F08 (Lapackeig)

Least Squares and Eigenvalue Problems (LAPACK)

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

Routine |
Mark of Introduction |
Purpose |
---|---|---|

f08aaf | 21 | dgels nagf_lapackeig_dgels Solves a real linear least squares problem of full rank |

f08abf | 25 | dgeqrt nagf_lapackeig_dgeqrt Performs a $QR$ factorization of real general rectangular matrix, with explicit blocking |

f08acf | 25 | dgemqrt nagf_lapackeig_dgemqrt Applies the orthogonal transformation determined by f08abf |

f08aef | 16 | dgeqrf nagf_lapackeig_dgeqrf Performs a $QR$ factorization of real general rectangular matrix |

f08aff | 16 | dorgqr nagf_lapackeig_dorgqr Forms all or part of orthogonal $Q$ from $QR$ factorization determined by f08aef, f08bef or f08bff |

f08agf | 16 | dormqr nagf_lapackeig_dormqr Applies an orthogonal transformation determined by f08aef, f08bef or f08bff |

f08ahf | 16 | dgelqf nagf_lapackeig_dgelqf Performs a $LQ$ factorization of real general rectangular matrix |

f08ajf | 16 | dorglq nagf_lapackeig_dorglq Forms all or part of orthogonal $Q$ from $LQ$ factorization determined by f08ahf |

f08akf | 16 | dormlq nagf_lapackeig_dormlq Applies the orthogonal transformation determined by f08ahf |

f08anf | 21 | zgels nagf_lapackeig_zgels Solves a complex linear least problem of full rank |

f08apf | 25 | zgeqrt nagf_lapackeig_zgeqrt Performs a $QR$ factorization of complex general rectangular matrix using recursive algorithm |

f08aqf | 25 | zgemqrt nagf_lapackeig_zgemqrt Applies the unitary transformation determined by f08apf |

f08asf | 16 | zgeqrf nagf_lapackeig_zgeqrf Performs a $QR$ factorization of complex general rectangular matrix |

f08atf | 16 | zungqr nagf_lapackeig_zungqr Forms all or part of unitary $Q$ from $QR$ factorization determined by f08asf, f08bsf or f08btf |

f08auf | 16 | zunmqr nagf_lapackeig_zunmqr Applies a unitary transformation determined by f08asf, f08bsf or f08btf |

f08avf | 16 | zgelqf nagf_lapackeig_zgelqf Performs a $LQ$ factorization of complex general rectangular matrix |

f08awf | 16 | zunglq nagf_lapackeig_zunglq Forms all or part of unitary $Q$ from $LQ$ factorization determined by f08avf |

f08axf | 16 | zunmlq nagf_lapackeig_zunmlq Applies the unitary transformation determined by f08avf |

f08baf | 21 | dgelsy nagf_lapackeig_dgelsy Computes the minimum-norm solution to a real linear least squares problem |

f08bbf | 25 | dtpqrt nagf_lapackeig_dtpqrt $QR$ factorization of real general triangular-pentagonal matrix |

f08bcf | 25 | dtpmqrt nagf_lapackeig_dtpmqrt Applies the orthogonal transformation determined by f08bbf |

f08bff | 22 | dgeqp3 nagf_lapackeig_dgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |

f08bhf | 22 | dtzrzf nagf_lapackeig_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |

f08bkf | 22 | dormrz nagf_lapackeig_dormrz Applies the orthogonal transformation determined by f08bhf |

f08bnf | 21 | zgelsy nagf_lapackeig_zgelsy Computes the minimum-norm solution to a complex linear least squares problem |

f08bpf | 25 | ztpqrt nagf_lapackeig_ztpqrt $QR$ factorization of complex triangular-pentagonal matrix |

f08bqf | 25 | ztpmqrt nagf_lapackeig_ztpmqrt Applies the unitary transformation determined by f08bpf |

f08btf | 22 | zgeqp3 nagf_lapackeig_zgeqp3 $QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |

f08bvf | 22 | ztzrzf nagf_lapackeig_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |

f08bxf | 22 | zunmrz nagf_lapackeig_zunmrz Applies the unitary transformation determined by f08bvf |

