F08 – least squares and eigenvalue problems (lapack)
- F08 Introduction
- f08aa – Solves a real linear least problem of full rank
- nag_lapack_dgels
- f08ab – Performs a QR factorization of real general rectangular matrix, with explicit blocking
- nag_lapack_dgeqrt
- f08ac – Applies the orthogonal transformation determined by f08ab
- nag_lapack_dgemqrt
- f08ae – Performs a QR factorization of real general rectangular matrix
- nag_lapack_dgeqrf
- f08af – Forms all or part of orthogonal Q from QR factorization determined by f08ae, f08be, f08bf
- nag_lapack_dorgqr
- f08ag – Applies an orthogonal transformation determined by f08ae, f08be, f08bf
- nag_lapack_dormqr
- f08ah – Performs a LQ factorization of real general rectangular matrix
- nag_lapack_dgelqf
- f08aj – Forms all or part of orthogonal Q from LQ factorization determined by f08ah
- nag_lapack_dorglq
- f08ak – Applies the orthogonal transformation determined by f08ah
- nag_lapack_dormlq
- f08an – Solves a complex linear least problem of full rank
- nag_lapack_zgels
- f08ap – Performs a QR factorization of complex general rectangular matrix using recursive algorithm
- nag_lapack_zgeqrt
- f08aq – Applies the unitary transformation determined by f08ap
- nag_lapack_zgemqrt
- f08as – Performs a QR factorization of complex general rectangular matrix
- nag_lapack_zgeqrf
- f08at – Forms all or part of unitary Q from QR factorization determined by f08as, f08bs, f08bt
- nag_lapack_zungqr
- f08au – Applies a unitary transformation determined by f08as, f08bs, f08bt
- nag_lapack_zunmqr
- f08av – Performs a LQ factorization of complex general rectangular matrix
- nag_lapack_zgelqf
- f08aw – Forms all or part of unitary Q from LQ factorization determined by f08av
- nag_lapack_zunglq
- f08ax – Applies the unitary transformation determined by f08av
- nag_lapack_zunmlq
- f08ba – Computes the minimum-norm solution to a real linear least squares problem
- nag_lapack_dgelsy
- f08bb – QR factorization of real general triangular-pentagonal matrix
- nag_lapack_dtpqrt
- f08bc – Applies the orthogonal transformation determined by f08bb
- nag_lapack_dtpmqrt
- f08be – QR factorization, with column pivoting, of real general rectangular matrix
- nag_lapack_dgeqpf
- f08bf – QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
- nag_lapack_dgeqp3
- f08bh – Reduces a real upper trapezoidal matrix to upper triangular form
- nag_lapack_dtzrzf
- f08bk – Applies the orthogonal transformation determined by f08bh
- nag_lapack_dormrz
- f08bn – Computes the minimum-norm solution to a complex linear least squares problem
- nag_lapack_zgelsy
- f08bp – QR factorization of complex triangular-pentagonal matrix
- nag_lapack_ztpqrt
- f08bq – Applies the unitary transformation determined by f08bp
- nag_lapack_ztpmqrt
- f08bs – QR factorization, with column pivoting, of complex general rectangular matrix
- nag_lapack_zgeqpf
- f08bt – QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
- nag_lapack_zgeqp3
- f08bv – Reduces a complex upper trapezoidal matrix to upper triangular form
- nag_lapack_ztzrzf
- f08bx – Applies the unitary transformation determined by f08bv
- nag_lapack_zunmrz
- f08ce – QL factorization of real general rectangular matrix
- nag_lapack_dgeqlf
- f08cf – Form all or part of orthogonal Q from QL factorization determined by f08ce
- nag_lapack_dorgql
- f08cg – Applies the orthogonal transformation determined by f08ce
- nag_lapack_dormql
- f08ch – RQ factorization of real general rectangular matrix
- nag_lapack_dgerqf
- f08cj – Form all or part of orthogonal Q from RQ factorization determined by f08ch
- nag_lapack_dorgrq
- f08ck – Applies the orthogonal transformation determined by f08ch
- nag_lapack_dormrq
- f08cs – QL factorization of complex general rectangular matrix
- nag_lapack_zgeqlf
- f08ct – Form all or part of unitary Q from QL factorization determined by f08cs
- nag_lapack_zungql
- f08cu – Applies the unitary transformation determined by f08cs
- nag_lapack_zunmql
- f08cv – RQ factorization of complex general rectangular matrix
- nag_lapack_zgerqf
- f08cw – Form all or part of unitary Q from RQ factorization determined by f08cv
- nag_lapack_zungrq
- f08cx – Applies the unitary transformation determined by f08cv
- nag_lapack_zunmrq
- f08fa – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
- nag_lapack_dsyev
- f08fb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
- nag_lapack_dsyevx
- f08fc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
- nag_lapack_dsyevd
- f08fd – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
- nag_lapack_dsyevr
- f08fe – Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
- nag_lapack_dsytrd
- f08ff – Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fe
- nag_lapack_dorgtr
- f08fg – Applies the orthogonal transformation determined by f08fe
- nag_lapack_dormtr
- f08fl – 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
