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

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 226 tuned routines and a total of 361 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.

There are 77 tuned LAPACK routines within the Library.

RoutineName |
Purpose |

F07ADF | $LU$ factorization of real $m$ 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 real $m$ 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), F08BEF (DGEQPF) or F08BFF (DGEQP3) |

F08AGF | Apply orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3) |

F08ASF | $QR$ factorization of complex general rectangular matrix |

F08ATF | Form all or part of unitary $Q$ from $QR$ factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) |

F08AUF | Apply unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) |

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) |

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 266 of these routines within the Library.

RoutineName |
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 |

C05QBF | Solution of a system of nonlinear equations using function values only (easy-to-use) |

C05QCF | Solution of a system of nonlinear equations using function values only (comprehensive) |

C05QDF | Solution of a system of nonlinear equations using function values only (reverse communication) |

C05RBF | Solution of a system of nonlinear equations using first derivatives (easy-to-use) |

C05RCF | Solution of a system of nonlinear equations using first derivatives (comprehensive) |

C05RDF | Solution of a system of nonlinear equations using first derivatives (reverse communication) |

D02AGF | Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined |

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 |

D02UEF | Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation |

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 |

E02JDF | Spline approximation to a set of scattered data using a two-stage approximation method |

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 |

F01EDF | Real symmetric matrix exponential |

F01EFF | Function of a real symmetric matrix |

F01ELF | Function of a real matrix (using numerical differentiation) |

F01FCF | Complex matrix exponential |

F01FDF | Complex Hermitian matrix exponential |

F01FFF | Function of a complex Hermitian matrix |

F01FLF | Function of a complex matrix (using numerical differentiation) |

F01JAF | Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix |

F01JBF | Condition number for a function of a real matrix (using numerical differentiation) |

F01JCF | Condition number for a function of a real matrix (using user-supplied derivatives) |

F01KAF | Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix |

F01KBF | Condition number for a function of a complex matrix (using numerical differentiation) |

F01KCF | Condition number for a function of a complex matrix (using user-supplied derivatives) |

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) |

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 $\text{}=n$) or minimal least squares (if rank $\text{}<n$) solution of $m$ real equations in $n$ unknowns, $m\ge n$ |

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 |

F07FCF | Uses the Cholesky factorization to compute the solution 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 |

F07FQF | Uses the Cholesky factorization to compute the solution 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 |

F07WDF | Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format |

F07WRF | Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format |

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) |

F08KHF | Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |

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 |

F12AUF | Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver |

F12FCF | Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FBF |

F12FGF | Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver |

G01HBF | Computes probabilities for the multivariate Normal distribution |

G01LBF | Computes a vector of values for the probability density function of the multivariate Normal distribution |

G02ABF | Computes the nearest correlation matrix to a real square matrix, augmented G02AAF to incorporate weights and bounds |

G02AEF | Computes the nearest correlation matrix with $k$-factor structure to a real square matrix |

G02AJF | Computes the nearest correlation matrix to a real square matrix, using element-wise weighting |

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 |

G02QFF | Linear quantile regression, simple interface, independent, identically distributed (IID) errors |

G02QGF | Linear quantile regression, comprehensive interface |

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 realisation 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 |

G12ABF | Computes rank statistics for comparing survival curves |

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, ${\chi}^{2}$ 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 ${\left({\epsilon}_{t-1}+\gamma \right)}^{2}$ |

G13FCF | Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ${\left(\left|{\epsilon}_{t-1}\right|+\gamma {\epsilon}_{t-1}\right)}^{2}$ |

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 |

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 149 of these routines within the Library.

RoutineName |
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 |

C06FXF | Three-dimensional complex discrete Fourier 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 multidimensional data (using complex data type) |

C06PJF | Multidimensional complex discrete Fourier transform of multidimensional 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 row ordered complex storage format for Hermitian sequences |

C06PQF | Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered 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 |

C06PVF | Two-dimensional real-to-complex discrete Fourier transform |

C06PWF | Two-dimensional complex-to-real discrete Fourier transform |

C06PXF | Three-dimensional complex discrete Fourier transform, complex data type |

C06PYF | Three-dimensional real-to-complex discrete Fourier transform |

C06PZF | Three-dimensional complex-to-real discrete Fourier transform |

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) |

C09EAF | Two-dimensional discrete wavelet transform |

C09EBF | Two-dimensional inverse discrete wavelet transform |

C09ECF | Two-dimensional multi-level discrete wavelet transform |

C09EDF | Two-dimensional inverse multi-level discrete wavelet transform |

C09FAF | Three-dimensional discrete wavelet transform |

C09FBF | Three-dimensional inverse discrete wavelet transform |

C09FCF | Three-dimensional multi-level discrete wavelet transform |

C09FDF | Three-dimensional inverse multi-level discrete wavelet transform |

D01DAF | Two-dimensional quadrature, finite region |

D01FCF | Multidimensional adaptive quadrature over hyper-rectangle |

D01GAF | One-dimensional quadrature, integration of function defined by data values, Gill–Miller method |