f08cef | 22 | dgeqlf nagf_lapackeig_dgeqlf $QL$ factorization of real general rectangular matrix |

f08cff | 22 | dorgql nagf_lapackeig_dorgql Form all or part of orthogonal $Q$ from $QL$ factorization determined by f08cef |

f08cgf | 22 | dormql nagf_lapackeig_dormql Applies the orthogonal transformation determined by f08cef |

f08chf | 22 | dgerqf nagf_lapackeig_dgerqf $RQ$ factorization of real general rectangular matrix |

f08cjf | 22 | dorgrq nagf_lapackeig_dorgrq Form all or part of orthogonal $Q$ from $RQ$ factorization determined by f08chf |

f08ckf | 22 | dormrq nagf_lapackeig_dormrq Applies the orthogonal transformation determined by f08chf |

f08csf | 22 | zgeqlf nagf_lapackeig_zgeqlf $QL$ factorization of complex general rectangular matrix |

f08ctf | 22 | zungql nagf_lapackeig_zungql Form all or part of unitary $Q$ from $QL$ factorization determined by f08csf |

f08cuf | 22 | zunmql nagf_lapackeig_zunmql Applies the unitary transformation determined by f08csf |

f08cvf | 22 | zgerqf nagf_lapackeig_zgerqf $RQ$ factorization of complex general rectangular matrix |

f08cwf | 22 | zungrq nagf_lapackeig_zungrq Form all or part of unitary $Q$ from $RQ$ factorization determined by f08cvf |

f08cxf | 22 | zunmrq nagf_lapackeig_zunmrq Applies the unitary transformation determined by f08cvf |

f08faf | 21 | dsyev nagf_lapackeig_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |

f08fbf | 21 | dsyevx nagf_lapackeig_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |

f08fcf | 19 | dsyevd nagf_lapackeig_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |

f08fdf | 21 | dsyevr nagf_lapackeig_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |

f08fef | 16 | dsytrd nagf_lapackeig_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |

f08fff | 16 | dorgtr nagf_lapackeig_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fef |

f08fgf | 16 | dormtr nagf_lapackeig_dormtr Applies the orthogonal transformation determined by f08fef |

f08flf | 22 | ddisna nagf_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 |

f08fnf | 21 | zheev nagf_lapackeig_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |

f08fpf | 21 | zheevx nagf_lapackeig_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |

f08fqf | 19 | zheevd nagf_lapackeig_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |

f08frf | 21 | zheevr nagf_lapackeig_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |

f08fsf | 16 | zhetrd nagf_lapackeig_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |

f08ftf | 16 | zungtr nagf_lapackeig_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsf |

f08fuf | 16 | zunmtr nagf_lapackeig_zunmtr Applies the unitary transformation matrix determined by f08fsf |

f08gaf | 21 | dspev nagf_lapackeig_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |

f08gbf | 21 | dspevx nagf_lapackeig_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |

f08gcf | 19 | dspevd nagf_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) |

f08gef | 16 | dsptrd nagf_lapackeig_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |

f08gff | 16 | dopgtr nagf_lapackeig_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gef |

f08ggf | 16 | dopmtr nagf_lapackeig_dopmtr Applies the orthogonal transformation determined by f08gef |

f08gnf | 21 | zhpev nagf_lapackeig_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |

f08gpf | 21 | zhpevx nagf_lapackeig_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |

f08gqf | 19 | zhpevd nagf_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) |

f08gsf | 16 | zhptrd nagf_lapackeig_zhptrd Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |

f08gtf | 16 | zupgtr nagf_lapackeig_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsf |

f08guf | 16 | zupmtr nagf_lapackeig_zupmtr Applies the unitary transformation matrix determined by f08gsf |

f08haf | 21 | dsbev nagf_lapackeig_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

f08hbf | 21 | dsbevx nagf_lapackeig_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |

f08hcf | 19 | dsbevd nagf_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) |

f08hef | 16 | dsbtrd nagf_lapackeig_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |

f08hnf | 21 | zhbev nagf_lapackeig_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |

f08hpf | 21 | zhbevx nagf_lapackeig_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |

f08hqf | 19 | zhbevd nagf_lapackeig_zhbevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |

f08hsf | 16 | zhbtrd nagf_lapackeig_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |

f08jaf | 21 | dstev nagf_lapackeig_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |

f08jbf | 21 | dstevx nagf_lapackeig_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |

f08jcf | 19 | dstevd nagf_lapackeig_dstevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |

f08jdf | 21 | dstevr nagf_lapackeig_dstevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |

f08jef | 16 | dsteqr nagf_lapackeig_dsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm |

f08jff | 16 | dsterf nagf_lapackeig_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm |

f08jgf | 16 | dpteqr nagf_lapackeig_dpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix |

f08jhf | 22 | dstedc nagf_lapackeig_dstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) |

f08jjf | 16 | dstebz nagf_lapackeig_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection |

f08jkf | 16 | dstein nagf_lapackeig_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |

f08jlf | 22 | dstegr nagf_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) |

f08jsf | 16 | zsteqr nagf_lapackeig_zsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm |

f08juf | 16 | zpteqr nagf_lapackeig_zpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix |

f08jvf | 22 | zstedc nagf_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) |

f08jxf | 16 | zstein nagf_lapackeig_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |

f08jyf | 22 | zstegr nagf_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) |

f08kaf | 21 | dgelss nagf_lapackeig_dgelss Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition |

f08kbf | 21 | dgesvd nagf_lapackeig_dgesvd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |

f08kcf | 21 | dgelsd nagf_lapackeig_dgelsd Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer) |

f08kdf | 21 | dgesdd nagf_lapackeig_dgesdd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |

f08kef | 16 | dgebrd nagf_lapackeig_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form |

f08kff | 16 | dorgbr nagf_lapackeig_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kef |

f08kgf | 16 | dormbr nagf_lapackeig_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kef |

f08khf | 23 | dgejsv nagf_lapackeig_dgejsv Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |

f08kjf | 23 | dgesvj nagf_lapackeig_dgesvj Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |

f08kmf | 27 | dgesvdx nagf_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 |

f08knf | 21 | zgelss nagf_lapackeig_zgelss Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition |

f08kpf | 21 | zgesvd nagf_lapackeig_zgesvd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors |

f08kqf | 21 | zgelsd nagf_lapackeig_zgelsd Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer) |

f08krf | 21 | zgesdd nagf_lapackeig_zgesdd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |

f08ksf | 16 | zgebrd nagf_lapackeig_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form |

f08ktf | 16 | zungbr nagf_lapackeig_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksf |

f08kuf | 16 | zunmbr nagf_lapackeig_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by f08ksf |

f08kvf | 27 | zgejsv nagf_lapackeig_zgejsv Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |

f08kwf | 27 | zgesvj nagf_lapackeig_zgesvj Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |

f08kzf | 27 | zgesvdx nagf_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 |

f08lef | 19 | dgbbrd nagf_lapackeig_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form |

f08lsf | 19 | zgbbrd nagf_lapackeig_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |

f08mbf | 27 | dbdsvdx nagf_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 |

f08mdf | 22 | dbdsdc nagf_lapackeig_dbdsdc Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) |

f08mef | 16 | dbdsqr nagf_lapackeig_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix |

f08msf | 16 | zbdsqr nagf_lapackeig_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix |

f08naf | 21 | dgeev nagf_lapackeig_dgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |

f08nbf | 21 | dgeevx nagf_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 |

f08nef | 16 | dgehrd nagf_lapackeig_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form |

f08nff | 16 | dorghr nagf_lapackeig_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef |

f08ngf | 16 | dormhr nagf_lapackeig_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef |

f08nhf | 16 | dgebal nagf_lapackeig_dgebal Balances a real general matrix |

f08njf | 16 | dgebak nagf_lapackeig_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhf |

f08nnf | 21 | zgeev nagf_lapackeig_zgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |

f08npf | 21 | zgeevx nagf_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 |

f08nsf | 16 | zgehrd nagf_lapackeig_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form |

f08ntf | 16 | zunghr nagf_lapackeig_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsf |

f08nuf | 16 | zunmhr nagf_lapackeig_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsf |

