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
    2  Tuned LAPACK Routines
    3  Routines Enhanced by Calling Tuned LAPACK Routines
    4  Tuned NAG-specific Routines
    5  Routines Enhanced by Calling Tuned NAG-specific Routines

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 204 tuned routines and a total of 337 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
F07ADFLU factorization of real m by n matrix
F07AEFSolution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF)
F07AHFRefined solution with error bounds of real system of linear equations, multiple right-hand sides
F07ARFLU factorization of complex m by n matrix
F07ASFSolution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF)
F07AVFRefined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07BDFLU factorization of real m by n band matrix
F07BEFSolution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF)
F07BHFRefined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BRFLU factorization of complex m by n band matrix
F07BSFSolution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF)
F07BVFRefined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07CHFRefined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
F07CVFRefined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
F07FDFCholesky factorization of real symmetric positive definite matrix
F07FEFSolution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF)
F07FHFRefined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
F07FRFCholesky factorization of complex Hermitian positive definite matrix
F07FSFSolution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF)
F07FVFRefined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
F07GEFSolution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GHFRefined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
F07GSFSolution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GVFRefined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
F07HEFSolution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (DPBTRF)
F07HHFRefined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
F07HSFSolution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (ZPBTRF)
F07HVFRefined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
F07JHFRefined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
F07JVFRefined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
F07MHFRefined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MVFRefined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07NVFRefined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07PHFRefined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PVFRefined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07QVFRefined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07THFError bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TVFError bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07UEFSolution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UHFError bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07USFSolution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UVFError bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07VEFSolution of real band triangular system of linear equations, multiple right-hand sides
F07VHFError bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VSFSolution of complex band triangular system of linear equations, multiple right-hand sides
F07VVFError bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
F08AEFQR factorization of real general rectangular matrix
F08AFFForm all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08AGFApply orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08ASFQR factorization of complex general rectangular matrix
F08ATFForm all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08AUFApply unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08FEFOrthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFFGenerate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FSFUnitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTFGenerate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08GFFGenerate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GTFGenerate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08HEFOrthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HSFUnitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JEFAll eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
F08JJFSelected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKFSelected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JSFAll eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JXFSelected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KEFOrthogonal reduction of real general rectangular matrix to bidiagonal form
F08KSFUnitary reduction of complex general rectangular matrix to bidiagonal form
F08MEFSVD of real bidiagonal matrix reduced from real general matrix
F08MSFSVD of real bidiagonal matrix reduced from complex general matrix
F08PKFSelected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PXFSelected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08TAFComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TBFComputes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TCFComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TNFComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TPFComputes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQFComputes 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 254 of these routines within the Library.
Routine
Name
Purpose
C02AKFAll zeros of real cubic equation
C02ALFAll zeros of real quartic equation
C02AMFAll zeros of complex cubic equation
C02ANFAll zeros of complex quartic equation
C05QBFSolution of a system of nonlinear equations using function values only (easy-to-use)
C05QCFSolution of a system of nonlinear equations using function values only (comprehensive)
C05QDFSolution of a system of nonlinear equations using function values only (reverse communication)
C05RBFSolution of a system of nonlinear equations using first derivatives (easy-to-use)
C05RCFSolution of a system of nonlinear equations using first derivatives (comprehensive)
C05RDFSolution of a system of nonlinear equations using first derivatives (reverse communication)
