 2 operation.

SHPR2-S

DHPR2-D

SSBMV-S Multiply a real vector by a real symmetric band matrix.

DSBMV-D

CSBMV-C

SSDI-S Diagonal Matrix Vector Multiply.

DSDI-D Routine to calculate the product X = DIAG*B, where DIAG

is a diagonal matrix.

SSMTV-S SLAP Column Format Sparse Matrix Transpose Vector Product.

DSMTV-D Routine to calculate the sparse matrix vector product:

Y = A'*X, where ' denotes transpose.

SSMV-S SLAP Column Format Sparse Matrix Vector Product.

DSMV-D Routine to calculate the sparse matrix vector product:

Y = A*X.

SSPMV-S Perform the matrix-vector operation.

DSPMV-D

CSPMV-C

SSPR-S Performs the symmetric rank 1 operation.

SSPR2-S Perform the symmetric rank 2 operation.

DSPR2-D

CSPR2-C

SSYMV-S Multiply a real vector by a real symmetric matrix.

DSYMV-D

CSYMV-C

SSYR-S Perform symmetric rank 1 update of a real symmetric matrix.

SSYR2-S Perform symmetric rank 2 update of a real symmetric matrix.

DSYR2-D

CSYR2-C

STBMV-S Multiply a real vector by a real triangular band matrix.

DTBMV-D

CTBMV-C

STBSV-S Solve a real triangular banded system of linear equations.

DTBSV-D

CTBSV-C

STPMV-S Perform one of the matrix-vector operations.

DTPMV-D

CTPMV-C

STPSV-S Solve one of the systems of equations.

DTPSV-D

CTPSV-C

STRMV-S Multiply a real vector by a real triangular matrix.

DTRMV-D

CTRMV-C

STRSV-S Solve a real triangular system of linear equations.

DTRSV-D

CTRSV-C

D1B6. Multiplication

SGEMM-S Multiply a real general matrix by a real general matrix.

DGEMM-D

CGEMM-C

CHEMM-C Multiply a complex general matrix by a complex Hermitian

SHEMM-S matrix.

DHEMM-D

CHER2K-C Perform Hermitian rank 2k update of a complex.

SHER2-S

DHER2-D

CHER2-C

CHERK-C Perform Hermitian rank k update of a complex Hermitian

SHERK-S matrix.

DHERK-D

SSYMM-S Multiply a real general matrix by a real symmetric matrix.

DSYMM-D

CSYMM-C

DSYR2K-D Perform one of the symmetric rank 2k operations.

SSYR2-S

DSYR2-D

CSYR2-C

SSYRK-S Perform symmetric rank k update of a real symmetric matrix.

DSYRK-D

CSYRK-C

STRMM-S Multiply a real general matrix by a real triangular matrix.

DTRMM-D

CTRMM-C

STRSM-S Solve a real triangular system of equations with multiple

DTRSM-D right-hand sides.

CTRSM-C

D1B9. Storage mode conversion

SS2Y-S SLAP Triad to SLAP Column Format Converter.

DS2Y-D Routine to convert from the SLAP Triad to SLAP Column

format.

D1B10. Elementary rotation (Givens transformation)

CSROT-C Apply a plane Givens rotation.

SROT-S

DROT-D

SROTG-S Construct a plane Givens rotation.

DROTG-D

CROTG-C

SROTMG-S Construct a modified Givens transformation.

DROTMG-D

D2. Solution of systems of linear equations (including inversion, LU and

related decompositions)

D2A. Real nonsymmetric matrices

D2A1. General

SGECO-S Factor a matrix using Gaussian elimination and estimate

DGECO-D the condition number of the matrix.

CGECO-C

SGEDI-S Compute the determinant and inverse of a matrix using the

DGEDI-D factors computed by SGECO or SGEFA.

CGEDI-C

SGEFA-S Factor a matrix using Gaussian elimination.

DGEFA-D

CGEFA-C

SGEFS-S Solve a general system of linear equations.

DGEFS-D

CGEFS-C

SGEIR-S Solve a general system of linear equations. Iterative

CGEIR-C refinement is used to obtain an error estimate.

SGESL-S Solve the real system A*X=B or TRANS(A)*X=B using the

DGESL-D factors of SGECO or SGEFA.

CGESL-C

SQRSL-S Apply the output of SQRDC to compute coordinate transfor-

DQRSL-D mations, projections, and least squares solutions.

CQRSL-C

D2A2. Banded

SGBCO-S Factor a band matrix by Gaussian elimination and

DGBCO-D estimate the condition number of the matrix.

CGBCO-C

SGBFA-S Factor a band matrix using Gaussian elimination.

DGBFA-D

CGBFA-C

SGBSL-S Solve the real band system A*X=B or TRANS(A)*X=B using

DGBSL-D the factors computed by SGBCO or SGBFA.

CGBSL-C

SNBCO-S Factor a band matrix using Gaussian elimination and

DNBCO-D estimate the condition number.

CNBCO-C

SNBFA-S Factor a real band matrix by elimination.

DNBFA-D

CNBFA-C

SNBFS-S Solve a general nonsymmetric banded system of linear

DNBFS-D equations.

CNBFS-C

SNBIR-S Solve a general nonsymmetric banded system of linear

CNBIR-C equations. Iterative refinement is used to obtain an error

estimate.

SNBSL-S Solve a real band system using the factors computed by

DNBSL-D SNBCO or SNBFA.

CNBSL-C

D2A2A. Tridiagonal

SGTSL-S Solve a tridiagonal linear system.

DGTSL-D

CGTSL-C

D2A3. Triangular

SSLI-S SLAP MSOLVE for Lower Triangle Matrix.

DSLI-D This routine acts as an interface between the SLAP generic

MSOLVE calling convention and the routine that actually

-1

computes L B = X.

SSLI2-S SLAP Lower Triangle Matrix Backsolve.

DSLI2-D Routine to solve a system of the form Lx = b , where L

is a lower triangular matrix.

STRCO-S Estimate the condition number of a triangular matrix.

DTRCO-D

CTRCO-C

STRDI-S Compute the determinant and inverse of a triangular matrix.

DTRDI-D

CTRDI-C

STRSL-S Solve a system of the form T*X=B or TRANS(T)*X=B, where

DTRSL-D T is a triangular matrix.

CTRSL-C

D2A4. Sparse

SBCG-S Preconditioned BiConjugate Gradient Sparse Ax = b Solver.

DBCG-D Routine to solve a Non-Symmetric linear system Ax = b

using the Preconditioned BiConjugate Gradient method.

SCGN-S Preconditioned CG Sparse Ax=b Solver for Normal Equations.

DCGN-D Routine to solve a general linear system Ax = b using the

Preconditioned Conjugate Gradient method applied to the

normal equations AA'y = b, x=A'y.

SCGS-S Preconditioned BiConjugate Gradient Squared Ax=b Solver.

DCGS-D Routine to solve a Non-Symmetric linear system Ax = b

using the Preconditioned BiConjugate Gradient Squared

method.

SGMRES-S Preconditioned GMRES Iterative Sparse Ax=b Solver.

DGMRES-D This routine uses the generalized minimum residual

(GMRES) method with preconditioning to solve

non-symmetric linear systems of the form: Ax = b.

SIR-S Preconditioned Iterative Refinement Sparse Ax = b Solver.

DIR-D Routine to solve a general linear system Ax = b using

iterative refinement with a matrix splitting.

SLPDOC-S Sparse Linear Algebra Package Version 2.0.2 Documentation.

DLPDOC-D Routines to solve large sparse symmetric and nonsymmetric

positive definite linear systems, Ax = b, using precondi-

tioned iterative methods.

SOMN-S Preconditioned Orthomin Sparse Iterative Ax=b Solver.

DOMN-D Routine to solve a general linear system Ax = b using

the Preconditioned Orthomin method.

SSDBCG-S Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.

DSDBCG-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient method with diagonal scaling.

SSDCGN-S Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.

DSDCGN-D Routine to solve a general linear system Ax = b using

diagonal scaling with the Conjugate Gradient method

applied to the the normal equations, viz., AA'y = b,

where x = A'y.

SSDCGS-S Diagonally Scaled CGS Sparse Ax=b Solver.

DSDCGS-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient Squared method with diagonal scaling.

SSDGMR-S Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.

DSDGMR-D This routine uses the generalized minimum residual

(GMRES) method with diagonal scaling to solve possibly

non-symmetric linear systems of the form: Ax = b.

SSDOMN-S Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.

DSDOMN-D Routine to solve a general linear system Ax = b using

the Orthomin method with diagonal scaling.

SSGS-S Gauss-Seidel Method Iterative Sparse Ax = b Solver.

DSGS-D Routine to solve a general linear system Ax = b using

Gauss-Seidel iteration.

SSILUR-S Incomplete LU Iterative Refinement Sparse Ax = b Solver.

DSILUR-D Routine to solve a general linear system Ax = b using

the incomplete LU decomposition with iterative refinement.

SSJAC-S Jacobi's Method Iterative Sparse Ax = b Solver.

DSJAC-D Routine to solve a general linear system Ax = b using

Jacobi iteration.

SSLUBC-S Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.

DSLUBC-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient method with Incomplete LU

decomposition preconditioning.

SSLUCN-S Incomplete LU CG Sparse Ax=b Solver for Normal Equations.

DSLUCN-D Routine to solve a general linear system Ax = b using the

incomplete LU decomposition with the Conjugate Gradient

method applied to the normal equations, viz., AA'y = b,

x = A'y.

SSLUCS-S Incomplete LU BiConjugate Gradient Squared Ax=b Solver.

DSLUCS-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient Squared method with Incomplete LU

decomposition preconditioning.

SSLUGM-S Incomplete LU GMRES Iterative Sparse Ax=b Solver.

DSLUGM-D This routine uses the generalized minimum residual

(GMRES) method with incomplete LU factorization for

preconditioning to solve possibly non-symmetric linear

systems of the form: Ax = b.

SSLUOM-S Incomplete LU Orthomin Sparse Iterative Ax=b Solver.

DSLUOM-D Routine to solve a general linear system Ax = b using

the Orthomin method with Incomplete LU decomposition.

D2B. Real symmetric matrices

D2B1. General

D2B1A. Indefinite

SSICO-S Factor a symmetric matrix by elimination with symmetric

DSICO-D pivoting and estimate the condition number of the matrix.

CHICO-C

CSICO-C

SSIDI-S Compute the determinant, inertia and inverse of a real

DSIDI-D symmetric matrix using the factors from SSIFA.

CHIDI-C

CSIDI-C

SSIFA-S Factor a real symmetric matrix by elimination with

DSIFA-D symmetric pivoting.

CHIFA-C

CSIFA-C

SSISL-S Solve a real symmetric system using the factors obtained

DSISL-D from SSIFA.

CHISL-C

CSISL-C

SSPCO-S Factor a real symmetric matrix stored in packed form

DSPCO-D by elimination with symmetric pivoting and estimate the

CHPCO-C condition number of the matrix.

CSPCO-C

SSPDI-S Compute the determinant, inertia, inverse of a real

DSPDI-D symmetric matrix stored in packed form using the factors

CHPDI-C from SSPFA.

CSPDI-C

SSPFA-S Factor a real symmetric matrix stored in packed form by

DSPFA-D elimination with symmetric pivoting.

CHPFA-C

CSPFA-C

SSPSL-S Solve a real symmetric system using the factors obtained

DSPSL-D from SSPFA.

CHPSL-C

CSPSL-C

D2B1B. Positive definite

SCHDC-S Compute the Cholesky decomposition of a positive definite

DCHDC-D matrix. A pivoting option allows the user to estimate the

CCHDC-C condition number of a positive definite matrix or determine

the rank of a positive semidefinite matrix.

SPOCO-S Factor a real symmetric positive definite matrix

DPOCO-D and estimate the condition number of the matrix.

CPOCO-C

SPODI-S Compute the determinant and inverse of a certain real

DPODI-D symmetric positive definite matrix using the factors

CPODI-C computed by SPOCO, SPOFA or SQRDC.

SPOFA-S Factor a real symmetric positive definite matrix.

DPOFA-D

CPOFA-C

SPOFS-S Solve a positive definite symmetric system of linear

DPOFS-D equations.

CPOFS-C

SPOIR-S Solve a positive definite symmetric system of linear

CPOIR-C equations. Iterative refinement is used to obtain an error

estimate.

SPOSL-S Solve the real symmetric positive definite linear system

DPOSL-D using the factors computed by SPOCO or SPOFA.

CPOSL-C

SPPCO-S Factor a symmetric positive definite matrix stored in

DPPCO-D packed form and estimate the condition number of the

CPPCO-C matrix.

SPPDI-S Compute the determinant and inverse of a real symmetric

DPPDI-D positive definite matrix using factors from SPPCO or SPPFA.

CPPDI-C

SPPFA-S Factor a real symmetric positive definite matrix stored in

DPPFA-D packed form.

CPPFA-C

SPPSL-S Solve the real symmetric positive definite system using

DPPSL-D the factors computed by SPPCO or SPPFA.

CPPSL-C

D2B2. Positive definite banded

SPBCO-S Factor a real symmetric positive definite matrix stored in

DPBCO-D band form and estimate the condition number of the matrix.

CPBCO-C

SPBFA-S Factor a real symmetric positive definite matrix stored in

DPBFA-D band form.

CPBFA-C

SPBSL-S Solve a real symmetric positive definite band system

DPBSL-D using the factors computed by SPBCO or SPBFA.

CPBSL-C

D2B2A. Tridiagonal

SPTSL-S Solve a positive definite tridiagonal linear system.

DPTSL-D

CPTSL-C

D2B4. Sparse

SBCG-S Preconditioned BiConjugate Gradient Sparse Ax = b Solver.

DBCG-D Routine to solve a Non-Symmetric linear system Ax = b

using the Preconditioned BiConjugate Gradient method.

SCG-S Preconditioned Conjugate Gradient Sparse Ax=b Solver.

DCG-D Routine to solve a symmetric positive definite linear

system Ax = b using the Preconditioned Conjugate

Gradient method.

SCGN-S Preconditioned CG Sparse Ax=b Solver for Normal Equations.

DCGN-D Routine to solve a general linear system Ax = b using the

Preconditioned Conjugate Gradient method applied to the

normal equations AA'y = b, x=A'y.

SCGS-S Preconditioned BiConjugate Gradient Squared Ax=b Solver.

DCGS-D Routine to solve a Non-Symmetric linear system Ax = b

using the Preconditioned BiConjugate Gradient Squared

method.

SGMRES-S Preconditioned GMRES Iterative Sparse Ax=b Solver.

DGMRES-D This routine uses the generalized minimum residual

(GMRES) method with preconditioning to solve

non-symmetric linear systems of the form: Ax = b.

SIR-S Preconditioned Iterative Refinement Sparse Ax = b Solver.

DIR-D Routine to solve a general linear system Ax = b using

iterative refinement with a matrix splitting.

SLPDOC-S Sparse Linear Algebra Package Version 2.0.2 Documentation.

DLPDOC-D Routines to solve large sparse symmetric and nonsymmetric

positive definite linear systems, Ax = b, using precondi-

tioned iterative methods.

SOMN-S Preconditioned Orthomin Sparse Iterative Ax=b Solver.

DOMN-D Routine to solve a general linear system Ax = b using

the Preconditioned Orthomin method.

SSDBCG-S Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.

DSDBCG-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient method with diagonal scaling.

SSDCG-S Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.

DSDCG-D Routine to solve a symmetric positive definite linear

system Ax = b using the Preconditioned Conjugate

Gradient method. The preconditioner is diagonal scaling.

SSDCGN-S Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.

DSDCGN-D Routine to solve a general linear system Ax = b using

diagonal scaling with the Conjugate Gradient method

applied to the the normal equations, viz., AA'y = b,

where x = A'y.

SSDCGS-S Diagonally Scaled CGS Sparse Ax=b Solver.

DSDCGS-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient Squared method with diagonal scaling.

SSDGMR-S Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.

DSDGMR-D This routine uses the generalized minimum residual

(GMRES) method with diagonal scaling to solve possibly

non-symmetric linear systems of the form: Ax = b.

SSDOMN-S Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.

DSDOMN-D Routine to solve a general linear system Ax = b using

the Orthomin method with diagonal scaling.

SSGS-S Gauss-Seidel Method Iterative Sparse Ax = b Solver.

DSGS-D Routine to solve a general linear system Ax = b using

Gauss-Seidel iteration.

SSICCG-S Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.

DSICCG-D Routine to solve a symmetric positive definite linear

system Ax = b using the incomplete Cholesky

Preconditioned Conjugate Gradient method.

SSILUR-S Incomplete LU Iterative Refinement Sparse Ax = b Solver.

DSILUR-D Routine to solve a general linear system Ax = b using

the incomplete LU decomposition with iterative refinement.

SSJAC-S Jacobi's Method Iterative Sparse Ax = b Solver.

DSJAC-D Routine to solve a general linear system Ax = b using

Jacobi iteration.

SSLUBC-S Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.

DSLUBC-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient method with Incomplete LU

decomposition preconditioning.

SSLUCN-S Incomplete LU CG Sparse Ax=b Solver for Normal Equations.

DSLUCN-D Routine to solve a general linear system Ax = b using the

incomplete LU decomposition with the Conjugate Gradient

method applied to the normal equations, viz., AA'y = b,

x = A'y.

SSLUCS-S Incomplete LU BiConjugate Gradient Squared Ax=b Solver.

DSLUCS-D Routine to solve a linear system Ax = b using the

BiConjugate Gradient Squared method with Incomplete LU

decomposition preconditioning.

SSLUGM-S Incomplete LU GMRES Iterative Sparse Ax=b Solver.

DSLUGM-D This routine uses the generalized minimum residual

(GMRES) method with incomplete LU factorization for

preconditioning to solve possibly non-symmetric linear

systems of the form: Ax = b.

SSLUOM-S Incomplete LU Orthomin Sparse Iterative Ax=b Solver.

DSLUOM-D Routine to solve a general linear system Ax = b using

the Orthomin method with Incomplete LU decomposition.

D2C. Complex non-Hermitian matrices

D2C1. General

CGECO-C Factor a matrix using Gaussian elimination and estimate

SGECO-S the condition number of the matrix.

DGECO-D

CGEDI-C Compute the determinant and inverse of a matrix using the

SGEDI-S factors computed by CGECO or CGEFA.

DGEDI-D

CGEFA-C Factor a matrix using Gaussian elimination.

SGEFA-S

DGEFA-D

CGEFS-C Solve a general system of linear equations.

SGEFS-S

DGEFS-D

CGEIR-C Solve a general system of linear equations. Iterative

SGEIR-S refinement is used to obtain an error estimate.

CGESL-C Solve the complex system A*X=B or CTRANS(A)*X=B using the

SGESL-S factors computed by CGECO or CGEFA.

