Tuned and Enhanced Routines in the NAG Library for SMP & Multicore (PDF version)
NAG Library Manual

NAG Library

Tuned and Enhanced Routines in the NAG Library for SMP & Multicore

+ Contents

1  Introduction

Tuned routines are user-callable routines that have been parallelized, or otherwise optimized, in the NAG Library for SMP & Multicore to give improved performance over the equivalent routines in the NAG Fortran Library or in the standard netlib version of LAPACK. Enhanced routines are defined to be those user-callable routines which internally call one or more of the tuned routines, and hence may also exhibit improved performance and scalability. There are a total of 169 tuned routines and a total of 312 enhanced routines within the Library.
The NAG Library for SMP & Multicore is designed to be used in conjunction with the appropriate vendor library on each platform, as it relies upon the vendor library for optimized BLAS and FFT routines. The vendor libraries generally include LAPACK as well, and the vendor may also have parallelized or otherwise optimized some of these LAPACK routines. For each implementation, the performance of the LAPACK routines listed in Section 2 has been investigated, and the best combination of NAG Library for SMP & Multicore and vendor library versions is selected. Thus, in a given implementation, not all of the routines listed in Section 2 will actually be the NAG Library for SMP & Multicore version – consult the Users' Note for your implementation for further information.

2  Tuned LAPACK Routines

There are 77 tuned LAPACK routines within the Library.
Routine
Name

Purpose
F07ADF LU factorization of realm by n matrix
F07AEF Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF)
F07AHF Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07ARF LU factorization of complex m by n matrix
F07ASF Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF)
F07AVF Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07BDF LU factorization of realm 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
F07FDF Cholesky factorization of real symmetric positive-definite matrix
F07FEF Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF)
F07FHF Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
F07FRF Cholesky factorization of complex Hermitian positive-definite matrix
F07FSF Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF)
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
F08AEF QR factorization of real general rectangular matrix
F08AFF Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AGF Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08ASF QR factorization of complex general rectangular matrix
F08ATF Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AUF Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08FEF Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FSF Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08GFF Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GTF Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
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
F08JEF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
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
F08JSF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JXF Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KEF Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KSF Unitary reduction of complex general rectangular matrix to bidiagonal form
F08MEF SVD of real bidiagonal matrix reduced from real general matrix
F08MSF SVD of real bidiagonal matrix reduced from complex general matrix
F08PKF Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
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)

3  Routines Enhanced by Calling Tuned LAPACK Routines

These routines call one or more of the tuned LAPACK routines as part of their core operations and may thereby exhibit improved performance and scalability. There are 239 of these routines within the Library.
Routine
Name