- nag_lapack_ddisna
- f08fn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
- nag_lapack_zheev
- f08fp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
- nag_lapack_zheevx
- f08fq – Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
- nag_lapack_zheevd
- f08fr – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
- nag_lapack_zheevr
- f08fs – Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
- nag_lapack_zhetrd
- f08ft – Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fs
- nag_lapack_zungtr
- f08fu – Applies the unitary transformation matrix determined by f08fs
- nag_lapack_zunmtr
- f08ga – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
- nag_lapack_dspev
- f08gb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
- nag_lapack_dspevx
- f08gc – 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)
- nag_lapack_dspevd
- f08ge – Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
- nag_lapack_dsptrd
- f08gf – Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08ge
- nag_lapack_dopgtr
- f08gg – Applies the orthogonal transformation determined by f08ge
- nag_lapack_dopmtr
- f08gn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
- nag_lapack_zhpev
- f08gp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
- nag_lapack_zhpevx
- f08gq – 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)
- nag_lapack_zhpevd
- f08gs – Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
- nag_lapack_zhptrd
- f08gt – Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gs
- nag_lapack_zupgtr
- f08gu – Applies the unitary transformation matrix determined by f08gs
- nag_lapack_zupmtr
- f08ha – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
- nag_lapack_dsbev
- f08hb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
- nag_lapack_dsbevx
- f08hc – 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)
- nag_lapack_dsbevd
- f08he – Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
- nag_lapack_dsbtrd
- f08hn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
- nag_lapack_zhbev
- f08hp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
- nag_lapack_zhbevx
- f08hq – Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
- nag_lapack_zhbevd
- f08hs – Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
- nag_lapack_zhbtrd
- f08ja – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
- nag_lapack_dstev
- f08jb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
- nag_lapack_dstevx
- f08jc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
- nag_lapack_dstevd
- f08jd – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
- nag_lapack_dstevr
- f08je – Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
- nag_lapack_dsteqr
- f08jf – Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
- nag_lapack_dsterf
- f08jg – Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
- nag_lapack_dpteqr
- f08jh – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
- nag_lapack_dstedc
- f08jj – Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
- nag_lapack_dstebz
- f08jk – Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
- nag_lapack_dstein
- f08jl – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
- nag_lapack_dstegr
- f08js – Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
- nag_lapack_zsteqr
- f08ju – Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
- nag_lapack_zpteqr
- f08jv – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
- nag_lapack_zstedc
- f08jx – Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
- nag_lapack_zstein
- f08jy – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
- nag_lapack_zstegr
- f08ka – Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
- nag_lapack_dgelss
- f08kb – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
- nag_lapack_dgesvd
- f08kc – Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
- nag_lapack_dgelsd
- f08kd – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
- nag_lapack_dgesdd
- f08ke – Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
- nag_lapack_dgebrd
- f08kf – Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08ke
- nag_lapack_dorgbr
- f08kg – Applies the orthogonal transformations from reduction to bidiagonal form determined by f08ke
- nag_lapack_dormbr
- f08kh – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned
Jacobi)
- nag_lapack_dgejsv
- f08kj – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast
Jacobi)
- nag_lapack_dgesvj
- f08kn – Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
- nag_lapack_zgelss
- f08kp – Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
- nag_lapack_zgesvd
- f08kq – Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
- nag_lapack_zgelsd
- f08kr – Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
(divide-and-conquer)
- nag_lapack_zgesdd
- f08ks – Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
- nag_lapack_zgebrd