D03FAF | Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates |

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 |

E01TKF | Interpolating functions, modified Shepard's method, four variables |

E01TLF | Interpolated values, evaluate interpolant computed by E01TKF, function and first derivatives, four variables |

E01TMF | Interpolating functions, modified Shepard's method, five variables |

E01TNF | Interpolated values, evaluate interpolant computed by E01TMF, function and first derivatives, five variables |

E01ZMF | Interpolating function, modified Shepard's method, $d$ dimensions |

E01ZNF | Interpolated values, evaluate interpolant computed by E01ZMF, function and first derivatives, $d$ dimensions |

E02BFF | Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points |

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 |

E05SAF | Global optimization using particle swarm algorithm (PSO), bound constraints only |

E05SBF | Global optimization using particle swarm algorithm (PSO), comprehensive |

E05UCF | Global optimization using multi-start, nonlinear constraints |

E05USF | Global optimization of a sum of squares problem using multi-start, nonlinear constraints |

F01CTF | Sum or difference of two real matrices, optional scaling and transposition |

F01CWF | Sum or difference of two complex matrices, optional scaling and transposition |

F01EJF | Real matrix logarithm |

F01EKF | Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm) |

F01EMF | Function of a real matrix (using user-supplied derivatives) |

F01FJF | Complex matrix logarithm |

F01FKF | Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm) |

F01FMF | Function of a complex matrix (using user-supplied derivatives) |

F05AAF | Gram–Schmidt orthogonalization 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 method or the MINRES algorithm |

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 | Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication |

F12AGF | Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver |

F12APF | Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication |

F12FBF | Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication |

G01ATF | Computes univariate summary information: mean, variance, skewness, kurtosis |

G01WAF | Computes the mean and standard deviation using a rolling window |

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 |

G02JDF | Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML) |

G02JEF | Hierarchical mixed effects regression using Maximum Likelihood (ML) |

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 |

G03GAF | Fits a Gaussian mixture model |

G05RCF | Generates a matrix of pseudorandom numbers from a Student's $t$-copula |

G05RDF | Generates a matrix of pseudorandom numbers from a Gaussian copula |

G05REF | Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula |

G05RFF | Generates a matrix of pseudorandom numbers from a bivariate Frank copula |

G05RGF | Generates a matrix of pseudorandom numbers from a bivariate Plackett copula |

G05RHF | Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula |

G05RJF | Generates a matrix of pseudorandom numbers from a multivariate Frank copula |

G05RKF | Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula |

G05RYF | Generates a matrix of pseudorandom numbers from a multivariate Student's $t$-distribution |

G05SAF | Generates a vector of pseudorandom numbers from a uniform distribution over $\left(0,1\right]$ |

G05SBF | Generates a vector of pseudorandom numbers from a beta distribution |

G05SCF | Generates a vector of pseudorandom numbers from a Cauchy distribution |

G05SDF | Generates a vector of pseudorandom numbers from a ${\chi}^{2}$ distribution |

G05SEF | Generates a vector of pseudorandom numbers from a Dirichlet distribution |

G05SFF | Generates a vector of pseudorandom numbers from an exponential distribution |

G05SGF | Generates a vector of pseudorandom numbers from an exponential mix distribution |

G05SHF | Generates a vector of pseudorandom numbers from an $F$-distribution |

G05SJF | Generates a vector of pseudorandom numbers from a gamma distribution |

G05SKF | Generates a vector of pseudorandom numbers from a Normal distribution |

G05SLF | Generates a vector of pseudorandom numbers from a logistic distribution |

G05SMF | Generates a vector of pseudorandom numbers from a log-normal distribution |

G05SNF | Generates a vector of pseudorandom numbers from a Student's $t$-distribution |

G05SPF | Generates a vector of pseudorandom numbers from a triangular distribution |

G05SQF | Generates a vector of pseudorandom numbers from a uniform distribution over $\left[a,b\right]$ |

G05SRF | Generates a vector of pseudorandom numbers from a von Mises distribution |

G05SSF | Generates a vector of pseudorandom numbers from a Weibull distribution |

G05XBF | Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm |

G05XDF | Backs out the increments from sample paths generated by a Brownian bridge algorithm |

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 |

G13MEF | Computes the iterated exponential moving average for a univariate inhomogeneous time series |

G13MFF | Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned |

G13MGF | Computes the exponential moving average for a univariate inhomogeneous time series |

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 |

S30NBF | Heston's model option pricing formula with Greeks |

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 |

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 165 of these routines within the Library.