D02AGFOrdinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02HAFOrdinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
D02HBFOrdinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
D02NEFImplicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D02SAFOrdinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02TKFOrdinary differential equations, general nonlinear boundary value problem, collocation technique
D02UEFSolve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
D03NCFFinite difference solution of the Black–Scholes equations
D05BDFNonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BEFNonlinear convolution Volterra–Abel equation, first kind, weakly singular
E04FCFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBFUnconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HEFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04NCFConvex QP problem or linearly-constrained linear least squares problem (dense)
E04UCFMinimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UFFMinimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04USFMinimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
F01ABFInverse of real symmetric positive definite matrix using iterative refinement
F01ADFInverse of real symmetric positive definite matrix
F01ECFReal matrix exponential
F01EDFReal symmetric matrix exponential
F01EFFFunction of a real symmetric matrix
F01FCFComplex matrix exponential
F01FDFComplex Hermitian matrix exponential
F01FFFFunction of a complex Hermitian matrix
F02ECFSelected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02FJFSelected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02GCFSelected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02WDFQR factorization, possibly followed by SVD
F02WGFComputes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F02WUFSVD of real upper triangular matrix (Black Box)
F02XUFSVD of complex upper triangular matrix (Black Box)
F04ABFSolution of real symmetric positive definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ASFSolution of real symmetric positive definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04BAFComputes the solution and error-bound to a real system of linear equations
F04BBFComputes the solution and error-bound to a real banded system of linear equations
F04BDFComputes the solution and error-bound to a real symmetric positive definite system of linear equations
F04BEFComputes the solution and error-bound to a real symmetric positive definite system of linear equations, packed storage
F04BFFComputes the solution and error-bound to a real symmetric positive definite banded system of linear equations
F04CAFComputes the solution and error-bound to a complex system of linear equations
F04CBFComputes the solution and error-bound to a complex banded system of linear equations
F04CDFComputes the solution and error-bound to a complex Hermitian positive definite system of linear equations
F04CEFComputes the solution and error-bound to a complex Hermitian positive definite system of linear equations, packed storage
F04CFFComputes the solution and error-bound to a complex Hermitian positive definite banded system of linear equations
F04JGFLeast squares (if rank =n) or minimal least squares (if rank <n) solution of m real equations in n unknowns, m≥n
F07AAFComputes the solution to a real system of linear equations
F07ABFUses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
F07ACFMixed precision real system solver
F07ANFComputes the solution to a complex system of linear equations
F07APFUses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
F07AQFMixed precision complex system solver
F07BAFComputes the solution to a real banded system of linear equations
F07BBFUses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
F07BNFComputes the solution to a complex banded system of linear equations
F07BPFUses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
F07CBFUses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
F07CPFUses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
F07FAFComputes the solution to a real symmetric positive definite system of linear equations
F07FBFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
F07FCFUses the Cholesky factorization to compute the solution for a real symmetric positive definite system of linear equations
F07FNFComputes the solution to a complex Hermitian positive definite system of linear equations
F07FPFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
F07FQFUses the Cholesky factorization to compute the solution for a complex Hermitian positive definite system of linear equations
F07GAFComputes the solution to a real symmetric positive definite system of linear equations, packed storage
F07GBFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
F07GNFComputes the solution to a complex Hermitian positive definite system of linear equations, packed storage
F07GPFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
F07HAFComputes the solution to a real symmetric positive definite banded system of linear equations
F07HBFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
F07HNFComputes the solution to a complex Hermitian positive definite banded system of linear equations
F07HPFUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
F07JBFUses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
F07JPFUses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
F07MBFUses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
F07MPFUses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
F07NPFUses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
F07PBFUses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage
F07PPFUses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage
F07QPFUses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage
F07WDFCholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
F07WRFCholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
F08AAFSolves an overdetermined or underdetermined real linear system
F08ANFSolves an overdetermined or underdetermined complex linear system
F08BAFComputes the minimum-norm solution to a real linear least squares problem
F08BFFQR factorization of real general rectangular matrix with column pivoting, using BLAS-3
F08BNFComputes the minimum-norm solution to a complex linear least squares problem
F08BTFQR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
F08FAFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCFComputes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FGFApply orthogonal transformation determined by F08FEF (DSYTRD)
F08FNFComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPFComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQFComputes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRFComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FUFApply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCFComputes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
F08GNFComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPFComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQFComputes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
F08HAFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCFComputes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer)
F08HNFComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPFComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQFComputes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08JAFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCFComputes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDFComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JGFComputes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
F08JHFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JLFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JUFComputes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
F08JVFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JYFComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KAFComputes the minimum-norm solution to a real linear least squares problem using singular value decomposition
F08KBFComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCFComputes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
F08KDFComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KFFGenerate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGFApply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KHFComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
F08KNFComputes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
F08KPFComputes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQFComputes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
F08KRFComputes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KTFGenerate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUFApply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08MDFComputes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08NAFComputes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBFComputes 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
F08NFFGenerate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGFApply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NNFComputes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPFComputes 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
F08NTFGenerate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUFApply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08PAFComputes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBFComputes 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
F08PEFComputes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PNFComputes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPFComputes 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
F08PSFComputes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08SAFComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBFComputes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCFComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SNFComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPFComputes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQFComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08UAFComputes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UBFComputes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UCFComputes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UNFComputes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UPFComputes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQFComputes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08WAFComputes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WBFComputes, 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
F08WNFComputes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WPFComputes, 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
F08XAFComputes, 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
F08XBFComputes, 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
F08XNFComputes, 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
F08XPFComputes, 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
F08ZAFSolves the real linear equality-constrained least squares (LSE) problem
F08ZBFSolves a real general Gauss–Markov linear model (GLM) problem
F08ZEFComputes a generalized QR factorization of a real matrix pair
F08ZFFComputes a generalized RQ factorization of a real matrix pair
F08ZNFSolves the complex linear equality-constrained least squares (LSE) problem
F08ZPFSolves a complex general Gauss–Markov linear model (GLM) problem
F08ZSFComputes a generalized QR factorization of a complex matrix pair
F08ZTFComputes a generalized RQ factorization of a complex matrix pair
F12FCFSelected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FBF
F12FGFSelected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
G01HBFComputes probabilities for the multivariate Normal distribution
G02ABFComputes the nearest correlation matrix to a real square matrix, augmented G02AAF to incorporate weights and bounds
G02AEFComputes the nearest correlation matrix with k-factor structure to a real square matrix
G02BYFComputes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF
G02CGFMultiple linear regression, from correlation coefficients, with constant term
G02CHFMultiple linear regression, from correlation-like coefficients, without constant term
G02DAFFits a general (multiple) linear regression model
