NAG Library
Keyword and GAMS Search

Reduction to standard form, generalized real symmetric-definite banded eigenproblem
Names: f01bvf; nagf_matop_real_symm_posdef_geneig
Keywords: eigenproblem, generalized; generalized eigenproblem; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4c1c

Computes selected eigenvalues and eigenvectors of a real general matrix
Names: f02ecc; nag_real_eigensystem_sel
Keywords: real, nonsymmetric matrix
GAMS: D4a2

Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
Names: f02ecf; nagf_eigen_real_gen_eigsys
Keywords: real, nonsymmetric matrix
GAMS: D4a2

Selected eigenvalues and eigenvectors of a real sparse general matrix
Names: f02ekc; nag_eigen_real_gen_sparse_arnoldi
Keywords: large scale eigenproblems; matrix, sparse; real, sparse matrix
GAMS: D4a7, D4a2

Selected eigenvalues and eigenvectors of a real sparse general matrix
Names: f02ekf; nagf_eigen_real_gen_sparse_arnoldi
Keywords: large scale eigenproblems; matrix, sparse; real, sparse matrix
GAMS: D4a7, D4a2

Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
Names: f02fjf; nagf_eigen_real_symm_sparse_eigsys
Keywords: matrix, sparse; real, sparse, symmetric matrix
GAMS: D4a7, D4b1

Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Names: f02fkc; nag_eigen_real_symm_sparse_arnoldi
Keywords: eigenproblem; eigenvalues; eigenvectors; large scale eigenproblems; matrix, sparse; real, sparse, symmetric matrix; sparse eigenproblem
GAMS: D4a7, D4a1

Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Names: f02fkf; nagf_eigen_real_symm_sparse_arnoldi
Keywords: eigenproblem; eigenvalues; eigenvectors; large scale eigenproblems; matrix, sparse; real, sparse, symmetric matrix; sparse eigenproblem
GAMS: D4a7, D4a1

Solves the quadratic eigenvalue problem for real matrices
Names: f02jcc; nag_eigen_real_gen_quad
Keywords: backward error; balancing; condition number; eigenproblem, quadratic; eigenvalues and eigenvectors
GAMS: D4b2

Solves the quadratic eigenvalue problem for real matrices
Names: f02jcf; nagf_eigen_real_gen_quad
Keywords: backward error; balancing; condition number; eigenproblem, quadratic; eigenvalues and eigenvectors
GAMS: D4b2

Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
Names: f02wgc; nag_real_partial_svd
Keywords: real, m×n matrix; SVD, singular value decomposition
GAMS: D6

Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
Names: f02wgf; nagf_eigen_real_gen_partialsvd
Keywords: real, m×n matrix; SVD, singular value decomposition
GAMS: D6

SVD of real upper triangular matrix (Black Box)
Names: f02wuf; nagf_eigen_real_triang_svd
Keywords: real, triangular matrix; SVD, singular value decomposition
GAMS: D6

Compute eigenvalue of 2×2 real symmetric matrix
Names: f06bpf; nagf_blas_deig2
Keywords: eigenvalues; elementary arithmetic
GAMS: D4a1

Solves a real linear least squares problem of full rank
Names: f08aac; nag_dgels; dgels
Keywords: DGELS; finance; LAPACK; linear least squares; LQ decomposition; overdetermined linear equations; QR factorization; real, m×n matrix; underdetermined linear system
GAMS: D9a1

Solves a real linear least squares problem of full rank
Names: f08aaf; nagf_lapackeig_dgels; dgels
Keywords: DGELS; finance; LAPACK; linear least squares; LQ decomposition; overdetermined linear equations; QR factorization; real, m×n matrix; underdetermined linear system
GAMS: D9a1

Performs a QR factorization of real general rectangular matrix, with explicit blocking
Names: f08abc; nag_dgeqrt; dgeqrt
Keywords: DGEQRT; explicit blocking; QR factorization; real, m by n matrix; recursive QR
GAMS: D5

Performs a QR factorization of real general rectangular matrix, with explicit blocking
Names: f08abf; nagf_lapackeig_dgeqrt; dgeqrt
Keywords: DGEQRT; explicit blocking; QR factorization; real, m by n matrix; recursive QR
GAMS: D5

Performs a QR factorization of real general rectangular matrix
Names: f08aec; nag_dgeqrf; dgeqrf
Keywords: DGEQRF; finance; LAPACK; QR factorization; real, m×n matrix
GAMS: D5

Performs a QR factorization of real general rectangular matrix
Names: f08aef; nagf_lapackeig_dgeqrf; dgeqrf
Keywords: DGEQRF; finance; LAPACK; QR factorization; real, m×n matrix
GAMS: D5

First order adjoint: Performs a QR factorization of real general rectangular matrix
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DGEQRF; finance; LAPACK; QR factorization; real, m×n matrix
GAMS: D5

Performs a LQ factorization of real general rectangular matrix
Names: f08ahc; nag_dgelqf; dgelqf
Keywords: DGELQF; LAPACK; LQ factorization; real, m×n matrix
GAMS: D5

Performs a LQ factorization of real general rectangular matrix
Names: f08ahf; nagf_lapackeig_dgelqf; dgelqf
Keywords: DGELQF; LAPACK; LQ factorization; real, m×n matrix
GAMS: D5

First order adjoint: Performs a LQ factorization of real general rectangular matrix
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DGELQF; LAPACK; LQ factorization; real, m×n matrix
GAMS: D5

Computes the minimum-norm solution to a real linear least squares problem
Names: f08bac; nag_dgelsy; dgelsy
Keywords: DGELSY; finance; LAPACK; linear least squares; minimal least squares; real, m×n matrix
GAMS: D9a1

Computes the minimum-norm solution to a real linear least squares problem
Names: f08baf; nagf_lapackeig_dgelsy; dgelsy
Keywords: DGELSY; finance; LAPACK; linear least squares; minimal least squares; real, m×n matrix
GAMS: D9a1

QR factorization of real general triangular-pentagonal matrix
Names: f08bbc; nag_dtpqrt; dtpqrt
Keywords: DTPQRT; explicit blocking; QR factorization; real, triangular-pentagonal matrix; recursive QR
GAMS: D5

QR factorization of real general triangular-pentagonal matrix
Names: f08bbf; nagf_lapackeig_dtpqrt; dtpqrt
Keywords: DTPQRT; explicit blocking; QR factorization; real, triangular-pentagonal matrix; recursive QR
GAMS: D5

QR factorization, with column pivoting, of real general rectangular matrix
Names: f08bec; nag_dgeqpf; dgeqpf
Keywords: DGEQPF; finance; LAPACK; orthogonal transformations; QR factorization; real, m×n matrix
GAMS: D5

QR factorization, with column pivoting, of real general rectangular matrix
Names: f08bef; nagf_lapackeig_dgeqpf; dgeqpf
Keywords: DGEQPF; finance; LAPACK; orthogonal transformations; QR factorization; real, m×n matrix
GAMS: D5

QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Names: f08bfc; nag_dgeqp3; dgeqp3
Keywords: DGEQP3; finance; LAPACK; orthogonal transformations; QR factorization; real, m×n matrix
GAMS: D5

QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Names: f08bff; nagf_lapackeig_dgeqp3; dgeqp3
Keywords: DGEQP3; finance; LAPACK; orthogonal transformations; QR factorization; real, m×n matrix
GAMS: D5

Reduces a real upper trapezoidal matrix to upper triangular form
Names: f08bhc; nag_dtzrzf; dtzrzf
Keywords: DTZRZF; LAPACK; matrix, upper trapezoidal; matrix, upper triangular; orthogonal transformations; real, trapezoidal matrix
GAMS: D5

Reduces a real upper trapezoidal matrix to upper triangular form
Names: f08bhf; nagf_lapackeig_dtzrzf; dtzrzf
Keywords: DTZRZF; LAPACK; matrix, upper trapezoidal; matrix, upper triangular; orthogonal transformations; real, trapezoidal matrix
GAMS: D5

QL factorization of real general rectangular matrix
Names: f08cec; nag_dgeqlf; dgeqlf
Keywords: DGEQLF; LAPACK; QL factorization; real, m×n matrix
GAMS: D5

QL factorization of real general rectangular matrix
Names: f08cef; nagf_lapackeig_dgeqlf; dgeqlf
Keywords: DGEQLF; LAPACK; QL factorization; real, m×n matrix
GAMS: D5

RQ factorization of real general rectangular matrix
Names: f08chc; nag_dgerqf; dgerqf
Keywords: DGERQF; LAPACK; real, m×n matrix; RQ factorizations
GAMS: D5

RQ factorization of real general rectangular matrix
Names: f08chf; nagf_lapackeig_dgerqf; dgerqf
Keywords: DGERQF; LAPACK; real, m×n matrix; RQ factorizations
GAMS: D5

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Names: f08fac; nag_dsyev; dsyev
Keywords: DSYEV; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Names: f08faf; nagf_lapackeig_dsyev; dsyev
Keywords: DSYEV; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1

First order adjoint: Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DSYEV; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Names: f08fbc; nag_dsyevx; dsyevx
Keywords: DSYEVX; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Names: f08fbf; nagf_lapackeig_dsyevx; dsyevx
Keywords: DSYEVX; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Names: f08fcc; nag_dsyevd; dsyevd
Keywords: divide-and-conquer method; DSYEVD; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1, D4c2a

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Names: f08fcf; nagf_lapackeig_dsyevd; dsyevd
Keywords: divide-and-conquer method; DSYEVD; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1, D4c2a

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Names: f08fc; nagcpp::lapackeig::dsyevd
Keywords: divide-and-conquer method; DSYEVD; eigenvalues; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4a1, D4c2a

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Names: f08fdc; nag_dsyevr; dsyevr
Keywords: dqds algorithm; DSYEVR; eigenvalues; eigenvectors; LAPACK; real, indefinite, symmetric matrix; relatively robust representations
GAMS: D4a1

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Names: f08fdf; nagf_lapackeig_dsyevr; dsyevr
Keywords: dqds algorithm; DSYEVR; eigenvalues; eigenvectors; LAPACK; real, indefinite, symmetric matrix; relatively robust representations
GAMS: D4a1

Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Names: f08fec; nag_dsytrd; dsytrd
Keywords: DSYTRD; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4c1b1

Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Names: f08fef; nagf_lapackeig_dsytrd; dsytrd
Keywords: DSYTRD; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4c1b1

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
Names: f08flc; nag_ddisna; ddisna
Keywords: complex, Hermitian, indefinite matrix; condition number, matrix; DDISNA; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4c, D6

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
Names: f08flf; nagf_lapackeig_ddisna; ddisna
Keywords: complex, Hermitian, indefinite matrix; condition number, matrix; DDISNA; eigenvectors; finance; LAPACK; real, indefinite, symmetric matrix
GAMS: D4c, D6

Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Names: f08fsc; nag_zhetrd; zhetrd
Keywords: complex, Hermitian, indefinite matrix; LAPACK; unitary transformations; ZHETRD
GAMS: D4c1b1

Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Names: f08fsf; nagf_lapackeig_zhetrd; zhetrd
Keywords: complex, Hermitian, indefinite matrix; LAPACK; unitary transformations; ZHETRD
GAMS: D4c1b1

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Names: f08gac; nag_dspev; dspev
Keywords: DSPEV; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; QR algorithm; real, indefinite, symmetric matrix
GAMS: D4a1

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Names: f08gaf; nagf_lapackeig_dspev; dspev
Keywords: DSPEV; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; QR algorithm; real, indefinite, symmetric matrix
GAMS: D4a1

First order adjoint: Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DSPEV; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; QR algorithm; real, indefinite, symmetric matrix
GAMS: D4a1

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Names: f08gbc; nag_dspevx; dspevx
Keywords: DSPEVX; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4a1

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Names: f08gbf; nagf_lapackeig_dspevx; dspevx
Keywords: DSPEVX; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4a1

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
Names: f08gcc; nag_dspevd; dspevd
Keywords: divide-and-conquer method; DSPEVD; eigenvalues; eigenvectors; LAPACK; Pal–Walker–Kahan (QL or QR) algorithm; real, indefinite, symmetric matrix
GAMS: D4a1, D4c2a

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
Names: f08gcf; nagf_lapackeig_dspevd; dspevd
Keywords: divide-and-conquer method; DSPEVD; eigenvalues; eigenvectors; LAPACK; Pal–Walker–Kahan (QL or QR) algorithm; real, indefinite, symmetric matrix
GAMS: D4a1, D4c2a

Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Names: f08gec; nag_dsptrd; dsptrd
Keywords: DSPTRD; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4c1b1

Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Names: f08gef; nagf_lapackeig_dsptrd; dsptrd
Keywords: DSPTRD; LAPACK; orthogonal transformations; real, indefinite, symmetric matrix
GAMS: D4c1b1

Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Names: f08gsc; nag_zhptrd; zhptrd
Keywords: complex, Hermitian, indefinite matrix; LAPACK; unitary transformations; ZHPTRD
GAMS: D4c1b1

Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Names: f08gsf; nagf_lapackeig_zhptrd; zhptrd
Keywords: complex, Hermitian, indefinite matrix; LAPACK; unitary transformations; ZHPTRD
GAMS: D4c1b1

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Names: f08hac; nag_dsbev; dsbev
Keywords: DSBEV; LAPACK; matrix, band; QR algorithm; real, band, symmetric matrix
GAMS: D4a6

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Names: f08haf; nagf_lapackeig_dsbev; dsbev
Keywords: DSBEV; LAPACK; matrix, band; QR algorithm; real, band, symmetric matrix
GAMS: D4a6

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Names: f08hbc; nag_dsbevx; dsbevx
Keywords: DSBEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; real, band, symmetric matrix
GAMS: D4a6

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Names: f08hbf; nagf_lapackeig_dsbevx; dsbevx
Keywords: DSBEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; real, band, symmetric matrix
GAMS: D4a6

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
Names: f08hcc; nag_dsbevd; dsbevd
Keywords: divide-and-conquer method; DSBEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; Pal–Walker–Kahan (QL or QR) algorithm; real, band, symmetric matrix
GAMS: D4a1, D4a6

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
Names: f08hcf; nagf_lapackeig_dsbevd; dsbevd
Keywords: divide-and-conquer method; DSBEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; Pal–Walker–Kahan (QL or QR) algorithm; real, band, symmetric matrix
GAMS: D4a1, D4a6

Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Names: f08hec; nag_dsbtrd; dsbtrd
Keywords: DSBTRD; LAPACK; matrix, band; orthogonal transformations; real, band, symmetric matrix
GAMS: D4c1b1

Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Names: f08hef; nagf_lapackeig_dsbtrd; dsbtrd
Keywords: DSBTRD; LAPACK; matrix, band; orthogonal transformations; real, band, symmetric matrix
GAMS: D4c1b1

Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Names: f08hsc; nag_zhbtrd; zhbtrd
Keywords: complex, band, Hermitian matrix; LAPACK; matrix, band; unitary transformations; ZHBTRD
GAMS: D4c1b1

Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Names: f08hsf; nagf_lapackeig_zhbtrd; zhbtrd
Keywords: complex, band, Hermitian matrix; LAPACK; matrix, band; unitary transformations; ZHBTRD
GAMS: D4c1b1

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Names: f08jac; nag_dstev; dstev
Keywords: DSTEV; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Names: f08jaf; nagf_lapackeig_dstev; dstev
Keywords: DSTEV; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Names: f08jbc; nag_dstevx; dstevx
Keywords: bisection method; DSTEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Names: f08jbf; nagf_lapackeig_dstevx; dstevx
Keywords: bisection method; DSTEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Names: f08jcc; nag_dstevd; dstevd
Keywords: divide-and-conquer method; DSTEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; Pal–Walker–Kahan (QL or QR) algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Names: f08jcf; nagf_lapackeig_dstevd; dstevd
Keywords: divide-and-conquer method; DSTEVX; eigenvalues; eigenvectors; LAPACK; matrix, band; Pal–Walker–Kahan (QL or QR) algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Names: f08jdc; nag_dstevr; dstevr
Keywords: dqds algorithm; DSTEVR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations
GAMS: D4a5

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Names: f08jdf; nagf_lapackeig_dstevr; dstevr
Keywords: dqds algorithm; DSTEVR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations
GAMS: D4a5

Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
Names: f08jec; nag_dsteqr; dsteqr
Keywords: DSTEQR; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
Names: f08jef; nagf_lapackeig_dsteqr; dsteqr
Keywords: DSTEQR; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
Names: f08jfc; nag_dsterf; dsterf
Keywords: DSTERF; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
Names: f08jff; nagf_lapackeig_dsterf; dsterf
Keywords: DSTERF; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Names: f08jgc; nag_dpteqr; dpteqr
Keywords: DPTEQR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Names: f08jgf; nagf_lapackeig_dpteqr; dpteqr
Keywords: DPTEQR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Names: f08jhc; nag_dstedc; dstedc
Keywords: divide-and-conquer method; DSTEDC; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Names: f08jhf; nagf_lapackeig_dstedc; dstedc
Keywords: divide-and-conquer method; DSTEDC; eigenvalues; eigenvectors; LAPACK; matrix, band; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Names: f08jjc; nag_dstebz; dstebz
Keywords: bisection method; DSTEBZ; eigenvalues; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Names: f08jjf; nagf_lapackeig_dstebz; dstebz
Keywords: bisection method; DSTEBZ; eigenvalues; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c2a

Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Names: f08jkc; nag_dstein; dstein
Keywords: DSTEIN; eigenvectors; inverse iteration; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c3

Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Names: f08jkf; nagf_lapackeig_dstein; dstein
Keywords: DSTEIN; eigenvectors; inverse iteration; LAPACK; matrix, band; real, symmetric, tridiagonal matrix
GAMS: D4a5, D4c3

Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Names: f08jlc; nag_dstegr; dstegr
Keywords: dqds algorithm; DSTEGR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations
GAMS: D4a5, D4c2a

Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Names: f08jlf; nagf_lapackeig_dstegr; dstegr
Keywords: dqds algorithm; DSTEGR; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations
GAMS: D4a5, D4c2a

Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
Names: f08jsc; nag_zsteqr; zsteqr
Keywords: eigenvalues; eigenvectors; LAPACK; QR algorithm; real, symmetric, tridiagonal matrix; ZSTEQR
GAMS: D4c2a, D4a5, D4a3

Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
Names: f08jsf; nagf_lapackeig_zsteqr; zsteqr
Keywords: eigenvalues; eigenvectors; LAPACK; QR algorithm; real, symmetric, tridiagonal matrix; ZSTEQR
GAMS: D4c2a, D4a5, D4a3

Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Names: f08juc; nag_zpteqr; zpteqr
Keywords: eigenvalues; eigenvectors; LAPACK; LDL^H decomposition; real, symmetric, tridiagonal matrix; ZPTEQR
GAMS: D4a5, D4c2a

Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Names: f08juf; nagf_lapackeig_zpteqr; zpteqr
Keywords: eigenvalues; eigenvectors; LAPACK; LDL^H decomposition; real, symmetric, tridiagonal matrix; ZPTEQR
GAMS: D4a5, D4c2a

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Names: f08jvc; nag_zstedc; zstedc
Keywords: divide-and-conquer method; eigenvalues; eigenvectors; LAPACK; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix; ZSTEDC
GAMS: D4c2a, D4a5, D4a3

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Names: f08jvf; nagf_lapackeig_zstedc; zstedc
Keywords: divide-and-conquer method; eigenvalues; eigenvectors; LAPACK; QL algorithm; QR algorithm; real, symmetric, tridiagonal matrix; ZSTEDC
GAMS: D4c2a, D4a5, D4a3

Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Names: f08jxc; nag_zstein; zstein
Keywords: eigenvectors; inverse iteration; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; ZSTEIN
GAMS: D4c3

Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Names: f08jxf; nagf_lapackeig_zstein; zstein
Keywords: eigenvectors; inverse iteration; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; ZSTEIN
GAMS: D4c3

Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Names: f08jyc; nag_zstegr; zstegr
Keywords: dqds algorithm; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations; ZSTEGR
GAMS: D4c2a, D4a5, D4a3

Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Names: f08jyf; nagf_lapackeig_zstegr; zstegr
Keywords: dqds algorithm; eigenvalues; eigenvectors; LAPACK; matrix, band; real, symmetric, tridiagonal matrix; relatively robust representations; ZSTEGR
GAMS: D4c2a, D4a5, D4a3

Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Names: f08kac; nag_dgelss; dgelss
Keywords: DGELSS; LAPACK; linear least squares; minimal least squares; real, m×n matrix; SVD, singular value decomposition
GAMS: D9a1

Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Names: f08kaf; nagf_lapackeig_dgelss; dgelss
Keywords: DGELSS; LAPACK; linear least squares; minimal least squares; real, m×n matrix; SVD, singular value decomposition
GAMS: D9a1

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Names: f08kbc; nag_dgesvd; dgesvd
Keywords: DGESVD; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Names: f08kbf; nagf_lapackeig_dgesvd; dgesvd
Keywords: DGESVD; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

First order adjoint: Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DGESVD; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Names: f08kcc; nag_dgelsd; dgelsd
Keywords: DGELSD; divide-and-conquer method; finance; LAPACK; linear least squares; minimal least squares; real, m×n matrix; SVD, singular value decomposition
GAMS: D9a1

Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Names: f08kcf; nagf_lapackeig_dgelsd; dgelsd
Keywords: DGELSD; divide-and-conquer method; finance; LAPACK; linear least squares; minimal least squares; real, m×n matrix; SVD, singular value decomposition
GAMS: D9a1

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Names: f08kdc; nag_dgesdd; dgesdd
Keywords: DGESDD; divide-and-conquer method; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Names: f08kdf; nagf_lapackeig_dgesdd; dgesdd
Keywords: DGESDD; divide-and-conquer method; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

First order adjoint: Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; symbolic adjoint; DGESDD; divide-and-conquer method; finance; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition
GAMS: D6

Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Names: f08kec; nag_dgebrd; dgebrd
Keywords: DGEBRD; LAPACK; orthogonal transformations; real, m×n matrix
GAMS: D6

Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Names: f08kef; nagf_lapackeig_dgebrd; dgebrd
Keywords: DGEBRD; LAPACK; orthogonal transformations; real, m×n matrix
GAMS: D6

First order adjoint: Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DGEBRD; LAPACK; orthogonal transformations; real, m×n matrix
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Names: f08khc; nag_dgejsv; dgejsv
Keywords: DGEJSV; Jacobi method; LAPACK; real, nonsymmetric matrix; singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Names: f08khf; nagf_lapackeig_dgejsv; dgejsv
Keywords: DGEJSV; Jacobi method; LAPACK; real, nonsymmetric matrix; singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Names: f08kjc; nag_dgesvj; dgesvj
Keywords: DGESVJ; Jacobi method; LAPACK; real, nonsymmetric matrix; singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Names: f08kjf; nagf_lapackeig_dgesvj; dgesvj
Keywords: DGESVJ; Jacobi method; LAPACK; real, nonsymmetric matrix; singular value decomposition
GAMS: D6

Computes all or selected singular values of the singular value decomposition of a real general matrix, optionally computing the corresponding left and right singular vectors
Names: f08kmc; nag_dgesvdx; dgesvdx
Keywords: DGESVDX; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition; TGK
GAMS: D6

Computes all or selected singular values of the singular value decomposition of a real general matrix, optionally computing the corresponding left and right singular vectors
Names: f08kmf; nagf_lapackeig_dgesvdx; dgesvdx
Keywords: DGESVDX; LAPACK; real, nonsymmetric matrix; SVD, singular value decomposition; TGK
GAMS: D6

Performs a reduction of real rectangular band matrix to upper bidiagonal form
Names: f08lec; nag_dgbbrd; dgbbrd
Keywords: DGBBRD; Givens rotations; LAPACK; matrix, band; real, band, m×n matrix
GAMS: D4c1b3

Performs a reduction of real rectangular band matrix to upper bidiagonal form
Names: f08lef; nagf_lapackeig_dgbbrd; dgbbrd
Keywords: DGBBRD; Givens rotations; LAPACK; matrix, band; real, band, m×n matrix
GAMS: D4c1b3

Reduction of complex rectangular band matrix to upper bidiagonal form
Names: f08lsc; nag_zgbbrd; zgbbrd
Keywords: Givens rotations; LAPACK; matrix, band; real, band, m×n matrix; ZGBBRD
GAMS: D4c1b3

Reduction of complex rectangular band matrix to upper bidiagonal form
Names: f08lsf; nagf_lapackeig_zgbbrd; zgbbrd
Keywords: Givens rotations; LAPACK; matrix, band; real, band, m×n matrix; ZGBBRD
GAMS: D4c1b3

Computes all or selected singular values of the singular value decomposition of a real square bidiagonal matrix, optionally computing the corresponding left and right singular vectors
Names: f08mbc; nag_dbdsvdx; dbdsvdx
Keywords: DBDSQR; differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition; TGK
GAMS: D6

Computes all or selected singular values of the singular value decomposition of a real square bidiagonal matrix, optionally computing the corresponding left and right singular vectors
Names: f08mbf; nagf_lapackeig_dbdsvdx; dbdsvdx
Keywords: DBDSQR; differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition; TGK
GAMS: D6

Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Names: f08mdc; nag_dbdsdc; dbdsdc
Keywords: DBDSDC; divide-and-conquer method; LAPACK; matrix, band; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition
GAMS: D6

Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Names: f08mdf; nagf_lapackeig_dbdsdc; dbdsdc
Keywords: DBDSDC; divide-and-conquer method; LAPACK; matrix, band; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition
GAMS: D6

Performs an SVD of real bidiagonal matrix reduced from real general matrix
Names: f08mec; nag_dbdsqr; dbdsqr
Keywords: DBDSQR; differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition
GAMS: D6

Performs an SVD of real bidiagonal matrix reduced from real general matrix
Names: f08mef; nagf_lapackeig_dbdsqr; dbdsqr
Keywords: DBDSQR; differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition
GAMS: D6

First order adjoint: Performs an SVD of real bidiagonal matrix reduced from real general matrix
Keywords: adjoint; algorithmic differentiation; automatic differentiation; AD; dco; DBDSQR; differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition
GAMS: D6

Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Names: f08msc; nag_zbdsqr; zbdsqr
Keywords: differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition; ZBDSQR
GAMS: D6

Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Names: f08msf; nagf_lapackeig_zbdsqr; zbdsqr
Keywords: differential qd algorithm; LAPACK; matrix, band; QL algorithm; QR algorithm; real, bidiagonal matrix; SVD, singular value decomposition; ZBDSQR
GAMS: D6

Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Names: f08nac; nag_dgeev; dgeev
Keywords: DGEEV; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; QR algorithm; real, nonsymmetric matrix
GAMS: D4a2

Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Names: f08naf; nagf_lapackeig_dgeev; dgeev
Keywords: DGEEV; eigenvalues; eigenvectors; LAPACK; orthogonal transformations; QR algorithm; real, nonsymmetric matrix
GAMS: D4a2

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
Names: f08nbc; nag_dgeevx; dgeevx
Keywords: balancing; condition number, matrix; DGEEVX; eigenvalues; eigenvectors; finance; forward error; LAPACK; orthogonal transformations; QR algorithm; real, nonsymmetric matrix
GAMS: D4a2

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
Names: f08nbf; nagf_lapackeig_dgeevx; dgeevx
Keywords: balancing; condition number, matrix; DGEEVX; eigenvalues; eigenvectors; finance; forward error; LAPACK; orthogonal transformations; QR algorithm; real, nonsymmetric matrix
GAMS: D4a2

Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Names: f08nec; nag_dgehrd; dgehrd
Keywords: DGEHRD; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4c1b2

Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Names: f08nef; nagf_lapackeig_dgehrd; dgehrd
Keywords: DGEHRD; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4c1b2

Balances a real general matrix
Names: f08nhc; nag_dgebal; dgebal
Keywords: balancing; DGEBAL; LAPACK; real, nonsymmetric matrix
GAMS: D4c1a

Balances a real general matrix
Names: f08nhf; nagf_lapackeig_dgebal; dgebal
Keywords: balancing; DGEBAL; LAPACK; real, nonsymmetric matrix
GAMS: D4c1a

Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc
Names: f08njc; nag_dgebak; dgebak
Keywords: balancing; DGEBAK; eigenvectors; LAPACK; real, nonsymmetric matrix
GAMS: D4c4

Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhf
Names: f08njf; nagf_lapackeig_dgebak; dgebak
Keywords: balancing; DGEBAK; eigenvectors; LAPACK; real, nonsymmetric matrix
GAMS: D4c4

Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Names: f08pac; nag_dgees; dgees
Keywords: DGEES; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors
GAMS: D4a2

Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Names: f08paf; nagf_lapackeig_dgees; dgees
Keywords: DGEES; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors
GAMS: D4a2

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
Names: f08pbc; nag_dgeesx; dgeesx
Keywords: condition number, matrix; DGEES; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors
GAMS: D4a2

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
Names: f08pbf; nagf_lapackeig_dgeesx; dgeesx
Keywords: condition number, matrix; DGEES; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors
GAMS: D4a2

Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Names: f08pec; nag_dhseqr; dhseqr
Keywords: DHSEQR; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form
GAMS: D4c2b

Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Names: f08pef; nagf_lapackeig_dhseqr; dhseqr
Keywords: DHSEQR; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form
GAMS: D4c2b

Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Names: f08pkc; nag_dhsein; dhsein
Keywords: DHSEIN; eigenvectors; inverse iteration; LAPACK; real, Hessenberg matrix
GAMS: D4c3

Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Names: f08pkf; nagf_lapackeig_dhsein; dhsein
Keywords: DHSEIN; eigenvectors; inverse iteration; LAPACK; real, Hessenberg matrix
GAMS: D4c3

Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Names: f08ppc; nag_zgeesx; zgeesx
Keywords: condition number, matrix; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors; ZGEESX
GAMS: D4a2

Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Names: f08ppf; nagf_lapackeig_zgeesx; zgeesx
Keywords: condition number, matrix; eigenvalues; LAPACK; real, nonsymmetric matrix; Schur form; Schur vectors; ZGEESX
GAMS: D4a2

Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Names: f08qfc; nag_dtrexc; dtrexc
Keywords: DTREXC; LAPACK; orthogonal transformations; real, nonsymmetric matrix; Schur form
GAMS: D4c

Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Names: f08qff; nagf_lapackeig_dtrexc; dtrexc
Keywords: DTREXC; LAPACK; orthogonal transformations; real, nonsymmetric matrix; Schur form
GAMS: D4c

Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Names: f08qgc; nag_dtrsen; dtrsen
Keywords: condition number, matrix; DTREXC; LAPACK; orthogonal transformations; Schur form
GAMS: D4c

Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Names: f08qgf; nagf_lapackeig_dtrsen; dtrsen
Keywords: condition number, matrix; DTREXC; LAPACK; orthogonal transformations; Schur form
GAMS: D4c

Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
Names: f08qhc; nag_dtrsyl; dtrsyl
Keywords: DTRSYL; LAPACK; real, quasi-triangular matrix; Sylvester equation
GAMS: D8

Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
Names: f08qhf; nagf_lapackeig_dtrsyl; dtrsyl
Keywords: DTRSYL; LAPACK; real, quasi-triangular matrix; Sylvester equation
GAMS: D8

Computes left and right eigenvectors of real upper quasi-triangular matrix
Names: f08qkc; nag_dtrevc; dtrevc
Keywords: DTREVC; eigenvectors; LAPACK; real, quasi-triangular matrix
GAMS: D4c3

Computes left and right eigenvectors of real upper quasi-triangular matrix
Names: f08qkf; nagf_lapackeig_dtrevc; dtrevc
Keywords: DTREVC; eigenvectors; LAPACK; real, quasi-triangular matrix
GAMS: D4c3

Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Names: f08qlc; nag_dtrsna; dtrsna
Keywords: condition number, matrix; DTRSNA; eigenvalues; eigenvectors; LAPACK; real, quasi-triangular matrix
GAMS: D4c

Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Names: f08qlf; nagf_lapackeig_dtrsna; dtrsna
Keywords: condition number, matrix; DTRSNA; eigenvalues; eigenvectors; LAPACK; real, quasi-triangular matrix
GAMS: D4c

Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Names: f08rac; nag_dorcsd; dorcsd
Keywords: complete CS decomposition; DORCSD; GSVD, generalized singular value decomposition; LAPACK; real, orthogonal matrix
GAMS: D6

Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Names: f08raf; nagf_lapackeig_dorcsd; dorcsd
Keywords: complete CS decomposition; DORCSD; GSVD, generalized singular value decomposition; LAPACK; real, orthogonal matrix
GAMS: D6

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Names: f08sac; nag_dsygv; dsygv
Keywords: DSYGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Names: f08saf; nagf_lapackeig_dsygv; dsygv
Keywords: DSYGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Names: f08sbc; nag_dsygvx; dsygvx
Keywords: DSYGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Names: f08sbf; nagf_lapackeig_dsygvx; dsygvx
Keywords: DSYGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Names: f08scc; nag_dsygvd; dsygvd
Keywords: divide-and-conquer method; DSYGVD; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Names: f08scf; nagf_lapackeig_dsygvd; dsygvd
Keywords: divide-and-conquer method; DSYGVD; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by f07fdc
Names: f08sec; nag_dsygst; dsygst
Keywords: DSYGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4c1c

Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by f07fdf
Names: f08sef; nagf_lapackeig_dsygst; dsygst
Keywords: DSYGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4c1c

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Names: f08tac; nag_dspgv; dspgv
Keywords: DSPGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Names: f08taf; nagf_lapackeig_dspgv; dspgv
Keywords: DSPGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Names: f08tbc; nag_dspgvx; dspgvx
Keywords: DSPGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Names: f08tbf; nagf_lapackeig_dspgvx; dspgvx
Keywords: DSPGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Names: f08tcc; nag_dspgvd; dspgvd
Keywords: divide-and-conquer method; DSPGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Names: f08tcf; nagf_lapackeig_dspgvd; dspgvd
Keywords: divide-and-conquer method; DSPGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4b1

Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by f07gdc
Names: f08tec; nag_dspgst; dspgst
Keywords: DSPGVX; eigenproblem, generalized; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4c1c

Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by f07gdf
Names: f08tef; nagf_lapackeig_dspgst; dspgst
Keywords: DSPGVX; eigenproblem, generalized; generalized eigenproblem; LAPACK; real, positive definite, symmetric matrix
GAMS: D4c1c

Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Names: f08uac; nag_dsbgv; dsbgv
Keywords: DSBGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Names: f08uaf; nagf_lapackeig_dsbgv; dsbgv
Keywords: DSBGV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Names: f08ubc; nag_dsbgvx; dsbgvx
Keywords: DSBGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Names: f08ubf; nagf_lapackeig_dsbgvx; dsbgvx
Keywords: DSBGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Names: f08ucc; nag_dsbgvd; dsbgvd
Keywords: divide-and-conquer method; DSBGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Names: f08ucf; nagf_lapackeig_dsbgvd; dsbgvd
Keywords: divide-and-conquer method; DSBGVX; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4b5

Performs a reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
Names: f08uec; nag_dsbgst; dsbgst
Keywords: DSBGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4c1c

Performs a reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
Names: f08uef; nagf_lapackeig_dsbgst; dsbgst
Keywords: DSBGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D4c1c

Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Names: f08ufc; nag_dpbstf; dpbstf
Keywords: Cholesky decomposition; DPBSTF; DSBGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D2b2

Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Names: f08uff; nagf_lapackeig_dpbstf; dpbstf
Keywords: Cholesky decomposition; DPBSTF; DSBGST; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; real, band, positive definite, symmetric matrix
GAMS: D2b2

Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Names: f08utc; nag_zpbstf; zpbstf
Keywords: complex, band, Hermitian, positive definite matrix; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; Split Cholesky factorization; ZPBSTF
GAMS: D2b2

Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Names: f08utf; nagf_lapackeig_zpbstf; zpbstf
Keywords: complex, band, Hermitian, positive definite matrix; eigenproblem, generalized; generalized eigenproblem; LAPACK; matrix, band; Split Cholesky factorization; ZPBSTF
GAMS: D2b2

Computes the generalized singular value decomposition of a real matrix pair
Names: f08vac; nag_dggsvd; dggsvd
Keywords: DGGSVD; GSVD, generalized singular value decomposition; LAPACK; real, nonsymmetric matrix; SVD, generalized
GAMS: D6

Computes the generalized singular value decomposition of a real matrix pair
Names: f08vaf; nagf_lapackeig_dggsvd; dggsvd
Keywords: DGGSVD; GSVD, generalized singular value decomposition; LAPACK; real, nonsymmetric matrix; SVD, generalized
GAMS: D6

Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Names: f08vcc; nag_dggsvd3; dggsvd3
Keywords: DGGSVD3; GSVD, generalized singular value decomposition; LAPACK; real, nonsymmetric matrix; SVD, generalized
GAMS: D6

Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Names: f08vcf; nagf_lapackeig_dggsvd3; dggsvd3
Keywords: DGGSVD3; GSVD, generalized singular value decomposition; LAPACK; real, nonsymmetric matrix; SVD, generalized
GAMS: D6

Produces orthogonal matrices that simultaneously reduce the m×n matrix A and the p×n matrix B to upper triangular form
Names: f08vec; nag_dggsvp; dggsvp
Keywords: DGGSVP; GSVD, generalized singular value decomposition; LAPACK; orthogonal transformations; real, m×n matrix; SVD, generalized
GAMS: D6

Produces orthogonal matrices that simultaneously reduce the m×n matrix A and the p×n matrix B to upper triangular form
Names: f08vef; nagf_lapackeig_dggsvp; dggsvp
Keywords: DGGSVP; GSVD, generalized singular value decomposition; LAPACK; orthogonal transformations; real, m×n matrix; SVD, generalized
GAMS: D6

Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m×n matrix A and the p×n matrix B to upper triangular form
Names: f08vgc; nag_dggsvp3; dggsvp3
Keywords: DGGSVP3; GSVD, generalized singular value decomposition; LAPACK; orthogonal transformations; real, m×n matrix; SVD, generalized
GAMS: D6

Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m×n matrix A and the p×n matrix B to upper triangular form
Names: f08vgf; nagf_lapackeig_dggsvp3; dggsvp3
Keywords: DGGSVP3; GSVD, generalized singular value decomposition; LAPACK; orthogonal transformations; real, m×n matrix; SVD, generalized
GAMS: D6

Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Names: f08wac; nag_dggev; dggev
Keywords: DGGEV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Names: f08waf; nagf_lapackeig_dggev; dggev
Keywords: DGGEV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

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
Names: f08wbc; nag_dggevx; dggevx
Keywords: balancing; condition number, matrix; DGGEVX; eigenproblem, generalized; eigenvalues; eigenvectors; finance; forward error; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

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
Names: f08wbf; nagf_lapackeig_dggevx; dggevx
Keywords: balancing; condition number, matrix; DGGEVX; eigenproblem, generalized; eigenvalues; eigenvectors; finance; forward error; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Names: f08wcc; nag_dggev3; dggev3
Keywords: DGGEV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Names: f08wcf; nagf_lapackeig_dggev3; dggev3
Keywords: DGGEV; eigenproblem, generalized; eigenvalues; eigenvectors; generalized eigenproblem; LAPACK; real, nonsymmetric matrix
GAMS: D4b2

Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Names: f08wec; nag_dgghrd; dgghrd
Keywords: DGGHRD; eigenproblem, generalized; generalized eigenproblem; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b2

Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Names: f08wef; nagf_lapackeig_dgghrd; dgghrd
Keywords: DGGHRD; eigenproblem, generalized; generalized eigenproblem; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b2

Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Names: f08wfc; nag_dgghd3; dgghd3
Keywords: DGGHD3; eigenproblem, generalized; generalized eigenproblem; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b2

Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Names: f08wff; nagf_lapackeig_dgghd3; dgghd3
Keywords: DGGHD3; eigenproblem, generalized; generalized eigenproblem; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b2

Balances a pair of real, square, matrices
Names: f08whc; nag_dggbal; dggbal
Keywords: balancing; DGGHRD; eigenproblem, generalized; generalized eigenproblem; LAPACK
GAMS: D4b2

Balances a pair of real, square, matrices
Names: f08whf; nagf_lapackeig_dggbal; dggbal
Keywords: balancing; DGGHRD; eigenproblem, generalized; generalized eigenproblem; LAPACK
GAMS: D4b2

Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc
Names: f08wjc; nag_dggbak; dggbak
Keywords: balancing; DGGBAK; eigenproblem, generalized; eigenvectors; generalized eigenproblem; LAPACK
GAMS: D4b2

Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whf
Names: f08wjf; nagf_lapackeig_dggbak; dggbak
Keywords: balancing; DGGBAK; eigenproblem, generalized; eigenvectors; generalized eigenproblem; LAPACK
GAMS: D4b2

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
Names: f08xac; nag_dgges; dgges
Keywords: DGGES; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

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
Names: f08xaf; nagf_lapackeig_dgges; dgges
Keywords: DGGES; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

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
Names: f08xbc; nag_dggesx; dggesx
Keywords: condition number, matrix; DGGESX; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

