F08 (Lapackeig)

Least Squares and Eigenvalue Problems (LAPACK)

F08 (Lapackeig) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Function |
Mark of Introduction |
Purpose |
---|---|---|

f08aac | 23 | nag_lapackeig_dgels Solves a real linear least squares problem of full rank |

f08abc | 24 | nag_lapackeig_dgeqrt Performs a $QR$ factorization of real general rectangular matrix, with explicit blocking |

f08acc | 24 | nag_lapackeig_dgemqrt Applies the orthogonal transformation determined by f08abc |

f08aec | 7 | nag_lapackeig_dgeqrf Performs a $QR$ factorization of real general rectangular matrix |

f08afc | 7 | nag_lapackeig_dorgqr Forms all or part of orthogonal $Q$ from $QR$ factorization determined by f08aec, f08bec or f08bfc |

f08agc | 7 | nag_lapackeig_dormqr Applies an orthogonal transformation determined by f08aec, f08bec or f08bfc |

f08ahc | 7 | nag_lapackeig_dgelqf Performs a $LQ$ factorization of real general rectangular matrix |

f08ajc | 7 | nag_lapackeig_dorglq Forms all or part of orthogonal $Q$ from $LQ$ factorization determined by f08ahc |

f08akc | 7 | nag_lapackeig_dormlq Applies the orthogonal transformation determined by f08ahc |

f08anc | 23 | nag_lapackeig_zgels Solves a complex linear least problem of full rank |

f08apc | 24 | nag_lapackeig_zgeqrt Performs a $QR$ factorization of complex general rectangular matrix using recursive algorithm |

f08aqc | 24 | nag_lapackeig_zgemqrt Applies the unitary transformation determined by f08apc |

f08asc | 7 | nag_lapackeig_zgeqrf Performs a $QR$ factorization of complex general rectangular matrix |

f08atc | 7 | nag_lapackeig_zungqr Forms all or part of unitary $Q$ from $QR$ factorization determined by f08asc, f08bsc or f08btc |

f08auc | 7 | nag_lapackeig_zunmqr Applies a unitary transformation determined by f08asc, f08bsc or f08btc |

f08avc | 7 | nag_lapackeig_zgelqf Performs a $LQ$ factorization of complex general rectangular matrix |

f08awc | 7 | nag_lapackeig_zunglq Forms all or part of unitary $Q$ from $LQ$ factorization determined by f08avc |

f08axc | 7 | nag_lapackeig_zunmlq Applies the unitary transformation determined by f08avc |

f08bac | 23 | nag_lapackeig_dgelsy Computes the minimum-norm solution to a real linear least squares problem |

f08bbc | 24 | nag_lapackeig_dtpqrt $QR$ factorization of real general triangular-pentagonal matrix |

f08bcc | 24 | nag_lapackeig_dtpmqrt Applies the orthogonal transformation determined by f08bbc |

f08bfc | 23 | nag_lapackeig_dgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |

f08bhc | 23 | nag_lapackeig_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |

f08bkc | 23 | nag_lapackeig_dormrz Applies the orthogonal transformation determined by f08bhc |

f08bnc | 23 | nag_lapackeig_zgelsy Computes the minimum-norm solution to a complex linear least squares problem |

f08bpc | 24 | nag_lapackeig_ztpqrt $QR$ factorization of complex triangular-pentagonal matrix |

f08bqc | 24 | nag_lapackeig_ztpmqrt Applies the unitary transformation determined by f08bpc |

f08btc | 23 | nag_lapackeig_zgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |

f08bvc | 23 | nag_lapackeig_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |

f08bxc | 23 | nag_lapackeig_zunmrz Applies the unitary transformation determined by f08bvc |

f08cec | 23 | nag_lapackeig_dgeqlf $QL$ factorization of real general rectangular matrix |

f08cfc | 23 | nag_lapackeig_dorgql Form all or part of orthogonal $Q$ from $QL$ factorization determined by f08cec |

f08cgc | 23 | nag_lapackeig_dormql Applies the orthogonal transformation determined by f08cec |

f08chc | 23 | nag_lapackeig_dgerqf $RQ$ factorization of real general rectangular matrix |

f08cjc | 23 | nag_lapackeig_dorgrq Form all or part of orthogonal $Q$ from $RQ$ factorization determined by f08chc |

f08ckc | 23 | nag_lapackeig_dormrq Applies the orthogonal transformation determined by f08chc |

f08csc | 23 | nag_lapackeig_zgeqlf $QL$ factorization of complex general rectangular matrix |

f08ctc | 23 | nag_lapackeig_zungql Form all or part of unitary $Q$ from $QL$ factorization determined by f08csc |

f08cuc | 23 | nag_lapackeig_zunmql Applies the unitary transformation determined by f08csc |

