NAG Fortran Library

Mark 19 News

1 Introduction

At Mark 19 of the Fortran Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1155 documented routines, of which 62 are new at this Mark. These extend the areas of fast Fourier transforms (FFTs), optimization, eigenvalue problems (LAPACK), sparse linear algebra, statistics, operations research (OR) and sorting as summarized below.

The most significant additions to the FFT chapter (Chapter C06) are as follows:

Coverage in the optimization chapter (Chapter E04) has been extended with the addition of a routine to solve sparse nonlinear programming problems.

New routines for solving eigenproblems (Chapter F08) are included for:

Coverage in the sparse linear algebra chapter (Chapter F11) has been extended to provide iterative methods and preconditioners for complex symmetric and non-Hermitian linear systems of equations.

Two of the new routines are in the statistics chapters (Chapter G01 to Chapter G13). They include facilities (in the stated chapters) for:

Coverage in the OR chapter (Chapter H) has been extended to provide solvers for dense and sparse integer quadratic programming problems.

A new routine for sorting a vector of complex numbers into the order specified by a vector of ranks is included in Chapter M01.

2 New Routines

The 62 new user-callable routines included in the NAG Fortran Library at Mark 19 are as follows.

C06PAF Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex data format for Hermitian sequences
C06PCF Single one-dimensional complex discrete Fourier transform, complex data format
C06PFF One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PJF Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PKF Circular convolution or correlation of two complex vectors
C06PPF Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences
C06PQF Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences and sequences stored as columns
C06PRF Multiple one-dimensional complex discrete Fourier transforms using complex data format
C06PSF Multiple one-dimensional complex discrete Fourier transforms using complex data format and sequences stored as columns
C06PUF Two-dimensional complex discrete Fourier transform, complex data format
C06PXF Three-dimensional complex discrete Fourier transform, complex data format
C06RAF Discrete sine transform (easy-to-use)
C06RBF Discrete cosine transform (easy-to-use)
C06RCF Discrete quarter-wave sine transform (easy-to-use)
C06RDF Discrete quarter-wave cosine transform (easy-to-use)
E04UGF NLP problem (sparse)
E04UHF Read optional parameter values for E04UGF from external file
E04UJF Supply optional parameter values to E04UGF
F08FCF (SSYEVD/DSYEVD) All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
F08FQF (CHEEVD/ZHEEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
F08GCF (SSPEVD/DSPEVD) All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
F08GQF (CHPEVD/ZHPEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
F08HCF (SSBEVD/DSBEVD) All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
F08HQF (CHBEVD/ZHBEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
F08JCF (SSTEVD/DSTEVD) All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
F08LEF (SGBBRD/DGBBRD) Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF (CGBBRD/ZGBBRD) Reduction of complex rectangular band matrix to upper bidiagonal form
F08UEF (SSBGST/DSBGST) Reduction of real symmetric-definite banded generalized eigenproblem Ax = lamda Bx to standard form Cy = lamda y, such that C has the same bandwidth as A
F08UFF (SPBSTF/DPBSTF) Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08USF (CHBGST/ZHBGST) Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = lamda Bx to standard form Cy = lamda y, such that C has the same bandwidth as A
F08UTF (CPBSTF/ZPBSTF) Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F11BDF Real sparse nonsymmetric linear systems, set-up for F11BEF
F11BEF Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BFF Real sparse nonsymmetric linear systems, diagnostic for F11BEF
F11BRF Complex sparse non-Hermitian linear systems, set-up for F11BSF
F11BSF Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BTF Complex sparse non-Hermitian linear systems, diagnostic for F11BSF
F11DNF Complex sparse non-Hermitian linear systems, incomplete LU factorization
F11DPF Solution of complex linear system involving incomplete LU preconditioning matrix generated by F11DNF
F11DQF Solution of complex sparse non-Hermitian linear system, RGMRES, CGS Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
F11DRF Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
F11DSF Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
F11JNF Complex sparse Hermitian matrix, incomplete Cholesky factorization
F11JPF Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
F11JQF Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
F11JRF Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
F11JSF Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11XNF Complex sparse non-Hermitian matrix vector multiply
F11XSF Complex sparse Hermitian matrix vector multiply
F11ZNF Complex sparse non-Hermitian matrix reorder routine
F11ZPF Complex sparse Hermitian matrix reorder routine
G11CAF Returns parameter estimates for the conditional analysis of stratified data
G12ZAF Creates the risk sets associated with the Cox proportional hazards model for fixed covariates
H02CBF Integer QP problem (dense)
H02CCF Read optional parameter values for H02CBF from external file
H02CDF Supply optional parameter values to H02CBF
H02CEF Integer LP or QP problem (sparse)
H02CFF Read optional parameter values for H02CEF from external file
H02CGF Supply optional parameter values to H02CEF
M01EDF Rearrange a vector according to given ranks, complex numbers
X04ACF Open unit number for reading, writing or appending, and associate unit with named file
X04ADF Close file associated with given unit number

3 Withdrawn Routines

The following routines have been withdrawn from the NAG Fortran Library at Mark 19. Warning of their withdrawal was included in the Mark 18 Library Manual, together with advice on which routines to use instead. See the document Advice on Replacement Calls for Superseded/Withdrawn Routines for more detailed guidance.

Withdrawn Routine Recommended Replacement
E04FDF E04FYF
E04GCF E04GYF
E04GEF E04GZF
E04HFF E04HYF
E04JAF E04JYF
E04KAF E04KYF
E04KCF E04KZF
E04LAF E04LYF
E04UPF E04UNF
F01MAF F11JAF
F02BBF F02FCF
F02BCF F02ECF
F02BDF F02GCF
F04MAF F11JCF
F04MBF F11GAF, F11GBF and F11GCF (or F11JCF or F11JEF)

4 Routines Scheduled for Withdrawal

The routines listed below are scheduled for withdrawal from the NAG Fortran Library, because improved routines have now been included in the Library. Users are advised to stop using routines which are scheduled for withdrawal immediately and to use recommended replacement routines instead. See the document Advice on Replacement Calls for Superseded/Withdrawn Routines for more detailed guidance, including advice on how to change a call to the old routine into a call to its recommended replacement.

The following routines will be withdrawn at Mark 20.

Routine Scheduled Recommended Replacement
for Withdrawal
E01SEF E01SGF
E01SFF E01SHF

The following routines have been superseded, but will not be withdrawn from the Library until Mark 21 at the earliest.

Superseded routine Recommended Replacement
F11BAF F11BDF
F11BBF F11BEF
F11BCF F11BFF


© The Numerical Algorithms Group Ltd, Oxford UK. 1999