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Mark 21 News – NAG SMP Library
1 Introduction
In this document we describe the differences between the last release ‘Release 2’ and this latest release, now named ‘Mark
21’, of the NAG SMP Library. There are two main differences:
- Release 2 was based on Mark 19 of the NAG Fortran Library while this latest release is based on Mark 21 of the NAG Fortran
Library; and
- in Mark 21, a larger number of routines have been specially tuned to maximize their performance on shared memory parallel
systems.
1.1 New Functionality
At Mark 21 of the NAG SMP Library new functionality has been introduced in addition to improvements in existing areas. The
Library now contains 1532 user-callable routines of which 1466 are documented and 374 are new at this mark.
New chapters on large scale eigenproblems and mesh generation have been introduced, and extensions have been included in
the areas of optimization, dense and banded linear algebra, direct solution of large scale linear systems, simple calculations
with statistics, regression, random numbers, zeros of polynomials, partial differential equations, time series analysis, and
special functions.
In addition the provision of thread safe versions of existing routines has been significantly extended in Chapter C05 ( Roots of One or More Transcendental Equations), Chapter D03 ( Partial Differential Equations), Chapter E04 ( Minimizing or Maximizing a Function) and Chapter G05 ( Random Number Generators) to aid users developing multithreaded applications.
The new chapter on Mesh Generation (Chapter D06) has routines for generating 2-D meshes together with a number of associated utility routines.
The new chapter on Large Scale Eigenproblems (Chapter F12) has routines for the solution of symmetric and nonsymmetric standard and generalized large scale eigenvalue problems. Chapter
F11 has been renamed as Large Scale Linear Systems, and new routines for the direct solution of sparse problems have been added.
Chapter E04 ( Minimizing or Maximizing a Function) has been updated with new routines for the solution of LP, QP and nonlinear programming problems with sparse linear constraints.
Chapters F07 F08 ( Linear Equations (LAPACK), respectivley) have been extended to include all the LAPACK driver routines, thus allowing the solution of most problems
with a call to a single routine rather than multiple calls to LAPACK computational routines. A comprehensive suite of driver
routines for the solution of dense and banded linear equations has also been added to Chapter F04 ( Simultaneous Linear Equations).
Routines for finding the roots of real and complex cubic and quartic equations have been added to Chapter C02 ( Zeros of Polynomials).
Chapter D03 ( Partial Differential Equations) now includes routines for solving Black–Scholes equations.
Routines for Landau and Vavilov distributions have been added to Chapter G01 ( Simple Calculations on Statistical Data), new routines for stepwise regression and mixed effects regression have been included in Chapter G02 ( Correlation and Regression Analysis), and a number of new random number generators, including Copulas and improved quasi-random number generators, generation
of univariate GARCH, asymmetric GARCH and EGARCH processes, and generators for further distributions have been added to Chapter
G05 ( Random Number Generators).
Chapter G13 ( Time Series Analysis) has been extended with routines for parameter estimation and forecasting for univariate regression GARCH, asymmetric GARCH
and EGARCH processes.
Chapter S ( Approximations of Special Functions) has new routines for polygamma functions, zeros of Bessel functions, Jacobian functions, elliptic integrals and Legendre
and associated Legendre functions. Variant routines for the log Gamma function, and Bessel function of the 1st kind have also
been added.
1.2 New SMP parallelism and other optimizations
SMP Parallel versions of many of the new Chapter F11 sparse direct solvers, and Chapter F12 sparse eigenproblem are included, and parallelism has been extended to many more LAPACK routines. In addition, improvements
in underlying NAG auxiliary routines improves the usage of the SMP optimized dense linear algebra by routines in the areas
of optimization, ODEs and PDEs, and statistics.
1.3 Documentation
The
NAG SMP Library Manual has undergone a fundamental change since Release 2 and the Essential Introduction and the Introduction to the NAG SMP Library are essential reading for all users of the
NAG SMP Library.
2 Tuned Routines
The following is a list of user-callable routines that have been parallelised, or otherwise optimized, since the last release.
There are 67 of these routines at this release in the area of dense and sparse linear algebra. See the document ‘ Tuned and Enhanced Routines in the NAG SMP Library’ for a full list of tuned routines.
