# NAG Library Chapter Contentsf08 – Least Squares and Eigenvalue Problems (LAPACK)

f08 Chapter Introduction – a description of the Chapter and an overview of the algorithms available

 FunctionName Mark ofIntroduction Purpose f08aac Example Text Example Data 23 nag_dgels Solves a real linear least squares problem of full rank f08abc Example Text Example Data 24 nag_dgeqrt Performs a $QR$ factorization of real general rectangular matrix, with explicit blocking f08acc 24 nag_dgemqrt Applies the orthogonal transformation determined by nag_dgeqrt (f08abc) f08aec Example Text Example Data 7 nag_dgeqrf Performs a $QR$ factorization of real general rectangular matrix f08afc Example Text Example Data 7 nag_dorgqr Forms all or part of orthogonal $Q$ from $QR$ factorization determined by nag_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc) f08agc 7 nag_dormqr Applies an orthogonal transformation determined by nag_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc) f08ahc Example Text Example Data 7 nag_dgelqf Performs a $LQ$ factorization of real general rectangular matrix f08ajc Example Text Example Data 7 nag_dorglq Forms all or part of orthogonal $Q$ from $LQ$ factorization determined by nag_dgelqf (f08ahc) f08akc 7 nag_dormlq Applies the orthogonal transformation determined by nag_dgelqf (f08ahc) f08anc Example Text Example Data 23 nag_zgels Solves a complex linear least problem of full rank f08apc Example Text Example Data 24 nag_zgeqrt Performs a $QR$ factorization of complex general rectangular matrix using recursive algorithm f08aqc 24 nag_zgemqrt Applies the unitary transformation determined by nag_zgeqrt (f08apc) f08asc Example Text Example Data 7 nag_zgeqrf Performs a $QR$ factorization of complex general rectangular matrix f08atc Example Text Example Data 7 nag_zungqr Forms all or part of unitary $Q$ from $QR$ factorization determined by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc) f08auc 7 nag_zunmqr Applies a unitary transformation determined by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc) f08avc Example Text Example Data 7 nag_zgelqf Performs a $LQ$ factorization of complex general rectangular matrix f08awc Example Text Example Data 7 nag_zunglq Forms all or part of unitary $Q$ from $LQ$ factorization determined by nag_zgelqf (f08avc) f08axc 7 nag_zunmlq Applies the unitary transformation determined by nag_zgelqf (f08avc) f08bac Example Text Example Data 23 nag_dgelsy Computes the minimum-norm solution to a real linear least squares problem f08bbc Example Text Example Data 24 nag_dtpqrt $QR$ factorization of real general triangular-pentagonal matrix f08bcc 24 nag_dtpmqrt Applies the orthogonal transformation determined by nag_dtpqrt (f08bbc) f08bec Example Text Example Data 7 nag_dgeqpf $QR$ factorization, with column pivoting, of real general rectangular matrix f08bfc Example Text Example Data 23 nag_dgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix f08bhc Example Text Example Data 23 nag_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form f08bkc 23 nag_dormrz Applies the orthogonal transformation determined by nag_dtzrzf (f08bhc) f08bnc Example Text Example Data 23 nag_zgelsy Computes the minimum-norm solution to a complex linear least squares problem f08bpc Example Text Example Data 24 nag_ztpqrt $QR$ factorization of complex triangular-pentagonal matrix f08bqc 24 nag_ztpmqrt Applies the unitary transformation determined by nag_ztpqrt (f08bpc) f08bsc Example Text Example Data 7 nag_zgeqpf $QR$ factorization, with column pivoting, of complex general rectangular matrix f08btc Example Text Example Data 23 nag_zgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix f08bvc Example Text Example Data 23 nag_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form f08bxc 23 nag_zunmrz Applies the unitary transformation determined by nag_ztzrzf (f08bvc) f08cec Example Text Example Data 23 nag_dgeqlf $QL$ factorization of real general rectangular matrix f08cfc Example Text Example Data 23 nag_dorgql Form all or part of orthogonal $Q$ from $QL$ factorization determined by nag_dgeqlf (f08cec) f08cgc 23 nag_dormql Applies the orthogonal transformation determined by nag_dgeqlf (f08cec) f08chc Example Text Example Data 23 nag_dgerqf $RQ$ factorization of real general rectangular matrix f08cjc Example Text Example Data 23 nag_dorgrq Form all or part of orthogonal $Q$ from $RQ$ factorization determined by nag_dgerqf (f08chc) f08ckc 23 nag_dormrq Applies the orthogonal transformation determined by nag_dgerqf (f08chc) f08csc Example Text Example Data 23 nag_zgeqlf $QL$ factorization of complex general rectangular matrix f08ctc Example Text Example Data 23 nag_zungql Form all or part of unitary $Q$ from $QL$ factorization determined by nag_zgeqlf (f08csc) f08cuc 23 nag_zunmql Applies the unitary transformation determined by nag_zgeqlf (f08csc) f08cvc Example Text Example Data 23 nag_zgerqf $RQ$ factorization of complex general rectangular matrix f08cwc Example Text Example Data 23 nag_zungrq Form all or part of unitary $Q$ from $RQ$ factorization determined by nag_zgerqf (f08cvc) f08cxc 23 nag_zunmrq Applies the unitary transformation determined by nag_zgerqf (f08cvc) f08fac Example Text Example Data 23 nag_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix f08fbc Example Text Example Data 23 nag_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix f08fcc Example Text Example Data 7 nag_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) f08fdc Example Text Example Data 23 nag_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) f08fec Example Text Example Data 7 nag_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form f08ffc Example Text Example Data 7 nag_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsytrd (f08fec) f08fgc Example Text Example