Purpose
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
C05NBF Solution of system of nonlinear equations using function values only (easy-to-use)
C05NCF Solution of system of nonlinear equations using function values only (comprehensive)
C05NDF Solution of system of nonlinear equations using function values only (reverse communication)
C05PBF Solution of system of nonlinear equations using first derivatives (easy-to-use)
C05PCF Solution of system of nonlinear equations using first derivatives (comprehensive)
C05PDF Solution of system of nonlinear equations using first derivatives (reverse communication)
D02HAF Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
D02HBF Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
D02NEF Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D02SAF Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02TKF Ordinary differential equations, general nonlinear boundary value problem, collocation technique
D03NCF Finite difference solution of the Black–Scholes equations
D05BDF Nonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BEF Nonlinear convolution Volterra–Abel equation, first kind, weakly singular
E04FCF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBF Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HEF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04NCF Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04UCF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UFF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04USF Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
F01ABF Inverse of real symmetric positive-definite matrix using iterative refinement
F01ADF Inverse of real symmetric positive-definite matrix
F01ECF Real matrix exponential
F02ECF Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02FJF Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02GCF Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02WDF QR factorization, possibly followed by SVD
F02WGF Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F02WUF SVD of real upper triangular matrix (Black Box)
F02XUF SVD of complex upper triangular matrix (Black Box)
F03ABF Determinant of real symmetric positive-definite matrix (Black Box)
F03AEF LLT factorization and determinant of real symmetric positive-definite matrix
F04ABF Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ASF Solution of real symmetric positive-definite 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
F04BBF Computes the solution and error-bound to a real banded 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
F04JGF Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of mreal equations in n unknowns, mn
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
F07ACF Mixed precision real system solver
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
F07AQF Mixed precision complex system solver
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 modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric 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
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
F08FCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FGF Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FNF Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FUF Apply unitary transformation matrix determined by F08FSF (ZHETRD)
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
F08GCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
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
F08GQF Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
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
F08HCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer)
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
F08HQF Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
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
F08JCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JGF Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
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)
F08JUF Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
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)
F08KFF Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
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)
F08KTF Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
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
F08NFF Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
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
F08NTF Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
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
F08PEF Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
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
F08PSF Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
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
F12FCF Returns the converged approximations (as determined by F12FBF) 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
G02CGF Multiple linear regression, from correlation coefficients, with constant term
G02CHF Multiple linear regression, from correlation-like coefficients, without constant term
G02DAF Fits a general (multiple) linear regression model
G02DDF Estimates of linear parameters and general linear regression model from updated model
G02EAF Computes residual sums of squares for all possible linear regressions for a set of independent variables
G02EEF Fits a linear regression model by forward selection
G02GAF Fits a generalized linear model with Normal errors
G02GBF Fits a generalized linear model with binomial errors
G02GCF Fits a generalized linear model with Poisson errors
G02GDF Fits a generalized linear model with gamma errors
G02HAF Robust regression, standard M-estimates
G02HDF Robust regression, compute regression with user-supplied functions and weights
G02HFF Robust regression, variance-covariance matrix following G02HDF
G02JAF Linear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JBF Linear mixed effects regression using Maximum Likelihood (ML)
G02KAF Ridge regression, optimizing a ridge regression parameter
G02KBF Ridge regression using a number of supplied ridge regression parameters
G02LAF Partial least-squares (PLS) regression using singular value decomposition
G02LCF PLS parameter estimates following partial least-squares regression by G02LAF or G02LBF
G03AAF Performs principal component analysis
G03ACF Performs canonical variate analysis
G03ADF Performs canonical correlation analysis
G03BAF Computes orthogonal rotations for loading matrix, generalized orthomax criterion
G03BCF Computes Procrustes rotations
G03BDF ProMax rotations
G03DAF Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
G03FAF Performs principal coordinate analysis, classical metric scaling
G04BBF Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
G04BCF Analysis of variance, general row and column design, treatment means and standard errors
G05PJF Generates a realization of a multivariate time series from a VARMA model
G08RAF Regression using ranks, uncensored data
G08RBF Regression using ranks, right-censored data
G11CAF Returns parameter estimates for the conditional analysis of stratified data
G11SAF Contingency table, latent variable model for binary data
G12BAF Fits Cox's proportional hazard model
G13AEF Univariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFF Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AJF Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13ASF Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
G13BAF Multivariate time series, filtering (pre-whitening) by an ARIMA model
G13BBF Multivariate time series, filtering by a transfer function model
G13BDF Multivariate time series, preliminary estimation of transfer function model
G13BEF Multivariate time series, estimation of multi-input model
G13BJF Multivariate time series, state set and forecasts from fully specified multi-input model
G13DBF Multivariate time series, multiple squared partial autocorrelations
G13DDF Multivariate time series, estimation of VARMA model
G13DJF Multivariate time series, forecasts and their standard errors
G13DNF Multivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
G13DPF Multivariate time series, partial autoregression matrices
G13DSF Multivariate time series, diagnostic checking of residuals, following G13DDF
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  Tuned NAG-specific Routines

These NAG-specific routines have been parallelized, or otherwise optimized, in the NAG Library for SMP & Multicore compared to the equivalent routine in the NAG Fortran Library. There are 92 of these routines within the Library.
Routine
Name

Purpose
C06FKF Circular convolution or correlation of two real vectors, extra workspace for greater speed
C06FPF Multiple one-dimensional real discrete Fourier transforms
C06FQF Multiple one-dimensional Hermitian discrete Fourier transforms
C06FRF Multiple one-dimensional complex discrete Fourier transforms
C06FUF Two-dimensional complex discrete Fourier transform
C06FXF Three-dimensional complex discrete Fourier transform
C06HAF Discrete sine transform
C06HBF Discrete cosine transform
C06HCF Discrete quarter-wave sine transform
C06HDF Discrete quarter-wave cosine transform
C06PAF Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
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 storage format for Hermitian sequences
C06PQF Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex storage format for Hermitian sequences
C06PRF Multiple one-dimensional complex discrete Fourier transforms using complex data type
C06PSF Multiple one-dimensional complex discrete Fourier transforms using complex data type and sequences stored as columns
C06PUF Two-dimensional complex discrete Fourier transform, complex data type
C06PXF Three-dimensional complex discrete Fourier transform, Complex data type
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)
D01DAF Two-dimensional quadrature, finite region
D01FCF Multi-dimensional adaptive quadrature over hyper-rectangle
D01GAF One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D03RAF General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RBF General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
E01SGF Interpolating functions, modified Shepard's method, two variables
E01SHF Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
E01TGF Interpolating functions, modified Shepard's method, three variables
E01THF Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables
E02CAF Least-squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
E02CBF Evaluation of fitted polynomial in two variables
E02DFF Evaluation of fitted bicubic spline at a mesh of points
F01CTF Sum or difference of two real matrices, optional scaling and transposition
F01CWF Sum or difference of two complex matrices, optional scaling and transposition
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)
F05AAF Gram–Schmidt orthogonalisation of n vectors of order m
F11BEF Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BSF Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11GEF Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos
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
F11XAF Real sparse nonsymmetric matrix vector multiply
F11XEF Real sparse symmetric matrix vector multiply
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
G02AAF Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
G02BAF Pearson product-moment correlation coefficients, all variables, no missing values
G02BDF Correlation-like coefficients (about zero), all variables, no missing values
G02BNF Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BPF Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQF Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BRF Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G03CAF Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03EAF Computes distance matrix
G03ECF Hierarchical cluster analysis
G05RCF Generates a matrix of pseudorandom numbers from a Student's t-copula
G05RDF Generates a matrix of pseudorandom numbers from a Gaussian copula
G05YJF Generates a Normal quasi-random number sequence
G05YKF Generates a log-normal quasi-random number sequence
G05YMF Generates a uniform quasi-random number sequence
G13EAF Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EBF Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
M01CAF Sort a vector, real numbers
M01CBF Sort a vector, integer numbers
M01CCF Sort a vector, character data
S30AAF Black–Scholes–Merton option pricing formula
S30ABF Black–Scholes–Merton option pricing formula with Greeks
S30BAF Floating-strike lookback option pricing formula
S30BBF Floating-strike lookback option pricing formula with Greeks
S30CAF Binary option: cash-or-nothing pricing formula
S30CBF Binary option: cash-or-nothing pricing formula with Greeks
S30CCF Binary option: asset-or-nothing pricing formula
S30CDF Binary option: asset-or-nothing pricing formula with Greeks
S30FAF Standard barrier option pricing formula
S30JAF Jump-diffusion, Merton's model, option pricing formula
S30JBF Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NAF Heston's model option pricing formula
S30QCF American option: Bjerksund and Stensland pricing formula
S30SAF Asian option: geometric continuous average rate pricing formula
S30SBF Asian option: geometric continuous average rate pricing formula with Greeks

5  Routines Enhanced by Calling Tuned NAG-specific Routines

These routines call one or more of the tuned NAG-specific routines as part of their core operations and may thereby exhibit improved performance and scalability. There are 128 of these routines within the Library.
Routine
Name

Purpose
D01PAF Multi-dimensional quadrature over an n-simplex
D02AGF Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02EJF Ordinary differential equations, stiff initial value problem, backward diffential formulae method, until function of solution is zero, intermediate output (simple driver)
D02NBF Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NCF Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NDF Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NGF Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NHF Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NJF Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NMF Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NNF Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D03FAF Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates
D03PCF General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PDF General system of parabolic PDEs, method of lines, Chebyshev C0 collocation, one space variable
D03PEF General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
D03PFF General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
D03PHF General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJF General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0 collocation, one space variable
D03PKF General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
D03PLF General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
D03PPF General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PRF General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
D03PSF General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, remeshing, one space variable
D05AAF Linear non-singular Fredholm integral equation, second kind, split kernel
D05ABF Linear non-singular Fredholm integral equation, second kind, smooth kernel
D06CBF Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CCF Renumbers a given mesh using Gibbs method
E02RAF Padé approximants
E04FCF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBF Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HEF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYF Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04NCF Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04UCF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UFF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
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)
E05JBF Global optimization by multi-level coordinate search, simple bounds, using function values only
F01ABF Inverse of real symmetric positive-definite matrix using iterative refinement
F02FJF Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02WDF QR factorization, possibly followed by SVD
F02WUF SVD of real upper triangular matrix (Black Box)
F02XUF SVD of complex upper triangular matrix (Black Box)
F03AAF Determinant of real matrix (Black Box)
F03ADF Determinant of complex matrix (Black Box)
F03AFF LU factorization and determinant of real matrix
F04ABF Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04AEF Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ASF Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04ATF Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04JGF Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of mreal equations in n unknowns, mn
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)
F11MDF Real sparse nonsymmetric linear systems, setup for F11MEF
G01AGF Lineprinter scatterplot of two variables
G01AHF Lineprinter scatterplot of one variable against Normal scores
G01ARF Constructs a stem and leaf plot
G01EMF Computes probability for the Studentized range statistic
G01HBF Computes probabilities for the multivariate Normal distribution
G01JDF Computes lower tail probability for a linear combination of (central) χ2 variables
G02CGF Multiple linear regression, from correlation coefficients, with constant term
G02CHF Multiple linear regression, from correlation-like coefficients, without constant term
G02DAF Fits a general (multiple) linear regression model
G02DDF Estimates of linear parameters and general linear regression model from updated model
G02DEF Add a new independent variable to a general linear regression model
G02DGF Fits a general linear regression model to new dependent variable
G02DKF Estimates and standard errors of parameters of a general linear regression model for given constraints
G02EEF Fits a linear regression model by forward selection
G02GAF Fits a generalized linear model with Normal errors
G02GBF Fits a generalized linear model with binomial errors
G02GCF Fits a generalized linear model with Poisson errors
G02GDF Fits a generalized linear model with gamma errors
G02GKF Estimates and standard errors of parameters of a general linear model for given constraints
G02HAF Robust regression, standard M-estimates
G02HDF Robust regression, compute regression with user-supplied functions and weights
G02HFF Robust regression, variance-covariance matrix following G02HDF
G02HKF Calculates a robust estimation of a correlation matrix, Huber's weight function
G02JAF Linear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JBF Linear mixed effects regression using Maximum Likelihood (ML)
G02KAF Ridge regression, optimizing a ridge regression parameter
G02KBF Ridge regression using a number of supplied ridge regression parameters
G03ACF Performs canonical variate analysis
G03ADF Performs canonical correlation analysis
G04EAF Computes orthogonal polynomials or dummy variables for factor/classification variable
G05PJF Generates a realization of a multivariate time series from a VARMA model
G05PYF Generates a random correlation matrix
G07BEF Computes maximum likelihood estimates for parameters of the Weibull distribution
G07DAF Robust estimation, median, median absolute deviation, robust standard deviation
G07DBF Robust estimation, M-estimates for location and scale parameters, standard weight functions
G07DCF Robust estimation, M-estimates for location and scale parameters, user-defined weight functions
G07DDF Computes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EAF Robust confidence intervals, one-sample
G07EBF Robust confidence intervals, two-sample
G08AGF Performs the Wilcoxon one-sample (matched pairs) signed rank test
G08AKF Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
G08CBF Performs the one-sample Kolmogorov–Smirnov test for standard distributions
G08CCF Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CDF Performs the two-sample Kolmogorov–Smirnov test
G08RAF Regression using ranks, uncensored data
G08RBF Regression using ranks, right-censored data
G11BBF Computes multiway table from set of classification factors using given percentile/quantile
G11BCF Computes marginal tables for multiway table computed by G11BAF or G11BBF
G11SAF Contingency table, latent variable model for binary data
G13ADF Univariate time series, preliminary estimation, seasonal ARIMA model
G13AEF Univariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFF Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AJF Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13BEF Multivariate time series, estimation of multi-input model
G13BJF Multivariate time series, state set and forecasts from fully specified multi-input model
G13DBF Multivariate time series, multiple squared partial autocorrelations
G13DDF Multivariate time series, estimation of VARMA model
G13DNF Multivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
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

Tuned and Enhanced Routines in the NAG Library for SMP & Multicore (PDF version)
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009