DGESL-D

CQRSL-C Apply the output of CQRDC to compute coordinate transfor-

SQRSL-S mations, projections, and least squares solutions.

DQRSL-D

CSICO-C Factor a complex symmetric matrix by elimination with

SSICO-S symmetric pivoting and estimate the condition number of the

DSICO-D matrix.

CHICO-C

CSIDI-C Compute the determinant and inverse of a complex symmetric

SSIDI-S matrix using the factors from CSIFA.

DSIDI-D

CHIDI-C

CSIFA-C Factor a complex symmetric matrix by elimination with

SSIFA-S symmetric pivoting.

DSIFA-D

CHIFA-C

CSISL-C Solve a complex symmetric system using the factors obtained

SSISL-S from CSIFA.

DSISL-D

CHISL-C

CSPCO-C Factor a complex symmetric matrix stored in packed form

SSPCO-S by elimination with symmetric pivoting and estimate the

DSPCO-D condition number of the matrix.

CHPCO-C

CSPDI-C Compute the determinant and inverse of a complex symmetric

SSPDI-S matrix stored in packed form using the factors from CSPFA.

DSPDI-D

CHPDI-C

CSPFA-C Factor a complex symmetric matrix stored in packed form by

SSPFA-S elimination with symmetric pivoting.

DSPFA-D

CHPFA-C

CSPSL-C Solve a complex symmetric system using the factors obtained

SSPSL-S from CSPFA.

DSPSL-D

CHPSL-C

D2C2. Banded

CGBCO-C Factor a band matrix by Gaussian elimination and

SGBCO-S estimate the condition number of the matrix.

DGBCO-D

CGBFA-C Factor a band matrix using Gaussian elimination.

SGBFA-S

DGBFA-D

CGBSL-C Solve the complex band system A*X=B or CTRANS(A)*X=B using

SGBSL-S the factors computed by CGBCO or CGBFA.

DGBSL-D

CNBCO-C Factor a band matrix using Gaussian elimination and

SNBCO-S estimate the condition number.

DNBCO-D

CNBFA-C Factor a band matrix by elimination.

SNBFA-S

DNBFA-D

CNBFS-C Solve a general nonsymmetric banded system of linear

SNBFS-S equations.

DNBFS-D

CNBIR-C Solve a general nonsymmetric banded system of linear

SNBIR-S equations. Iterative refinement is used to obtain an error

estimate.

CNBSL-C Solve a complex band system using the factors computed by

SNBSL-S CNBCO or CNBFA.

DNBSL-D

D2C2A. Tridiagonal

CGTSL-C Solve a tridiagonal linear system.

SGTSL-S

DGTSL-D

D2C3. Triangular

CTRCO-C Estimate the condition number of a triangular matrix.

STRCO-S

DTRCO-D

CTRDI-C Compute the determinant and inverse of a triangular matrix.

STRDI-S

DTRDI-D

CTRSL-C Solve a system of the form T*X=B or CTRANS(T)*X=B, where

STRSL-S T is a triangular matrix. Here CTRANS(T) is the conjugate

DTRSL-D transpose.

D2D. Complex Hermitian matrices

D2D1. General

D2D1A. Indefinite

CHICO-C Factor a complex Hermitian matrix by elimination with sym-

SSICO-S metric pivoting and estimate the condition of the matrix.

DSICO-D

CSICO-C

CHIDI-C Compute the determinant, inertia and inverse of a complex

SSIDI-S Hermitian matrix using the factors obtained from CHIFA.

DSISI-D

CSIDI-C

CHIFA-C Factor a complex Hermitian matrix by elimination

SSIFA-S (symmetric pivoting).

DSIFA-D

CSIFA-C

CHISL-C Solve the complex Hermitian system using factors obtained

SSISL-S from CHIFA.

DSISL-D

CSISL-C

CHPCO-C Factor a complex Hermitian matrix stored in packed form by

SSPCO-S elimination with symmetric pivoting and estimate the

DSPCO-D condition number of the matrix.

CSPCO-C

CHPDI-C Compute the determinant, inertia and inverse of a complex

SSPDI-S Hermitian matrix stored in packed form using the factors

DSPDI-D obtained from CHPFA.

DSPDI-C

CHPFA-C Factor a complex Hermitian matrix stored in packed form by

SSPFA-S elimination with symmetric pivoting.

DSPFA-D

DSPFA-C

CHPSL-C Solve a complex Hermitian system using factors obtained

SSPSL-S from CHPFA.

DSPSL-D

CSPSL-C

D2D1B. Positive definite

CCHDC-C Compute the Cholesky decomposition of a positive definite

SCHDC-S matrix. A pivoting option allows the user to estimate the

DCHDC-D condition number of a positive definite matrix or determine

the rank of a positive semidefinite matrix.

CPOCO-C Factor a complex Hermitian positive definite matrix

SPOCO-S and estimate the condition number of the matrix.

DPOCO-D

CPODI-C Compute the determinant and inverse of a certain complex

SPODI-S Hermitian positive definite matrix using the factors

DPODI-D computed by CPOCO, CPOFA, or CQRDC.

CPOFA-C Factor a complex Hermitian positive definite matrix.

SPOFA-S

DPOFA-D

CPOFS-C Solve a positive definite symmetric complex system of

SPOFS-S linear equations.

DPOFS-D

CPOIR-C Solve a positive definite Hermitian system of linear

SPOIR-S equations. Iterative refinement is used to obtain an

error estimate.

CPOSL-C Solve the complex Hermitian positive definite linear system

SPOSL-S using the factors computed by CPOCO or CPOFA.

DPOSL-D

CPPCO-C Factor a complex Hermitian positive definite matrix stored

SPPCO-S in packed form and estimate the condition number of the

DPPCO-D matrix.

CPPDI-C Compute the determinant and inverse of a complex Hermitian

SPPDI-S positive definite matrix using factors from CPPCO or CPPFA.

DPPDI-D

CPPFA-C Factor a complex Hermitian positive definite matrix stored

SPPFA-S in packed form.

DPPFA-D

CPPSL-C Solve the complex Hermitian positive definite system using

SPPSL-S the factors computed by CPPCO or CPPFA.

DPPSL-D

D2D2. Positive definite banded

CPBCO-C Factor a complex Hermitian positive definite matrix stored

SPBCO-S in band form and estimate the condition number of the

DPBCO-D matrix.

CPBFA-C Factor a complex Hermitian positive definite matrix stored

SPBFA-S in band form.

DPBFA-D

CPBSL-C Solve the complex Hermitian positive definite band system

SPBSL-S using the factors computed by CPBCO or CPBFA.

DPBSL-D

D2D2A. Tridiagonal

CPTSL-C Solve a positive definite tridiagonal linear system.

SPTSL-S

DPTSL-D

D2E. Associated operations (e.g., matrix reorderings)

SLLTI2-S SLAP Backsolve routine for LDL' Factorization.

DLLTI2-D Routine to solve a system of the form L*D*L' X = B,

where L is a unit lower triangular matrix and D is a

diagonal matrix and ' means transpose.

SS2LT-S Lower Triangle Preconditioner SLAP Set Up.

DS2LT-D Routine to store the lower triangle of a matrix stored

in the SLAP Column format.

SSD2S-S Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.

DSD2S-D Routine to compute the inverse of the diagonal of the

matrix A*A', where A is stored in SLAP-Column format.

SSDS-S Diagonal Scaling Preconditioner SLAP Set Up.

DSDS-D Routine to compute the inverse of the diagonal of a matrix

stored in the SLAP Column format.

SSDSCL-S Diagonal Scaling of system Ax = b.

DSDSCL-D This routine scales (and unscales) the system Ax = b

by symmetric diagonal scaling.

SSICS-S Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.

DSICS-D Routine to generate the Incomplete Cholesky decomposition,

L*D*L-trans, of a symmetric positive definite matrix, A,

which is stored in SLAP Column format. The unit lower

triangular matrix L is stored by rows, and the inverse of

the diagonal matrix D is stored.

SSILUS-S Incomplete LU Decomposition Preconditioner SLAP Set Up.

DSILUS-D Routine to generate the incomplete LDU decomposition of a

matrix. The unit lower triangular factor L is stored by

rows and the unit upper triangular factor U is stored by

columns. The inverse of the diagonal matrix D is stored.

No fill in is allowed.

SSLLTI-S SLAP MSOLVE for LDL' (IC) Factorization.

DSLLTI-D This routine acts as an interface between the SLAP generic

MSOLVE calling convention and the routine that actually

-1

computes (LDL') B = X.

SSLUI-S SLAP MSOLVE for LDU Factorization.

DSLUI-D This routine acts as an interface between the SLAP generic

MSOLVE calling convention and the routine that actually

-1

computes (LDU) B = X.

SSLUI2-S SLAP Backsolve for LDU Factorization.

DSLUI2-D Routine to solve a system of the form L*D*U X = B,

where L is a unit lower triangular matrix, D is a diagonal

matrix, and U is a unit upper triangular matrix.

SSLUI4-S SLAP Backsolve for LDU Factorization.

DSLUI4-D Routine to solve a system of the form (L*D*U)' X = B,

where L is a unit lower triangular matrix, D is a diagonal

matrix, and U is a unit upper triangular matrix and '

denotes transpose.

SSLUTI-S SLAP MTSOLV for LDU Factorization.

DSLUTI-D This routine acts as an interface between the SLAP generic

MTSOLV calling convention and the routine that actually

-T

computes (LDU) B = X.

SSMMI2-S SLAP Backsolve for LDU Factorization of Normal Equations.

DSMMI2-D To solve a system of the form (L*D*U)*(L*D*U)' X = B,

where L is a unit lower triangular matrix, D is a diagonal

matrix, and U is a unit upper triangular matrix and '

denotes transpose.

SSMMTI-S SLAP MSOLVE for LDU Factorization of Normal Equations.

DSMMTI-D This routine acts as an interface between the SLAP generic

MMTSLV calling convention and the routine that actually

-1

computes [(LDU)*(LDU)'] B = X.

D3. Determinants

D3A. Real nonsymmetric matrices

D3A1. General

SGEDI-S Compute the determinant and inverse of a matrix using the

DGEDI-D factors computed by SGECO or SGEFA.

CGEDI-C

D3A2. Banded

SGBDI-S Compute the determinant of a band matrix using the factors

DGBDI-D computed by SGBCO or SGBFA.

CGBDI-C

SNBDI-S Compute the determinant of a band matrix using the factors

DNBDI-D computed by SNBCO or SNBFA.

CNBDI-C

D3A3. Triangular

STRDI-S Compute the determinant and inverse of a triangular matrix.

DTRDI-D

CTRDI-C

D3B. Real symmetric matrices

D3B1. General

D3B1A. Indefinite

SSIDI-S Compute the determinant, inertia and inverse of a real

DSIDI-D symmetric matrix using the factors from SSIFA.

CHIDI-C

CSIDI-C

SSPDI-S Compute the determinant, inertia, inverse of a real

DSPDI-D symmetric matrix stored in packed form using the factors

CHPDI-C from SSPFA.

CSPDI-C

D3B1B. Positive definite

SPODI-S Compute the determinant and inverse of a certain real

DPODI-D symmetric positive definite matrix using the factors

CPODI-C computed by SPOCO, SPOFA or SQRDC.

SPPDI-S Compute the determinant and inverse of a real symmetric

DPPDI-D positive definite matrix using factors from SPPCO or SPPFA.

CPPDI-C

D3B2. Positive definite banded

SPBDI-S Compute the determinant of a symmetric positive definite

DPBDI-D band matrix using the factors computed by SPBCO or SPBFA.

CPBDI-C

D3C. Complex non-Hermitian matrices

D3C1. General

CGEDI-C Compute the determinant and inverse of a matrix using the

SGEDI-S factors computed by CGECO or CGEFA.

DGEDI-D

CSIDI-C Compute the determinant and inverse of a complex symmetric

SSIDI-S matrix using the factors from CSIFA.

DSIDI-D

CHIDI-C

CSPDI-C Compute the determinant and inverse of a complex symmetric

SSPDI-S matrix stored in packed form using the factors from CSPFA.

DSPDI-D

CHPDI-C

D3C2. Banded

CGBDI-C Compute the determinant of a complex band matrix using the

SGBDI-S factors from CGBCO or CGBFA.

DGBDI-D

CNBDI-C Compute the determinant of a band matrix using the factors

SNBDI-S computed by CNBCO or CNBFA.

DNBDI-D

D3C3. Triangular

CTRDI-C Compute the determinant and inverse of a triangular matrix.

STRDI-S

DTRDI-D

D3D. Complex Hermitian matrices

D3D1. General

D3D1A. Indefinite

CHIDI-C Compute the determinant, inertia and inverse of a complex

SSIDI-S Hermitian matrix using the factors obtained from CHIFA.

DSISI-D

CSIDI-C

CHPDI-C Compute the determinant, inertia and inverse of a complex

SSPDI-S Hermitian matrix stored in packed form using the factors

DSPDI-D obtained from CHPFA.

DSPDI-C

D3D1B. Positive definite

CPODI-C Compute the determinant and inverse of a certain complex

SPODI-S Hermitian positive definite matrix using the factors

DPODI-D computed by CPOCO, CPOFA, or CQRDC.

CPPDI-C Compute the determinant and inverse of a complex Hermitian

SPPDI-S positive definite matrix using factors from CPPCO or CPPFA.

DPPDI-D

D3D2. Positive definite banded

CPBDI-C Compute the determinant of a complex Hermitian positive

SPBDI-S definite band matrix using the factors computed by CPBCO or

DPBDI-D CPBFA.

D4. Eigenvalues, eigenvectors

EISDOC-A Documentation for EISPACK, a collection of subprograms for

solving matrix eigen-problems.

D4A. Ordinary eigenvalue problems (Ax = (lambda) * x)

D4A1. Real symmetric

RS-S Compute the eigenvalues and, optionally, the eigenvectors

CH-C of a real symmetric matrix.

RSP-S Compute the eigenvalues and, optionally, the eigenvectors

of a real symmetric matrix packed into a one dimensional

array.

SSIEV-S Compute the eigenvalues and, optionally, the eigenvectors

CHIEV-C of a real symmetric matrix.

SSPEV-S Compute the eigenvalues and, optionally, the eigenvectors

of a real symmetric matrix stored in packed form.

D4A2. Real nonsymmetric

RG-S Compute the eigenvalues and, optionally, the eigenvectors

CG-C of a real general matrix.

SGEEV-S Compute the eigenvalues and, optionally, the eigenvectors

CGEEV-C of a real general matrix.

D4A3. Complex Hermitian

CH-C Compute the eigenvalues and, optionally, the eigenvectors

RS-S of a complex Hermitian matrix.

CHIEV-C Compute the eigenvalues and, optionally, the eigenvectors

SSIEV-S of a complex Hermitian matrix.

D4A4. Complex non-Hermitian

CG-C Compute the eigenvalues and, optionally, the eigenvectors

RG-S of a complex general matrix.

CGEEV-C Compute the eigenvalues and, optionally, the eigenvectors

SGEEV-S of a complex general matrix.

D4A5. Tridiagonal

BISECT-S Compute the eigenvalues of a symmetric tridiagonal matrix

in a given interval using Sturm sequencing.

IMTQL1-S Compute the eigenvalues of a symmetric tridiagonal matrix

using the implicit QL method.

IMTQL2-S Compute the eigenvalues and eigenvectors of a symmetric

tridiagonal matrix using the implicit QL method.

IMTQLV-S Compute the eigenvalues of a symmetric tridiagonal matrix

using the implicit QL method. Eigenvectors may be computed

later.

RATQR-S Compute the largest or smallest eigenvalues of a symmetric

tridiagonal matrix using the rational QR method with Newton

correction.

RST-S Compute the eigenvalues and, optionally, the eigenvectors

of a real symmetric tridiagonal matrix.

RT-S Compute the eigenvalues and eigenvectors of a special real

tridiagonal matrix.

TQL1-S Compute the eigenvalues of symmetric tridiagonal matrix by

the QL method.

TQL2-S Compute the eigenvalues and eigenvectors of symmetric

tridiagonal matrix.

TQLRAT-S Compute the eigenvalues of symmetric tridiagonal matrix

using a rational variant of the QL method.

TRIDIB-S Compute the eigenvalues of a symmetric tridiagonal matrix

in a given interval using Sturm sequencing.

TSTURM-S Find those eigenvalues of a symmetric tridiagonal matrix

in a given interval and their associated eigenvectors by

Sturm sequencing.

D4A6. Banded

BQR-S Compute some of the eigenvalues of a real symmetric

matrix using the QR method with shifts of origin.

RSB-S Compute the eigenvalues and, optionally, the eigenvectors

of a symmetric band matrix.

D4B. Generalized eigenvalue problems (e.g., Ax = (lambda)*Bx)

D4B1. Real symmetric

RSG-S Compute the eigenvalues and, optionally, the eigenvectors

of a symmetric generalized eigenproblem.

RSGAB-S Compute the eigenvalues and, optionally, the eigenvectors

of a symmetric generalized eigenproblem.

RSGBA-S Compute the eigenvalues and, optionally, the eigenvectors

of a symmetric generalized eigenproblem.

D4B2. Real general

RGG-S Compute the eigenvalues and eigenvectors for a real

generalized eigenproblem.

D4C. Associated operations

D4C1. Transform problem

D4C1A. Balance matrix

BALANC-S Balance a real general matrix and isolate eigenvalues

CBAL-C whenever possible.

D4C1B. Reduce to compact form

D4C1B1. Tridiagonal

BANDR-S Reduce a real symmetric band matrix to symmetric

tridiagonal matrix and, optionally, accumulate

orthogonal similarity transformations.

HTRID3-S Reduce a complex Hermitian (packed) matrix to a real

symmetric tridiagonal matrix by unitary similarity

transformations.

HTRIDI-S Reduce a complex Hermitian matrix to a real symmetric

tridiagonal matrix using unitary similarity

transformations.

TRED1-S Reduce a real symmetric matrix to symmetric tridiagonal

matrix using orthogonal similarity transformations.

TRED2-S Reduce a real symmetric matrix to a symmetric tridiagonal

matrix using and accumulating orthogonal transformations.

TRED3-S Reduce a real symmetric matrix stored in packed form to

symmetric tridiagonal matrix using orthogonal

transformations.

D4C1B2. Hessenberg

ELMHES-S Reduce a real general matrix to upper Hessenberg form

COMHES-C using stabilized elementary similarity transformations.

ORTHES-S Reduce a real general matrix to upper Hessenberg form

CORTH-C using orthogonal similarity transformations.

D4C1B3. Other

QZHES-S The first step of the QZ algorithm for solving generalized

matrix eigenproblems. Accepts a pair of real general

matrices and reduces one of them to upper Hessenberg

and the other to upper triangular form using orthogonal

transformations. Usually followed by QZIT, QZVAL, QZVEC.