Data 7 nag_dormtr Applies the orthogonal transformation determined by nag_dsytrd (f08fec) f08flc 23 nag_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 Example Text Example Data 23 nag_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix f08fpc Example Text Example Data 23 nag_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix f08fqc Example Text Example Data 7 nag_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) f08frc Example Text Example Data 23 nag_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) f08fsc Example Text Example Data 7 nag_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form f08ftc Example Text Example Data 7 nag_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhetrd (f08fsc) f08fuc Example Text Example Data 7 nag_zunmtr Applies the unitary transformation matrix determined by nag_zhetrd (f08fsc) f08gac Example Text Example Data 23 nag_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage f08gbc Example Text Example Data 23 nag_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage f08gcc Example Text Example Data 7 nag_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 Example Text Example Data 7 nag_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage f08gfc Example Text Example Data 7 nag_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsptrd (f08gec) f08ggc Example Text Example Data 7 nag_dopmtr Applies the orthogonal transformation determined by nag_dsptrd (f08gec) f08gnc Example Text Example Data 23 nag_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage f08gpc Example Text Example Data 23 nag_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage f08gqc Example Text Example Data 7 nag_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 Example Text Example Data 7 nag_zhptrd Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage f08gtc Example Text Example Data 7 nag_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by nag_zhptrd (f08gsc) f08guc Example Text Example Data 7 nag_zupmtr Applies the unitary transformation matrix determined by nag_zhptrd (f08gsc) f08hac Example Text Example Data 23 nag_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix f08hbc Example Text Example Data 23 nag_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix f08hcc Example Text Example Data 7 nag_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 Example Text Example Data 7 nag_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form f08hnc Example Text Example Data 23 nag_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix f08hpc Example Text Example Data 23 nag_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix f08hqc Example Text Example Data 7 nag_zhbevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer) f08hsc Example Text Example Data 7 nag_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form f08jac Example Text Example Data 23 nag_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix f08jbc Example Text Example Data 23 nag_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix f08jcc Example Text Example Data 7 nag_dstevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) f08jdc Example Text Example Data 23 nag_dstevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) f08jec Example Text Example Data 7 nag_dsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm f08jfc Example Text Example Data 7 nag_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm f08jgc Example Text Example Data 7 nag_dpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix f08jhc Example Text Example Data 23 nag_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_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection f08jkc 7 nag_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array f08jlc Example Text Example Data 23 nag_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_zsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm f08juc Example Text Example Data 7 nag_zpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix f08jvc Example Text Example Data 23 nag_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_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array f08jyc Example Text Example Data 23 nag_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 Example Text Example Data 23 nag_dgelss Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition f08kbc Example Text Example Data 23 nag_dgesvd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors f08kcc Example Text Example Data 23 nag_dgelsd Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer) f08kdc Example Text Example Data 23 nag_dgesdd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) f08kec Example Text Example Data 7 nag_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form f08kfc Example Text Example Data 7 nag_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by nag_dgebrd (f08kec) f08kgc Example Text Example Data 7 nag_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by nag_dgebrd (f08kec) f08khc Example Text Example Data 23 nag_dgejsv Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) f08kjc Example Text Example Data 23 nag_dgesvj Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi) f08knc Example Text Example Data 23 nag_zgelss Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition f08kpc Example Text Example Data 23 nag_zgesvd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors f08kqc Example Text Example Data 23 nag_zgelsd Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer) f08krc Example Text Example Data 23 nag_zgesdd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) f08ksc Example Text Example Data 7 nag_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form f08ktc Example Text Example Data 7 nag_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by nag_zgebrd (f08ksc) f08kuc Example