NAG Fortran Library Manual, Mark 21 : News
1 Introduction
At Mark 21 of the NAG Fortran Library new functionality has been introduced in addition to improvements in existing areas.
The Library now contains 1533 user-callable routines, all of which are documented, and 285 are new at this mark.
A new chapter on large scale eigenproblems has 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 statistical calculations, regression,
random numbers, and special functions.
The new Chapter F12 (Large Scale Eigenproblems) 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.
Chapter F07 (Linear Equations (LAPACK)) and Chapter F08 (Least-squares and Eigenvalue Problems (LAPACK)) 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 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 have been added
to Chapter G05 (Random Number Generators).
Variant routines for the log Gamma function, and Bessel function of the 1st kind have been added to Chapter S (Approximations of Special Functions).
The NAG Fortran Library Manual has undergone a fundamental change since Mark 20 and the Essential Introduction is essential reading for all users of the NAG Fortran Library.
2 New Routines
The 285 new user-callable routines included in the Fortran Library at Mark 21 are as follows.
A00ACF | Check availability of a valid licence key |
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 INTEGER argument |
E04NUF | Set a single option for E04NQF from a double precision argument |
E04NXF | Get the setting of an INTEGER valued option of E04NQF |
E04NYF | Get the setting of a double precision valued option of E04NQF |
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 INTEGER argument |
E04VNF | Set a single option for E04VHF from a double precision argument |
E04VRF | Get the setting of an INTEGER valued option of E04VHF |
E04VSF | Get the setting of a double precision valued option of E04VHF |
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 INTEGER argument |
E04WHF | Set a single option for E04WDF from a double precision argument |
E04WJF | Determine whether an E04WDF option has been set or not |
E04WKF | Get the setting of an INTEGER valued option of E04WDF |
E04WLF | Get the setting of a double precision 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 modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal system of linear equations |
F07JDF | Computes the modified Cholesky factorization of a real symmetric positive-definite tridiagonal matrix |
F07JEF | Solves a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF) |
F07JGF | Computes the reciprocal of the condition number of a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (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 modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal system of linear equations |
F07JRF | Computes the modified Cholesky factorization of a complex Hermitian positive-definite tridiagonal matrix |
F07JSF | Solves a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF) |
F07JUF | Computes the reciprocal of the condition number of a complex Hermitian positive-definite tridiagonal system using the modified Cholesky 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 |
F07MBF | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations |
F07MNF | Computes the solution to a complex Hermitian system of linear equations |
F07MPF | Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations |
F07NNF | Computes the solution to a complex symmetric system of linear equations |
F07NPF | Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations |
F07PAF | Computes the solution to a real symmetric system of linear equations, packed storage |
F07PBF | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage |
F07PNF | Computes the solution to a complex Hermitian 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 |
F07QNF | Computes the solution to a complex symmetric 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 |
F08BHF | Reduces a real upper trapezoidal matrix to upper triangular form |
F08BKF | Apply orthogonal transformation determined by F08BHF (DTZRZF) |
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 |
F08BVF | Reduces a complex upper trapezoidal matrix to upper triangular form |
F08BXF | Apply unitary transformation determined by F08BVF (ZTZRZF) |
F08CEF | QL factorization of real general rectangular matrix |
F08CFF | Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF) |
F08CGF | Apply orthogonal transformation determined by F08CEF (DGEQLF) |
F08CHF | RQ factorization of real general rectangular matrix |
F08CJF | Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF) |
F08CKF | Apply orthogonal transformation determined by F08CHF (DGERQF) |
F08CSF | QL factorization of complex general rectangular matrix |
F08CTF | Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF) |
F08CUF | Apply unitary transformation determined by F08CSF (ZGEQLF) |
F08CVF | RQ factorization of complex general rectangular matrix |
F08CWF | Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF) |
F08CXF | Apply unitary transformation determined by F08CVF (ZGERQF) |
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) |
F08FLF | Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix |
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) |
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) |
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) |
F08VAF | Computes the generalized singular value decomposition of a real matrix pair |
F08VEF | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair |
F08VNF | Computes the generalized singular value decomposition of a complex matrix pair |
F08VSF | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair |
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 |
F08YEF | Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
F08YFF | Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
F08YGF | Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces |
F08YHF | Solves the real-valued generalized Sylvester equation |
F08YLF | Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form |
F08YSF | Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
F08YTF | Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
F08YUF | Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces |
F08YVF | Solves the complex generalized Sylvester equation |
F08YYF | Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form |
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 |
F11MDF | Real sparse nonsymmetric linear systems, setup for F11MEF |
F11MEF | LU factorization of real sparse matrix |
F11MFF | Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) |
F11MGF | Estimate condition number of real matrix, matrix already factorized by F11MEF |
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 |
F11MLF | 1-norm, ∞-norm, largest absolute element, real general matrix |
F11MMF | Real sparse nonsymmetric linear systems, diagnostic for F11MEF |
F12AAF | Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem |
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 |
F12ACF | Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real nonsymmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12ADF | Set a single option from a string (F12ABF/F12ACF/F12AGF) |
F12AEF | Provides monitoring information for F12ABF |
F12AFF | Initialization routine for (F12AGF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (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 |
F12ANF | Initialization routine for (F12APF) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem |
F12APF | Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem |
F12AQF | Returns the converged approximations (as determined by F12ABF) to eigenvalues of a complex sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12ARF | Set a single option from a string (F12APF/F12AQF) |
F12ASF | Provides monitoring information for F12APF |
F12FAF | Initialization routine for (F12FBF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem |
F12FBF | Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem |
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 |
F12FDF | Set a single option from a string (F12FBF/F12FCF/F12FGF) |
F12FEF | Provides monitoring information for F12FBF |
F12FFF | Initialization routine for (F12FGF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem |
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 |
G01ETF | Landau distribution function Φ (λ) |
G01EUF | Vavilov distribution function Φ_{V}(λ;κ,β^{2}) |
G01FTF | Landau inverse function Ψ(x) |
G01MTF | Landau density function φ (λ) |
G01MUF | Vavilov density function φ_{V} (λ;κ,β^{2}) |
G01PTF | Landau first moment function Φ_{1}(x) |
G01QTF | Landau second moment function Φ_{2}(x) |
G01RTF | Landau derivative function φ′(λ) |
G01ZUF | Initialization routine for G01MUF and G01EUF |
G02EFF | Stepwise linear regression |
G02JAF | Linear mixed effects regression using Restricted Maximum Likelihood (REML) |
G02JBF | Linear mixed effects regression using Maximum Likelihood (ML) |
G05LXF | Generates a matrix of random numbers from a multivariate Student's t-distribution, seeds and generator passed explicitly |
G05LYF | Generates a matrix of random numbers from a multivariate Normal distribution, seeds and generator passed explicitly |
G05RAF | Generates a matrix of random numbers from a Gaussian Copula, seeds and generator passed explicitly |
G05RBF | Generates a matrix of random numbers from a Student's t-Copula, seeds and generator passed explicitly |
G05YCF | Initializes the Faure generator (G05YDF/G05YJF/G05YKF) |
G05YDF | Generates a sequence of quasi-random numbers using Faure's method |
G05YEF | Initializes the Sobol generator (G05YFF/G05YJF/G05YKF) |
G05YFF | Generates a sequence of quasi-random numbers using Sobol's method |
G05YGF | Initializes the Neiderreiter generator (G05YHF/G05YJF/G05YKF) |
G05YHF | Generates a sequence of quasi-random numbers using Neiderreiter's method |
G05YJF | Generates a Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method |
G05YKF | Generates a log-Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method |
S14AGF | Logarithm of the Gamma function lnΓ(z) |
S18GKF | Bessel function of the 1st kind J_{α±n}(z) |
3 Withdrawn Routines
The following routines have been withdrawn from the NAG Fortran Library at Mark 21. Warning of their withdrawal was included
in the NAG Fortran Library Manual at Mark 20, together with advice on which routines to use instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Routines’ for more detailed guidance.
4 Routines Scheduled for Withdrawal
The routines listed below are scheduled for withdrawal from the 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 Withdrawn/Superseded 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 22.
Routine Scheduled for Withdrawal |
Replacement Routine(s) |
E04UNF | E04USF/E04USA |
F11GAF | F11GDF |
F11GBF | F11GEF |
F11GCF | F11GFF |
G05CAF | G05KAF |
G05CBF | G05KBF |
G05CCF | G05KCF |
G05CFF | F06DFF |
G05CGF | F06DFF |
G05DAF | G05LGF |
G05DBF | G05LJF |
G05DCF | G05LNF |
G05DDF | G05LAF |
G05DEF | G05LKF |
G05DFF | G05LLF |
G05DHF | G05LCF |
G05DJF | G05LBF |
G05DKF | G05LDF |
G05DPF | G05LMF |
G05DRF | G05MEF |
G05DYF | G05MAF |
G05DZF | G05KEF |
G05EAF | G05LZF |
G05EBF | G05MAF |
G05ECF | G05MKF |
G05EDF | G05MJF |
G05EEF | G05MCF |
G05EFF | G05MLF |
G05EGF | G05PAF |
G05EHF | G05NAF |
G05EJF | G05NBF |
G05EWF | G05PAF |
G05EXF | G05MZF |
G05EYF | G05MZF |
G05EZF | G05LZF |
G05FAF | G05LGF |
G05FBF | G05LJF |
G05FDF | G05LAF |
G05FEF | G05LEF |
G05FFF | G05LFF |
G05FSF | G05LPF |
G05GAF | G05QAF |
G05GBF | G05QBF |
G05HDF | G05PCF |
G05ZAF | No replacement document required |
The following routines have been superseded, but will not be withdrawn from the Library until Mark 23 at the earliest.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2006