- f08kt – Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ks
- nag_lapack_zungbr
- f08ku – Applies the unitary transformations from reduction to bidiagonal form determined by f08ks
- nag_lapack_zunmbr
- f08le – Performs a reduction of real rectangular band matrix to upper bidiagonal form
- nag_lapack_dgbbrd
- f08ls – Reduction of complex rectangular band matrix to upper bidiagonal form
- nag_lapack_zgbbrd
- f08md – Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
- nag_lapack_dbdsdc
- f08me – Performs an SVD of real bidiagonal matrix reduced from real general matrix
- nag_lapack_dbdsqr
- f08ms – Performs an SVD of real bidiagonal matrix reduced from complex general matrix
- nag_lapack_zbdsqr
- f08na – Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
- nag_lapack_dgeev
- f08nb – 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
- nag_lapack_dgeevx
- f08ne – Performs an orthogonal reduction of real general matrix to upper Hessenberg form
- nag_lapack_dgehrd
- f08nf – Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08ne
- nag_lapack_dorghr
- f08ng – Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08ne
- nag_lapack_dormhr
- f08nh – Balances a real general matrix
- nag_lapack_dgebal
- f08nj – Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nh
- nag_lapack_dgebak
- f08nn – Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
- nag_lapack_zgeev
- f08np – 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
- nag_lapack_zgeevx
- f08ns – Performs a unitary reduction of complex general matrix to upper Hessenberg form
- nag_lapack_zgehrd
- f08nt – Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08ns
- nag_lapack_zunghr
- f08nu – Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08ns
- nag_lapack_zunmhr
- f08nv – Balances a complex general matrix
- nag_lapack_zgebal
- f08nw – Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nv
- nag_lapack_zgebak
- f08pa – Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
- nag_lapack_dgees
- f08pb – 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
- nag_lapack_dgeesx
- f08pe – Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
- nag_lapack_dhseqr
- f08pk – Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
- nag_lapack_dhsein
- f08pn – Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
- nag_lapack_zgees
- f08pp – 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
- nag_lapack_zgeesx
- f08ps – Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
- nag_lapack_zhseqr
- f08px – Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
- nag_lapack_zhsein
- f08qf – Reorders a Schur factorization of real matrix using orthogonal similarity transformation
- nag_lapack_dtrexc
- f08qg – Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
- nag_lapack_dtrsen
- f08qh – Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
- nag_lapack_dtrsyl
- f08qk – Computes left and right eigenvectors of real upper quasi-triangular matrix
- nag_lapack_dtrevc
- f08ql – Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
- nag_lapack_dtrsna
- f08qt – Reorders a Schur factorization of complex matrix using unitary similarity transformation
- nag_lapack_ztrexc
- f08qu – Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues,
with estimates of sensitivities
- nag_lapack_ztrsen
- f08qv – Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
- nag_lapack_ztrsyl
- f08qx – Computes left and right eigenvectors of complex upper triangular matrix
- nag_lapack_ztrevc
- f08qy – Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
- nag_lapack_ztrsna
- f08ra – Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
- nag_lapack_dorcsd
- f08rn – Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
- nag_lapack_zuncsd
- f08sa – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
- nag_lapack_dsygv
- f08sb – Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
- nag_lapack_dsygvx
- f08sc – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
- nag_lapack_dsygvd
- f08se – Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by f07fd
- nag_lapack_dsygst
- f08sn – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
- nag_lapack_zhegv
- f08sp – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
- nag_lapack_zhegvx
- f08sq – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
- nag_lapack_zhegvd
- f08ss – Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by f07fr
- nag_lapack_zhegst
- f08ta – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
- nag_lapack_dspgv
- f08tb – Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
- nag_lapack_dspgvx
- f08tc – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
- nag_lapack_dspgvd
- f08te – Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by f07gd
- nag_lapack_dspgst
- f08tn – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed
storage
- nag_lapack_zhpgv
- f08tp – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem,