QZIT-S The second step of the QZ algorithm for generalized

eigenproblems. Accepts an upper Hessenberg and an upper

triangular matrix and reduces the former to

quasi-triangular form while preserving the form of the

latter. Usually preceded by QZHES and followed by QZVAL

and QZVEC.

D4C1C. Standardize problem

FIGI-S Transforms certain real non-symmetric tridiagonal matrix

to symmetric tridiagonal matrix.

FIGI2-S Transforms certain real non-symmetric tridiagonal matrix

to symmetric tridiagonal matrix.

REDUC-S Reduce a generalized symmetric eigenproblem to a standard

symmetric eigenproblem using Cholesky factorization.

REDUC2-S Reduce a certain generalized symmetric eigenproblem to a

standard symmetric eigenproblem using Cholesky

factorization.

D4C2. Compute eigenvalues of matrix in compact form

D4C2A. Tridiagonal

BISECT-S Compute the eigenvalues of a symmetric tridiagonal matrix

in a given interval using Sturm sequencing.

IMTQL1-S Compute the eigenvalues of a symmetric tridiagonal matrix

using the implicit QL method.

IMTQL2-S Compute the eigenvalues and eigenvectors of a symmetric

tridiagonal matrix using the implicit QL method.

IMTQLV-S Compute the eigenvalues of a symmetric tridiagonal matrix

using the implicit QL method. Eigenvectors may be computed

later.

RATQR-S Compute the largest or smallest eigenvalues of a symmetric

tridiagonal matrix using the rational QR method with Newton

correction.

TQL1-S Compute the eigenvalues of symmetric tridiagonal matrix by

the QL method.

TQL2-S Compute the eigenvalues and eigenvectors of symmetric

tridiagonal matrix.

TQLRAT-S Compute the eigenvalues of symmetric tridiagonal matrix

using a rational variant of the QL method.

TRIDIB-S Compute the eigenvalues of a symmetric tridiagonal matrix

in a given interval using Sturm sequencing.

TSTURM-S Find those eigenvalues of a symmetric tridiagonal matrix

in a given interval and their associated eigenvectors by

Sturm sequencing.

D4C2B. Hessenberg

COMLR-C Compute the eigenvalues of a complex upper Hessenberg

matrix using the modified LR method.

COMLR2-C Compute the eigenvalues and eigenvectors of a complex upper

Hessenberg matrix using the modified LR method.

HQR-S Compute the eigenvalues of a real upper Hessenberg matrix

COMQR-C using the QR method.

HQR2-S Compute the eigenvalues and eigenvectors of a real upper

COMQR2-C Hessenberg matrix using QR method.

INVIT-S Compute the eigenvectors of a real upper Hessenberg

CINVIT-C matrix associated with specified eigenvalues by inverse

iteration.

D4C2C. Other

QZVAL-S The third step of the QZ algorithm for generalized

eigenproblems. Accepts a pair of real matrices, one in

quasi-triangular form and the other in upper triangular

form and computes the eigenvalues of the associated

eigenproblem. Usually preceded by QZHES, QZIT, and

followed by QZVEC.

D4C3. Form eigenvectors from eigenvalues

BANDV-S Form the eigenvectors of a real symmetric band matrix

associated with a set of ordered approximate eigenvalues

by inverse iteration.

QZVEC-S The optional fourth step of the QZ algorithm for

generalized eigenproblems. Accepts a matrix in

quasi-triangular form and another in upper triangular

and computes the eigenvectors of the triangular problem

and transforms them back to the original coordinates

Usually preceded by QZHES, QZIT, and QZVAL.

TINVIT-S Compute the eigenvectors of symmetric tridiagonal matrix

corresponding to specified eigenvalues, using inverse

iteration.

D4C4. Back transform eigenvectors

BAKVEC-S Form the eigenvectors of a certain real non-symmetric

tridiagonal matrix from a symmetric tridiagonal matrix

output from FIGI.

BALBAK-S Form the eigenvectors of a real general matrix from the

CBABK2-C eigenvectors of matrix output from BALANC.

ELMBAK-S Form the eigenvectors of a real general matrix from the

COMBAK-C eigenvectors of the upper Hessenberg matrix output from

ELMHES.

ELTRAN-S Accumulates the stabilized elementary similarity

transformations used in the reduction of a real general

matrix to upper Hessenberg form by ELMHES.

HTRIB3-S Compute the eigenvectors of a complex Hermitian matrix from

the eigenvectors of a real symmetric tridiagonal matrix

output from HTRID3.

HTRIBK-S Form the eigenvectors of a complex Hermitian matrix from

the eigenvectors of a real symmetric tridiagonal matrix

output from HTRIDI.

ORTBAK-S Form the eigenvectors of a general real matrix from the

CORTB-C eigenvectors of the upper Hessenberg matrix output from

ORTHES.

ORTRAN-S Accumulate orthogonal similarity transformations in the

reduction of real general matrix by ORTHES.

REBAK-S Form the eigenvectors of a generalized symmetric

eigensystem from the eigenvectors of derived matrix output

from REDUC or REDUC2.

REBAKB-S Form the eigenvectors of a generalized symmetric

eigensystem from the eigenvectors of derived matrix output

from REDUC2.

TRBAK1-S Form the eigenvectors of real symmetric matrix from

the eigenvectors of a symmetric tridiagonal matrix formed

by TRED1.

TRBAK3-S Form the eigenvectors of a real symmetric matrix from the

eigenvectors of a symmetric tridiagonal matrix formed

by TRED3.

D5. QR decomposition, Gram-Schmidt orthogonalization

LLSIA-S Solve a linear least squares problems by performing a QR

DLLSIA-D factorization of the matrix using Householder

transformations. Emphasis is put on detecting possible

rank deficiency.

SGLSS-S Solve a linear least squares problems by performing a QR

DGLSS-D factorization of the matrix using Householder

transformations. Emphasis is put on detecting possible

rank deficiency.

SQRDC-S Use Householder transformations to compute the QR

DQRDC-D factorization of an N by P matrix. Column pivoting is a

CQRDC-C users option.

D6. Singular value decomposition

SSVDC-S Perform the singular value decomposition of a rectangular

DSVDC-D matrix.

CSVDC-C

D7. Update matrix decompositions

D7B. Cholesky

SCHDD-S Downdate an augmented Cholesky decomposition or the

DCHDD-D triangular factor of an augmented QR decomposition.

CCHDD-C

SCHEX-S Update the Cholesky factorization A=TRANS(R)*R of A

DCHEX-D positive definite matrix A of order P under diagonal

CCHEX-C permutations of the form TRANS(E)*A*E, where E is a

permutation matrix.

SCHUD-S Update an augmented Cholesky decomposition of the

DCHUD-D triangular part of an augmented QR decomposition.

CCHUD-C

D9. Overdetermined or underdetermined systems of equations, singular systems,

pseudo-inverses (search also classes D5, D6, K1a, L8a)

BNDACC-S Compute the LU factorization of a banded matrices using

DBNDAC-D sequential accumulation of rows of the data matrix.

Exactly one right-hand side vector is permitted.

BNDSOL-S Solve the least squares problem for a banded matrix using

DBNDSL-D sequential accumulation of rows of the data matrix.

Exactly one right-hand side vector is permitted.

HFTI-S Solve a linear least squares problems by performing a QR

DHFTI-D factorization of the matrix using Householder

transformations.

LLSIA-S Solve a linear least squares problems by performing a QR

DLLSIA-D factorization of the matrix using Householder

transformations. Emphasis is put on detecting possible

rank deficiency.

LSEI-S Solve a linearly constrained least squares problem with

DLSEI-D equality and inequality constraints, and optionally compute

a covariance matrix.

MINFIT-S Compute the singular value decomposition of a rectangular

matrix and solve the related linear least squares problem.

SGLSS-S Solve a linear least squares problems by performing a QR

DGLSS-D factorization of the matrix using Householder

transformations. Emphasis is put on detecting possible

rank deficiency.

SQRSL-S Apply the output of SQRDC to compute coordinate transfor-

DQRSL-D mations, projections, and least squares solutions.

CQRSL-C

ULSIA-S Solve an underdetermined linear system of equations by

DULSIA-D performing an LQ factorization of the matrix using

Householder transformations. Emphasis is put on detecting

possible rank deficiency.

E. Interpolation

BSPDOC-A Documentation for BSPLINE, a package of subprograms for

working with piecewise polynomial functions

in B-representation.

E1. Univariate data (curve fitting)

E1A. Polynomial splines (piecewise polynomials)

BINT4-S Compute the B-representation of a cubic spline

DBINT4-D which interpolates given data.

BINTK-S Compute the B-representation of a spline which interpolates

DBINTK-D given data.

BSPDOC-A Documentation for BSPLINE, a package of subprograms for

working with piecewise polynomial functions

in B-representation.

PCHDOC-A Documentation for PCHIP, a Fortran package for piecewise

cubic Hermite interpolation of data.

PCHIC-S Set derivatives needed to determine a piecewise monotone

DPCHIC-D piecewise cubic Hermite interpolant to given data.

User control is available over boundary conditions and/or

treatment of points where monotonicity switches direction.

PCHIM-S Set derivatives needed to determine a monotone piecewise

DPCHIM-D cubic Hermite interpolant to given data. Boundary values

are provided which are compatible with monotonicity. The

interpolant will have an extremum at each point where mono-

tonicity switches direction. (See PCHIC if user control is

desired over boundary or switch conditions.)

PCHSP-S Set derivatives needed to determine the Hermite represen-

DPCHSP-D tation of the cubic spline interpolant to given data, with

specified boundary conditions.

E1B. Polynomials

POLCOF-S Compute the coefficients of the polynomial fit (including

DPOLCF-D Hermite polynomial fits) produced by a previous call to

POLINT.

POLINT-S Produce the polynomial which interpolates a set of discrete

DPLINT-D data points.

E3. Service routines (e.g., grid generation, evaluation of fitted functions)

(search also class N5)

BFQAD-S Compute the integral of a product of a function and a

DBFQAD-D derivative of a B-spline.

BSPDR-S Use the B-representation to construct a divided difference

DBSPDR-D table preparatory to a (right) derivative calculation.

BSPEV-S Calculate the value of the spline and its derivatives from

DBSPEV-D the B-representation.

BSPPP-S Convert the B-representation of a B-spline to the piecewise

DBSPPP-D polynomial (PP) form.

BSPVD-S Calculate the value and all derivatives of order less than

DBSPVD-D NDERIV of all basis functions which do not vanish at X.

BSPVN-S Calculate the value of all (possibly) nonzero basis

DBSPVN-D functions at X.

BSQAD-S Compute the integral of a K-th order B-spline using the

DBSQAD-D B-representation.

BVALU-S Evaluate the B-representation of a B-spline at X for the

DBVALU-D function value or any of its derivatives.

CHFDV-S Evaluate a cubic polynomial given in Hermite form and its

DCHFDV-D first derivative at an array of points. While designed for

use by PCHFD, it may be useful directly as an evaluator

for a piecewise cubic Hermite function in applications,

such as graphing, where the interval is known in advance.

If only function values are required, use CHFEV instead.

CHFEV-S Evaluate a cubic polynomial given in Hermite form at an

DCHFEV-D array of points. While designed for use by PCHFE, it may

be useful directly as an evaluator for a piecewise cubic

Hermite function in applications, such as graphing, where

the interval is known in advance.

INTRV-S Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT

DINTRV-D such that XT(ILEFT) .LE. X where XT(*) is a subdivision

of the X interval.

PCHBS-S Piecewise Cubic Hermite to B-Spline converter.

DPCHBS-D

PCHCM-S Check a cubic Hermite function for monotonicity.

DPCHCM-D

PCHFD-S Evaluate a piecewise cubic Hermite function and its first

DPCHFD-D derivative at an array of points. May be used by itself

for Hermite interpolation, or as an evaluator for PCHIM

or PCHIC. If only function values are required, use

PCHFE instead.

PCHFE-S Evaluate a piecewise cubic Hermite function at an array of

DPCHFE-D points. May be used by itself for Hermite interpolation,

or as an evaluator for PCHIM or PCHIC.

PCHIA-S Evaluate the definite integral of a piecewise cubic

DPCHIA-D Hermite function over an arbitrary interval.

PCHID-S Evaluate the definite integral of a piecewise cubic

DPCHID-D Hermite function over an interval whose endpoints are data

points.

PFQAD-S Compute the integral on (X1,X2) of a product of a function

DPFQAD-D F and the ID-th derivative of a B-spline,

(PP-representation).

POLYVL-S Calculate the value of a polynomial and its first NDER

DPOLVL-D derivatives where the polynomial was produced by a previous

call to POLINT.

PPQAD-S Compute the integral on (X1,X2) of a K-th order B-spline

DPPQAD-D using the piecewise polynomial (PP) representation.

PPVAL-S Calculate the value of the IDERIV-th derivative of the

DPPVAL-D B-spline from the PP-representation.

F. Solution of nonlinear equations

F1. Single equation

F1A. Smooth

F1A1. Polynomial

F1A1A. Real coefficients

RPQR79-S Find the zeros of a polynomial with real coefficients.

CPQR79-C

RPZERO-S Find the zeros of a polynomial with real coefficients.

CPZERO-C

F1A1B. Complex coefficients

CPQR79-C Find the zeros of a polynomial with complex coefficients.

RPQR79-S

CPZERO-C Find the zeros of a polynomial with complex coefficients.

RPZERO-S

F1B. General (no smoothness assumed)

FZERO-S Search for a zero of a function F(X) in a given interval

DFZERO-D (B,C). It is designed primarily for problems where F(B)

and F(C) have opposite signs.

F2. System of equations

F2A. Smooth

SNSQ-S Find a zero of a system of a N nonlinear functions in N

DNSQ-D variables by a modification of the Powell hybrid method.

SNSQE-S An easy-to-use code to find a zero of a system of N

DNSQE-D nonlinear functions in N variables by a modification of

the Powell hybrid method.

SOS-S Solve a square system of nonlinear equations.

DSOS-D

F3. Service routines (e.g., check user-supplied derivatives)

CHKDER-S Check the gradients of M nonlinear functions in N

DCKDER-D variables, evaluated at a point X, for consistency

with the functions themselves.

G. Optimization (search also classes K, L8)

G2. Constrained

G2A. Linear programming

G2A2. Sparse matrix of constraints

SPLP-S Solve linear programming problems involving at

DSPLP-D most a few thousand constraints and variables.

Takes advantage of sparsity in the constraint matrix.

G2E. Quadratic programming

SBOCLS-S Solve the bounded and constrained least squares

DBOCLS-D problem consisting of solving the equation

E*X = F (in the least squares sense)

subject to the linear constraints

C*X = Y.

SBOLS-S Solve the problem

DBOLS-D E*X = F (in the least squares sense)

with bounds on selected X values.

G2H. General nonlinear programming

G2H1. Simple bounds

SBOCLS-S Solve the bounded and constrained least squares

DBOCLS-D problem consisting of solving the equation

E*X = F (in the least squares sense)

subject to the linear constraints

C*X = Y.

SBOLS-S Solve the problem

DBOLS-D E*X = F (in the least squares sense)

with bounds on selected X values.

G2H2. Linear equality or inequality constraints

SBOCLS-S Solve the bounded and constrained least squares

DBOCLS-D problem consisting of solving the equation

E*X = F (in the least squares sense)

subject to the linear constraints

C*X = Y.

SBOLS-S Solve the problem

DBOLS-D E*X = F (in the least squares sense)

with bounds on selected X values.

G4. Service routines

G4C. Check user-supplied derivatives

CHKDER-S Check the gradients of M nonlinear functions in N

DCKDER-D variables, evaluated at a point X, for consistency

with the functions themselves.

H. Differentiation, integration

H1. Numerical differentiation

CHFDV-S Evaluate a cubic polynomial given in Hermite form and its

DCHFDV-D first derivative at an array of points. While designed for

use by PCHFD, it may be useful directly as an evaluator

for a piecewise cubic Hermite function in applications,

such as graphing, where the interval is known in advance.

If only function values are required, use CHFEV instead.

PCHFD-S Evaluate a piecewise cubic Hermite function and its first

DPCHFD-D derivative at an array of points. May be used by itself

for Hermite interpolation, or as an evaluator for PCHIM

or PCHIC. If only function values are required, use

PCHFE instead.

H2. Quadrature (numerical evaluation of definite integrals)

QPDOC-A Documentation for QUADPACK, a package of subprograms for

automatic evaluation of one-dimensional definite integrals.

H2A. One-dimensional integrals

H2A1. Finite interval (general integrand)

H2A1A. Integrand available via user-defined procedure

H2A1A1. Automatic (user need only specify required accuracy)

GAUS8-S Integrate a real function of one variable over a finite

DGAUS8-D interval using an adaptive 8-point Legendre-Gauss

algorithm. Intended primarily for high accuracy

integration or integration of smooth functions.

QAG-S The routine calculates an approximation result to a given

DQAG-D definite integral I = integral of F over (A,B),

hopefully satisfying following claim for accuracy

ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGE-S The routine calculates an approximation result to a given

DQAGE-D definite integral I = Integral of F over (A,B),

hopefully satisfying following claim for accuracy

ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGS-S The routine calculates an approximation result to a given

DQAGS-D Definite integral I = Integral of F over (A,B),

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGSE-S The routine calculates an approximation result to a given

DQAGSE-D definite integral I = Integral of F over (A,B),

hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QNC79-S Integrate a function using a 7-point adaptive Newton-Cotes

DQNC79-D quadrature rule.

QNG-S The routine calculates an approximation result to a

DQNG-D given definite integral I = integral of F over (A,B),

hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

H2A1A2. Nonautomatic

QK15-S To compute I = Integral of F over (A,B), with error

DQK15-D estimate

J = integral of ABS(F) over (A,B)

QK21-S To compute I = Integral of F over (A,B), with error

DQK21-D estimate

J = Integral of ABS(F) over (A,B)

QK31-S To compute I = Integral of F over (A,B) with error

DQK31-D estimate

J = Integral of ABS(F) over (A,B)

QK41-S To compute I = Integral of F over (A,B), with error

DQK41-D estimate

J = Integral of ABS(F) over (A,B)

QK51-S To compute I = Integral of F over (A,B) with error

DQK51-D estimate

J = Integral of ABS(F) over (A,B)

QK61-S To compute I = Integral of F over (A,B) with error

DQK61-D estimate

J = Integral of ABS(F) over (A,B)

H2A1B. Integrand available only on grid

H2A1B2. Nonautomatic

AVINT-S Integrate a function tabulated at arbitrarily spaced

DAVINT-D abscissas using overlapping parabolas.

PCHIA-S Evaluate the definite integral of a piecewise cubic

DPCHIA-D Hermite function over an arbitrary interval.

PCHID-S Evaluate the definite integral of a piecewise cubic

DPCHID-D Hermite function over an interval whose endpoints are data

points.