Note: on some implementations, the equivalent vendor library routines may be substituted for some of the following list – consult
the Users' Note for your implementation for further information.
| F04AFF |
Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix
already factorized by F03AEF)
|
| F04AGF |
Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F03AEF)
|
| F04AHF |
Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AFF)
|
| F04AJF |
Solution of real simultaneous linear equations (coefficient matrix already factorized by F03AFF)
|
| F07AHF |
Refined solution with error bounds of real system of linear equations, multiple right-hand sides |
| F07AVF |
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides |
| F07BDF |
LU factorization of real m by n band matrix
|
| F07BEF |
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF) |
| F07BHF |
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides |
| F07BRF |
LU factorization of complex m by n band matrix
|
| F07BSF |
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF) |
| F07BVF |
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides |
| F07CHF |
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides |
| F07CVF |
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides |
| F07FHF |
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides |
| F07FVF |
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand
sides
|
| F07GEF |
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized
by F07GDF (DPPTRF), packed storage
|
| F07GHF |
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides,
packed storage
|
| F07GSF |
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized
by F07GRF (ZPPTRF), packed storage
|
| F07GVF |
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand
sides, packed storage
|
| F07HEF |
Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized
by F07HDF (DPBTRF) |
| F07HHF |
Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand
sides
|
| F07HSF |
Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already
factorized by F07HRF (ZPBTRF) |
| F07HVF |
Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand
sides
|
| F07JHF |
Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand
sides
|
| F07JVF |
Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple
right-hand sides
|
| F07MHF |
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides |
| F07MVF |
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides |
| F07NVF |
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides |
| F07PHF |
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed
storage
|
| F07PVF |
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides,
packed storage
|
| F07QVF |
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage |
| F07THF |
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides |
| F07TVF |
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides |
| F07UEF |
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage |
| F07UHF |
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage |
| F07USF |
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage |
| F07UVF |
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage |
| F07VEF |
Solution of real band triangular system of linear equations, multiple right-hand sides |
| F07VHF |
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides |
| F07VSF |
Solution of complex band triangular system of linear equations, multiple right-hand sides |
| F07VVF |
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides |
| F08HEF |
Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| F08HSF |
Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| F08JJF |
Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| F08JKF |
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| F08JXF |
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| F08PEF |
Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| F08PKF |
Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| F08PSF |
Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| F08PXF |
Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| F08TAF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed
storage
|
| F08TBF |
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed
storage
|
| F08TCF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed
storage (divide-and-conquer)
|
| F08TNF |
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed
storage
|
| F08TPF |
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem,
packed storage
|
| F08TQF |
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem,
packed storage (divide-and-conquer)
|
| F11BSF |
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS,Bi-CGSTAB or TFQMR method |
| F11GSF |
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos |
| F11MEF |
LU factorization of real sparse matrix
|
| F11MFF |
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) |
| F11MHF |
Refined solution with error bounds of real system of linear equations, multiple right-hand sides |
| F11MKF |
Real sparse nonsymmetric matrix matrix multiply, compressed column storage |
| F11XNF |
Complex sparse non-Hermitian matrix vector multiply |
| F11XSF |
Complex sparse Hermitian matrix vector multiply |
| F12ABF |
Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues
and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
|
| F12AGF |
Computes approximations to selected eigenvalues of a real nonsymmetric banded (standard or generalized) eigenproblem and,
optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant
subspace
|
3 Enhanced Routines
These routines call one or more of the tuned routines as part of their core operations and may thereby exhibit improved performance
and scalability. There are 162 newly enhanced routines at this mark; these include the areas of zeros of polynomials, PDEs,
optimization, dense and sparse linear algebra, and multivariate statistics.