packed storage
- nag_lapack_zhpgvx
- f08tq – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem,
packed storage (divide-and-conquer)
- nag_lapack_zhpgvd
- f08ts – Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by f07gr
- nag_lapack_zhpgst
- f08ua – Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
- nag_lapack_dsbgv
- f08ub – Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
- nag_lapack_dsbgvx
- f08uc – Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
- nag_lapack_dsbgvd
- f08ue – Performs a reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
- nag_lapack_dsbgst
- f08uf – Computes a split Cholesky factorization of real symmetric positive definite band matrix A
- nag_lapack_dpbstf
- f08un – Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
- nag_lapack_zhbgv
- f08up – Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
- nag_lapack_zhbgvx
- f08uq – Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
(divide-and-conquer)
- nag_lapack_zhbgvd
- f08us – Performs a reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λ y, such that C has the same bandwidth as A
- nag_lapack_zhbgst
- f08ut – Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
- nag_lapack_zpbstf
- f08va – Computes the generalized singular value decomposition of a real matrix pair
- nag_lapack_dggsvd
- f08ve – Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
- nag_lapack_dggsvp
- f08vn – Computes the generalized singular value decomposition of a complex matrix pair
- nag_lapack_zggsvd
- f08vs – 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
- nag_lapack_zggsvp
- f08wa – Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
- nag_lapack_dggev
- f08wb – 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
- nag_lapack_dggevx
- f08we – Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
- nag_lapack_dgghrd
- f08wh – Balances a pair of real, square, matrices
- nag_lapack_dggbal
- f08wj – Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08wh
- nag_lapack_dggbak
- f08wn – Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized
eigenvectors
- nag_lapack_zggev
- f08wp – 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
- nag_lapack_zggevx
- f08ws – Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
- nag_lapack_zgghrd
- f08wv – Balances a pair of complex, square, matrices
- nag_lapack_zggbal
- f08ww – Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wv
- nag_lapack_zggbak
- f08xa – 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
- nag_lapack_dgges
- f08xb – 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
- nag_lapack_dggesx
- f08xe – Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
- nag_lapack_dhgeqz
- f08xn – 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_lapack_zgges
- f08xp – 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
- nag_lapack_zggesx
- f08xs – Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex,
square, matrices
- nag_lapack_zhgeqz
- f08ye – Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
- nag_lapack_dtgsja
- f08yf – Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
- nag_lapack_dtgexc
- f08yg – 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
- nag_lapack_dtgsen
- f08yh – Solves the real-valued, generalized, quasi-trangular, Sylvester equation
- nag_lapack_dtgsyl
- f08yk – Computes right and left generalized eigenvectors of the matrix pair (AB)) which is assumed to be in generalized upper Schur form
- nag_lapack_dtgevc
- f08yl – Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
- nag_lapack_dtgsna
- f08ys – Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
- nag_lapack_ztgsja
- f08yt – Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
- nag_lapack_ztgexc
- f08yu – 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
- nag_lapack_ztgsen
- f08yv – Solves the complex generalized Sylvester equation
- nag_lapack_ztgsyl
- f08yx – Computes left and right eigenvectors of a pair of complex upper triangular matrices
- nag_lapack_ztgevc
- f08yy – Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized
Schur canonical form
- nag_lapack_ztgsna
- f08za – Solves the real linear equality-constrained least squares (LSE) problem
- nag_lapack_dgglse
- f08zb – Solves a real general Gauss–Markov linear model (GLM) problem
- nag_lapack_dggglm
- f08ze – Computes a generalized QR factorization of a real matrix pair
- nag_lapack_dggqrf
- f08zf – Computes a generalized RQ factorization of a real matrix pair
- nag_lapack_dggrqf
- f08zn – Solves the complex linear equality-constrained least squares (LSE) problem
- nag_lapack_zgglse
- f08zp – Solves a complex general Gauss–Markov linear model (GLM) problem
- nag_lapack_zggglm
- f08zs – Computes a generalized QR factorization of a complex matrix pair
- nag_lapack_zggqrf
- f08zt – Computes a generalized RQ factorization of a complex matrix pair
- nag_lapack_zggrqf