H2A2. Finite interval (specific or special type integrand including weight

functions, oscillating and singular integrands, principal value

integrals, splines, etc.)

H2A2A. Integrand available via user-defined procedure

H2A2A1. Automatic (user need only specify required accuracy)

BFQAD-S Compute the integral of a product of a function and a

DBFQAD-D derivative of a B-spline.

BSQAD-S Compute the integral of a K-th order B-spline using the

DBSQAD-D B-representation.

PFQAD-S Compute the integral on (X1,X2) of a product of a function

DPFQAD-D F and the ID-th derivative of a B-spline,

(PP-representation).

PPQAD-S Compute the integral on (X1,X2) of a K-th order B-spline

DPPQAD-D using the piecewise polynomial (PP) representation.

QAGP-S The routine calculates an approximation result to a given

DQAGP-D definite integral I = Integral of F over (A,B),

hopefully satisfying following claim for accuracy

break points of the integration interval, where local

difficulties of the integrand may occur(e.g. SINGULARITIES,

DISCONTINUITIES), are provided by the user.

QAGPE-S Approximate a given definite integral I = Integral of F

DQAGPE-D over (A,B), hopefully satisfying the accuracy claim:

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

Break points of the integration interval, where local

difficulties of the integrand may occur (e.g. singularities

or discontinuities) are provided by the user.

QAWC-S The routine calculates an approximation result to a

DQAWC-D Cauchy principal value I = INTEGRAL of F*W over (A,B)

(W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying

following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

QAWCE-S The routine calculates an approximation result to a

DQAWCE-D CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)

(W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying

following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

QAWO-S Calculate an approximation to a given definite integral

DQAWO-D I = Integral of F(X)*W(X) over (A,B), where

W(X) = COS(OMEGA*X)

or W(X) = SIN(OMEGA*X),

hopefully satisfying the following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWOE-S Calculate an approximation to a given definite integral

DQAWOE-D I = Integral of F(X)*W(X) over (A,B), where

W(X) = COS(OMEGA*X)

or W(X) = SIN(OMEGA*X),

hopefully satisfying the following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWS-S The routine calculates an approximation result to a given

DQAWS-D definite integral I = Integral of F*W over (A,B),

(where W shows a singular behaviour at the end points

see parameter INTEGR).

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWSE-S The routine calculates an approximation result to a given

DQAWSE-D definite integral I = Integral of F*W over (A,B),

(where W shows a singular behaviour at the end points,

see parameter INTEGR).

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QMOMO-S This routine computes modified Chebyshev moments. The K-th

DQMOMO-D modified Chebyshev moment is defined as the integral over

(-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev

polynomial of degree K.

H2A2A2. Nonautomatic

QC25C-S To compute I = Integral of F*W over (A,B) with

DQC25C-D error estimate, where W(X) = 1/(X-C)

QC25F-S To compute the integral I=Integral of F(X) over (A,B)

DQC25F-D Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)

and to compute J=Integral of ABS(F) over (A,B). For small

value of OMEGA or small intervals (A,B) 15-point GAUSS-

KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

QC25S-S To compute I = Integral of F*W over (BL,BR), with error

DQC25S-D estimate, where the weight function W has a singular

behaviour of ALGEBRAICO-LOGARITHMIC type at the points

A and/or B. (BL,BR) is a part of (A,B).

QK15W-S To compute I = Integral of F*W over (A,B), with error

DQK15W-D estimate

J = Integral of ABS(F*W) over (A,B)

H2A3. Semi-infinite interval (including e**(-x) weight function)

H2A3A. Integrand available via user-defined procedure

H2A3A1. Automatic (user need only specify required accuracy)

QAGI-S The routine calculates an approximation result to a given

DQAGI-D INTEGRAL I = Integral of F over (BOUND,+INFINITY)

OR I = Integral of F over (-INFINITY,BOUND)

OR I = Integral of F over (-INFINITY,+INFINITY)

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGIE-S The routine calculates an approximation result to a given

DQAGIE-D integral I = Integral of F over (BOUND,+INFINITY)

or I = Integral of F over (-INFINITY,BOUND)

or I = Integral of F over (-INFINITY,+INFINITY),

hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

QAWF-S The routine calculates an approximation result to a given

DQAWF-D Fourier integral

I = Integral of F(X)*W(X) over (A,INFINITY)

where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.EPSABS.

QAWFE-S The routine calculates an approximation result to a

DQAWFE-D given Fourier integral

I = Integral of F(X)*W(X) over (A,INFINITY)

where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),

hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.EPSABS.

H2A3A2. Nonautomatic

QK15I-S The original (infinite integration range is mapped

DQK15I-D onto the interval (0,1) and (A,B) is a part of (0,1).

it is the purpose to compute

I = Integral of transformed integrand over (A,B),

J = Integral of ABS(Transformed Integrand) over (A,B).

H2A4. Infinite interval (including e**(-x**2)) weight function)

H2A4A. Integrand available via user-defined procedure

H2A4A1. Automatic (user need only specify required accuracy)

QAGI-S The routine calculates an approximation result to a given

DQAGI-D INTEGRAL I = Integral of F over (BOUND,+INFINITY)

OR I = Integral of F over (-INFINITY,BOUND)

OR I = Integral of F over (-INFINITY,+INFINITY)

Hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGIE-S The routine calculates an approximation result to a given

DQAGIE-D integral I = Integral of F over (BOUND,+INFINITY)

or I = Integral of F over (-INFINITY,BOUND)

or I = Integral of F over (-INFINITY,+INFINITY),

hopefully satisfying following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

H2A4A2. Nonautomatic

QK15I-S The original (infinite integration range is mapped

DQK15I-D onto the interval (0,1) and (A,B) is a part of (0,1).

it is the purpose to compute

I = Integral of transformed integrand over (A,B),

J = Integral of ABS(Transformed Integrand) over (A,B).

DERKF-S Solve an initial value problem in ordinary differential

DDERKF-D equations using a Runge-Kutta-Fehlberg scheme.

DEABM-S Solve an initial value problem in ordinary differential

DDEABM-D equations using an Adams-Bashforth method.

SDRIV1-S The function of SDRIV1 is to solve N (200 or fewer)

DDRIV1-D ordinary differential equations of the form

CDRIV1-C dY(I)/dT = F(Y(I),T), given the initial conditions

Y(I) = YI. SDRIV1 uses single precision arithmetic.

SDRIV2-S The function of SDRIV2 is to solve N ordinary differential

DDRIV2-D equations of the form dY(I)/dT = F(Y(I),T), given the

CDRIV2-C initial conditions Y(I) = YI. The program has options to

allow the solution of both stiff and non-stiff differential

equations. SDRIV2 uses single precision arithmetic.

SDRIV3-S The function of SDRIV3 is to solve N ordinary differential

DDRIV3-D equations of the form dY(I)/dT = F(Y(I),T), given the

CDRIV3-C initial conditions Y(I) = YI. The program has options to

allow the solution of both stiff and non-stiff differential

equations. Other important options are available. SDRIV3

uses single precision arithmetic.

SINTRP-S Approximate the solution at XOUT by evaluating the

DINTP-D polynomial computed in STEPS at XOUT. Must be used in

conjunction with STEPS.

STEPS-S Integrate a system of first order ordinary differential

DSTEPS-D equations one step.

DEBDF-S Solve an initial value problem in ordinary differential

DDEBDF-D equations using backward differentiation formulas. It is

intended primarily for stiff problems.

SDASSL-S This code solves a system of differential/algebraic

DDASSL-D equations of the form G(T,Y,YPRIME) = 0.

SDRIV1-S The function of SDRIV1 is to solve N (200 or fewer)

DDRIV1-D ordinary differential equations of the form

CDRIV1-C dY(I)/dT = F(Y(I),T), given the initial conditions

Y(I) = YI. SDRIV1 uses single precision arithmetic.

SDRIV2-S The function of SDRIV2 is to solve N ordinary differential

DDRIV2-D equations of the form dY(I)/dT = F(Y(I),T), given the

CDRIV2-C initial conditions Y(I) = YI. The program has options to

allow the solution of both stiff and non-stiff differential

equations. SDRIV2 uses single precision arithmetic.

SDRIV3-S The function of SDRIV3 is to solve N ordinary differential

DDRIV3-D equations of the form dY(I)/dT = F(Y(I),T), given the

CDRIV3-C initial conditions Y(I) = YI. The program has options to

allow the solution of both stiff and non-stiff differential

equations. Other important options are available. SDRIV3

uses single precision arithmetic.

BVSUP-S Solve a linear two-point boundary value problem using

DBVSUP-D superposition coupled with an orthonormalization procedure

and a variable-step integration scheme.

system)

HSTCRT-S Solve the standard five-point finite difference

approximation on a staggered grid to the Helmholtz equation

in Cartesian coordinates.

HSTCSP-S Solve the standard five-point finite difference

approximation on a staggered grid to the modified Helmholtz

equation in spherical coordinates assuming axisymmetry

(no dependence on longitude).

HSTCYL-S Solve the standard five-point finite difference

approximation on a staggered grid to the modified

Helmholtz equation in cylindrical coordinates.

HSTPLR-S Solve the standard five-point finite difference

approximation on a staggered grid to the Helmholtz equation

in polar coordinates.

HSTSSP-S Solve the standard five-point finite difference

approximation on a staggered grid to the Helmholtz

equation in spherical coordinates and on the surface of

the unit sphere (radius of 1).

HW3CRT-S Solve the standard seven-point finite difference

approximation to the Helmholtz equation in Cartesian

coordinates.

HWSCRT-S Solves the standard five-point finite difference

approximation to the Helmholtz equation in Cartesian

coordinates.

HWSCSP-S Solve a finite difference approximation to the modified

Helmholtz equation in spherical coordinates assuming

axisymmetry (no dependence on longitude).

HWSCYL-S Solve a standard finite difference approximation

to the Helmholtz equation in cylindrical coordinates.

HWSPLR-S Solve a finite difference approximation to the Helmholtz

equation in polar coordinates.

HWSSSP-S Solve a finite difference approximation to the Helmholtz

equation in spherical coordinates and on the surface of the

unit sphere (radius of 1).

SEPELI-S Discretize and solve a second and, optionally, a fourth

order finite difference approximation on a uniform grid to

the general separable elliptic partial differential

equation on a rectangle with any combination of periodic or

mixed boundary conditions.

SEPX4-S Solve for either the second or fourth order finite

difference approximation to the solution of a separable

elliptic partial differential equation on a rectangle.

Any combination of periodic or mixed boundary conditions is

allowed.

BLKTRI-S Solve a block tridiagonal system of linear equations

CBLKTR-C (usually resulting from the discretization of separable

two-dimensional elliptic equations).

GENBUN-S Solve by a cyclic reduction algorithm the linear system

CMGNBN-C of equations that results from a finite difference

approximation to certain 2-d elliptic PDE's on a centered

grid .

POIS3D-S Solve a three-dimensional block tridiagonal linear system

which arises from a finite difference approximation to a

three-dimensional Poisson equation using the Fourier

transform package FFTPAK written by Paul Swarztrauber.

POISTG-S Solve a block tridiagonal system of linear equations

that results from a staggered grid finite difference

approximation to 2-D elliptic PDE's.

J. Integral transforms

J1. Fast Fourier transforms (search class L10 for time series analysis)

FFTDOC-A Documentation for FFTPACK, a collection of Fast Fourier

Transform routines.

J1A. One-dimensional

J1A1. Real

EZFFTB-S A simplified real, periodic, backward fast Fourier

transform.

EZFFTF-S Compute a simplified real, periodic, fast Fourier forward

transform.

EZFFTI-S Initialize a work array for EZFFTF and EZFFTB.

RFFTB1-S Compute the backward fast Fourier transform of a real

CFFTB1-C coefficient array.

RFFTF1-S Compute the forward transform of a real, periodic sequence.

CFFTF1-C

RFFTI1-S Initialize a real and an integer work array for RFFTF1 and

CFFTI1-C RFFTB1.

J1A2. Complex

CFFTB1-C Compute the unnormalized inverse of CFFTF1.

RFFTB1-S

CFFTF1-C Compute the forward transform of a complex, periodic

RFFTF1-S sequence.

CFFTI1-C Initialize a real and an integer work array for CFFTF1 and

RFFTI1-S CFFTB1.

J1A3. Trigonometric (sine, cosine)

COSQB-S Compute the unnormalized inverse cosine transform.

COSQF-S Compute the forward cosine transform with odd wave numbers.

COSQI-S Initialize a work array for COSQF and COSQB.

COST-S Compute the cosine transform of a real, even sequence.

COSTI-S Initialize a work array for COST.

SINQB-S Compute the unnormalized inverse of SINQF.

SINQF-S Compute the forward sine transform with odd wave numbers.

SINQI-S Initialize a work array for SINQF and SINQB.

SINT-S Compute the sine transform of a real, odd sequence.

SINTI-S Initialize a work array for SINT.

J4. Hilbert transforms

QAWC-S The routine calculates an approximation result to a

DQAWC-D Cauchy principal value I = INTEGRAL of F*W over (A,B)

(W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying

following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

QAWCE-S The routine calculates an approximation result to a

DQAWCE-D CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)

(W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying

following claim for accuracy

ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

QC25C-S To compute I = Integral of F*W over (A,B) with

DQC25C-D error estimate, where W(X) = 1/(X-C)

K. Approximation (search also class L8)

BSPDOC-A Documentation for BSPLINE, a package of subprograms for

working with piecewise polynomial functions

in B-representation.

K1. Least squares (L-2) approximation

K1A. Linear least squares (search also classes D5, D6, D9)

K1A1. Unconstrained

K1A1A. Univariate data (curve fitting)

K1A1A1. Polynomial splines (piecewise polynomials)

EFC-S Fit a piecewise polynomial curve to discrete data.

DEFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

FC-S Fit a piecewise polynomial curve to discrete data.

DFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

Equality and inequality constraints can be imposed on the

fitted curve.

K1A1A2. Polynomials

PCOEF-S Convert the POLFIT coefficients to Taylor series form.

DPCOEF-D

POLFIT-S Fit discrete data in a least squares sense by polynomials

DPOLFT-D in one variable.

K1A2. Constrained

K1A2A. Linear constraints

EFC-S Fit a piecewise polynomial curve to discrete data.

DEFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

FC-S Fit a piecewise polynomial curve to discrete data.

DFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

Equality and inequality constraints can be imposed on the

fitted curve.

LSEI-S Solve a linearly constrained least squares problem with

DLSEI-D equality and inequality constraints, and optionally compute

a covariance matrix.

SBOCLS-S Solve the bounded and constrained least squares

DBOCLS-D problem consisting of solving the equation

E*X = F (in the least squares sense)

subject to the linear constraints

C*X = Y.

SBOLS-S Solve the problem

DBOLS-D E*X = F (in the least squares sense)

with bounds on selected X values.

WNNLS-S Solve a linearly constrained least squares problem with

DWNNLS-D equality constraints and nonnegativity constraints on

selected variables.

K1B. Nonlinear least squares

K1B1. Unconstrained

SCOV-S Calculate the covariance matrix for a nonlinear data

DCOV-D fitting problem. It is intended to be used after a

successful return from either SNLS1 or SNLS1E.

K1B1A. Smooth functions

K1B1A1. User provides no derivatives

SNLS1-S Minimize the sum of the squares of M nonlinear functions

DNLS1-D in N variables by a modification of the Levenberg-Marquardt

algorithm.

SNLS1E-S An easy-to-use code which minimizes the sum of the squares

DNLS1E-D of M nonlinear functions in N variables by a modification

of the Levenberg-Marquardt algorithm.

K1B1A2. User provides first derivatives

SNLS1-S Minimize the sum of the squares of M nonlinear functions

DNLS1-D in N variables by a modification of the Levenberg-Marquardt

algorithm.

SNLS1E-S An easy-to-use code which minimizes the sum of the squares

DNLS1E-D of M nonlinear functions in N variables by a modification

of the Levenberg-Marquardt algorithm.

K6. Service routines (e.g., mesh generation, evaluation of fitted functions)

(search also class N5)

BFQAD-S Compute the integral of a product of a function and a

DBFQAD-D derivative of a B-spline.

DBSPDR-D Use the B-representation to construct a divided difference

BSPDR-S table preparatory to a (right) derivative calculation.

BSPEV-S Calculate the value of the spline and its derivatives from

DBSPEV-D the B-representation.

BSPPP-S Convert the B-representation of a B-spline to the piecewise

DBSPPP-D polynomial (PP) form.

BSPVD-S Calculate the value and all derivatives of order less than

DBSPVD-D NDERIV of all basis functions which do not vanish at X.

BSPVN-S Calculate the value of all (possibly) nonzero basis

DBSPVN-D functions at X.

BSQAD-S Compute the integral of a K-th order B-spline using the

DBSQAD-D B-representation.

BVALU-S Evaluate the B-representation of a B-spline at X for the

DBVALU-D function value or any of its derivatives.

INTRV-S Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT

DINTRV-D such that XT(ILEFT) .LE. X where XT(*) is a subdivision

of the X interval.

PFQAD-S Compute the integral on (X1,X2) of a product of a function

DPFQAD-D F and the ID-th derivative of a B-spline,

(PP-representation).

PPQAD-S Compute the integral on (X1,X2) of a K-th order B-spline

DPPQAD-D using the piecewise polynomial (PP) representation.

PPVAL-S Calculate the value of the IDERIV-th derivative of the

DPPVAL-D B-spline from the PP-representation.

PVALUE-S Use the coefficients generated by POLFIT to evaluate the

DP1VLU-D polynomial fit of degree L, along with the first NDER of

its derivatives, at a specified point.

L. Statistics, probability

L5. Function evaluation (search also class C)

L5A. Univariate

L5A1. Cumulative distribution functions, probability density functions

L5A1E. Error function, exponential, extreme value

ERF-S Compute the error function.

DERF-D

ERFC-S Compute the complementary error function.

DERFC-D

L6. Pseudo-random number generation

L6A. Univariate

L6A14. Negative binomial, normal

RGAUSS-S Generate a normally distributed (Gaussian) random number.

L6A21. Uniform

RAND-S Generate a uniformly distributed random number.

RUNIF-S Generate a uniformly distributed random number.

L7. Experimental design, including analysis of variance

L7A. Univariate

L7A3. Analysis of covariance

CV-S Evaluate the variance function of the curve obtained

DCV-D by the constrained B-spline fitting subprogram FC.

L8. Regression (search also classes G, K)

L8A. Linear least squares (L-2) (search also classes D5, D6, D9)

L8A3. Piecewise polynomial (i.e. multiphase or spline)

EFC-S Fit a piecewise polynomial curve to discrete data.

DEFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

FC-S Fit a piecewise polynomial curve to discrete data.

DFC-D The piecewise polynomials are represented as B-splines.

The fitting is done in a weighted least squares sense.

Equality and inequality constraints can be imposed on the

fitted curve.