G02DDFEstimates of linear parameters and general linear regression model from updated model
G02EAFComputes residual sums of squares for all possible linear regressions for a set of independent variables
G02EEFFits a linear regression model by forward selection
G02GAFFits a generalized linear model with Normal errors
G02GBFFits a generalized linear model with binomial errors
G02GCFFits a generalized linear model with Poisson errors
G02GDFFits a generalized linear model with gamma errors
G02HAFRobust regression, standard M-estimates
G02HDFRobust regression, compute regression with user-supplied functions and weights
G02HFFRobust regression, variance-covariance matrix following G02HDF
G02JAFLinear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JBFLinear mixed effects regression using Maximum Likelihood (ML)
G02KAFRidge regression, optimizing a ridge regression parameter
G02KBFRidge regression using a number of supplied ridge regression parameters
G02LAFPartial least squares (PLS) regression using singular value decomposition
G02LCFPLS parameter estimates following partial least squares regression by G02LAF or G02LBF
G02QFFQuantile linear regression, simple interface, independent, identically distributed (IID) errors
G02QGFQuantile linear regression, comprehensive interface
G03AAFPerforms principal component analysis
G03ACFPerforms canonical variate analysis
G03ADFPerforms canonical correlation analysis
G03BAFComputes orthogonal rotations for loading matrix, generalized orthomax criterion
G03BCFComputes Procrustes rotations
G03BDFProMax rotations
G03DAFComputes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
G03FAFPerforms principal coordinate analysis, classical metric scaling
G04BBFAnalysis of variance, randomized block or completely randomized design, treatment means and standard errors
G04BCFAnalysis of variance, general row and column design, treatment means and standard errors
G05PJFGenerates a realization of a multivariate time series from a VARMA model
G08RAFRegression using ranks, uncensored data
G08RBFRegression using ranks, right-censored data
G11CAFReturns parameter estimates for the conditional analysis of stratified data
G11SAFContingency table, latent variable model for binary data
G12ABFComputes rank statistics for comparing survival curves
G12BAFFits Cox's proportional hazard model
G13AEFUnivariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFFUnivariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AJFUnivariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13ASFUnivariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
G13BAFMultivariate time series, filtering (pre-whitening) by an ARIMA model
G13BBFMultivariate time series, filtering by a transfer function model
G13BDFMultivariate time series, preliminary estimation of transfer function model
G13BEFMultivariate time series, estimation of multi-input model
G13BJFMultivariate time series, state set and forecasts from fully specified multi-input model
G13DBFMultivariate time series, multiple squared partial autocorrelations
G13DDFMultivariate time series, estimation of VARMA model
G13DJFMultivariate time series, forecasts and their standard errors
G13DNFMultivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
G13DPFMultivariate time series, partial autoregression matrices
G13DSFMultivariate time series, diagnostic checking of residuals, following G13DDF
G13DXFCalculates the zeros of a vector autoregressive (or moving average) operator
G13FAFUnivariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form εt-1+γ2
G13FCFUnivariate time series, parameter estimation for a GARCH process with asymmetry of the form εt-1+γεt-12
G13FEFUnivariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FGFUnivariate 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 127 of these routines within the Library.
Routine
Name
Purpose
C06FKFCircular convolution or correlation of two real vectors, extra workspace for greater speed
C06FPFMultiple one-dimensional real discrete Fourier transforms
C06FQFMultiple one-dimensional Hermitian discrete Fourier transforms
C06FRFMultiple one-dimensional complex discrete Fourier transforms
C06FUFTwo-dimensional complex discrete Fourier transform
C06FXFThree-dimensional complex discrete Fourier transform
C06HAFDiscrete sine transform
C06HBFDiscrete cosine transform
C06HCFDiscrete quarter-wave sine transform
C06HDFDiscrete quarter-wave cosine transform
C06PAFSingle one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
C06PFFOne-dimensional complex discrete Fourier transform of multidimensional data (using complex data type)
C06PJFMultidimensional complex discrete Fourier transform of multidimensional data (using complex data type)
C06PKFCircular convolution or correlation of two complex vectors
C06PPFMultiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
C06PQFMultiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
C06PRFMultiple one-dimensional complex discrete Fourier transforms using complex data type
C06PSFMultiple one-dimensional complex discrete Fourier transforms using complex data type and sequences stored as columns
C06PUFTwo-dimensional complex discrete Fourier transform, complex data type
C06PXFThree-dimensional complex discrete Fourier transform, complex data type
C06RAFDiscrete sine transform (easy-to-use)
C06RBFDiscrete cosine transform (easy-to-use)
C06RCFDiscrete quarter-wave sine transform (easy-to-use)
C06RDFDiscrete quarter-wave cosine transform (easy-to-use)
C09EAFTwo-dimensional discrete wavelet transform
C09EBFTwo-dimensional inverse discrete wavelet transform
C09ECFTwo-dimensional multi-level discrete wavelet transform
C09EDFTwo-dimensional inverse multi-level discrete wavelet transform
D01DAFTwo-dimensional quadrature, finite region
D01FCFMultidimensional adaptive quadrature over hyper-rectangle
D01GAFOne-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D03FAFElliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates
D03RAFGeneral system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RBFGeneral system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
E01SGFInterpolating functions, modified Shepard's method, two variables
E01SHFInterpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