| C02AKF |
All zeros of real cubic equation |
| C02ALF |
All zeros of real quartic equation |
| C02AMF |
All zeros of complex cubic equation |
| C02ANF |
All zeros of complex quartic equation |
| D03FAF |
Elliptic PDE, Helmholtz equation, three-dimensional Cartesian co-ordinates |
| D03NCF |
Finite difference solution of the Black–Scholes equations |
| E02RAF |
Padé-approximants |
| E04USF |
Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives
(comprehensive)
|
| E04YCF |
Covariance matrix for nonlinear least-squares problem (unconstrained) |
| F02ECF |
Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box) |
| F02WDF |
QR factorization, possibly followed by SVD
|
| F02WEF |
SVD of real matrix (Black Box) |
| F02WUF |
SVD of real upper triangular matrix (Black Box) |
| F02XEF |
SVD of complex matrix (Black Box) |
| F02XUF |
SVD of complex upper triangular matrix (Black Box) |
| F03ADF |
Determinant of complex matrix (Black Box) |
| F03AFF |
LU factorization and determinant of real matrix
|
| F04ADF |
Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box) |
| F04AEF |
Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) |
| F04ATF |
Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box) |
| F04BAF |
Computes the solution and error-bound to a real system of linear equations |
| F04BDF |
Computes the solution and error-bound to a real symmetric positive-definite system of linear equations |
| F04BEF |
Computes the solution and error-bound to a real symmetric positive-definite system of linear equations, packed storage |
| F04BFF |
Computes the solution and error-bound to a real symmetric positive-definite banded system of linear equations |
| F04CAF |
Computes the solution and error-bound to a complex system of linear equations |
| F04CBF |
Computes the solution and error-bound to a complex banded system of linear equations |
| F04CDF |
Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations |
| F04CEF |
Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations, packed storage |
| F04CFF |
Computes the solution and error-bound to a complex Hermitian positive-definite banded system of linear equations |
| F04JDF |
Minimal least-squares solution of m real equations in n unknowns, rank ≤m, m≤n |
| F04JGF |
Least-squares (if rank =n) or minimal least-squares (if rank <n) solution of m real equations in n unknowns, rank ≤n, m≥n |
| F07AAF |
Computes the solution to a real system of linear equations |
| F07ABF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
|
| F07ANF |
Computes the solution to a complex system of linear equations |
| F07APF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
|
| F07BAF |
Computes the solution to a real banded system of linear equations |
| F07BBF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
|
| F07BNF |
Computes the solution to a complex banded system of linear equations |
| F07BPF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
|
| F07CBF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
|
| F07CPF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
|
| F07FAF |
Computes the solution to a real symmetric positive-definite system of linear equations |
| F07FBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
system of linear equations
|
| F07FNF |
Computes the solution to a complex Hermitian positive-definite system of linear equations |
| F07FPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
system of linear equations
|
| F07GAF |
Computes the solution to a real symmetric positive-definite system of linear equations, packed storage |
| F07GBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
system of linear equations, packed storage
|
| F07GNF |
Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage |
| F07GPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
system of linear equations, packed storage
|
| F07HAF |
Computes the solution to a real symmetric positive-definite banded system of linear equations |
| F07HBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
banded system of linear equations
|
| F07HNF |
Computes the solution to a complex Hermitian positive-definite banded system of linear equations |
| F07HPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
banded system of linear equations
|
| F07JBF |
Uses the L×D×L′ factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal
system of linear equations
|
| F07JPF |
Uses the L×D×L′ factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal
system of linear equations
|
| F07MBF |
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations |
| F07MPF |
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations |
| F07NPF |
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations |
| F07PBF |
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage |
| F07PPF |
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed
storage
|
| F07QPF |
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed
storage
|
| F08AAF |
Solves an overdetermined or underdetermined real linear system |
| F08ANF |
Solves an overdetermined or underdetermined complex linear system |
| F08BAF |
Computes the minimum-norm solution to a real linear least-squares problem |
| F08BFF |
QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
|
| F08BNF |
Computes the minimum-norm solution to a complex linear least-squares problem |
| F08BTF |
QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
|
| F08FAF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FBF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FDF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| F08FNF |
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FPF |
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FRF |
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| F08GAF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GBF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GNF |
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GPF |
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08HAF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HBF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HNF |
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HPF |
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08JAF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JBF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JDF |
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |
| F08JHF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this
form (divide-and-conquer)
|
| F08JLF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced
to this form (Relatively Robust Representations)
|
| F08JVF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix
reduced to this form (divide-and-conquer)
|
| F08JYF |
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix
reduced to this form (Relatively Robust Representations)
|
| F08KAF |
Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition |
| F08KBF |
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |
| F08KCF |
Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer) |
| F08KDF |
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |
| F08KNF |
Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition |
| F08KPF |
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors |
| F08KQF |
Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer) |
| F08KRF |
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
(divide-and-conquer)
|
| F08MDF |
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) |
| F08NAF |
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |
| F08NBF |
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally,
the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
|
| F08NNF |
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |
| F08NPF |
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally,
the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
|
| F08PAF |
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors |
| F08PBF |
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors;
also, optionally, computes reciprocal condition numbers for selected eigenvalues
|
| F08PNF |
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors |
| F08PPF |
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors;
also, optionally, computes reciprocal condition numbers for selected eigenvalues
|
| F08SAF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SBF |
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SCF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
| F08SNF |
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SPF |
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SQF |
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
| F08UAF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UBF |
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UCF |
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
(divide-and-conquer)
|
| F08UNF |
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UPF |
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UQF |
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
(divide-and-conquer)
|
| F08WAF |
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized
eigenvectors
|
| F08WBF |
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized
eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for
the right eigenvectors
|
| F08WNF |
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized
eigenvectors
|
| F08WPF |
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized
eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for
the right eigenvectors
|
| F08XAF |
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally,
the left and/or right matrices of Schur vectors
|
| F08XBF |
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally,
the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
|
| F08XNF |
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally,
the left and/or right matrices of Schur vectors
|
| F08XPF |
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally,
the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
|
| F08ZAF |
Solves the real linear equality-constrained least-squares (LSE) problem |
| F08ZBF |
Solves a real general Gauss–Markov linear model (GLM) problem |
| F08ZEF |
Computes a generalized QR factorization of a real matrix pair
|
| F08ZFF |
Computes a generalized RQ factorization of a real matrix pair
|
| F08ZNF |
Solves the complex linear equality-constrained least-squares (LSE) problem |
| F08ZPF |
Solves a complex general Gauss–Markov linear model (GLM) problem |
| F08ZSF |
Computes a generalized QR factorization of a complex matrix pair
|
| F08ZTF |
Computes a generalized RQ factorization of a complex matrix pair
|
| F11DCF |
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF |
| F11DEF |
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner
(Black Box)
|
| F11DKF |
Real sparse nonsymmetric linear systems, line Jacobi preconditioner |
| F11DQF |
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by
F11DNF (Black Box)
|
| F11DSF |
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner
Black Box
|
| F11DXF |
Complex sparse nonsymmetric linear systems, line Jacobi preconditioner |
| F11JCF |
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
|
| F11JEF |
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) |
| F11JQF |
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
|
| F11JSF |
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black
Box)
|
| F12FCF |
Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real symmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate
eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
|
| F12FGF |
Computes approximations to selected eigenvalues of a real symmetric banded (standard or generalized) eigenproblem and, optionally,
the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
|
| G01HBF |
Computes probabilities for the multivariate Normal distribution |
| G02BYF |
Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF |
| G02DDF |
Estimates of linear parameters and general linear regression model from updated model |
| G02DKF |
Estimates and standard errors of parameters of a general linear regression model for given constraints |
| G02GKF |
Estimates and standard errors of parameters of a general linear model for given constraints |
| G02HDF |
Robust regression, compute regression with user-supplied functions and weights |
| G02JAF |
Linear mixed effects regression using Restricted Maximum Likelihood (REML) |
| G03FAF |
Performs principal co-ordinate analysis, classical metric scaling |
| G05PCF |
Generates a realisation of a multivariate time series from a VARMA model |
| G11CAF |
Returns parameter estimates for the conditional analysis of stratified data |
| G12BAF |
Fits Cox's proportional hazard model |
| G13ADF |
Univariate time series, preliminary estimation, seasonal ARIMA model |
| G13DXF |
Calculates the zeros of a vector autoregressive (or moving average) operator |
| G13FAF |
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the
form (εt-1+γ)2 |
| G13FCF |
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|εt-1|+γεt-1)2 |
| G13FEF |
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process |
| G13FGF |
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process |
4 New Routines
The 374 new user-callable routines included in the SMP Library at Mark 21 are as follows.
| A00ACF |
Check availability of a valid licence key |
| C02AKF |
All zeros of real cubic equation |
| C02ALF |
All zeros of real quartic equation |
| C02AMF |
All zeros of complex cubic equation |
| C02ANF |
All zeros of complex quartic equation |
| D03NCF |
Finite difference solution of the Black–Scholes equations |
| D03NDF |
Analytic solution of the Black–Scholes equations |
| D03NEF |
Compute average values for D03NDF |
| D06AAF |
Generates a two-dimensional mesh using a simple incremental method |
| D06ABF |
Generates a two-dimensional mesh using a Delaunay–Voronoi process |
| D06ACF |
Generates a two-dimensional mesh using an Advancing-front method |
| D06BAF |
Generates a boundary mesh |
| D06CAF |
Uses a barycentering technique to smooth a given mesh |
| D06CBF |
Generates a sparsity pattern of a Finite Element matrix associated with a given mesh |
| D06CCF |
Renumbers a given mesh using Gibbs method |
| D06DAF |
Generates a mesh resulting from an affine transformation of a given mesh |
| D06DBF |
Joins together two given adjacent (possibly overlapping) meshes |
| E04NPF |
Initialization routine for E04NQF |
| E04NQF |
LP or QP problem (suitable for sparse problems) |
| E04NRF |
Supply optional parameter values for E04NQF from external file
|
| E04NSF |
Set a single option for E04NQF from a character string
|
| E04NTF |
Set a single option for E04NQF from an argument
|
| E04NUF |
Set a single option for E04NQF from a argument
|
| E04NXF |
Get the setting of an valued option of E04NQF |
| E04NYF |
Get the setting of a valued option of E04NQF |
| E04USF |
Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives
(comprehensive)
|
| E04VGF |
Initialization routine for E04VHF |
| E04VHF |
General sparse nonlinear optimizer |
| E04VJF |
Determine the pattern of nonzeros in the Jacobian matrix for E04VHF |
| E04VKF |
Supply optional parameter values for E04VHF from external file
|
| E04VLF |
Set a single option for E04VHF from a character string
|
| E04VMF |
Set a single option for E04VHF from an argument
|
| E04VNF |
Set a single option for E04VHF from a argument
|
| E04VRF |
Get the setting of an valued option of E04VHF |
| E04VSF |
Get the setting of a valued option of E04VHF |
| E04WBF |
Initialization routine for
|
| E04WCF |
Initialization routine for E04WDF |
| E04WDF |
Solves the nonlinear programming (NP) problem |
| E04WEF |
Supply optional parameter values for E04WDF from external file
|
| E04WFF |
Set a single option for E04WDF from a character string
|
| E04WGF |
Set a single option for E04WDF from an argument
|
| E04WHF |
Set a single option for E04WDF from a argument
|
| E04WKF |
Get the setting of an valued option of E04WDF |
| E04WLF |
Get the setting of a valued option of E04WDF |
| F04BAF |
Computes the solution and error-bound to a real system of linear equations |
| F04BBF |
Computes the solution and error-bound to a real banded system of linear equations |
| F04BCF |
Computes the solution and error-bound to a real tridiagonal system of linear equations |
| F04BDF |
Computes the solution and error-bound to a real symmetric positive-definite system of linear equations |
| F04BEF |
Computes the solution and error-bound to a real symmetric positive-definite system of linear equations, packed storage |
| F04BFF |
Computes the solution and error-bound to a real symmetric positive-definite banded system of linear equations |
| F04BGF |
Computes the solution and error-bound to a real symmetric positive-definite tridiagonal system of linear equations |
| F04BHF |
Computes the solution and error-bound to a real symmetric system of linear equations |
| F04BJF |
Computes the solution and error-bound to a real symmetric system of linear equations, packed storage |
| F04CAF |
Computes the solution and error-bound to a complex system of linear equations |
| F04CBF |
Computes the solution and error-bound to a complex banded system of linear equations |
| F04CCF |
Computes the solution and error-bound to a complex tridiagonal system of linear equations |
| F04CDF |
Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations |
| F04CEF |
Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations, packed storage |
| F04CFF |
Computes the solution and error-bound to a complex Hermitian positive-definite banded system of linear equations |
| F04CGF |
Computes the solution and error-bound to a complex Hermitian positive-definite tridiagonal system of linear equations |
| F04CHF |
Computes the solution and error-bound to a complex Hermitian system of linear equations |
| F04CJF |
Computes the solution and error-bound to a complex Hermitian system of linear equations, packed storage |
| F04DHF |
Computes the solution and error-bound to a complex symmetric system of linear equations |
| F04DJF |
Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage. |
| F06FEF |
Multiply real vector by reciprocal of scalar |
| F06KEF |
Multiply complex vector by reciprocal of real scalar |
| F06RNF |
1-norm, ∞-norm, Frobenius norm, largest absolute element, real tridiagonal matrix
|
| F06RPF |
1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
|
| F06TAF |
Matrix-vector product, complex symmetric matrix |
| F06TBF |
Rank-1 update, complex symetric matrix |
| F06TCF |
Matrix-vector product, complex symmetric packed matrix |