N. Data handling (search also class L2)

N1. Input, output

SBHIN-S Read a Sparse Linear System in the Boeing/Harwell Format.

DBHIN-D The matrix is read in and if the right hand side is also

present in the input file then it too is read in. The

matrix is then modified to be in the SLAP Column format.

SCPPLT-S Printer Plot of SLAP Column Format Matrix.

DCPPLT-D Routine to print out a SLAP Column format matrix in a

"printer plot" graphical representation.

STIN-S Read in SLAP Triad Format Linear System.

DTIN-D Routine to read in a SLAP Triad format matrix and right

hand side and solution to the system, if known.

STOUT-S Write out SLAP Triad Format Linear System.

DTOUT-D Routine to write out a SLAP Triad format matrix and right

hand side and solution to the system, if known.

N6. Sorting

N6A. Internal

N6A1. Passive (i.e. construct pointer array, rank)

N6A1A. Integer

IPSORT-I Return the permutation vector generated by sorting a given

SPSORT-S array and, optionally, rearrange the elements of the array.

DPSORT-D The array may be sorted in increasing or decreasing order.

HPSORT-H A slightly modified quicksort algorithm is used.

N6A1B. Real

SPSORT-S Return the permutation vector generated by sorting a given

DPSORT-D array and, optionally, rearrange the elements of the array.

IPSORT-I The array may be sorted in increasing or decreasing order.

HPSORT-H A slightly modified quicksort algorithm is used.

N6A1C. Character

HPSORT-H Return the permutation vector generated by sorting a

SPSORT-S substring within a character array and, optionally,

DPSORT-D rearrange the elements of the array. The array may be

IPSORT-I sorted in forward or reverse lexicographical order. A

slightly modified quicksort algorithm is used.

N6A2. Active

N6A2A. Integer

IPSORT-I Return the permutation vector generated by sorting a given

SPSORT-S array and, optionally, rearrange the elements of the array.

DPSORT-D The array may be sorted in increasing or decreasing order.

HPSORT-H A slightly modified quicksort algorithm is used.

ISORT-I Sort an array and optionally make the same interchanges in

SSORT-S an auxiliary array. The array may be sorted in increasing

DSORT-D or decreasing order. A slightly modified QUICKSORT

algorithm is used.

N6A2B. Real

SPSORT-S Return the permutation vector generated by sorting a given

DPSORT-D array and, optionally, rearrange the elements of the array.

IPSORT-I The array may be sorted in increasing or decreasing order.

HPSORT-H A slightly modified quicksort algorithm is used.

SSORT-S Sort an array and optionally make the same interchanges in

DSORT-D an auxiliary array. The array may be sorted in increasing

ISORT-I or decreasing order. A slightly modified QUICKSORT

algorithm is used.

N6A2C. Character

HPSORT-H Return the permutation vector generated by sorting a

SPSORT-S substring within a character array and, optionally,

DPSORT-D rearrange the elements of the array. The array may be

IPSORT-I sorted in forward or reverse lexicographical order. A

slightly modified quicksort algorithm is used.

N8. Permuting

SPPERM-S Rearrange a given array according to a prescribed

DPPERM-D permutation vector.

IPPERM-I

HPPERM-H

R. Service routines

R1. Machine-dependent constants

I1MACH-I Return integer machine dependent constants.

R1MACH-S Return floating point machine dependent constants.

D1MACH-D

R2. Error checking (e.g., check monotonicity)

GAMLIM-S Compute the minimum and maximum bounds for the argument in

DGAMLM-D the Gamma function.

R3. Error handling

FDUMP-A Symbolic dump (should be locally written).

R3A. Set criteria for fatal errors

XSETF-A Set the error control flag.

R3B. Set unit number for error messages

XSETUA-A Set logical unit numbers (up to 5) to which error

messages are to be sent.

XSETUN-A Set output file to which error messages are to be sent.

R3C. Other utility programs

NUMXER-I Return the most recent error number.

XERCLR-A Reset current error number to zero.

XERDMP-A Print the error tables and then clear them.

XERMAX-A Set maximum number of times any error message is to be

printed.

XERMSG-A Process error messages for SLATEC and other libraries.

XGETF-A Return the current value of the error control flag.

XGETUA-A Return unit number(s) to which error messages are being

sent.

XGETUN-A Return the (first) output file to which error messages

are being sent.

Z. Other

AAAAAA-A SLATEC Common Mathematical Library disclaimer and version.

BSPDOC-A Documentation for BSPLINE, a package of subprograms for

working with piecewise polynomial functions

in B-representation.

EISDOC-A Documentation for EISPACK, a collection of subprograms for

solving matrix eigen-problems.

FFTDOC-A Documentation for FFTPACK, a collection of Fast Fourier

Transform routines.

FUNDOC-A Documentation for FNLIB, a collection of routines for

evaluating elementary and special functions.

PCHDOC-A Documentation for PCHIP, a Fortran package for piecewise

cubic Hermite interpolation of data.

QPDOC-A Documentation for QUADPACK, a package of subprograms for

automatic evaluation of one-dimensional definite integrals.

SLPDOC-S Sparse Linear Algebra Package Version 2.0.2 Documentation.

DLPDOC-D Routines to solve large sparse symmetric and nonsymmetric

positive definite linear systems, Ax = b, using precondi-

tioned iterative methods.

SECTION II. Subsidiary Routines

ASYIK Subsidiary to BESI and BESK

ASYJY Subsidiary to BESJ and BESY

BCRH Subsidiary to CBLKTR

BDIFF Subsidiary to BSKIN

BESKNU Subsidiary to BESK

BESYNU Subsidiary to BESY

BKIAS Subsidiary to BSKIN

BKISR Subsidiary to BSKIN

BKSOL Subsidiary to BVSUP

BLKTR1 Subsidiary to BLKTRI

BNFAC Subsidiary to BINT4 and BINTK

BNSLV Subsidiary to BINT4 and BINTK

BSGQ8 Subsidiary to BFQAD

BSPLVD Subsidiary to FC

BSPLVN Subsidiary to FC

BSRH Subsidiary to BLKTRI

BVDER Subsidiary to BVSUP

BVPOR Subsidiary to BVSUP

C1MERG Merge two strings of complex numbers. Each string is

ascending by the real part.

C9LGMC Compute the log gamma correction factor so that

LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z

+ C9LGMC(Z).

C9LN2R Evaluate LOG(1+Z) from second order relative accuracy so

that LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

CACAI Subsidiary to CAIRY

CACON Subsidiary to CBESH and CBESK

CASYI Subsidiary to CBESI and CBESK

CBINU Subsidiary to CAIRY, CBESH, CBESI, CBESJ, CBESK and CBIRY

CBKNU Subsidiary to CAIRY, CBESH, CBESI and CBESK

CBLKT1 Subsidiary to CBLKTR

CBUNI Subsidiary to CBESI and CBESK

CBUNK Subsidiary to CBESH and CBESK

CCMPB Subsidiary to CBLKTR

CDCOR Subroutine CDCOR computes corrections to the Y array.

CDCST CDCST sets coefficients used by the core integrator CDSTP.

CDIV Compute the complex quotient of two complex numbers.

CDNTL Subroutine CDNTL is called to set parameters on the first

call to CDSTP, on an internal restart, or when the user has

altered MINT, MITER, and/or H.

CDNTP Subroutine CDNTP interpolates the K-th derivative of Y at

TOUT, using the data in the YH array. If K has a value

greater than NQ, the NQ-th derivative is calculated.

CDPSC Subroutine CDPSC computes the predicted YH values by

effectively multiplying the YH array by the Pascal triangle

matrix when KSGN is +1, and performs the inverse function

when KSGN is -1.

CDPST Subroutine CDPST evaluates the Jacobian matrix of the right

hand side of the differential equations.

CDSCL Subroutine CDSCL rescales the YH array whenever the step

size is changed.

CDSTP CDSTP performs one step of the integration of an initial

value problem for a system of ordinary differential

equations.

CDZRO CDZRO searches for a zero of a function F(N, T, Y, IROOT)

between the given values B and C until the width of the

interval (B, C) has collapsed to within a tolerance

specified by the stopping criterion,

ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).

CFFTB Compute the unnormalized inverse of CFFTF.

CFFTF Compute the forward transform of a complex, periodic

sequence.

CFFTI Initialize a work array for CFFTF and CFFTB.

CFOD Subsidiary to DEBDF

CHFCM Check a single cubic for monotonicity.

CHFIE Evaluates integral of a single cubic for PCHIA

CHKPR4 Subsidiary to SEPX4

CHKPRM Subsidiary to SEPELI

CHKSN4 Subsidiary to SEPX4

CHKSNG Subsidiary to SEPELI

CKSCL Subsidiary to CBKNU, CUNK1 and CUNK2

CMLRI Subsidiary to CBESI and CBESK

CMPCSG Subsidiary to CMGNBN

CMPOSD Subsidiary to CMGNBN

CMPOSN Subsidiary to CMGNBN

CMPOSP Subsidiary to CMGNBN

CMPTR3 Subsidiary to CMGNBN

CMPTRX Subsidiary to CMGNBN

COMPB Subsidiary to BLKTRI

COSGEN Subsidiary to GENBUN

COSQB1 Compute the unnormalized inverse of COSQF1.

COSQF1 Compute the forward cosine transform with odd wave numbers.

CPADD Subsidiary to CBLKTR

CPEVL Subsidiary to CPZERO

CPEVLR Subsidiary to CPZERO

CPROC Subsidiary to CBLKTR

CPROCP Subsidiary to CBLKTR

CPROD Subsidiary to BLKTRI

CPRODP Subsidiary to BLKTRI

CRATI Subsidiary to CBESH, CBESI and CBESK

CS1S2 Subsidiary to CAIRY and CBESK

CSCALE Subsidiary to BVSUP

CSERI Subsidiary to CBESI and CBESK

CSHCH Subsidiary to CBESH and CBESK

CSROOT Compute the complex square root of a complex number.

CUCHK Subsidiary to SERI, CUOIK, CUNK1, CUNK2, CUNI1, CUNI2 and

CKSCL

CUNHJ Subsidiary to CBESI and CBESK

CUNI1 Subsidiary to CBESI and CBESK

CUNI2 Subsidiary to CBESI and CBESK

CUNIK Subsidiary to CBESI and CBESK

CUNK1 Subsidiary to CBESK

CUNK2 Subsidiary to CBESK

CUOIK Subsidiary to CBESH, CBESI and CBESK

CWRSK Subsidiary to CBESI and CBESK

D1MERG Merge two strings of ascending double precision numbers.

D1MPYQ Subsidiary to DNSQ and DNSQE

D1UPDT Subsidiary to DNSQ and DNSQE

D9AIMP Evaluate the Airy modulus and phase.

D9ATN1 Evaluate DATAN(X) from first order relative accuracy so

that DATAN(X) = X + X**3*D9ATN1(X).

D9B0MP Evaluate the modulus and phase for the J0 and Y0 Bessel

functions.

D9B1MP Evaluate the modulus and phase for the J1 and Y1 Bessel

functions.

D9CHU Evaluate for large Z Z**A * U(A,B,Z) where U is the

logarithmic confluent hypergeometric function.

D9GMIC Compute the complementary incomplete Gamma function for A

near a negative integer and X small.

D9GMIT Compute Tricomi's incomplete Gamma function for small

arguments.

D9KNUS Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*

K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

D9LGIC Compute the log complementary incomplete Gamma function

for large X and for A .LE. X.

D9LGIT Compute the logarithm of Tricomi's incomplete Gamma

function with Perron's continued fraction for large X and

A .GE. X.

D9LGMC Compute the log Gamma correction factor so that

LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X

+ D9LGMC(X).

D9LN2R Evaluate LOG(1+X) from second order relative accuracy so

that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

DASYIK Subsidiary to DBESI and DBESK

DASYJY Subsidiary to DBESJ and DBESY

DBDIFF Subsidiary to DBSKIN

DBKIAS Subsidiary to DBSKIN

DBKISR Subsidiary to DBSKIN

DBKSOL Subsidiary to DBVSUP

DBNFAC Subsidiary to DBINT4 and DBINTK

DBNSLV Subsidiary to DBINT4 and DBINTK

DBOLSM Subsidiary to DBOCLS and DBOLS

DBSGQ8 Subsidiary to DBFQAD

DBSKNU Subsidiary to DBESK

DBSYNU Subsidiary to DBESY

DBVDER Subsidiary to DBVSUP

DBVPOR Subsidiary to DBVSUP

DCFOD Subsidiary to DDEBDF

DCHFCM Check a single cubic for monotonicity.

DCHFIE Evaluates integral of a single cubic for DPCHIA

DCHKW SLAP WORK/IWORK Array Bounds Checker.

This routine checks the work array lengths and interfaces

to the SLATEC error handler if a problem is found.

DCOEF Subsidiary to DBVSUP

DCSCAL Subsidiary to DBVSUP and DSUDS

DDAINI Initialization routine for DDASSL.

DDAJAC Compute the iteration matrix for DDASSL and form the

LU-decomposition.

DDANRM Compute vector norm for DDASSL.

DDASLV Linear system solver for DDASSL.

DDASTP Perform one step of the DDASSL integration.

DDATRP Interpolation routine for DDASSL.

DDAWTS Set error weight vector for DDASSL.

DDCOR Subroutine DDCOR computes corrections to the Y array.

DDCST DDCST sets coefficients used by the core integrator DDSTP.

DDES Subsidiary to DDEABM

DDNTL Subroutine DDNTL is called to set parameters on the first

call to DDSTP, on an internal restart, or when the user has

altered MINT, MITER, and/or H.

DDNTP Subroutine DDNTP interpolates the K-th derivative of Y at

TOUT, using the data in the YH array. If K has a value

greater than NQ, the NQ-th derivative is calculated.

DDOGLG Subsidiary to DNSQ and DNSQE

DDPSC Subroutine DDPSC computes the predicted YH values by

effectively multiplying the YH array by the Pascal triangle

matrix when KSGN is +1, and performs the inverse function

when KSGN is -1.

DDPST Subroutine DDPST evaluates the Jacobian matrix of the right

hand side of the differential equations.

DDSCL Subroutine DDSCL rescales the YH array whenever the step

size is changed.

DDSTP DDSTP performs one step of the integration of an initial

value problem for a system of ordinary differential

equations.

DDZRO DDZRO searches for a zero of a function F(N, T, Y, IROOT)

between the given values B and C until the width of the

interval (B, C) has collapsed to within a tolerance

specified by the stopping criterion,

ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).

DEFCMN Subsidiary to DEFC

DEFE4 Subsidiary to SEPX4

DEFEHL Subsidiary to DERKF

DEFER Subsidiary to SEPELI

DENORM Subsidiary to DNSQ and DNSQE

DERKFS Subsidiary to DERKF

DES Subsidiary to DEABM

DEXBVP Subsidiary to DBVSUP

DFCMN Subsidiary to FC

DFDJC1 Subsidiary to DNSQ and DNSQE

DFDJC3 Subsidiary to DNLS1 and DNLS1E

DFEHL Subsidiary to DDERKF

DFSPVD Subsidiary to DFC

DFSPVN Subsidiary to DFC

DFULMT Subsidiary to DSPLP

DGAMLN Compute the logarithm of the Gamma function

DGAMRN Subsidiary to DBSKIN

DH12 Subsidiary to DHFTI, DLSEI and DWNNLS

DHELS Internal routine for DGMRES.

DHEQR Internal routine for DGMRES.

DHKSEQ Subsidiary to DBSKIN

DHSTRT Subsidiary to DDEABM, DDEBDF and DDERKF

DHVNRM Subsidiary to DDEABM, DDEBDF and DDERKF

DINTYD Subsidiary to DDEBDF

DJAIRY Subsidiary to DBESJ and DBESY

DLPDP Subsidiary to DLSEI

DLSI Subsidiary to DLSEI

DLSOD Subsidiary to DDEBDF

DLSSUD Subsidiary to DBVSUP and DSUDS

DMACON Subsidiary to DBVSUP

DMGSBV Subsidiary to DBVSUP

DMOUT Subsidiary to DBOCLS and DFC

DMPAR Subsidiary to DNLS1 and DNLS1E

DOGLEG Subsidiary to SNSQ and SNSQE

DOHTRL Subsidiary to DBVSUP and DSUDS

DORTH Internal routine for DGMRES.

DORTHR Subsidiary to DBVSUP and DSUDS

DPCHCE Set boundary conditions for DPCHIC

DPCHCI Set interior derivatives for DPCHIC

DPCHCS Adjusts derivative values for DPCHIC

DPCHDF Computes divided differences for DPCHCE and DPCHSP

DPCHKT Compute B-spline knot sequence for DPCHBS.

DPCHNG Subsidiary to DSPLP

DPCHST DPCHIP Sign-Testing Routine

DPCHSW Limits excursion from data for DPCHCS

DPIGMR Internal routine for DGMRES.

DPINCW Subsidiary to DSPLP

DPINIT Subsidiary to DSPLP

DPINTM Subsidiary to DSPLP

DPJAC Subsidiary to DDEBDF

DPLPCE Subsidiary to DSPLP

DPLPDM Subsidiary to DSPLP

DPLPFE Subsidiary to DSPLP

DPLPFL Subsidiary to DSPLP

DPLPMN Subsidiary to DSPLP

DPLPMU Subsidiary to DSPLP

DPLPUP Subsidiary to DSPLP

DPNNZR Subsidiary to DSPLP

DPOPT Subsidiary to DSPLP

DPPGQ8 Subsidiary to DPFQAD

DPRVEC Subsidiary to DBVSUP

DPRWPG Subsidiary to DSPLP

DPRWVR Subsidiary to DSPLP

DPSIXN Subsidiary to DEXINT

DQCHEB This routine computes the CHEBYSHEV series expansion

of degrees 12 and 24 of a function using A

FAST FOURIER TRANSFORM METHOD

F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),

F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),

Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

DQELG The routine determines the limit of a given sequence of

approximations, by means of the Epsilon algorithm of

P.Wynn. An estimate of the absolute error is also given.

The condensed Epsilon table is computed. Only those

elements needed for the computation of the next diagonal

are preserved.

DQFORM Subsidiary to DNSQ and DNSQE

DQPSRT This routine maintains the descending ordering in the

list of the local error estimated resulting from the

interval subdivision process. At each call two error

estimates are inserted using the sequential search

method, top-down for the largest error estimate and

bottom-up for the smallest error estimate.

DQRFAC Subsidiary to DNLS1, DNLS1E, DNSQ and DNSQE

DQRSLV Subsidiary to DNLS1 and DNLS1E

DQWGTC This function subprogram is used together with the

routine DQAWC and defines the WEIGHT function.

DQWGTF This function subprogram is used together with the

routine DQAWF and defines the WEIGHT function.

DQWGTS This function subprogram is used together with the

routine DQAWS and defines the WEIGHT function.