Text Example Data 7 nag_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by nag_zgebrd (f08ksc) f08lec Example Text Example Data 7 nag_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form f08lsc Example Text Example Data 7 nag_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form f08mdc Example Text Example Data 23 nag_dbdsdc Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) f08mec Example Text Example Data 7 nag_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix f08msc 7 nag_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix f08nac Example Text Example Data 23 nag_dgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix f08nbc Example Text Example Data 23 nag_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 Example Text Example Data 7 nag_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form f08nfc Example Text Example Data 7 nag_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec) f08ngc Example Text Example Data 7 nag_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec) f08nhc Example Text Example Data 7 nag_dgebal Balances a real general matrix f08njc 7 nag_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to nag_dgebal (f08nhc) f08nnc Example Text Example Data 23 nag_zgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix f08npc Example Text Example Data 23 nag_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 Example Text Example Data 7 nag_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form f08ntc Example Text Example Data 7 nag_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc) f08nuc Example Text Example Data 7 nag_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc) f08nvc Example Text Example Data 7 nag_zgebal Balances a complex general matrix f08nwc 7 nag_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to nag_zgebal (f08nvc) f08pac Example Text Example Data 23 nag_dgees Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors f08pbc Example Text Example Data 23 nag_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 Example Text Example Data 7 nag_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix f08pkc 7 nag_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration f08pnc Example Text Example Data 23 nag_zgees Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f08ppc Example Text Example Data 23 nag_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 Example Text Example Data 7 nag_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix f08pxc 7 nag_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration f08qfc Example Text Example Data 7 nag_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation f08qgc Example Text Example Data 7 nag_dtrsen Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities f08qhc Example Text Example Data 7 nag_dtrsyl Solves the real Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper quasi-triangular or transposes f08qkc 7 nag_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix f08qlc Example Text Example Data 7 nag_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix f08qtc Example Text Example Data 7 nag_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation f08quc Example Text Example Data 7 nag_ztrsen Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities f08qvc Example Text Example Data 7 nag_ztrsyl Solves the complex Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper triangular or conjugate-transposes f08qxc 7 nag_ztrevc Computes left and right eigenvectors of complex upper triangular matrix f08qyc Example Text Example Data 7 nag_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix f08rac Example Text Example Data 24 nag_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices f08rnc Example Text Example Data 24 nag_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices f08sac Example Text Example Data 23 nag_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem f08sbc Example Text Example Data 23 nag_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem f08scc Example Text Example Data 23 nag_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) f08sec Example Text Example Data 7 nag_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 nag_dpotrf (f07fdc) f08snc Example Text Example Data 23 nag_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem f08spc Example Text Example Data 23 nag_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem f08sqc Example Text Example Data 23 nag_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) f08ssc Example Text Example Data 7 nag_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 nag_zpotrf (f07frc) f08tac Example Text Example Data 23 nag_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage f08tbc Example Text Example Data 23 nag_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage f08tcc Example Text Example Data 23 nag_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) f08tec Example Text Example Data 7 nag_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 nag_dpptrf (f07gdc) f08tnc Example Text Example Data 23 nag_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage f08tpc Example Text Example Data 23 nag_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage f08tqc Example Text Example Data 23 nag_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) f08tsc Example Text Example Data 7 nag_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 nag_zpptrf (f07grc) f08uac Example Text Example Data 23 nag_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem f08ubc Example Text Example Data 23 nag_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem f08ucc Example Text Example Data 23 nag_dsbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer) f08uec Example Text Example Data 7 nag_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_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$ f08unc Example Text Example Data 23 nag_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem f08upc Example Text Example Data 23 nag_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem f08uqc Example Text Example Data 23 nag_zhbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer) f08usc Example Text Example Data 7 nag_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_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix $A$ f08vac Example Text Example Data 9 nag_dggsvd Computes the generalized singular value decomposition of a real matrix pair f08vcc Example Text Example Data 26.0 nag_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair f08vec Example Text Example Data 23 nag_dggsvp Produces orthogonal matrices that simultaneously reduce the $m$ by $n$ matrix $A$ and the $p$ by $n$ matrix $B$ to upper triangular form f08vgc Example Text Example Data 26.0 nag_dggsvp3 Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the $m$ by $n$ matrix $A$ and the $p$ by $n$ matrix $B$ to upper triangular form f08vnc Example Text Example Data 9 nag_zggsvd Computes the generalized singular value decomposition of a complex matrix pair f08vqc Example Text Example Data 26.0 nag_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair f08vsc Example Text Example Data 23 nag_zggsvp Produces unitary matrices that simultaneously reduce the complex, $m$ by $n$, matrix $A$ and the complex, $p$ by $n$, matrix $B$ to upper triangular form f08vuc Example Text Example Data 26.0 nag_zggsvp3 Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, $m$ by $n$, matrix $A$ and the complex, $p$ by $n$, matrix $B$ to upper triangular form f08wac Example Text Example Data 23 nag_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors f08wbc Example Text Example Data 23 nag_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 Example Text Example Data 26.0 nag_dggev3 Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors f08wec 7 nag_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form f08wfc 26.0 nag_dgghd3 Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form f08whc 7 nag_dggbal Balances a pair of real, square, matrices f08wjc 7 nag_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to nag_dggbal (f08whc) f08wnc Example Text Example Data 23 nag_zggev Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors f08wpc Example Text Example Data 23 nag_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 Example Text Example Data 26.0 nag_zggev3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors f08wsc 7 nag_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form f08wtc 26.0 nag_zgghd3 Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form f08wvc 7 nag_zggbal Balances a pair of complex, square, matrices f08wwc 7 nag_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to nag_zggbal (f08wvc) f08xac Example Text Example Data 23 nag_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 f08xbc Example Text Example Data 23 nag_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 Example Text Example Data 26.0 nag_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 Example Text Example Data 7 nag_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices f08xnc Example Text Example Data 23 nag_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 f08xpc Example Text Example Data 23 nag_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 Example Text Example Data 26.0 nag_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 Example Text Example Data 7 nag_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices f08yec Example Text Example Data 23 nag_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair f08yfc Example Text Example Data 23 nag_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation f08ygc Example Text Example Data 23 nag_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 Example Text Example Data 23 nag_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation f08ykc Example Text Example Data 7 nag_dtgevc Computes right and left generalized eigenvectors of the matrix pair $\left(A,B\right)$ which is assumed to be in generalized upper Schur form f08ylc Example Text Example Data 23 nag_dtgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form f08ysc Example Text Example Data 23 nag_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair f08ytc Example Text Example Data 23 nag_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation f08yuc Example Text Example Data 23 nag_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 Example Text Example Data 23 nag_ztgsyl Solves the complex generalized Sylvester equation f08yxc Example Text Example Data 7 nag_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices f08yyc Example Text Example Data 23 nag_ztgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form f08zac Example Text Example Data 9 nag_dgglse Solves the real linear equality-constrained least squares (LSE) problem f08zbc Example Text Example Data 9 nag_dggglm Solves a real general Gauss–Markov linear model (GLM) problem f08zec Example Text Example Data 23 nag_dggqrf Computes a generalized $QR$ factorization of a real matrix pair f08zfc Example Text Example Data 23 nag_dggrqf Computes a generalized $RQ$ factorization of a real matrix pair f08znc Example Text Example Data 9 nag_zgglse Solves the complex linear equality-constrained least squares (LSE) problem f08zpc Example Text Example Data 9 nag_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem f08zsc Example Text Example Data 23 nag_zggqrf Computes a generalized $QR$ factorization of a complex matrix pair f08ztc Example Text Example Data 23 nag_zggrqf Computes a generalized $RQ$ factorization of a complex matrix pair
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017