F08 Chapter Contents : NAG Library Manual, Mark 27

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 $Q R$ 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 $Q R$ factorization of real general rectangular matrix
f08aff	16	dorgqr nagf_lapackeig_dorgqr Forms all or part of orthogonal $Q$ from $Q R$ 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 $L Q$ factorization of real general rectangular matrix
f08ajf	16	dorglq nagf_lapackeig_dorglq Forms all or part of orthogonal $Q$ from $L Q$ 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 $Q R$ 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 $Q R$ factorization of complex general rectangular matrix
f08atf	16	zungqr nagf_lapackeig_zungqr Forms all or part of unitary $Q$ from $Q R$ 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 $L Q$ factorization of complex general rectangular matrix
f08awf	16	zunglq nagf_lapackeig_zunglq Forms all or part of unitary $Q$ from $L Q$ 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 $Q R$ 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 $Q R$ 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 $Q R$ 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 $Q R$ 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 $Q L$ factorization of real general rectangular matrix
f08cff	22	dorgql nagf_lapackeig_dorgql Form all or part of orthogonal $Q$ from $Q L$ factorization determined by f08cef
f08cgf	22	dormql nagf_lapackeig_dormql Applies the orthogonal transformation determined by f08cef
f08chf	22	dgerqf nagf_lapackeig_dgerqf $R Q$ factorization of real general rectangular matrix
f08cjf	22	dorgrq nagf_lapackeig_dorgrq Form all or part of orthogonal $Q$ from $R Q$ factorization determined by f08chf
f08ckf	22	dormrq nagf_lapackeig_dormrq Applies the orthogonal transformation determined by f08chf
f08csf	22	zgeqlf nagf_lapackeig_zgeqlf $Q L$ factorization of complex general rectangular matrix
f08ctf	22	zungql nagf_lapackeig_zungql Form all or part of unitary $Q$ from $Q L$ factorization determined by f08csf
f08cuf	22	zunmql nagf_lapackeig_zunmql Applies the unitary transformation determined by f08csf
f08cvf	22	zgerqf nagf_lapackeig_zgerqf $R Q$ factorization of complex general rectangular matrix
f08cwf	22	zungrq nagf_lapackeig_zungrq Form all or part of unitary $Q$ from $R Q$ 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 $Q L$ or $Q R$ 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 $Q L$ or $Q R$ 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 $Q L$ or $Q R$ 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 $Q L$ or $Q R$ algorithm
f08jff	16	dsterf nagf_lapackeig_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $Q L$ or $Q R$ 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 $Q L$ or $Q R$ 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 $A X + X B = C$ , $A$ 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 $A X + X B = C$ , $A$ 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 $A x = λ B x$ , $A B x = λ x$ or $B A x = λ x$ , $B$ 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 $A x = λ B x$ , $A B x = λ x$ or $B A x = λ x$ , $B$ 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 $A x = λ B x$ , $A B x = λ x$ or $B A x = λ x$ , 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 $A x = λ B x$ , $A B x = λ x$ or $B A x = λ x$ , 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 $A x = λ B x$ to standard form $C y = λ y$ , 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 $A x = λ B x$ to standard form $C y = λ y$ , 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 $Q R$ factorization of a real matrix pair
f08zff	22	dggrqf nagf_lapackeig_dggrqf Computes a generalized $R Q$ 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 $Q R$ factorization of a complex matrix pair
f08ztf	22	zggrqf nagf_lapackeig_zggrqf Computes a generalized $R Q$ factorization of a complex matrix pair
f08bef	16 (Deprecated)	dgeqpf nagf_lapackeig_dgeqpf $Q R$ factorization, with column pivoting, of real general rectangular matrix
f08bsf	16 (Deprecated)	zgeqpf nagf_lapackeig_zgeqpf $Q R$ 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

NAG FL InterfaceF08 (Lapackeig)Least Squares and Eigenvalue Problems (LAPACK)

NAG FL Interface
F08 (Lapackeig)
Least Squares and Eigenvalue Problems (LAPACK)