DREADP Subsidiary to DSPLP

DREORT Subsidiary to DBVSUP

DRKFAB Subsidiary to DBVSUP

DRKFS Subsidiary to DDERKF

DRLCAL Internal routine for DGMRES.

DRSCO Subsidiary to DDEBDF

DSLVS Subsidiary to DDEBDF

DSOSEQ Subsidiary to DSOS

DSOSSL Subsidiary to DSOS

DSTOD Subsidiary to DDEBDF

DSTOR1 Subsidiary to DBVSUP

DSTWAY Subsidiary to DBVSUP

DSUDS Subsidiary to DBVSUP

DSVCO Subsidiary to DDEBDF

DU11LS Subsidiary to DLLSIA

DU11US Subsidiary to DULSIA

DU12LS Subsidiary to DLLSIA

DU12US Subsidiary to DULSIA

DUSRMT Subsidiary to DSPLP

DVECS Subsidiary to DBVSUP

DVNRMS Subsidiary to DDEBDF

DVOUT Subsidiary to DSPLP

DWNLIT Subsidiary to DWNNLS

DWNLSM Subsidiary to DWNNLS

DWNLT1 Subsidiary to WNLIT

DWNLT2 Subsidiary to WNLIT

DWNLT3 Subsidiary to WNLIT

DWRITP Subsidiary to DSPLP

DWUPDT Subsidiary to DNLS1 and DNLS1E

DX Subsidiary to SEPELI

DX4 Subsidiary to SEPX4

DXLCAL Internal routine for DGMRES.

DXPMU To compute the values of Legendre functions for DXLEGF.

Method: backward mu-wise recurrence for P(-MU,NU,X) for

fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,

P(-MU1,NU1,X) and store in ascending mu order.

DXPMUP To compute the values of Legendre functions for DXLEGF.

This subroutine transforms an array of Legendre functions

of the first kind of negative order stored in array PQA

into Legendre functions of the first kind of positive

order stored in array PQA. The original array is destroyed.

DXPNRM To compute the values of Legendre functions for DXLEGF.

This subroutine transforms an array of Legendre functions

of the first kind of negative order stored in array PQA

into normalized Legendre polynomials stored in array PQA.

The original array is destroyed.

DXPQNU To compute the values of Legendre functions for DXLEGF.

This subroutine calculates initial values of P or Q using

power series, then performs forward nu-wise recurrence to

obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise

recurrence is stable for P for all mu and for Q for mu=0,1.

DXPSI To compute values of the Psi function for DXLEGF.

DXQMU To compute the values of Legendre functions for DXLEGF.

Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed

nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

DXQNU To compute the values of Legendre functions for DXLEGF.

Method: backward nu-wise recurrence for Q(MU,NU,X) for

fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,

Q(MU1,NU2,X).

DY Subsidiary to SEPELI

DY4 Subsidiary to SEPX4

DYAIRY Subsidiary to DBESJ and DBESY

EFCMN Subsidiary to EFC

ENORM Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE

EXBVP Subsidiary to BVSUP

EZFFT1 EZFFTI calls EZFFT1 with appropriate work array

partitioning.

FCMN Subsidiary to FC

FDJAC1 Subsidiary to SNSQ and SNSQE

FDJAC3 Subsidiary to SNLS1 and SNLS1E

FULMAT Subsidiary to SPLP

GAMLN Compute the logarithm of the Gamma function

GAMRN Subsidiary to BSKIN

H12 Subsidiary to HFTI, LSEI and WNNLS

HKSEQ Subsidiary to BSKIN

HSTART Subsidiary to DEABM, DEBDF and DERKF

HSTCS1 Subsidiary to HSTCSP

HVNRM Subsidiary to DEABM, DEBDF and DERKF

HWSCS1 Subsidiary to HWSCSP

HWSSS1 Subsidiary to HWSSSP

I1MERG Merge two strings of ascending integers.

IDLOC Subsidiary to DSPLP

INDXA Subsidiary to BLKTRI

INDXB Subsidiary to BLKTRI

INDXC Subsidiary to BLKTRI

INTYD Subsidiary to DEBDF

INXCA Subsidiary to CBLKTR

INXCB Subsidiary to CBLKTR

INXCC Subsidiary to CBLKTR

IPLOC Subsidiary to SPLP

ISDBCG Preconditioned BiConjugate Gradient Stop Test.

This routine calculates the stop test for the BiConjugate

Gradient iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISDCG Preconditioned Conjugate Gradient Stop Test.

This routine calculates the stop test for the Conjugate

Gradient iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISDCGN Preconditioned CG on Normal Equations Stop Test.

This routine calculates the stop test for the Conjugate

Gradient iteration scheme applied to the normal equations.

It returns a non-zero if the error estimate (the type of

which is determined by ITOL) is less than the user

specified tolerance TOL.

ISDCGS Preconditioned BiConjugate Gradient Squared Stop Test.

This routine calculates the stop test for the BiConjugate

Gradient Squared iteration scheme. It returns a non-zero

if the error estimate (the type of which is determined by

ITOL) is less than the user specified tolerance TOL.

ISDGMR Generalized Minimum Residual Stop Test.

This routine calculates the stop test for the Generalized

Minimum RESidual (GMRES) iteration scheme. It returns a

non-zero if the error estimate (the type of which is

determined by ITOL) is less than the user specified

tolerance TOL.

ISDIR Preconditioned Iterative Refinement Stop Test.

This routine calculates the stop test for the iterative

refinement iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISDOMN Preconditioned Orthomin Stop Test.

This routine calculates the stop test for the Orthomin

iteration scheme. It returns a non-zero if the error

estimate (the type of which is determined by ITOL) is

less than the user specified tolerance TOL.

ISSBCG Preconditioned BiConjugate Gradient Stop Test.

This routine calculates the stop test for the BiConjugate

Gradient iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISSCG Preconditioned Conjugate Gradient Stop Test.

This routine calculates the stop test for the Conjugate

Gradient iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISSCGN Preconditioned CG on Normal Equations Stop Test.

This routine calculates the stop test for the Conjugate

Gradient iteration scheme applied to the normal equations.

It returns a non-zero if the error estimate (the type of

which is determined by ITOL) is less than the user

specified tolerance TOL.

ISSCGS Preconditioned BiConjugate Gradient Squared Stop Test.

This routine calculates the stop test for the BiConjugate

Gradient Squared iteration scheme. It returns a non-zero

if the error estimate (the type of which is determined by

ITOL) is less than the user specified tolerance TOL.

ISSGMR Generalized Minimum Residual Stop Test.

This routine calculates the stop test for the Generalized

Minimum RESidual (GMRES) iteration scheme. It returns a

non-zero if the error estimate (the type of which is

determined by ITOL) is less than the user specified

tolerance TOL.

ISSIR Preconditioned Iterative Refinement Stop Test.

This routine calculates the stop test for the iterative

refinement iteration scheme. It returns a non-zero if the

error estimate (the type of which is determined by ITOL)

is less than the user specified tolerance TOL.

ISSOMN Preconditioned Orthomin Stop Test.

This routine calculates the stop test for the Orthomin

iteration scheme. It returns a non-zero if the error

estimate (the type of which is determined by ITOL) is

less than the user specified tolerance TOL.

IVOUT Subsidiary to SPLP

J4SAVE Save or recall global variables needed by error

handling routines.

JAIRY Subsidiary to BESJ and BESY

LA05AD Subsidiary to DSPLP

LA05AS Subsidiary to SPLP

LA05BD Subsidiary to DSPLP

LA05BS Subsidiary to SPLP

LA05CD Subsidiary to DSPLP

LA05CS Subsidiary to SPLP

LA05ED Subsidiary to DSPLP

LA05ES Subsidiary to SPLP

LMPAR Subsidiary to SNLS1 and SNLS1E

LPDP Subsidiary to LSEI

LSAME Test two characters to determine if they are the same

letter, except for case.

LSI Subsidiary to LSEI

LSOD Subsidiary to DEBDF

LSSODS Subsidiary to BVSUP

LSSUDS Subsidiary to BVSUP

MACON Subsidiary to BVSUP

MC20AD Subsidiary to DSPLP

MC20AS Subsidiary to SPLP

MGSBV Subsidiary to BVSUP

MINSO4 Subsidiary to SEPX4

MINSOL Subsidiary to SEPELI

MPADD Subsidiary to DQDOTA and DQDOTI

MPADD2 Subsidiary to DQDOTA and DQDOTI

MPADD3 Subsidiary to DQDOTA and DQDOTI

MPBLAS Subsidiary to DQDOTA and DQDOTI

MPCDM Subsidiary to DQDOTA and DQDOTI

MPCHK Subsidiary to DQDOTA and DQDOTI

MPCMD Subsidiary to DQDOTA and DQDOTI

MPDIVI Subsidiary to DQDOTA and DQDOTI

MPERR Subsidiary to DQDOTA and DQDOTI

MPMAXR Subsidiary to DQDOTA and DQDOTI

MPMLP Subsidiary to DQDOTA and DQDOTI

MPMUL Subsidiary to DQDOTA and DQDOTI

MPMUL2 Subsidiary to DQDOTA and DQDOTI

MPMULI Subsidiary to DQDOTA and DQDOTI

MPNZR Subsidiary to DQDOTA and DQDOTI

MPOVFL Subsidiary to DQDOTA and DQDOTI

MPSTR Subsidiary to DQDOTA and DQDOTI

MPUNFL Subsidiary to DQDOTA and DQDOTI

OHTROL Subsidiary to BVSUP

OHTROR Subsidiary to BVSUP

ORTHO4 Subsidiary to SEPX4

ORTHOG Subsidiary to SEPELI

ORTHOL Subsidiary to BVSUP

ORTHOR Subsidiary to BVSUP

PASSB Calculate the fast Fourier transform of subvectors of

arbitrary length.

PASSB2 Calculate the fast Fourier transform of subvectors of

length two.

PASSB3 Calculate the fast Fourier transform of subvectors of

length three.

PASSB4 Calculate the fast Fourier transform of subvectors of

length four.

PASSB5 Calculate the fast Fourier transform of subvectors of

length five.

PASSF Calculate the fast Fourier transform of subvectors of

arbitrary length.

PASSF2 Calculate the fast Fourier transform of subvectors of

length two.

PASSF3 Calculate the fast Fourier transform of subvectors of

length three.

PASSF4 Calculate the fast Fourier transform of subvectors of

length four.

PASSF5 Calculate the fast Fourier transform of subvectors of

length five.

PCHCE Set boundary conditions for PCHIC

PCHCI Set interior derivatives for PCHIC

PCHCS Adjusts derivative values for PCHIC

PCHDF Computes divided differences for PCHCE and PCHSP

PCHKT Compute B-spline knot sequence for PCHBS.

PCHNGS Subsidiary to SPLP

PCHST PCHIP Sign-Testing Routine

PCHSW Limits excursion from data for PCHCS

PGSF Subsidiary to CBLKTR

PIMACH Subsidiary to HSTCSP, HSTSSP and HWSCSP

PINITM Subsidiary to SPLP

PJAC Subsidiary to DEBDF

PNNZRS Subsidiary to SPLP

POISD2 Subsidiary to GENBUN

POISN2 Subsidiary to GENBUN

POISP2 Subsidiary to GENBUN

POS3D1 Subsidiary to POIS3D

POSTG2 Subsidiary to POISTG

PPADD Subsidiary to BLKTRI

PPGQ8 Subsidiary to PFQAD

PPGSF Subsidiary to CBLKTR

PPPSF Subsidiary to CBLKTR

PPSGF Subsidiary to BLKTRI

PPSPF Subsidiary to BLKTRI

PROC Subsidiary to CBLKTR

PROCP Subsidiary to CBLKTR

PROD Subsidiary to BLKTRI

PRODP Subsidiary to BLKTRI

PRVEC Subsidiary to BVSUP

PRWPGE Subsidiary to SPLP

PRWVIR Subsidiary to SPLP

PSGF Subsidiary to BLKTRI

PSIXN Subsidiary to EXINT

PYTHAG Compute the complex square root of a complex number without

destructive overflow or underflow.

QCHEB This routine computes the CHEBYSHEV series expansion

of degrees 12 and 24 of a function using A

FAST FOURIER TRANSFORM METHOD

F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),

F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),

Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

QELG The routine determines the limit of a given sequence of

approximations, by means of the Epsilon algorithm of

P. Wynn. An estimate of the absolute error is also given.

The condensed Epsilon table is computed. Only those

elements needed for the computation of the next diagonal

are preserved.

QFORM Subsidiary to SNSQ and SNSQE

QPSRT Subsidiary to QAGE, QAGIE, QAGPE, QAGSE, QAWCE, QAWOE and

QAWSE

QRFAC Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE

QRSOLV Subsidiary to SNLS1 and SNLS1E

QS2I1D Sort an integer array, moving an integer and DP array.

This routine sorts the integer array IA and makes the same

interchanges in the integer array JA and the double pre-

cision array A. The array IA may be sorted in increasing

order or decreasing order. A slightly modified QUICKSORT

algorithm is used.

QS2I1R Sort an integer array, moving an integer and real array.

This routine sorts the integer array IA and makes the same

interchanges in the integer array JA and the real array A.

The array IA may be sorted in increasing order or decreas-

ing order. A slightly modified QUICKSORT algorithm is

used.

QWGTC This function subprogram is used together with the

routine QAWC and defines the WEIGHT function.

QWGTF This function subprogram is used together with the

routine QAWF and defines the WEIGHT function.

QWGTS This function subprogram is used together with the

routine QAWS and defines the WEIGHT function.

R1MPYQ Subsidiary to SNSQ and SNSQE

R1UPDT Subsidiary to SNSQ and SNSQE

R9AIMP Evaluate the Airy modulus and phase.

R9ATN1 Evaluate ATAN(X) from first order relative accuracy so that

ATAN(X) = X + X**3*R9ATN1(X).

R9CHU Evaluate for large Z Z**A * U(A,B,Z) where U is the

logarithmic confluent hypergeometric function.

R9GMIC Compute the complementary incomplete Gamma function for A

near a negative integer and for small X.

R9GMIT Compute Tricomi's incomplete Gamma function for small

arguments.

R9KNUS Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*

K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

R9LGIC Compute the log complementary incomplete Gamma function

for large X and for A .LE. X.

R9LGIT Compute the logarithm of Tricomi's incomplete Gamma

function with Perron's continued fraction for large X and

A .GE. X.

R9LGMC Compute the log Gamma correction factor so that

LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X

+ R9LGMC(X).

R9LN2R Evaluate LOG(1+X) from second order relative accuracy so

that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

RADB2 Calculate the fast Fourier transform of subvectors of

length two.

RADB3 Calculate the fast Fourier transform of subvectors of

length three.

RADB4 Calculate the fast Fourier transform of subvectors of

length four.

RADB5 Calculate the fast Fourier transform of subvectors of

length five.

RADBG Calculate the fast Fourier transform of subvectors of

arbitrary length.

RADF2 Calculate the fast Fourier transform of subvectors of

length two.

RADF3 Calculate the fast Fourier transform of subvectors of

length three.

RADF4 Calculate the fast Fourier transform of subvectors of

length four.

RADF5 Calculate the fast Fourier transform of subvectors of

length five.

RADFG Calculate the fast Fourier transform of subvectors of

arbitrary length.

REORT Subsidiary to BVSUP

RFFTB Compute the backward fast Fourier transform of a real

coefficient array.

RFFTF Compute the forward transform of a real, periodic sequence.

RFFTI Initialize a work array for RFFTF and RFFTB.

RKFAB Subsidiary to BVSUP

RSCO Subsidiary to DEBDF

RWUPDT Subsidiary to SNLS1 and SNLS1E

S1MERG Merge two strings of ascending real numbers.

SBOLSM Subsidiary to SBOCLS and SBOLS

SCHKW SLAP WORK/IWORK Array Bounds Checker.

This routine checks the work array lengths and interfaces

to the SLATEC error handler if a problem is found.

SCLOSM Subsidiary to SPLP

SCOEF Subsidiary to BVSUP

SDAINI Initialization routine for SDASSL.

SDAJAC Compute the iteration matrix for SDASSL and form the

LU-decomposition.

SDANRM Compute vector norm for SDASSL.

SDASLV Linear system solver for SDASSL.

SDASTP Perform one step of the SDASSL integration.

SDATRP Interpolation routine for SDASSL.

SDAWTS Set error weight vector for SDASSL.

SDCOR Subroutine SDCOR computes corrections to the Y array.

SDCST SDCST sets coefficients used by the core integrator SDSTP.

SDNTL Subroutine SDNTL is called to set parameters on the first

call to SDSTP, on an internal restart, or when the user has

altered MINT, MITER, and/or H.

SDNTP Subroutine SDNTP interpolates the K-th derivative of Y at

TOUT, using the data in the YH array. If K has a value

greater than NQ, the NQ-th derivative is calculated.

SDPSC Subroutine SDPSC computes the predicted YH values by

effectively multiplying the YH array by the Pascal triangle

matrix when KSGN is +1, and performs the inverse function

when KSGN is -1.

SDPST Subroutine SDPST evaluates the Jacobian matrix of the right

hand side of the differential equations.

SDSCL Subroutine SDSCL rescales the YH array whenever the step

size is changed.

SDSTP SDSTP performs one step of the integration of an initial

value problem for a system of ordinary differential

equations.

SDZRO SDZRO searches for a zero of a function F(N, T, Y, IROOT)

between the given values B and C until the width of the

interval (B, C) has collapsed to within a tolerance

specified by the stopping criterion,

ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).

SHELS Internal routine for SGMRES.

SHEQR Internal routine for SGMRES.

SLVS Subsidiary to DEBDF

SMOUT Subsidiary to FC and SBOCLS

SODS Subsidiary to BVSUP

SOPENM Subsidiary to SPLP

SORTH Internal routine for SGMRES.

SOSEQS Subsidiary to SOS

SOSSOL Subsidiary to SOS

SPELI4 Subsidiary to SEPX4

SPELIP Subsidiary to SEPELI

SPIGMR Internal routine for SGMRES.

SPINCW Subsidiary to SPLP

SPINIT Subsidiary to SPLP

SPLPCE Subsidiary to SPLP

SPLPDM Subsidiary to SPLP

SPLPFE Subsidiary to SPLP

SPLPFL Subsidiary to SPLP

SPLPMN Subsidiary to SPLP

SPLPMU Subsidiary to SPLP

SPLPUP Subsidiary to SPLP

SPOPT Subsidiary to SPLP

SREADP Subsidiary to SPLP

SRLCAL Internal routine for SGMRES.

STOD Subsidiary to DEBDF

STOR1 Subsidiary to BVSUP

STWAY Subsidiary to BVSUP

SUDS Subsidiary to BVSUP

SVCO Subsidiary to DEBDF

SVD Perform the singular value decomposition of a rectangular

matrix.