RoutineName |
Purpose |

C05QSF | Solution of a sparse system of nonlinear equations using function values only (easy-to-use) |

D01GBF | Multidimensional quadrature over hyper-rectangle, Monte–Carlo method |

D01GCF | Multidimensional quadrature, general product region, number-theoretic method |

D01GDF | Multidimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines |

D01PAF | Multidimensional quadrature over an $n$-simplex |

D02EJF | Ordinary differential equations, stiff initial value problem, backward differentiation 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) |

D02UAF | Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid |

D02UBF | Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial |

D03PCF | General system of parabolic PDEs, method of lines, finite differences, one space variable |

D03PDF | General system of parabolic PDEs, method of lines, Chebyshev ${C}^{0}$ collocation, one space variable |

D03PEF | General system of first-order PDEs, method of lines, Keller box discretization, 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 ${C}^{0}$ collocation, one space variable |

D03PKF | General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, 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 discretization, remeshing, one space variable |

D03PSF | General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable |

D05AAF | Linear nonsingular Fredholm integral equation, second kind, split kernel |

D05ABF | Linear nonsingular 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) |

E04UGF | NLP problem (sparse) |

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) |

F01ABF | Inverse of real symmetric positive definite matrix using iterative refinement |

F01ELF | Function of a real matrix (using numerical differentiation) |

F01FLF | Function of a complex matrix (using numerical differentiation) |

F01GAF | Action of a real matrix exponential on a real matrix |

F01GBF | Action of a real matrix exponential on a real matrix (reverse communication) |

F01HAF | Action of a complex matrix exponential on a complex matrix |

F01HBF | Action of a complex matrix exponential on a complex matrix (reverse communication) |

F01JAF | Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix |

F01JBF | Condition number for a function of a real matrix (using numerical differentiation) |

F01JCF | Condition number for a function of a real matrix (using user-supplied derivatives) |

F01KAF | Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix |

F01KBF | Condition number for a function of a complex matrix (using numerical differentiation) |

F01KCF | Condition number for a function of a complex matrix (using user-supplied derivatives) |

F02EKF | Selected eigenvalues and eigenvectors of a real sparse general matrix |

F02FJF | Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (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) |

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 $\text{}=n$) or minimal least squares (if rank $\text{}<n$) solution of $m$ real equations in $n$ unknowns, $m\ge n$ |

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) |

F11DGF | Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete $LU$ block diagonal preconditioner computed by F11DFF |

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 |

F11DUF | Solution of complex sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete $LU$ block diagonal preconditioner computed by F11DTF |

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 |

F12AUF | Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver |

F12FGF | Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver |

G01AGF | Lineprinter scatterplot of two variables |

G01AHF | Lineprinter scatterplot of one variable against Normal scores |

G01ANF | Calculates approximate quantiles from a data stream of known size |

G01APF | Calculates approximate quantiles from a data stream of unknown size |

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) ${\chi}^{2}$ variables |

G02ABF | Computes the nearest correlation matrix to a real square matrix, augmented G02AAF to incorporate weights and bounds |

G02AEF | Computes the nearest correlation matrix with $k$-factor structure to a real square matrix |

G02AJF | Computes the nearest correlation matrix to a real square matrix, using element-wise weighting |

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 |

G05PDF | Generates a realisation of a time series from a GARCH process with asymmetry of the form ${\left({\epsilon}_{t-1}+\gamma \right)}^{2}$ |

G05PEF | Generates a realisation of a time series from a GARCH process with asymmetry of the form ${\left(\left|{\epsilon}_{t-1}\right|+\gamma {\epsilon}_{t-1}\right)}^{2}$ |

G05PFF | Generates a realisation of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process |

G05PGF | Generates a realisation of a time series from an exponential GARCH (EGARCH) process |

G05PJF | Generates a realisation of a multivariate time series from a VARMA model |

G05PYF | Generates a random correlation matrix |

G05RZF | Generates a matrix of pseudorandom numbers from a multivariate Normal distribution |

G05ZPF | Generates realisations of a one-dimensional random field |

G05ZQF | Setup for simulating two-dimensional random fields, user-defined variogram |

G05ZRF | Setup for simulating two-dimensional random fields, preset variogram |

G05ZSF | Generates realisations of a two-dimensional random field |

G05ZTF | Generates realisations of fractional Brownian motion |

G07BEF | Computes maximum likelihood estimates for parameters of the Weibull distribution |

G07BFF | Estimates parameter values of the generalized Pareto 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 |

G12ABF | Computes rank statistics for comparing survival curves |

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 |

G13BCF | Multivariate time series, cross-correlations |

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, ${\chi}^{2}$ 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 ${\left({\epsilon}_{t-1}+\gamma \right)}^{2}$ |

G13FCF | Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ${\left(\left|{\epsilon}_{t-1}\right|+\gamma {\epsilon}_{t-1}\right)}^{2}$ |

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 |