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:
New routines for solving eigenproblems (Chapter F08) are included for:
Two of the new routines are in the statistics chapters (Chapter G01 to Chapter G13). They include facilities (in the stated chapters) for:
A new routine for sorting a vector of complex numbers into the order specified by a vector of ranks is included in Chapter M01.
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 |
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) |
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 |
Superseded routine | Recommended Replacement |
F11BAF | F11BDF |
F11BBF | F11BEF |
F11BCF | F11BFF |