SVECS Subsidiary to BVSUP

SVOUT Subsidiary to SPLP

SWRITP Subsidiary to SPLP

SXLCAL Internal routine for SGMRES.

TEVLC Subsidiary to CBLKTR

TEVLS Subsidiary to BLKTRI

TRI3 Subsidiary to GENBUN

TRIDQ Subsidiary to POIS3D

TRIS4 Subsidiary to SEPX4

TRISP Subsidiary to SEPELI

TRIX Subsidiary to GENBUN

U11LS Subsidiary to LLSIA

U11US Subsidiary to ULSIA

U12LS Subsidiary to LLSIA

U12US Subsidiary to ULSIA

USRMAT Subsidiary to SPLP

VNWRMS Subsidiary to DEBDF

WNLIT Subsidiary to WNNLS

WNLSM Subsidiary to WNNLS

WNLT1 Subsidiary to WNLIT

WNLT2 Subsidiary to WNLIT

WNLT3 Subsidiary to WNLIT

XERBLA Error handler for the Level 2 and Level 3 BLAS Routines.

XERCNT Allow user control over handling of errors.

XERHLT Abort program execution and print error message.

XERPRN Print error messages processed by XERMSG.

XERSVE Record that an error has occurred.

XPMU To compute the values of Legendre functions for XLEGF.

Method: backward mu-wise recurrence for P(-MU,NU,X) for

fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,

P(-MU1,NU1,X) and store in ascending mu order.

XPMUP To compute the values of Legendre functions for XLEGF.

This subroutine transforms an array of Legendre functions

of the first kind of negative order stored in array PQA

into Legendre functions of the first kind of positive

order stored in array PQA. The original array is destroyed.

XPNRM To compute the values of Legendre functions for XLEGF.

This subroutine transforms an array of Legendre functions

of the first kind of negative order stored in array PQA

into normalized Legendre polynomials stored in array PQA.

The original array is destroyed.

XPQNU To compute the values of Legendre functions for XLEGF.

This subroutine calculates initial values of P or Q using

power series, then performs forward nu-wise recurrence to

obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise

recurrence is stable for P for all mu and for Q for mu=0,1.

XPSI To compute values of the Psi function for XLEGF.

XQMU To compute the values of Legendre functions for XLEGF.

Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed

nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

XQNU To compute the values of Legendre functions for XLEGF.

Method: backward nu-wise recurrence for Q(MU,NU,X) for

fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,

Q(MU1,NU2,X).

YAIRY Subsidiary to BESJ and BESY

ZABS Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZACAI Subsidiary to ZAIRY

ZACON Subsidiary to ZBESH and ZBESK

ZASYI Subsidiary to ZBESI and ZBESK

ZBINU Subsidiary to ZAIRY, ZBESH, ZBESI, ZBESJ, ZBESK and ZBIRY

ZBKNU Subsidiary to ZAIRY, ZBESH, ZBESI and ZBESK

ZBUNI Subsidiary to ZBESI and ZBESK

ZBUNK Subsidiary to ZBESH and ZBESK

ZDIV Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZEXP Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZKSCL Subsidiary to ZBESK

ZLOG Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZMLRI Subsidiary to ZBESI and ZBESK

ZMLT Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZRATI Subsidiary to ZBESH, ZBESI and ZBESK

ZS1S2 Subsidiary to ZAIRY and ZBESK

ZSERI Subsidiary to ZBESI and ZBESK

ZSHCH Subsidiary to ZBESH and ZBESK

ZSQRT Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and

ZBIRY

ZUCHK Subsidiary to SERI, ZUOIK, ZUNK1, ZUNK2, ZUNI1, ZUNI2 and

ZKSCL

ZUNHJ Subsidiary to ZBESI and ZBESK

ZUNI1 Subsidiary to ZBESI and ZBESK

ZUNI2 Subsidiary to ZBESI and ZBESK

ZUNIK Subsidiary to ZBESI and ZBESK

ZUNK1 Subsidiary to ZBESK

ZUNK2 Subsidiary to ZBESK

ZUOIK Subsidiary to ZBESH, ZBESI and ZBESK

ZWRSK Subsidiary to ZBESI and ZBESK

SECTION III. Alphabetic List of Routines and Categories

As stated in the introduction, an asterisk (*) immediately

preceeding a routine name indicates a subsidiary routine.

AAAAAA Z ACOSH C4C

AI C10D AIE C10D

ALBETA C7B ALGAMS C7A

ALI C5 ALNGAM C7A

ALNREL C4B ASINH C4C

*ASYIK *ASYJY

ATANH C4C AVINT H2A1B2

BAKVEC D4C4 BALANC D4C1A

BALBAK D4C4 BANDR D4C1B1

BANDV D4C3 *BCRH

*BDIFF BESI C10B3

BESI0 C10B1 BESI0E C10B1

BESI1 C10B1 BESI1E C10B1

BESJ C10A3 BESJ0 C10A1

BESJ1 C10A1 BESK C10B3

BESK0 C10B1 BESK0E C10B1

BESK1 C10B1 BESK1E C10B1

BESKES C10B3 *BESKNU

BESKS C10B3 BESY C10A3

BESY0 C10A1 BESY1 C10A1

*BESYNU BETA C7B

BETAI C7F BFQAD H2A2A1, E3, K6

BI C10D BIE C10D

BINOM C1 BINT4 E1A

BINTK E1A BISECT D4A5, D4C2A

*BKIAS *BKISR

*BKSOL *BLKTR1

BLKTRI I2B4B BNDACC D9

BNDSOL D9 *BNFAC

*BNSLV BQR D4A6

*BSGQ8 BSKIN C10F

BSPDOC E, E1A, K, Z BSPDR E3

BSPEV E3, K6 *BSPLVD

*BSPLVN BSPPP E3, K6

BSPVD E3, K6 BSPVN E3, K6

BSQAD H2A2A1, E3, K6 *BSRH

BVALU E3, K6 *BVDER

*BVPOR BVSUP I1B1

C0LGMC C7A *C1MERG

*C9LGMC C7A *C9LN2R C4B

*CACAI *CACON

CACOS C4A CACOSH C4C

CAIRY C10D CARG A4A

CASIN C4A CASINH C4C

*CASYI CATAN C4A

CATAN2 C4A CATANH C4C

CAXPY D1A7 CBABK2 D4C4

CBAL D4C1A CBESH C10A4

CBESI C10B4 CBESJ C10A4

CBESK C10B4 CBESY C10A4

CBETA C7B *CBINU

CBIRY C10D *CBKNU

*CBLKT1 CBLKTR I2B4B

CBRT C2 *CBUNI

*CBUNK CCBRT C2

CCHDC D2D1B CCHDD D7B

CCHEX D7B CCHUD D7B

*CCMPB CCOPY D1A5

CCOSH C4C CCOT C4A

CDCDOT D1A4 *CDCOR

*CDCST *CDIV

*CDNTL *CDNTP

CDOTC D1A4 CDOTU D1A4

*CDPSC *CDPST

CDRIV1 I1A2, I1A1B CDRIV2 I1A2, I1A1B

CDRIV3 I1A2, I1A1B *CDSCL

*CDSTP *CDZRO

CEXPRL C4B *CFFTB J1A2

CFFTB1 J1A2 *CFFTF J1A2

CFFTF1 J1A2 *CFFTI J1A2

CFFTI1 J1A2 *CFOD

CG D4A4 CGAMMA C7A

CGAMR C7A CGBCO D2C2

CGBDI D3C2 CGBFA D2C2

CGBMV D1B4 CGBSL D2C2

CGECO D2C1 CGEDI D2C1, D3C1

CGEEV D4A4 CGEFA D2C1

CGEFS D2C1 CGEIR D2C1

CGEMM D1B6 CGEMV D1B4

CGERC D1B4 CGERU D1B4

CGESL D2C1 CGTSL D2C2A

CH D4A3 CHBMV D1B4

CHEMM D1B6 CHEMV D1B4

CHER D1B4 CHER2 D1B4

CHER2K D1B6 CHERK D1B6

*CHFCM CHFDV E3, H1

CHFEV E3 *CHFIE

CHICO D2D1A CHIDI D2D1A, D3D1A

CHIEV D4A3 CHIFA D2D1A

CHISL D2D1A CHKDER F3, G4C

*CHKPR4 *CHKPRM

*CHKSN4 *CHKSNG

CHPCO D2D1A CHPDI D2D1A, D3D1A

CHPFA D2D1A CHPMV D1B4

CHPR D1B4 CHPR2 D1B4

CHPSL D2D1A CHU C11

CINVIT D4C2B *CKSCL

CLBETA C7B CLNGAM C7A

CLNREL C4B CLOG10 C4B

CMGNBN I2B4B *CMLRI

*CMPCSG *CMPOSD

*CMPOSN *CMPOSP

*CMPTR3 *CMPTRX

CNBCO D2C2 CNBDI D3C2

CNBFA D2C2 CNBFS D2C2

CNBIR D2C2 CNBSL D2C2

COMBAK D4C4 COMHES D4C1B2

COMLR D4C2B COMLR2 D4C2B

*COMPB COMQR D4C2B

COMQR2 D4C2B CORTB D4C4

CORTH D4C1B2 COSDG C4A

*COSGEN COSQB J1A3

*COSQB1 J1A3 COSQF J1A3

*COSQF1 J1A3 COSQI J1A3

COST J1A3 COSTI J1A3

COT C4A *CPADD

CPBCO D2D2 CPBDI D3D2

CPBFA D2D2 CPBSL D2D2

*CPEVL *CPEVLR

CPOCO D2D1B CPODI D2D1B, D3D1B

CPOFA D2D1B CPOFS D2D1B

CPOIR D2D1B CPOSL D2D1B

CPPCO D2D1B CPPDI D2D1B, D3D1B

CPPFA D2D1B CPPSL D2D1B

CPQR79 F1A1B *CPROC

*CPROCP *CPROD

*CPRODP CPSI C7C

CPTSL D2D2A CPZERO F1A1B

CQRDC D5 CQRSL D9, D2C1

*CRATI CROTG D1B10

*CS1S2 CSCAL D1A6

*CSCALE *CSERI

CSEVL C3A2 *CSHCH

CSICO D2C1 CSIDI D2C1, D3C1

CSIFA D2C1 CSINH C4C

CSISL D2C1 CSPCO D2C1

CSPDI D2C1, D3C1 CSPFA D2C1

CSPSL D2C1 *CSROOT

CSROT D1B10 CSSCAL D1A6

CSVDC D6 CSWAP D1A5

CSYMM D1B6 CSYR2K D1B6

CSYRK D1B6 CTAN C4A

CTANH C4C CTBMV D1B4

CTBSV D1B4 CTPMV D1B4

CTPSV D1B4 CTRCO D2C3

CTRDI D2C3, D3C3 CTRMM D1B6

CTRMV D1B4 CTRSL D2C3

CTRSM D1B6 CTRSV D1B4

*CUCHK *CUNHJ

*CUNI1 *CUNI2

*CUNIK *CUNK1

*CUNK2 *CUOIK

CV L7A3 *CWRSK

D1MACH R1 *D1MERG

*D1MPYQ *D1UPDT

*D9AIMP C10D *D9ATN1 C4A

*D9B0MP C10A1 *D9B1MP C10A1

*D9CHU C11 *D9GMIC C7E

*D9GMIT C7E *D9KNUS C10B3

*D9LGIC C7E *D9LGIT C7E

*D9LGMC C7E *D9LN2R C4B

D9PAK A6B D9UPAK A6B

DACOSH C4C DAI C10D

DAIE C10D DASINH C4C

DASUM D1A3A *DASYIK

*DASYJY DATANH C4C

DAVINT H2A1B2 DAWS C8C

DAXPY D1A7 DBCG D2A4, D2B4

*DBDIFF DBESI C10B3

DBESI0 C10B1 DBESI1 C10B1

DBESJ C10A3 DBESJ0 C10A1

DBESJ1 C10A1 DBESK C10B3

DBESK0 C10B1 DBESK1 C10B1

DBESKS C10B3 DBESY C10A3

DBESY0 C10A1 DBESY1 C10A1

DBETA C7B DBETAI C7F

DBFQAD H2A2A1, E3, K6 DBHIN N1

DBI C10D DBIE C10D

DBINOM C1 DBINT4 E1A

DBINTK E1A *DBKIAS

*DBKISR *DBKSOL

DBNDAC D9 DBNDSL D9

*DBNFAC *DBNSLV

DBOCLS K1A2A, G2E, G2H1, G2H2 DBOLS K1A2A, G2E, G2H1, G2H2

*DBOLSM *DBSGQ8

DBSI0E C10B1 DBSI1E C10B1

DBSK0E C10B1 DBSK1E C10B1

DBSKES C10B3 DBSKIN C10F

*DBSKNU DBSPDR E3, K6

DBSPEV E3, K6 DBSPPP E3, K6

DBSPVD E3, K6 DBSPVN E3, K6

DBSQAD H2A2A1, E3, K6 *DBSYNU

DBVALU E3, K6 *DBVDER

*DBVPOR DBVSUP I1B1

DCBRT C2 DCDOT D1A4

*DCFOD DCG D2B4

DCGN D2A4, D2B4 DCGS D2A4, D2B4

DCHDC D2B1B DCHDD D7B

DCHEX D7B *DCHFCM

DCHFDV E3, H1 DCHFEV E3

*DCHFIE *DCHKW R2

DCHU C11 DCHUD D7B

DCKDER F3, G4C *DCOEF

DCOPY D1A5 DCOPYM D1A5

DCOSDG C4A DCOT C4A

DCOV K1B1 DCPPLT N1

*DCSCAL DCSEVL C3A2

DCV L7A3 *DDAINI

*DDAJAC *DDANRM

*DDASLV DDASSL I1A2

*DDASTP *DDATRP

DDAWS C8C *DDAWTS

*DDCOR *DDCST

DDEABM I1A1B DDEBDF I1A2

DDERKF I1A1A *DDES

*DDNTL *DDNTP

*DDOGLG DDOT D1A4

*DDPSC *DDPST

DDRIV1 I1A2, I1A1B DDRIV2 I1A2, I1A1B

DDRIV3 I1A2, I1A1B *DDSCL

*DDSTP *DDZRO

DE1 C5 DEABM I1A1B

DEBDF I1A2 DEFC K1A1A1, K1A2A, L8A3

*DEFCMN *DEFE4

*DEFEHL *DEFER

DEI C5 *DENORM

DERF C8A, L5A1E DERFC C8A, L5A1E

DERKF I1A1A *DERKFS

*DES *DEXBVP

DEXINT C5 DEXPRL C4B

DFAC C1 DFC K1A1A1, K1A2A, L8A3

*DFCMN *DFDJC1

*DFDJC3 *DFEHL

*DFSPVD *DFSPVN

*DFULMT DFZERO F1B

DGAMI C7E DGAMIC C7E

DGAMIT C7E DGAMLM C7A, R2

*DGAMLN C7A DGAMMA C7A

DGAMR C7A *DGAMRN

DGAUS8 H2A1A1 DGBCO D2A2

DGBDI D3A2 DGBFA D2A2

DGBMV D1B4 DGBSL D2A2

DGECO D2A1 DGEDI D3A1, D2A1

DGEFA D2A1 DGEFS D2A1

DGEMM D1B6 DGEMV D1B4

DGER D1B4 DGESL D2A1

DGLSS D9, D5 DGMRES D2A4, D2B4

DGTSL D2A2A *DH12

*DHELS D2A4, D2B4 *DHEQR D2A4, D2B4

DHFTI D9 *DHKSEQ

*DHSTRT *DHVNRM

DINTP I1A1B DINTRV E3, K6

*DINTYD DIR D2A4, D2B4

*DJAIRY DLBETA C7B

DLGAMS C7A DLI C5

DLLSIA D9, D5 DLLTI2 D2E

DLNGAM C7A DLNREL C4B

DLPDOC D2A4, D2B4, Z *DLPDP

DLSEI K1A2A, D9 *DLSI

*DLSOD *DLSSUD

*DMACON *DMGSBV

*DMOUT *DMPAR

DNBCO D2A2 DNBDI D3A2

DNBFA D2A2 DNBFS D2A2

DNBSL D2A2 DNLS1 K1B1A1, K1B1A2

DNLS1E K1B1A1, K1B1A2 DNRM2 D1A3B

DNSQ F2A DNSQE F2A

*DOGLEG *DOHTRL

DOMN D2A4, D2B4 *DORTH D2A4, D2B4

*DORTHR DP1VLU K6

DPBCO D2B2 DPBDI D3B2

DPBFA D2B2 DPBSL D2B2

DPCHBS E3 *DPCHCE

*DPCHCI DPCHCM E3

*DPCHCS *DPCHDF

DPCHFD E3, H1 DPCHFE E3

DPCHIA E3, H2A1B2 DPCHIC E1A

DPCHID E3, H2A1B2 DPCHIM E1A

*DPCHKT E3 *DPCHNG

DPCHSP E1A *DPCHST

*DPCHSW DPCOEF K1A1A2

DPFQAD H2A2A1, E3, K6 *DPIGMR D2A4, D2B4

*DPINCW *DPINIT

*DPINTM *DPJAC

DPLINT E1B *DPLPCE

*DPLPDM *DPLPFE

*DPLPFL *DPLPMN

*DPLPMU *DPLPUP

*DPNNZR DPOCH C1, C7A

DPOCH1 C1, C7A DPOCO D2B1B

DPODI D2B1B, D3B1B DPOFA D2B1B

DPOFS D2B1B DPOLCF E1B

DPOLFT K1A1A2 DPOLVL E3

*DPOPT DPOSL D2B1B

DPPCO D2B1B DPPDI D2B1B, D3B1B

DPPERM N8 DPPFA D2B1B

*DPPGQ8 DPPQAD H2A2A1, E3, K6

DPPSL D2B1B DPPVAL E3, K6

*DPRVEC *DPRWPG

*DPRWVR DPSI C7C

DPSIFN C7C *DPSIXN

DPSORT N6A1B, N6A2B DPTSL D2B2A

DQAG H2A1A1 DQAGE H2A1A1

DQAGI H2A3A1, H2A4A1 DQAGIE H2A3A1, H2A4A1

DQAGP H2A2A1 DQAGPE H2A2A1

DQAGS H2A1A1 DQAGSE H2A1A1

DQAWC H2A2A1, J4 DQAWCE H2A2A1, J4

DQAWF H2A3A1 DQAWFE H2A3A1

DQAWO H2A2A1 DQAWOE H2A2A1

DQAWS H2A2A1 DQAWSE H2A2A1

DQC25C H2A2A2, J4 DQC25F H2A2A2

DQC25S H2A2A2 *DQCHEB

DQDOTA D1A4 DQDOTI D1A4

*DQELG *DQFORM

DQK15 H2A1A2 DQK15I H2A3A2, H2A4A2

DQK15W H2A2A2 DQK21 H2A1A2

DQK31 H2A1A2 DQK41 H2A1A2

DQK51 H2A1A2 DQK61 H2A1A2

DQMOMO H2A2A1, C3A2 DQNC79 H2A1A1

DQNG H2A1A1 *DQPSRT

DQRDC D5 *DQRFAC

DQRSL D9, D2A1 *DQRSLV

*DQWGTC *DQWGTF

*DQWGTS DRC C14

DRC3JJ C19 DRC3JM C19

DRC6J C19 DRD C14

*DREADP *DREORT

DRF C14 DRJ C14

*DRKFAB *DRKFS

*DRLCAL D2A4, D2B4 DROT D1A8

DROTG D1B10 DROTM D1A8

DROTMG D1B10 *DRSCO

DS2LT D2E DS2Y D1B9

DSBMV D1B4 DSCAL D1A6

DSD2S D2E DSDBCG D2A4, D2B4

DSDCG D2B4 DSDCGN D2A4, D2B4

DSDCGS D2A4, D2B4 DSDGMR D2A4, D2B4

DSDI D1B4 DSDOMN D2A4, D2B4

DSDOT D1A4 DSDS D2E

DSDSCL D2E DSGS D2A4, D2B4

DSICCG D2B4 DSICO D2B1A

DSICS D2E DSIDI D2B1A, D3B1A

DSIFA D2B1A DSILUR D2A4, D2B4

DSILUS D2E DSINDG C4A

DSISL D2B1A DSJAC D2A4, D2B4

DSLI D2A3 DSLI2 D2A3

DSLLTI D2E DSLUBC D2A4, D2B4

DSLUCN D2A4, D2B4 DSLUCS D2A4, D2B4

DSLUGM D2A4, D2B4 DSLUI D2E

DSLUI2 D2E DSLUI4 D2E

DSLUOM D2A4, D2B4 DSLUTI D2E

*DSLVS DSMMI2 D2E

DSMMTI D2E DSMTV D1B4

DSMV D1B4 DSORT N6A2B

DSOS F2A *DSOSEQ

*DSOSSL DSPCO D2B1A

DSPDI D2B1A, D3B1A DSPENC C5

DSPFA D2B1A DSPLP G2A2

DSPMV D1B4 DSPR D1B4

DSPR2 D1B4 DSPSL D2B1A

DSTEPS I1A1B *DSTOD

*DSTOR1 *DSTWAY

*DSUDS *DSVCO

DSVDC D6 DSWAP D1A5

DSYMM D1B6 DSYMV D1B4

DSYR D1B4 DSYR2 D1B4

DSYR2K D1B6 DSYRK D1B6

DTBMV D1B4 DTBSV D1B4

DTIN N1 DTOUT N1

DTPMV D1B4 DTPSV D1B4

DTRCO D2A3 DTRDI D2A3, D3A3

DTRMM D1B6 DTRMV D1B4

DTRSL D2A3 DTRSM D1B6

DTRSV D1B4 *DU11LS

*DU11US *DU12LS

*DU12US DULSIA D9

*DUSRMT *DVECS

*DVNRMS *DVOUT

*DWNLIT *DWNLSM

*DWNLT1 *DWNLT2

*DWNLT3 DWNNLS K1A2A

*DWRITP *DWUPDT

*DX *DX4

DXADD A3D DXADJ A3D

DXC210 A3D DXCON A3D

*DXLCAL D2A4, D2B4 DXLEGF C3A2, C9

DXNRMP C3A2, C9 *DXPMU C3A2, C9

*DXPMUP C3A2, C9 *DXPNRM C3A2, C9

*DXPQNU C3A2, C9 *DXPSI C7C

*DXQMU C3A2, C9 *DXQNU C3A2, C9

DXRED A3D DXSET A3D

*DY *DY4

*DYAIRY E1 C5

EFC K1A1A1, K1A2A, L8A3 *EFCMN

EI C5 EISDOC D4, Z

ELMBAK D4C4 ELMHES D4C1B2

ELTRAN D4C4 *ENORM

ERF C8A, L5A1E ERFC C8A, L5A1E

*EXBVP EXINT C5

EXPREL C4B *EZFFT1

EZFFTB J1A1 EZFFTF J1A1

EZFFTI J1A1 FAC C1

FC K1A1A1, K1A2A, L8A3 *FCMN

*FDJAC1 *FDJAC3

FDUMP R3 FFTDOC J1, Z

FIGI D4C1C FIGI2 D4C1C

*FULMAT FUNDOC C, Z

FZERO F1B GAMI C7E

GAMIC C7E GAMIT C7E

GAMLIM C7A, R2 *GAMLN C7A

GAMMA C7A GAMR C7A

*GAMRN GAUS8 H2A1A1

GENBUN I2B4B *H12

HFTI D9 *HKSEQ

HPPERM N8 HPSORT N6A1C, N6A2C

HQR D4C2B HQR2 D4C2B

*HSTART HSTCRT I2B1A1A

*HSTCS1 HSTCSP I2B1A1A

HSTCYL I2B1A1A HSTPLR I2B1A1A

HSTSSP I2B1A1A HTRIB3 D4C4

HTRIBK D4C4 HTRID3 D4C1B1

HTRIDI D4C1B1 *HVNRM

HW3CRT I2B1A1A HWSCRT I2B1A1A

*HWSCS1 HWSCSP I2B1A1A

HWSCYL I2B1A1A HWSPLR I2B1A1A

*HWSSS1 HWSSSP I2B1A1A

I1MACH R1 *I1MERG

ICAMAX D1A2 ICOPY D1A5

IDAMAX D1A2 *IDLOC

IMTQL1 D4A5, D4C2A IMTQL2 D4A5, D4C2A

IMTQLV D4A5, D4C2A *INDXA

*INDXB *INDXC

INITDS C3A2 INITS C3A2

INTRV E3, K6 *INTYD

INVIT D4C2B *INXCA

*INXCB *INXCC

*IPLOC IPPERM N8

IPSORT N6A1A, N6A2A ISAMAX D1A2

*ISDBCG D2A4, D2B4 *ISDCG D2B4

*ISDCGN D2A4, D2B4 *ISDCGS D2A4, D2B4

*ISDGMR D2A4, D2B4 *ISDIR D2A4, D2B4

*ISDOMN D2A4, D2B4 ISORT N6A2A

*ISSBCG D2A4, D2B4 *ISSCG D2B4

*ISSCGN D2A4, D2B4 *ISSCGS D2A4, D2B4

*ISSGMR D2A4, D2B4 *ISSIR D2A4, D2B4

*ISSOMN D2A4, D2B4 ISWAP D1A5

*IVOUT *J4SAVE

*JAIRY *LA05AD

*LA05AS *LA05BD

*LA05BS *LA05CD

*LA05CS *LA05ED

*LA05ES LLSIA D9, D5

*LMPAR *LPDP

*LSAME R, N3 LSEI K1A2A, D9

*LSI *LSOD

*LSSODS *LSSUDS

*MACON *MC20AD

*MC20AS *MGSBV

MINFIT D9 *MINSO4

*MINSOL *MPADD

*MPADD2 *MPADD3

*MPBLAS *MPCDM

*MPCHK *MPCMD

*MPDIVI *MPERR

*MPMAXR *MPMLP

*MPMUL *MPMUL2

*MPMULI *MPNZR

*MPOVFL *MPSTR

*MPUNFL NUMXER R3C

*OHTROL *OHTROR

ORTBAK D4C4 ORTHES D4C1B2

*ORTHO4 *ORTHOG

*ORTHOL *ORTHOR

ORTRAN D4C4 *PASSB

*PASSB2 *PASSB3

*PASSB4 *PASSB5

*PASSF *PASSF2

*PASSF3 *PASSF4

*PASSF5 PCHBS E3

*PCHCE *PCHCI

PCHCM E3 *PCHCS

*PCHDF PCHDOC E1A, Z

PCHFD E3, H1 PCHFE E3

PCHIA E3, H2A1B2 PCHIC E1A

PCHID E3, H2A1B2 PCHIM E1A

*PCHKT E3 *PCHNGS

PCHSP E1A *PCHST

*PCHSW PCOEF K1A1A2

PFQAD H2A2A1, E3, K6 *PGSF

*PIMACH *PINITM

*PJAC *PNNZRS

POCH C1, C7A POCH1 C1, C7A

POIS3D I2B4B *POISD2

*POISN2 *POISP2

POISTG I2B4B POLCOF E1B

POLFIT K1A1A2 POLINT E1B

POLYVL E3 *POS3D1

*POSTG2 *PPADD

*PPGQ8 *PPGSF

*PPPSF PPQAD H2A2A1, E3, K6

*PPSGF *PPSPF

PPVAL E3, K6 *PROC

*PROCP *PROD

*PRODP *PRVEC

*PRWPGE *PRWVIR

*PSGF PSI C7C

PSIFN C7C *PSIXN

PVALUE K6 *PYTHAG

QAG H2A1A1 QAGE H2A1A1

QAGI H2A3A1, H2A4A1 QAGIE H2A3A1, H2A4A1

QAGP H2A2A1 QAGPE H2A2A1

QAGS H2A1A1 QAGSE H2A1A1

QAWC H2A2A1, J4 QAWCE H2A2A1, J4

QAWF H2A3A1 QAWFE H2A3A1

QAWO H2A2A1 QAWOE H2A2A1

QAWS H2A2A1 QAWSE H2A2A1

QC25C H2A2A2, J4 QC25F H2A2A2

QC25S H2A2A2 *QCHEB

*QELG *QFORM

QK15 H2A1A2 QK15I H2A3A2, H2A4A2

QK15W H2A2A2 QK21 H2A1A2

QK31 H2A1A2 QK41 H2A1A2

QK51 H2A1A2 QK61 H2A1A2

QMOMO H2A2A1, C3A2 QNC79 H2A1A1

QNG H2A1A1 QPDOC H2, Z

*QPSRT *QRFAC

*QRSOLV *QS2I1D N6A2A

*QS2I1R N6A2A *QWGTC

*QWGTF *QWGTS

QZHES D4C1B3 QZIT D4C1B3

QZVAL D4C2C QZVEC D4C3

R1MACH R1 *R1MPYQ

*R1UPDT *R9AIMP C10D

*R9ATN1 C4A *R9CHU C11

*R9GMIC C7E *R9GMIT C7E

*R9KNUS C10B3 *R9LGIC C7E

*R9LGIT C7E *R9LGMC C7E

*R9LN2R C4B R9PAK A6B

R9UPAK A6B *RADB2

*RADB3 *RADB4

*RADB5 *RADBG

*RADF2 *RADF3

*RADF4 *RADF5

*RADFG RAND L6A21

RATQR D4A5, D4C2A RC C14

RC3JJ C19 RC3JM C19

RC6J C19 RD C14

REBAK D4C4 REBAKB D4C4

REDUC D4C1C REDUC2 D4C1C

*REORT RF C14

*RFFTB J1A1 RFFTB1 J1A1

*RFFTF J1A1 RFFTF1 J1A1

*RFFTI J1A1 RFFTI1 J1A1

RG D4A2 RGAUSS L6A14

RGG D4B2 RJ C14

*RKFAB RPQR79 F1A1A

RPZERO F1A1A RS D4A1

RSB D4A6 *RSCO

RSG D4B1 RSGAB D4B1

RSGBA D4B1 RSP D4A1

RST D4A5 RT D4A5

RUNIF L6A21 *RWUPDT

*S1MERG SASUM D1A3A

SAXPY D1A7 SBCG D2A4, D2B4

SBHIN N1 SBOCLS K1A2A, G2E, G2H1, G2H2

SBOLS K1A2A, G2E, G2H1, G2H2 *SBOLSM

SCASUM D1A3A SCG D2B4

SCGN D2A4, D2B4 SCGS D2A4, D2B4

SCHDC D2B1B SCHDD D7B

SCHEX D7B *SCHKW R2

SCHUD D7B *SCLOSM

SCNRM2 D1A3B *SCOEF

SCOPY D1A5 SCOPYM D1A5

SCOV K1B1 SCPPLT N1

*SDAINI *SDAJAC

*SDANRM *SDASLV

SDASSL I1A2 *SDASTP

*SDATRP *SDAWTS

*SDCOR *SDCST

*SDNTL *SDNTP

SDOT D1A4 *SDPSC

*SDPST SDRIV1 I1A2, I1A1B

SDRIV2 I1A2, I1A1B SDRIV3 I1A2, I1A1B

*SDSCL SDSDOT D1A4

*SDSTP *SDZRO

SEPELI I2B1A2 SEPX4 I2B1A2

SGBCO D2A2 SGBDI D3A2

SGBFA D2A2 SGBMV D1B4

SGBSL D2A2 SGECO D2A1

SGEDI D2A1, D3A1 SGEEV D4A2

SGEFA D2A1 SGEFS D2A1

SGEIR D2A1 SGEMM D1B6

SGEMV D1B4 SGER D1B4

SGESL D2A1 SGLSS D9, D5

SGMRES D2A4, D2B4 SGTSL D2A2A

*SHELS D2A4, D2B4 *SHEQR D2A4, D2B4

SINDG C4A SINQB J1A3

SINQF J1A3 SINQI J1A3

SINT J1A3 SINTI J1A3

SINTRP I1A1B SIR D2A4, D2B4

SLLTI2 D2E SLPDOC D2A4, D2B4, Z

*SLVS *SMOUT

SNBCO D2A2 SNBDI D3A2

SNBFA D2A2 SNBFS D2A2

SNBIR D2A2 SNBSL D2A2

SNLS1 K1B1A1, K1B1A2 SNLS1E K1B1A1, K1B1A2

SNRM2 D1A3B SNSQ F2A

SNSQE F2A *SODS

SOMN D2A4, D2B4 *SOPENM

*SORTH D2A4, D2B4 SOS F2A

*SOSEQS *SOSSOL

SPBCO D2B2 SPBDI D3B2

SPBFA D2B2 SPBSL D2B2

*SPELI4 *SPELIP

SPENC C5 *SPIGMR D2A4, D2B4

*SPINCW *SPINIT

SPLP G2A2 *SPLPCE

*SPLPDM *SPLPFE

*SPLPFL *SPLPMN

*SPLPMU *SPLPUP

SPOCO D2B1B SPODI D2B1B, D3B1B

SPOFA D2B1B SPOFS D2B1B

SPOIR D2B1B *SPOPT

SPOSL D2B1B SPPCO D2B1B

SPPDI D2B1B, D3B1B SPPERM N8

SPPFA D2B1B SPPSL D2B1B

SPSORT N6A1B, N6A2B SPTSL D2B2A

SQRDC D5 SQRSL D9, D2A1

*SREADP *SRLCAL D2A4, D2B4

SROT D1A8 SROTG D1B10

SROTM D1A8 SROTMG D1B10

SS2LT D2E SS2Y D1B9

SSBMV D1B4 SSCAL D1A6

SSD2S D2E SSDBCG D2A4, D2B4

SSDCG D2B4 SSDCGN D2A4, D2B4

SSDCGS D2A4, D2B4 SSDGMR D2A4, D2B4

SSDI D1B4 SSDOMN D2A4, D2B4

SSDS D2E SSDSCL D2E

SSGS D2A4, D2B4 SSICCG D2B4

SSICO D2B1A SSICS D2E

SSIDI D2B1A, D3B1A SSIEV D4A1

SSIFA D2B1A SSILUR D2A4, D2B4

SSILUS D2E SSISL D2B1A

SSJAC D2A4, D2B4 SSLI D2A3

SSLI2 D2A3 SSLLTI D2E

SSLUBC D2A4, D2B4 SSLUCN D2A4, D2B4

SSLUCS D2A4, D2B4 SSLUGM D2A4, D2B4

SSLUI D2E SSLUI2 D2E

SSLUI4 D2E SSLUOM D2A4, D2B4

SSLUTI D2E SSMMI2 D2E

SSMMTI D2E SSMTV D1B4

SSMV D1B4 SSORT N6A2B

SSPCO D2B1A SSPDI D2B1A, D3B1A

SSPEV D4A1 SSPFA D2B1A

SSPMV D1B4 SSPR D1B4

SSPR2 D1B4 SSPSL D2B1A

SSVDC D6 SSWAP D1A5

SSYMM D1B6 SSYMV D1B4

SSYR D1B4 SSYR2 D1B4

SSYR2K D1B6 SSYRK D1B6

STBMV D1B4 STBSV D1B4

STEPS I1A1B STIN N1

*STOD *STOR1

STOUT N1 STPMV D1B4

STPSV D1B4 STRCO D2A3

STRDI D2A3, D3A3 STRMM D1B6

STRMV D1B4 STRSL D2A3

STRSM D1B6 STRSV D1B4

*STWAY *SUDS

*SVCO *SVD

*SVECS *SVOUT

*SWRITP *SXLCAL D2A4, D2B4

*TEVLC *TEVLS

TINVIT D4C3 TQL1 D4A5, D4C2A

TQL2 D4A5, D4C2A TQLRAT D4A5, D4C2A

TRBAK1 D4C4 TRBAK3 D4C4

TRED1 D4C1B1 TRED2 D4C1B1

TRED3 D4C1B1 *TRI3

TRIDIB D4A5, D4C2A *TRIDQ

*TRIS4 *TRISP

*TRIX TSTURM D4A5, D4C2A

*U11LS *U11US

*U12LS *U12US

ULSIA D9 *USRMAT

*VNWRMS *WNLIT

*WNLSM *WNLT1

*WNLT2 *WNLT3

WNNLS K1A2A XADD A3D

XADJ A3D XC210 A3D

XCON A3D *XERBLA R3

XERCLR R3C *XERCNT R3C

XERDMP R3C *XERHLT R3C

XERMAX R3C XERMSG R3C

*XERPRN R3C *XERSVE R3

XGETF R3C XGETUA R3C

XGETUN R3C XLEGF C3A2, C9

XNRMP C3A2, C9 *XPMU C3A2, C9

*XPMUP C3A2, C9 *XPNRM C3A2, C9

*XPQNU C3A2, C9 *XPSI C7C

*XQMU C3A2, C9 *XQNU C3A2, C9

XRED A3D XSET A3D

XSETF R3A XSETUA R3B

XSETUN R3B *YAIRY

*ZABS *ZACAI

*ZACON ZAIRY C10D

*ZASYI ZBESH C10A4

ZBESI C10B4 ZBESJ C10A4

ZBESK C10B4 ZBESY C10A4

*ZBINU ZBIRY C10D

*ZBKNU *ZBUNI

*ZBUNK *ZDIV

*ZEXP *ZKSCL

*ZLOG *ZMLRI

*ZMLT *ZRATI

*ZS1S2 *ZSERI

*ZSHCH *ZSQRT

*ZUCHK *ZUNHJ

*ZUNI1 *ZUNI2

*ZUNIK *ZUNK1

*ZUNK2 *ZUOIK

*ZWRSK

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