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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
which are otherwise equivalent. The names of equivalent routines are listed
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,
I integer, H character, L logical, and A is a pseudo-type given to routines
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
directly by library users. They are listed here so that users will be able
to avoid duplicating names that are used by the CML and for the benefit of
programmers who may be able to use them in the construction of new routines
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
has at least one category. An asterisk (*) immediately preceding a 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).
I. Differential and integral equations
I1. Ordinary differential equations
I1A. Initial value problems
I1A1. General, nonstiff or mildly stiff
I1A1A. One-step methods (e.g., Runge-Kutta)
DERKF-S Solve an initial value problem in ordinary differential
DDERKF-D equations using a Runge-Kutta-Fehlberg scheme.
I1A1B. Multistep methods (e.g., Adams' predictor-corrector)
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.
I1A2. Stiff and mixed algebraic-differential equations
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.
I1B. Multipoint boundary value problems
I1B1. Linear
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.
I2. Partial differential equations
I2B. Elliptic boundary value problems
I2B1. Linear
I2B1A. Second order
I2B1A1. Poisson (Laplace) or Helmholz equation
I2B1A1A. Rectangular domain (or topologically rectangular in the coordinate
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).
I2B1A2. Other separable problems
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.
I2B4. Service routines
I2B4B. Solution of discretized elliptic equations
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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