Keyword : Symmetric

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	$L D L^{T}$ 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- $2 k$ 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- $2 k$ 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 $Q L$ or $Q R$ algorithm
F08JFF	All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $Q L$ or $Q R$ 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 $Q L$ or $Q R$ 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

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