f08cvc | 23 | nag_lapackeig_zgerqf $RQ$ factorization of complex general rectangular matrix |

f08cwc | 23 | nag_lapackeig_zungrq Form all or part of unitary $Q$ from $RQ$ factorization determined by f08cvc |

f08cxc | 23 | nag_lapackeig_zunmrq Applies the unitary transformation determined by f08cvc |

f08fac | 23 | nag_lapackeig_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |

f08fbc | 23 | nag_lapackeig_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |

f08fcc | 7 | nag_lapackeig_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |

f08fdc | 23 | nag_lapackeig_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |

f08fec | 7 | nag_lapackeig_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |

f08ffc | 7 | nag_lapackeig_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec |

f08fgc | 7 | nag_lapackeig_dormtr Applies the orthogonal transformation determined by f08fec |

f08flc | 23 | nag_lapackeig_ddisna 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 |

f08fnc | 23 | nag_lapackeig_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |

f08fpc | 23 | nag_lapackeig_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |

f08fqc | 7 | nag_lapackeig_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |

f08frc | 23 | nag_lapackeig_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |

f08fsc | 7 | nag_lapackeig_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |

f08ftc | 7 | nag_lapackeig_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc |

f08fuc | 7 | nag_lapackeig_zunmtr Applies the unitary transformation matrix determined by f08fsc |

f08gac | 23 | nag_lapackeig_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |

f08gbc | 23 | nag_lapackeig_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |

f08gcc | 7 | nag_lapackeig_dspevd 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) |

f08gec | 7 | nag_lapackeig_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |

f08gfc | 7 | nag_lapackeig_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec |

f08ggc | 7 | nag_lapackeig_dopmtr Applies the orthogonal transformation determined by f08gec |

f08gnc | 23 | nag_lapackeig_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |

f08gpc | 23 | nag_lapackeig_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |

f08gqc | 7 | nag_lapackeig_zhpevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the $QL$ or $QR$ algorithm) |

f08gsc | 7 | nag_lapackeig_zhptrd Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |

f08gtc | 7 | nag_lapackeig_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsc |

f08guc | 7 | nag_lapackeig_zupmtr Applies the unitary transformation matrix determined by f08gsc |

f08hac | 23 | nag_lapackeig_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

f08hbc | 23 | nag_lapackeig_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

f08hcc | 7 | nag_lapackeig_dsbevd 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) |

f08hec | 7 | nag_lapackeig_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |

f08hnc | 23 | nag_lapackeig_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |

f08hpc | 23 | nag_lapackeig_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |

f08hqc | 7 | nag_lapackeig_zhbevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |

f08hsc | 7 | nag_lapackeig_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |

f08jac | 23 | nag_lapackeig_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |

f08jbc | 23 | nag_lapackeig_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |

f08jcc | 7 | nag_lapackeig_dstevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |

f08jdc | 23 | nag_lapackeig_dstevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |

f08jec | 7 | nag_lapackeig_dsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm |

f08jfc | 7 | nag_lapackeig_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm |

f08jgc | 7 | nag_lapackeig_dpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix |

f08jhc | 23 | nag_lapackeig_dstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) |

f08jjc | 7 | nag_lapackeig_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection |

f08jkc | 7 | nag_lapackeig_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |

f08jlc | 23 | nag_lapackeig_dstegr 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) |

f08jsc | 7 | nag_lapackeig_zsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm |

f08juc | 7 | nag_lapackeig_zpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix |

f08jvc | 23 | nag_lapackeig_zstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer) |

f08jxc | 7 | nag_lapackeig_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |

f08jyc | 23 | nag_lapackeig_zstegr 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) |

f08kac | 23 | nag_lapackeig_dgelss Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition |

f08kbc | 23 | nag_lapackeig_dgesvd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |

f08kcc | 23 | nag_lapackeig_dgelsd Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer) |

f08kdc | 23 | nag_lapackeig_dgesdd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |

f08kec | 7 | nag_lapackeig_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form |

f08kfc | 7 | nag_lapackeig_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec |

f08kgc | 7 | nag_lapackeig_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kec |

f08khc | 23 | nag_lapackeig_dgejsv Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |

f08kjc | 23 | nag_lapackeig_dgesvj Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |

f08kmc | 27 | nag_lapackeig_dgesvdx 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 |

f08knc | 23 | nag_lapackeig_zgelss Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition |

f08kpc | 23 | nag_lapackeig_zgesvd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors |

f08kqc | 23 | nag_lapackeig_zgelsd Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer) |

f08krc | 23 | nag_lapackeig_zgesdd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |

f08ksc | 7 | nag_lapackeig_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form |

f08ktc | 7 | nag_lapackeig_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksc |

f08kuc | 7 | nag_lapackeig_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by f08ksc |

f08kvc | 27 | nag_lapackeig_zgejsv Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |

f08kwc | 27 | nag_lapackeig_zgesvj Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |

f08kzc | 27 | nag_lapackeig_zgesvdx Computes all or selected singular values of the singular value decomposition of a complex general matrix, optionally computing the corresponding left and right singular vectors |

f08lec | 7 | nag_lapackeig_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form |

f08lsc | 7 | nag_lapackeig_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |

f08mbc | 27 | nag_lapackeig_dbdsvdx 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 |

f08mdc | 23 | nag_lapackeig_dbdsdc Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) |

f08mec | 7 | nag_lapackeig_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix |

f08msc | 7 | nag_lapackeig_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix |

f08nac | 23 | nag_lapackeig_dgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |

f08nbc | 23 | nag_lapackeig_dgeevx 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 |

f08nec | 7 | nag_lapackeig_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form |

f08nfc | 7 | nag_lapackeig_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec |

f08ngc | 7 | nag_lapackeig_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec |

f08nhc | 7 | nag_lapackeig_dgebal Balances a real general matrix |

f08njc | 7 | nag_lapackeig_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc |

f08nnc | 23 | nag_lapackeig_zgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |

f08npc | 23 | nag_lapackeig_zgeevx Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |

f08nsc | 7 | nag_lapackeig_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form |

f08ntc | 7 | nag_lapackeig_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsc |

f08nuc | 7 | nag_lapackeig_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsc |

f08nvc | 7 | nag_lapackeig_zgebal Balances a complex general matrix |

f08nwc | 7 | nag_lapackeig_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvc |

f08pac | 23 | nag_lapackeig_dgees Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors |

f08pbc | 23 | nag_lapackeig_dgeesx 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 |

f08pec | 7 | nag_lapackeig_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |

f08pkc | 7 | nag_lapackeig_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |

f08pnc | 23 | nag_lapackeig_zgees Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors |

f08ppc | 23 | nag_lapackeig_zgeesx 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 |

f08psc | 7 | nag_lapackeig_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |

f08pxc | 7 | nag_lapackeig_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |

f08qfc | 7 | nag_lapackeig_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation |

f08qgc | 7 | nag_lapackeig_dtrsen Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |

f08qhc | 7 | nag_lapackeig_dtrsyl Solves the real Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper quasi-triangular or transposes |

f08qkc | 7 | nag_lapackeig_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |

f08qlc | 7 | nag_lapackeig_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |

f08qtc | 7 | nag_lapackeig_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation |

f08quc | 7 | nag_lapackeig_ztrsen Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |

f08qvc | 7 | nag_lapackeig_ztrsyl Solves the complex Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper triangular or conjugate-transposes |

f08qxc | 7 | nag_lapackeig_ztrevc Computes left and right eigenvectors of complex upper triangular matrix |

f08qyc | 7 | nag_lapackeig_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |

f08rac | 24 | nag_lapackeig_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices |

f08rnc | 24 | nag_lapackeig_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices |

f08sac | 23 | nag_lapackeig_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |

f08sbc | 23 | nag_lapackeig_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |

f08scc | 23 | nag_lapackeig_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |

f08sec | 7 | nag_lapackeig_dsygst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, $B$ factorized by f07fdc |

f08snc | 23 | nag_lapackeig_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |

f08spc | 23 | nag_lapackeig_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |

f08sqc | 23 | nag_lapackeig_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |

f08ssc | 7 | nag_lapackeig_zhegst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, $B$ factorized by f07frc |

f08tac | 23 | nag_lapackeig_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |

f08tbc | 23 | nag_lapackeig_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |

f08tcc | 23 | nag_lapackeig_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) |

f08tec | 7 | nag_lapackeig_dspgst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, packed storage, $B$ factorized by f07gdc |

f08tnc | 23 | nag_lapackeig_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |

f08tpc | 23 | nag_lapackeig_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |

f08tqc | 23 | nag_lapackeig_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) |

f08tsc | 7 | nag_lapackeig_zhpgst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, packed storage, $B$ factorized by f07grc |

f08uac | 23 | nag_lapackeig_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |

f08ubc | 23 | nag_lapackeig_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |

f08ucc | 23 | nag_lapackeig_dsbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer) |

f08uec | 7 | nag_lapackeig_dsbgst Performs a reduction of real symmetric-definite banded generalized eigenproblem $Ax=\lambda Bx$ to standard form $Cy=\lambda y$, such that $C$ has the same bandwidth as $A$ |

f08ufc | 7 | nag_lapackeig_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$ |

f08unc | 23 | nag_lapackeig_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |

f08upc | 23 | nag_lapackeig_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |

f08uqc | 23 | nag_lapackeig_zhbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer) |

f08usc | 7 | nag_lapackeig_zhbgst Performs a reduction of complex Hermitian-definite banded generalized eigenproblem $Ax=\lambda Bx$ to standard form $Cy=\lambda y$, such that $C$ has the same bandwidth as $A$ |