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
Names: f08xbf; nagf_lapackeig_dggesx; dggesx
Keywords: condition number, matrix; DGGESX; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Names: f08xcc; nag_dgges3; dgges3
Keywords: DGGES3; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Names: f08xcf; nagf_lapackeig_dgges3; dgges3
Keywords: DGGES3; eigenvalues; generalized Schur form; LAPACK; real, nonsymmetric matrix; Schur form, generalized; Schur vectors
GAMS: D4b2

Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Names: f08xec; nag_dhgeqz; dhgeqz
Keywords: DHGEQZ; eigenvalues; generalized Schur form; LAPACK; real, Hessenberg matrix
GAMS: D4b2

Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Names: f08xef; nagf_lapackeig_dhgeqz; dhgeqz
Keywords: DHGEQZ; eigenvalues; generalized Schur form; LAPACK; real, Hessenberg matrix
GAMS: D4b2

Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Names: f08yec; nag_dtgsja; dtgsja
Keywords: DTGSJA; GSVD, generalized singular value decomposition; LAPACK; real, trapezoidal matrix; real, triangular matrix; SVD, generalized
GAMS: D6

Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Names: f08yef; nagf_lapackeig_dtgsja; dtgsja
Keywords: DTGSJA; GSVD, generalized singular value decomposition; LAPACK; real, trapezoidal matrix; real, triangular matrix; SVD, generalized
GAMS: D6

Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Names: f08yfc; nag_dtgexc; dtgexc
Keywords: DTGEXC; generalized Schur form; LAPACK; orthogonal transformations
GAMS: D4c

Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Names: f08yff; nagf_lapackeig_dtgexc; dtgexc
Keywords: DTGEXC; generalized Schur form; LAPACK; orthogonal transformations
GAMS: D4c

Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Names: f08ygc; nag_dtgsen; dtgsen
Keywords: condition number, matrix; DTGSEN; eigenvalues; generalized Schur form; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b, D4c

Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Names: f08ygf; nagf_lapackeig_dtgsen; dtgsen
Keywords: condition number, matrix; DTGSEN; eigenvalues; generalized Schur form; LAPACK; orthogonal transformations; real, nonsymmetric matrix
GAMS: D4b, D4c

Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Names: f08yhc; nag_dtgsyl; dtgsyl
Keywords: DTGSYL; LAPACK; real, quasi-triangular matrix; Sylvester equation
GAMS: D8

Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Names: f08yhf; nagf_lapackeig_dtgsyl; dtgsyl
Keywords: DTGSYL; LAPACK; real, quasi-triangular matrix; Sylvester equation
GAMS: D8

Computes right and left generalized eigenvectors of the matrix pair (A,B) which is assumed to be in generalized upper Schur form
Names: f08ykc; nag_dtgevc; dtgevc
Keywords: DTGEVC; eigenvectors; generalized Schur form; LAPACK
GAMS: D4b2

Computes right and left generalized eigenvectors of the matrix pair (A,B) which is assumed to be in generalized upper Schur form
Names: f08ykf; nagf_lapackeig_dtgevc; dtgevc
Keywords: DTGEVC; eigenvectors; generalized Schur form; LAPACK
GAMS: D4b2

Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Names: f08ylc; nag_dtgsna; dtgsna
Keywords: condition number, matrix; DTGSNA; generalized Schur form; LAPACK; real, nonsymmetric matrix
GAMS: D4c

Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Names: f08ylf; nagf_lapackeig_dtgsna; dtgsna
Keywords: condition number, matrix; DTGSNA; generalized Schur form; LAPACK; real, nonsymmetric matrix
GAMS: D4c

Solves the real linear equality-constrained least squares (LSE) problem
Names: f08zac; nag_dgglse; dgglse
Keywords: DGGLSE; LAPACK; linear least squares; real, m×n matrix; RQ factorizations
GAMS: D9b1

Solves the real linear equality-constrained least squares (LSE) problem
Names: f08zaf; nagf_lapackeig_dgglse; dgglse
Keywords: DGGLSE; LAPACK; linear least squares; real, m×n matrix; RQ factorizations
GAMS: D9b1

Solves a real general Gauss–Markov linear model (GLM) problem
Names: f08zbc; nag_dggglm; dggglm
Keywords: DGGGLM; Gauss–Markov linear model; LAPACK; QR factorization; real, m×n matrix
GAMS: D9b1

Solves a real general Gauss–Markov linear model (GLM) problem
Names: f08zbf; nagf_lapackeig_dggglm; dggglm
Keywords: DGGGLM; Gauss–Markov linear model; LAPACK; QR factorization; real, m×n matrix
GAMS: D9b1

Computes a generalized QR factorization of a real matrix pair
Names: f08zec; nag_dggqrf; dggqrf
Keywords: DGGQRF; LAPACK; QR factorization; real, m×n matrix
GAMS: D5

Computes a generalized QR factorization of a real matrix pair
Names: f08zef; nagf_lapackeig_dggqrf; dggqrf
Keywords: DGGQRF; LAPACK; QR factorization; real, m×n matrix
GAMS: D5

Computes a generalized RQ factorization of a real matrix pair
Names: f08zfc; nag_dggrqf; dggrqf
Keywords: DGGRQF; LAPACK; real, m×n matrix; RQ factorizations
GAMS: D5

Computes a generalized RQ factorization of a real matrix pair
Names: f08zff; nagf_lapackeig_dggrqf; dggrqf
Keywords: DGGRQF; LAPACK; real, m×n matrix; RQ factorizations
GAMS: D5

Initialization routine for (f12abc) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
Names: f12aac; nag_real_sparse_eigensystem_init
Keywords: eigenproblem; eigenproblem, initialization; real, sparse matrix
GAMS: D4c1b3

Initialization routine for (f12abf) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
Names: f12aaf; nagf_sparseig_real_init
Keywords: eigenproblem; eigenproblem, initialization; real, sparse matrix
GAMS: D4c1b3

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Names: f12abc; nag_real_sparse_eigensystem_iter
Keywords: eigenproblem; eigenvalues; eigenvectors; real, sparse matrix; sparse eigenproblem
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Names: f12abf; nagf_sparseig_real_iter
Keywords: eigenproblem; eigenvalues; eigenvectors; real, sparse matrix; sparse eigenproblem
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for f12abc
Names: f12acc; nag_real_sparse_eigensystem_sol
Keywords: eigenproblem; eigenvalues; eigenvectors; real, sparse matrix; sparse eigenproblem
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for f12abf
Names: f12acf; nagf_sparseig_real_proc
Keywords: eigenproblem; eigenvalues; eigenvectors; real, sparse matrix; sparse eigenproblem
GAMS: D4a7

Set a single option from a string (f12abc/f12acc/f12agc)
Names: f12adc; nag_real_sparse_eigensystem_option
Keywords: real, sparse matrix; sparse eigenproblem, options
GAMS: D4c1b3

Set a single option from a string (f12abf/f12acf/f12agf)
Names: f12adf; nagf_sparseig_real_option
Keywords: real, sparse matrix; sparse eigenproblem, options
GAMS: D4c1b3