| F06TDF |
Rank-1 update, complex symetric packed matrix |
| F06UNF |
1-norm, ∞-norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
|
| F06UPF |
1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
|
| F07AAF |
Computes the solution to a real system of linear equations |
| F07ABF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
|
| F07AFF |
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number |
| F07ANF |
Computes the solution to a complex system of linear equations |
| F07APF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
|
| F07ATF |
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number |
| F07BAF |
Computes the solution to a real banded system of linear equations |
| F07BBF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
|
| F07BFF |
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number |
| F07BNF |
Computes the solution to a complex banded system of linear equations |
| F07BPF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
|
| F07BTF |
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number |
| F07CAF |
Computes the solution to a real tridiagonal system of linear equations |
| F07CBF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
|
| F07CDF |
LU factorization of real tridiagonal matrix
|
| F07CEF |
Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF) |
| F07CGF |
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF) |
| F07CHF |
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides |
| F07CNF |
Computes the solution to a complex tridiagonal system of linear equations |
| F07CPF |
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
|
| F07CRF |
LU factorization of complex tridiagonal matrix
|
| F07CSF |
Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF) |
| F07CUF |
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF) |
| F07CVF |
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides |
| F07FAF |
Computes the solution to a real symmetric positive-definite system of linear equations |
| F07FBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
system of linear equations
|
| F07FFF |
Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition
number
|
| F07FNF |
Computes the solution to a complex Hermitian positive-definite system of linear equations |
| F07FPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
system of linear equations
|
| F07FTF |
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition
number
|
| F07GAF |
Computes the solution to a real symmetric positive-definite system of linear equations, packed storage |
| F07GBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
system of linear equations, packed storage
|
| F07GFF |
Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition
number, packed storage
|
| F07GNF |
Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage |
| F07GPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
system of linear equations, packed storage
|
| F07GTF |
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition
number, packed storage
|
| F07HAF |
Computes the solution to a real symmetric positive-definite banded system of linear equations |
| F07HBF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite
banded system of linear equations
|
| F07HFF |
Computes row and column scalings intended to equilibrate a real symmetric positive-definite banded matrix and reduce its condition
number
|
| F07HNF |
Computes the solution to a complex Hermitian positive-definite banded system of linear equations |
| F07HPF |
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite
banded system of linear equations
|
| F07HTF |
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite banded matrix and reduce its
condition number
|
| F07JAF |
Computes the solution to a real symmetric positive-definite tridiagonal system of linear equations |
| F07JBF |
Uses the L×D×L′ factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal
system of linear equations
|
| F07JDF |
Computes the L×D×L′ factorization of a real symmetric positive-definite tridiagonal matrix
|
| F07JEF |
Solution of real symmetric tridiagonal linear system, matrix already factorized by F07JDF (DPTTRF) |
| F07JGF |
Computes the reciprocal of the condition number of a real symmetric positive-definite tridiagonal system using the L×D×L′ factorization computed byF07JDF (DPTTRF) |
| F07JHF |
Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand
sides
|
| F07JNF |
Computes the solution to a complex Hermitian positive-definite tridiagonal system of linear equations |
| F07JPF |
Uses the L×D×L′ factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal
system of linear equations
|
| F07JRF |
Computes the L×D×L′ factorization of a complex Hermitian positive-definite tridiagonal matrix
|
| F07JSF |
Solves a complex Hermitian positive-definite tridiagonal system using the L×D×L′ factorization computed by F07JRF (ZPTTRF) |
| F07JUF |
Computes the reciprocal of the condition number of a complex Hermitian positive-definite tridiagonal system using the L×D×L′ factorization computed by F07JRF (ZPTTRF) |
| F07JVF |
Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple
right-hand sides
|
| F07MAF |
Computes the solution to a real symmetric system of linear equations |
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