f08utc | 7 | nag_lapackeig_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix $A$ |

f08vcc | 26 | nag_lapackeig_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair |

f08vgc | 26 | nag_lapackeig_dggsvp3 Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the $m\times n$ matrix $A$ and the $p\times n$ matrix $B$ to upper triangular form |

f08vqc | 26 | nag_lapackeig_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair |

f08vuc | 26 | nag_lapackeig_zggsvp3 Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, $m\times n$, matrix $A$ and the complex, $p\times n$, matrix $B$ to upper triangular form |

f08wbc | 23 | nag_lapackeig_dggevx 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 |

f08wcc | 26 | nag_lapackeig_dggev3 Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wfc | 26 | nag_lapackeig_dgghd3 Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |

f08whc | 7 | nag_lapackeig_dggbal Balances a pair of real, square, matrices |

f08wjc | 7 | nag_lapackeig_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc |

f08wpc | 23 | nag_lapackeig_zggevx Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |

f08wqc | 26 | nag_lapackeig_zggev3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wtc | 26 | nag_lapackeig_zgghd3 Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |

f08wvc | 7 | nag_lapackeig_zggbal Balances a pair of complex, square, matrices |

f08wwc | 7 | nag_lapackeig_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvc |

f08xbc | 23 | nag_lapackeig_dggesx 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 |

f08xcc | 26 | nag_lapackeig_dgges3 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 |

f08xec | 7 | nag_lapackeig_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |

f08xpc | 23 | nag_lapackeig_zggesx Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |

f08xqc | 26 | nag_lapackeig_zgges3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors |

f08xsc | 7 | nag_lapackeig_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices |

f08yec | 23 | nag_lapackeig_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |

f08yfc | 23 | nag_lapackeig_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |

f08ygc | 23 | nag_lapackeig_dtgsen 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 |

f08yhc | 23 | nag_lapackeig_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation |

f08ykc | 7 | nag_lapackeig_dtgevc Computes right and left generalized eigenvectors of the matrix pair $(A,B)$ which is assumed to be in generalized upper Schur form |

f08ylc | 23 | nag_lapackeig_dtgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form |

f08ysc | 23 | nag_lapackeig_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |

f08ytc | 23 | nag_lapackeig_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |

f08yuc | 23 | nag_lapackeig_ztgsen Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces |

f08yvc | 23 | nag_lapackeig_ztgsyl Solves the complex generalized Sylvester equation |

f08yxc | 7 | nag_lapackeig_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices |

f08yyc | 23 | nag_lapackeig_ztgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form |

f08zac | 9 | nag_lapackeig_dgglse Solves the real linear equality-constrained least squares (LSE) problem |

f08zbc | 9 | nag_lapackeig_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |

f08zec | 23 | nag_lapackeig_dggqrf Computes a generalized $QR$ factorization of a real matrix pair |

f08zfc | 23 | nag_lapackeig_dggrqf Computes a generalized $RQ$ factorization of a real matrix pair |

f08znc | 9 | nag_lapackeig_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |

f08zpc | 9 | nag_lapackeig_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |

f08zsc | 23 | nag_lapackeig_zggqrf Computes a generalized $QR$ factorization of a complex matrix pair |

f08ztc | 23 | nag_lapackeig_zggrqf Computes a generalized $RQ$ factorization of a complex matrix pair |

f08bec | 7
(Deprecated) |
nag_lapackeig_dgeqpf $QR$ factorization, with column pivoting, of real general rectangular matrix |

f08bsc | 7
(Deprecated) |
nag_lapackeig_zgeqpf $QR$ factorization, with column pivoting, of complex general rectangular matrix |

f08vac | 9
(Deprecated) |
nag_lapackeig_dggsvd Computes the generalized singular value decomposition of a real matrix pair |

f08vec | 23
(Deprecated) |
nag_lapackeig_dggsvp Produces orthogonal matrices that simultaneously reduce the $m\times n$ matrix $A$ and the $p\times n$ matrix $B$ to upper triangular form |

f08vnc | 9
(Deprecated) |
nag_lapackeig_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |

f08vsc | 23
(Deprecated) |
nag_lapackeig_zggsvp Produces unitary matrices that simultaneously reduce the complex, $m\times n$, matrix $A$ and the complex, $p\times n$, matrix $B$ to upper triangular form |

f08wac | 23
(Deprecated) |
nag_lapackeig_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wec | 7
(Deprecated) |
nag_lapackeig_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |

f08wnc | 23
(Deprecated) |
nag_lapackeig_zggev Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wsc | 7
(Deprecated) |
nag_lapackeig_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |

f08xac | 23
(Deprecated) |
nag_lapackeig_dgges 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 |

f08xnc | 23
(Deprecated) |
nag_lapackeig_zgges Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors |