SLATEC Table of Contents
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.