f08nvf | 16 | zgebal nagf_lapackeig_zgebal Balances a complex general matrix |

f08nwf | 16 | zgebak nagf_lapackeig_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvf |

f08paf | 21 | dgees nagf_lapackeig_dgees Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors |

f08pbf | 21 | dgeesx nagf_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 |

f08pef | 16 | dhseqr nagf_lapackeig_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |

f08pkf | 16 | dhsein nagf_lapackeig_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |

f08pnf | 21 | zgees nagf_lapackeig_zgees Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors |

f08ppf | 21 | zgeesx nagf_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 |

f08psf | 16 | zhseqr nagf_lapackeig_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |

f08pxf | 16 | zhsein nagf_lapackeig_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |

f08qff | 16 | dtrexc nagf_lapackeig_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation |

f08qgf | 16 | dtrsen nagf_lapackeig_dtrsen Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |

f08qhf | 16 | dtrsyl nagf_lapackeig_dtrsyl Solves the real Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper quasi-triangular or transposes |

f08qkf | 16 | dtrevc nagf_lapackeig_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |

f08qlf | 16 | dtrsna nagf_lapackeig_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |

f08qtf | 16 | ztrexc nagf_lapackeig_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation |

f08quf | 16 | ztrsen nagf_lapackeig_ztrsen Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |

f08qvf | 16 | ztrsyl nagf_lapackeig_ztrsyl Solves the complex Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper triangular or conjugate-transposes |

f08qxf | 16 | ztrevc nagf_lapackeig_ztrevc Computes left and right eigenvectors of complex upper triangular matrix |

f08qyf | 16 | ztrsna nagf_lapackeig_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |

f08raf | 25 | dorcsd nagf_lapackeig_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices |

f08rnf | 25 | zuncsd nagf_lapackeig_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices |

f08saf | 21 | dsygv nagf_lapackeig_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |

f08sbf | 21 | dsygvx nagf_lapackeig_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |

f08scf | 21 | dsygvd nagf_lapackeig_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |

f08sef | 16 | dsygst nagf_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 f07fdf |

f08snf | 21 | zhegv nagf_lapackeig_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |

f08spf | 21 | zhegvx nagf_lapackeig_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |

f08sqf | 21 | zhegvd nagf_lapackeig_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |

f08ssf | 16 | zhegst nagf_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 f07frf |

f08taf | 21 | dspgv nagf_lapackeig_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |

f08tbf | 21 | dspgvx nagf_lapackeig_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |

f08tcf | 21 | dspgvd nagf_lapackeig_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) |

f08tef | 16 | dspgst nagf_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 f07gdf |

f08tnf | 21 | zhpgv nagf_lapackeig_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |

f08tpf | 21 | zhpgvx nagf_lapackeig_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |

f08tqf | 21 | zhpgvd nagf_lapackeig_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) |

f08tsf | 16 | zhpgst nagf_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 f07grf |

f08uaf | 21 | dsbgv nagf_lapackeig_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |

f08ubf | 21 | dsbgvx nagf_lapackeig_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |

f08ucf | 21 | dsbgvd nagf_lapackeig_dsbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer) |

f08uef | 19 | dsbgst nagf_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 $A$ |

f08uff | 19 | dpbstf nagf_lapackeig_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$ |

f08unf | 21 | zhbgv nagf_lapackeig_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |

f08upf | 21 | zhbgvx nagf_lapackeig_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |

f08uqf | 21 | zhbgvd nagf_lapackeig_zhbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer) |

f08usf | 19 | zhbgst nagf_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 $A$ |

f08utf | 19 | zpbstf nagf_lapackeig_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix $A$ |

f08vcf | 26 | dggsvd3 nagf_lapackeig_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair |

f08vgf | 26 | dggsvp3 nagf_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 |

f08vqf | 26 | zggsvd3 nagf_lapackeig_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair |

f08vuf | 26 | zggsvp3 nagf_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 |

f08wbf | 21 | dggevx nagf_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 |

f08wcf | 26 | dggev3 nagf_lapackeig_dggev3 Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wff | 26 | dgghd3 nagf_lapackeig_dgghd3 Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |

f08whf | 20 | dggbal nagf_lapackeig_dggbal Balances a pair of real, square, matrices |

f08wjf | 20 | dggbak nagf_lapackeig_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whf |

f08wpf | 21 | zggevx nagf_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 |

f08wqf | 26 | zggev3 nagf_lapackeig_zggev3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wtf | 26 | zgghd3 nagf_lapackeig_zgghd3 Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |

f08wvf | 20 | zggbal nagf_lapackeig_zggbal Balances a pair of complex, square, matrices |

f08wwf | 20 | zggbak nagf_lapackeig_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvf |

f08xbf | 21 | dggesx nagf_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 |

f08xcf | 26 | dgges3 nagf_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 |

f08xef | 20 | dhgeqz nagf_lapackeig_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |

f08xpf | 21 | zggesx nagf_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 |

f08xqf | 26 | zgges3 nagf_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 |

f08xsf | 20 | zhgeqz nagf_lapackeig_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices |

f08yef | 22 | dtgsja nagf_lapackeig_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |

f08yff | 22 | dtgexc nagf_lapackeig_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |

f08ygf | 22 | dtgsen nagf_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 |

f08yhf | 22 | dtgsyl nagf_lapackeig_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation |

f08ykf | 20 | dtgevc nagf_lapackeig_dtgevc Computes right and left generalized eigenvectors of the matrix pair $(A,B)$ which is assumed to be in generalized upper Schur form |

f08ylf | 22 | dtgsna nagf_lapackeig_dtgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form |

f08ysf | 22 | ztgsja nagf_lapackeig_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |

f08ytf | 22 | ztgexc nagf_lapackeig_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |

f08yuf | 22 | ztgsen nagf_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 |

f08yvf | 22 | ztgsyl nagf_lapackeig_ztgsyl Solves the complex generalized Sylvester equation |

f08yxf | 20 | ztgevc nagf_lapackeig_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices |

f08yyf | 22 | ztgsna nagf_lapackeig_ztgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form |

f08zaf | 21 | dgglse nagf_lapackeig_dgglse Solves the real linear equality-constrained least squares (LSE) problem |

f08zbf | 21 | dggglm nagf_lapackeig_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |

f08zef | 22 | dggqrf nagf_lapackeig_dggqrf Computes a generalized $QR$ factorization of a real matrix pair |

f08zff | 22 | dggrqf nagf_lapackeig_dggrqf Computes a generalized $RQ$ factorization of a real matrix pair |

f08znf | 21 | zgglse nagf_lapackeig_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |

f08zpf | 21 | zggglm nagf_lapackeig_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |

f08zsf | 22 | zggqrf nagf_lapackeig_zggqrf Computes a generalized $QR$ factorization of a complex matrix pair |

f08ztf | 22 | zggrqf nagf_lapackeig_zggrqf Computes a generalized $RQ$ factorization of a complex matrix pair |

f08bef | 16
(Deprecated) |
dgeqpf nagf_lapackeig_dgeqpf $QR$ factorization, with column pivoting, of real general rectangular matrix |

f08bsf | 16
(Deprecated) |
zgeqpf nagf_lapackeig_zgeqpf $QR$ factorization, with column pivoting, of complex general rectangular matrix |

f08vaf | 21
(Deprecated) |
dggsvd nagf_lapackeig_dggsvd Computes the generalized singular value decomposition of a real matrix pair |

f08vef | 22
(Deprecated) |
dggsvp nagf_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 |

f08vnf | 21
(Deprecated) |
zggsvd nagf_lapackeig_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |

f08vsf | 22
(Deprecated) |
zggsvp nagf_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 |

f08waf | 21
(Deprecated) |
dggev nagf_lapackeig_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wef | 20
(Deprecated) |
dgghrd nagf_lapackeig_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |

f08wnf | 21
(Deprecated) |
zggev nagf_lapackeig_zggev Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |

f08wsf | 20
(Deprecated) |
zgghrd nagf_lapackeig_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |

f08xaf | 21
(Deprecated) |
dgges nagf_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 |

f08xnf | 21
(Deprecated) |
zgges nagf_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 |