E01TGFInterpolating functions, modified Shepard's method, three variables
E01THFInterpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables
E01TKFInterpolating functions, modified Shepard's method, four variables
E01TLFInterpolated values, evaluate interpolant computed by E01TKF, function and first derivatives, four variables
E01TMFInterpolating functions, modified Shepard's method, five variables
E01TNFInterpolated values, evaluate interpolant computed by E01TMF, function and first derivatives, five variables
E02CAFLeast squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
E02CBFEvaluation of fitted polynomial in two variables
E02DFFEvaluation of fitted bicubic spline at a mesh of points
E05SAFGlobal optimization using particle swarm algorithm (PSO), bound constraints only
E05SBFGlobal optimization using particle swarm algorithm (PSO), comprehensive
F01CTFSum or difference of two real matrices, optional scaling and transposition
F01CWFSum or difference of two complex matrices, optional scaling and transposition
F05AAFGram–Schmidt orthogonalisation of n vectors of order m
F11BEFReal sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BSFComplex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11GEFReal sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
F11GSFComplex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
F11MEFLU factorization of real sparse matrix
F11MFFSolution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F11MHFRefined solution with error bounds of real system of linear equations, multiple right-hand sides
F11MKFReal sparse nonsymmetric matrix-matrix multiply, compressed column storage
F11XAFReal sparse nonsymmetric matrix vector multiply
F11XEFReal sparse symmetric matrix vector multiply
F11XNFComplex sparse non-Hermitian matrix vector multiply
F11XSFComplex sparse Hermitian matrix vector multiply
F12ABFSelected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
F12AGFSelected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
F12APFSelected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
F12FBFSelected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
G02AAFComputes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
G02BAFPearson product-moment correlation coefficients, all variables, no missing values
G02BDFCorrelation-like coefficients (about zero), all variables, no missing values
G02BNFKendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BPFKendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQFKendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BRFKendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G02JDFHierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
G02JEFHierarchical mixed effects regression using Maximum Likelihood (ML)
G03CAFComputes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03EAFComputes distance matrix
G03ECFHierarchical cluster analysis
G05RCFGenerates a matrix of pseudorandom numbers from a Student's t-copula
G05RDFGenerates a matrix of pseudorandom numbers from a Gaussian copula
G05REFGenerates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
G05RFFGenerates a matrix of pseudorandom numbers from a bivariate Frank copula
G05RGFGenerates a matrix of pseudorandom numbers from a bivariate Plackett copula
G05RHFGenerates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
G05RJFGenerates a matrix of pseudorandom numbers from a multivariate Frank copula
G05RKFGenerates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
G05RYFGenerates a matrix of pseudorandom numbers from a multivariate Student's t-distribution
G05SAFGenerates a vector of pseudorandom numbers from a uniform distribution over 0,1
G05SBFGenerates a vector of pseudorandom numbers from a beta distribution
G05SCFGenerates a vector of pseudorandom numbers from a Cauchy distribution
G05SDFGenerates a vector of pseudorandom numbers from a χ2 distribution
G05SEFGenerates a vector of pseudorandom numbers from a Dirichlet distribution
G05SFFGenerates a vector of pseudorandom numbers from an exponential distribution
G05SGFGenerates a vector of pseudorandom numbers from an exponential mix distribution
G05SHFGenerates a vector of pseudorandom numbers from an F-distribution
G05SJFGenerates a vector of pseudorandom numbers from a gamma distribution
G05SKFGenerates a vector of pseudorandom numbers from a Normal distribution
G05SLFGenerates a vector of pseudorandom numbers from a logistic distribution
G05SMFGenerates a vector of pseudorandom numbers from a log-normal distribution
G05SNFGenerates a vector of pseudorandom numbers from a Student's t-distribution
G05SPFGenerates a vector of pseudorandom numbers from a triangular distribution
G05SQFGenerates a vector of pseudorandom numbers from a uniform distribution over a,b
G05SRFGenerates a vector of pseudorandom numbers from a von Mises distribution
G05SSFGenerates a vector of pseudorandom numbers from a Weibull distribution
G05YJFGenerates a Normal quasi-random number sequence
G05YKFGenerates a log-normal quasi-random number sequence
G05YMFGenerates a uniform quasi-random number sequence
G13EAFCombined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EBFCombined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
M01CAFSort a vector, real numbers
M01CBFSort a vector, integer numbers
M01CCFSort a vector, character data
S30AAFBlack–Scholes–Merton option pricing formula
S30ABFBlack–Scholes–Merton option pricing formula with Greeks
S30BAFFloating-strike lookback option pricing formula
S30BBFFloating-strike lookback option pricing formula with Greeks
S30CAFBinary option: cash-or-nothing pricing formula
S30CBFBinary option: cash-or-nothing pricing formula with Greeks
S30CCFBinary option: asset-or-nothing pricing formula
S30CDFBinary option: asset-or-nothing pricing formula with Greeks
S30FAFStandard barrier option pricing formula
S30JAFJump-diffusion, Merton's model, option pricing formula
S30JBFJump-diffusion, Merton's model, option pricing formula with Greeks
S30NAFHeston's model option pricing formula
S30QCFAmerican option: Bjerksund and Stensland pricing formula
S30SAFAsian option: geometric continuous average rate pricing formula
S30SBFAsian 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 143 of these routines within the Library.
Routine
Name
Purpose
C05QSFSolution of a sparse system of nonlinear equations using function values only (easy-to-use)
D01GBFMultidimensional quadrature over hyper-rectangle, Monte–Carlo method
D01GCFMultidimensional quadrature, general product region, number-theoretic method
D01GDFMultidimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
D01PAFMultidimensional quadrature over an n-simplex
D02EJFOrdinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
D02NBFExplicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NCFExplicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NDFExplicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NGFImplicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NHFImplicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NJFImplicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NMFExplicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NNFImplicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02UAFCoefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
D02UBFFunction or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
D03PCFGeneral system of parabolic PDEs, method of lines, finite differences, one space variable
D03PDFGeneral system of parabolic PDEs, method of lines, Chebyshev C0 collocation, one space variable
D03PEFGeneral system of first-order PDEs, method of lines, Keller box discretization, one space variable
D03PFFGeneral 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
D03PHFGeneral system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJFGeneral system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0 collocation, one space variable
D03PKFGeneral system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
D03PLFGeneral 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
D03PPFGeneral system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PRFGeneral system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
D03PSFGeneral system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
D05AAFLinear non-singular Fredholm integral equation, second kind, split kernel
D05ABFLinear non-singular Fredholm integral equation, second kind, smooth kernel
D06CBFGenerates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CCFRenumbers a given mesh using Gibbs method
E02RAFPadé approximants
E04FCFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBFUnconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HEFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYFUnconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04NCFConvex QP problem or linearly-constrained linear least squares problem (dense)
E04UCFMinimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UFFMinimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UGFNLP problem (sparse)
E04USFMinimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
E04YCFCovariance matrix for nonlinear least squares problem (unconstrained)
F01ABFInverse of real symmetric positive definite matrix using iterative refinement
F02FJFSelected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02WDFQR factorization, possibly followed by SVD
F02WGFComputes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F02WUFSVD of real upper triangular matrix (Black Box)
F02XUFSVD of complex upper triangular matrix (Black Box)
F04ABFSolution of real symmetric positive definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04AEFSolution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ASFSolution of real symmetric positive definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04ATFSolution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04JGFLeast squares (if rank =n) or minimal least squares (if rank <n) solution of m real equations in n unknowns, m≥n
F11DCFSolution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
F11DEFSolution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
F11DKFReal sparse nonsymmetric linear systems, line Jacobi preconditioner
F11DQFSolution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
F11DSFSolution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
F11DXFComplex sparse nonsymmetric linear systems, line Jacobi preconditioner
F11JCFSolution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
F11JEFSolution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11JQFSolution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
F11JSFSolution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11MDFReal sparse nonsymmetric linear systems, setup for F11MEF
F12FGFSelected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
G01AGFLineprinter scatterplot of two variables
G01AHFLineprinter scatterplot of one variable against Normal scores
G01ANFCalculates approximate quantiles from a data stream of known size
G01APFCalculates approximate quantiles from a data stream of unknown size
G01ARFConstructs a stem and leaf plot
G01EMFComputes probability for the Studentized range statistic
G01HBFComputes probabilities for the multivariate Normal distribution