Provides monitoring information for f12abc
Names: f12aec; nag_real_sparse_eigensystem_monit
Keywords: eigenproblem; monitoring information; real, sparse matrix; sparse eigenproblems, monitoring
GAMS: D4c1b3

Provides monitoring information for f12abf
Names: f12aef; nagf_sparseig_real_monit
Keywords: eigenproblem; monitoring information; real, sparse matrix; sparse eigenproblems, monitoring
GAMS: D4c1b3

Initialization routine for (f12agc) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
Names: f12afc; nag_real_banded_sparse_eigensystem_init
Keywords: eigenproblem, initialization; real, band matrix
GAMS: D4c1b3

Initialization routine for (f12agf) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
Names: f12aff; nagf_sparseig_real_band_init
Keywords: eigenproblem, initialization; real, band matrix
GAMS: D4c1b3

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Names: f12agc; nag_real_banded_sparse_eigensystem_sol
Keywords: eigenproblem, banded; eigenvalues; eigenvectors; real, band matrix
GAMS: D4a6

Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Names: f12agf; nagf_sparseig_real_band_solve
Keywords: eigenproblem, banded; eigenvalues; eigenvectors; real, band matrix
GAMS: D4a6

Initialization routine for (f12fbc) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
Names: f12fac; nag_real_symm_sparse_eigensystem_init
Keywords: eigenproblem, initialization; real, sparse, symmetric matrix
GAMS: D4c1b3

Initialization routine for (f12fbf) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
Names: f12faf; nagf_sparseig_real_symm_init
Keywords: eigenproblem, initialization; real, sparse, symmetric matrix
GAMS: D4c1b3

Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Names: f12fbc; nag_real_symm_sparse_eigensystem_iter
Keywords: eigenvalues; eigenvectors; real, sparse, symmetric matrix; sparse eigenproblem
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Names: f12fbf; nagf_sparseig_real_symm_iter
Keywords: eigenvalues; eigenvectors; real, sparse, symmetric matrix; sparse eigenproblem
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for f12fbc
Names: f12fcc; nag_real_symm_sparse_eigensystem_sol
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, postprocessing
GAMS: D4a7

Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for f12fbf
Names: f12fcf; nagf_sparseig_real_symm_proc
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, postprocessing
GAMS: D4a7

Set a single option from a string (f12fbc/f12fcc/f12fgc)
Names: f12fdc; nag_real_symm_sparse_eigensystem_option
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, options
GAMS: D4c1b3

Set a single option from a string (f12fbf/f12fcf/f12fgf)
Names: f12fdf; nagf_sparseig_real_symm_option
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, options
GAMS: D4c1b3

Provides monitoring information for f12fbc
Names: f12fec; nag_real_symm_sparse_eigensystem_monit
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, monitoring
GAMS: D4c1b3

Provides monitoring information for f12fbf
Names: f12fef; nagf_sparseig_real_symm_monit
Keywords: real, sparse, symmetric matrix; sparse eigenproblem, monitoring
GAMS: D4c1b3

Initialization routine for (f12fgc) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
Names: f12ffc; nag_real_symm_banded_sparse_eigensystem_init
Keywords: eigenproblem, initialization; real, band, symmetric matrix
GAMS: D4c1b3

Initialization routine for (f12fgf) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
Names: f12fff; nagf_sparseig_real_symm_band_init
Keywords: eigenproblem, initialization; real, band, symmetric matrix
GAMS: D4c1b3

Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Names: f12fgc; nag_real_symm_banded_sparse_eigensystem_sol
Keywords: eigenproblem, banded; eigenvalues; eigenvectors; real, band, symmetric matrix
GAMS: D4a6

Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Names: f12fgf; nagf_sparseig_real_symm_band_solve
Keywords: eigenproblem, banded; eigenvalues; eigenvectors; real, band, symmetric matrix
GAMS: D4a6

Initialization routine for (f12jjc, f12jkc, f12jrc, f12jsc, f12jtc, f12juc and f12jvc) computing eigenvalues within a selected region of the complex plane, and eigenvectors, of a standard, generalized or polynomial eigenproblem
Names: f12jac; nag_sparseig_feast_init
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Initialization routine for (f12jjf, f12jkf, f12jrf, f12jsf, f12jtf, f12juf and f12jvf) computing eigenvalues within a selected region of the complex plane, and eigenvectors, of a standard, generalized or polynomial eigenproblem
Names: f12jaf; nagf_sparseig_feast_init
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Set a single option from a string (f12jjc, f12jkc, f12jrc, f12jsc, f12jtc, f12juc and f12jvc)
Names: f12jbc; nag_sparseig_feast_option
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Set a single option from a string (f12jjf, f12jkf, f12jrf, f12jsf, f12jtf, f12juf and f12jvf)
Names: f12jbf; nagf_sparseig_feast_option
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Setup routine for f12jjc and f12jrc. Computes nodes and weights for an elliptical contour, symmetric about the real line
Names: f12jec; nag_sparseig_feast_symm_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Setup routine for f12jjf and f12jrf. Computes nodes and weights for an elliptical contour, symmetric about the real line
Names: f12jef; nagf_sparseig_feast_symm_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Setup routine for f12jkc, f12jsc, f12jtc, f12juc and f12jvc. Computes nodes and weights for an elliptical contour in the complex plane
Names: f12jfc; nag_sparseig_feast_gen_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real matrix
GAMS:

Setup routine for f12jkf, f12jsf, f12jtf, f12juf and f12jvf. Computes nodes and weights for an elliptical contour in the complex plane
Names: f12jff; nagf_sparseig_feast_gen_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real matrix
GAMS:

Setup routine for f12jkc, f12jsc, f12jtc, f12juc and f12jvc. Creates nodes and weights for a custom contour in the complex plane
Names: f12jgc; nag_sparseig_feast_custom_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real matrix
GAMS:

Setup routine for f12jkf, f12jsf, f12jtf, f12juf and f12jvf. Creates nodes and weights for a custom contour in the complex plane
Names: f12jgf; nagf_sparseig_feast_custom_contour
Keywords: complex, Hermitian matrix; eigenvalues; eigenvectors; real matrix
GAMS:

Selected eigenvalues and eigenvectors of a real symmetric eigenproblem, reverse communication driver
Names: f12jjc; nag_sparseig_feast_real_symm_solve
Keywords: eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Selected eigenvalues and eigenvectors of a real symmetric eigenproblem, reverse communication driver
Names: f12jjf; nagf_sparseig_feast_real_symm_solve
Keywords: eigenvalues; eigenvectors; real, symmetric matrix
GAMS:

Selected eigenvalues and eigenvectors of a real nonsymmetric eigenproblem, reverse communication driver
Names: f12jkc; nag_sparseig_feast_real_gen_solve
Keywords: eigenvalues; eigenvectors; real, nonsymmetric matrix
GAMS:

Selected eigenvalues and eigenvectors of a real nonsymmetric eigenproblem, reverse communication driver
Names: f12jkf; nagf_sparseig_feast_real_gen_solve
Keywords: eigenvalues; eigenvectors; real, nonsymmetric matrix
GAMS: