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

F01ADF | Inverse of real symmetric positive definite matrix |

F01EDF | Real symmetric matrix exponential |

F01EFF | Function of a real symmetric matrix |

F01MCF | $LD{L}^{\mathrm{T}}$ factorization of real symmetric positive definite variable-bandwidth matrix |

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

F03BFF | Determinant of real symmetric positive definite matrix |

F03BHF | Determinant of real symmetric positive definite banded matrix |

F04ABF | Solution of real symmetric positive definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) |

F04ASF | Solution of real symmetric positive definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box) |

F04BDF | Computes the solution and error-bound to a real symmetric positive definite system of linear equations |

F04BEF | Computes the solution and error-bound to a real symmetric positive definite system of linear equations, packed storage |

F04BFF | Computes the solution and error-bound to a real symmetric positive definite banded system of linear equations |

F04BGF | Computes the solution and error-bound to a real symmetric positive definite tridiagonal system of linear equations |

F04BHF | Computes the solution and error-bound to a real symmetric system of linear equations |

F04BJF | Computes the solution and error-bound to a real symmetric system of linear equations, packed storage |

F04DHF | Computes the solution and error-bound to a complex symmetric system of linear equations |

F04DJF | Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage |

F04FEF | Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side |

F04FFF | Solution of real symmetric positive definite Toeplitz system, one right-hand side |

F04MCF | Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF) |

F04MEF | Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix |

F04MFF | Update solution of real symmetric positive definite Toeplitz system |

F06BHF | Apply real similarity rotation to 2 by 2 symmetric matrix |

F06BPF | Compute eigenvalue of 2 by 2 real symmetric matrix |

F06FPF | Apply real symmetric plane rotation to two vectors |

F06PCF | Matrix-vector product, real symmetric matrix |

F06PDF | Matrix-vector product, real symmetric band matrix |

F06PEF | Matrix-vector product, real symmetric packed matrix |

F06PPF | Rank-1 update, real symmetric matrix |

F06PQF | Rank-1 update, real symmetric packed matrix |

F06PRF | Rank-2 update, real symmetric matrix |

F06PSF | Rank-2 update, real symmetric packed matrix |

F06QMF | Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations |

F06RCF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, real symmetric matrix |

F06RDF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage |

F06REF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, real symmetric band matrix |

F06RPF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix |

F06TAF | Matrix-vector product, complex symmetric matrix |

F06TBF | Rank-1 update, complex symmetric matrix |

F06TCF | Matrix-vector product, complex symmetric packed matrix |

F06TDF | Rank-1 update, complex symmetric packed matrix |

F06UFF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, complex symmetric matrix |

F06UGF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage |

F06UHF | $1$-norm, $\infty $-norm, Frobenius norm, largest absolute element, complex symmetric band matrix |

F06WAF | 1-norm, $\infty $-norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format |

F06WCF | Rank-$k$ update of a real symmetric matrix, Rectangular Full Packed format |

F06WQF | Rank-$k$ update of a complex Hermitian matrix, Rectangular Full Packed format |

F06YCF | Matrix-matrix product, one real symmetric matrix, one real rectangular matrix |

F06YPF | Rank-$k$ update of a real symmetric matrix |

F06YRF | Rank-$2k$ update of a real symmetric matrix |

F06ZTF | Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix |

F06ZUF | Rank-$k$ update of a complex symmetric matrix |

F06ZWF | Rank-$2k$ update of a complex symmetric matrix |

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 |

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 |

F07FFF | Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number |

F07FGF | Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FDF |

F07FHF | Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides |

F07FJF | Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF |

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 |

F07GDF | Cholesky factorization of real symmetric positive definite matrix, packed storage |

F07GEF | Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage |

F07GFF | Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage |

F07GGF | Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage |

F07GHF | Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage |

F07GJF | Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, 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 |

F07HDF | Cholesky factorization of real symmetric positive definite band matrix |

F07HEF | Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF |

F07HFF | Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number |

F07HGF | Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF |

F07HHF | Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides |

F07JAF | Computes the solution to a real symmetric positive definite tridiagonal system of linear equations |

F07JBF | Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations |

F07JDF | Computes the modified Cholesky factorization of a real symmetric positive definite tridiagonal matrix |

F07JEF | Solves a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by F07JDF |

F07JGF | Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by F07JDF |

F07JHF | Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides |

F07KDF | Cholesky factorization of real symmetric positive semidefinite matrix |

F07MAF | Computes the solution to a real symmetric system of linear equations |

F07MBF | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations |

F07MDF | Bunch–Kaufman factorization of real symmetric indefinite matrix |

F07MEF | Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF |

F07MGF | Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF |

F07MHF | Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides |

F07MJF | Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF |

F07NRF | Bunch–Kaufman factorization of complex symmetric matrix |

F07NSF | Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF |

F07NUF | Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF |

F07NVF | Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides |

F07NWF | Inverse of complex symmetric matrix, matrix already factorized by F07NRF |

F07PAF | Computes the solution to a real symmetric system of linear equations, packed storage |

F07PBF | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage |

F07PDF | Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage |

F07PEF | Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage |

F07PGF | Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage |

F07PHF | Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage |

F07PJF | Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage |

F07QNF | Computes the solution to a complex symmetric system of linear equations, packed storage |

F07QPF | Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage |

F07QRF | Bunch–Kaufman factorization of complex symmetric matrix, packed storage |

F07QSF | Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage |

F07QUF | Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage |

F07QVF | Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage |

F07QWF | Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage |

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

F07WEF | Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF, Rectangular Full Packed format |

F07WJF | Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format |

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) |

F08FEF | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |

F08FLF | Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix |

F08FSF | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |

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) |

F08GEF | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |

F08GSF | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |

F08HAF | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

F08HBF | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

F08HCF | Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer) |

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 |

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) |

F08JEF | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm |

F08JFF | All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm |

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) |

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 |

F08JLF | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) |

F08JSF | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm |

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) |

F08JXF | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |

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) |

F08UFF | Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$ |

F11GDF | Real sparse symmetric linear systems, setup for F11GEF |

F11GEF | Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm |

F11GFF | Real sparse symmetric linear systems, diagnostic for F11GEF |

F11JAF | Real sparse symmetric matrix, incomplete Cholesky factorization |

F11JCF | Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box) |

F11JDF | Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix |

F11JEF | Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) |

F11XEF | Real sparse symmetric matrix vector multiply |

F11ZBF | Real sparse symmetric matrix reorder routine |

© The Numerical Algorithms Group Ltd, Oxford UK. 2013