G01JDFComputes lower tail probability for a linear combination of (central) χ2 variables
G02ABFComputes the nearest correlation matrix to a real square matrix, augmented G02AAF to incorporate weights and bounds
G02AEFComputes the nearest correlation matrix with k-factor structure to a real square matrix
G02CGFMultiple linear regression, from correlation coefficients, with constant term
G02CHFMultiple linear regression, from correlation-like coefficients, without constant term
G02DAFFits a general (multiple) linear regression model
G02DDFEstimates of linear parameters and general linear regression model from updated model
G02DEFAdd a new independent variable to a general linear regression model
G02DGFFits a general linear regression model to new dependent variable
G02DKFEstimates and standard errors of parameters of a general linear regression model for given constraints
G02EEFFits a linear regression model by forward selection
G02GAFFits a generalized linear model with Normal errors
G02GBFFits a generalized linear model with binomial errors
G02GCFFits a generalized linear model with Poisson errors
G02GDFFits a generalized linear model with gamma errors
G02GKFEstimates and standard errors of parameters of a general linear model for given constraints
G02HAFRobust regression, standard M-estimates
G02HDFRobust regression, compute regression with user-supplied functions and weights
G02HFFRobust regression, variance-covariance matrix following G02HDF
G02HKFCalculates a robust estimation of a correlation matrix, Huber's weight function
G02JAFLinear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JBFLinear mixed effects regression using Maximum Likelihood (ML)
G02KAFRidge regression, optimizing a ridge regression parameter
G02KBFRidge regression using a number of supplied ridge regression parameters
G03ACFPerforms canonical variate analysis
G03ADFPerforms canonical correlation analysis
G04EAFComputes orthogonal polynomials or dummy variables for factor/classification variable
G05PDFGenerates a realization of a time series from a GARCH process with asymmetry of the form εt-1+γ2
G05PEFGenerates a realization of a time series from a GARCH process with asymmetry of the form εt-1+γ εt-12
G05PFFGenerates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05PGFGenerates a realization of a time series from an exponential GARCH (EGARCH) process
G05PJFGenerates a realization of a multivariate time series from a VARMA model
G05PYFGenerates a random correlation matrix
G05RZFGenerates a matrix of pseudorandom numbers from a multivariate Normal distribution
G07BEFComputes maximum likelihood estimates for parameters of the Weibull distribution
G07BFFEstimates parameter values of the generalized Pareto distribution
G07DAFRobust estimation, median, median absolute deviation, robust standard deviation
G07DBFRobust estimation, M-estimates for location and scale parameters, standard weight functions
G07DCFRobust estimation, M-estimates for location and scale parameters, user-defined weight functions
G07DDFComputes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EAFRobust confidence intervals, one-sample
G07EBFRobust confidence intervals, two-sample
G08AGFPerforms the Wilcoxon one-sample (matched pairs) signed rank test
G08AKFComputes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
G08CBFPerforms the one-sample Kolmogorov–Smirnov test for standard distributions
G08CCFPerforms the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CDFPerforms the two-sample Kolmogorov–Smirnov test
G08RAFRegression using ranks, uncensored data
G08RBFRegression using ranks, right-censored data
G11BBFComputes multiway table from set of classification factors using given percentile/quantile
G11BCFComputes marginal tables for multiway table computed by G11BAF or G11BBF
G11SAFContingency table, latent variable model for binary data
G12ABFComputes rank statistics for comparing survival curves
G13ADFUnivariate time series, preliminary estimation, seasonal ARIMA model
G13AEFUnivariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFFUnivariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AJFUnivariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13BCFMultivariate time series, cross-correlations
G13BEFMultivariate time series, estimation of multi-input model
G13BJFMultivariate time series, state set and forecasts from fully specified multi-input model
G13DBFMultivariate time series, multiple squared partial autocorrelations
G13DDFMultivariate time series, estimation of VARMA model
G13DNFMultivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
G13FAFUnivariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form εt-1+γ2
G13FCFUnivariate time series, parameter estimation for a GARCH process with asymmetry of the form εt-1+γεt-12
G13FEFUnivariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FGFUnivariate 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. 2012