## F08 – Least Squares and Eigenvalue Problems (LAPACK)

• F08 Introduction
• f08aa – Solves an overdetermined or underdetermined real linear system
• nag_lapack_dgels – f08aa
• f08ae – QR factorization of real general rectangular matrix
• nag_lapack_dgeqrf – f08ae
• f08af – Form all or part of orthogonal Q from QR factorization determined by f08ae, f08be, f08bf
• nag_lapack_dorgqr – f08af
• f08ag – Apply orthogonal transformation determined by f08ae, f08be, f08bf
• nag_lapack_dormqr – f08ag
• f08ah – LQ factorization of real general rectangular matrix
• nag_lapack_dgelqf – f08ah
• f08aj – Form all or part of orthogonal Q from LQ factorization determined by f08ah
• nag_lapack_dorglq – f08aj
• f08ak – Apply orthogonal transformation determined by f08ah
• nag_lapack_dormlq – f08ak
• f08an – Solves an overdetermined or underdetermined complex linear system
• nag_lapack_zgels – f08an
• f08as – QR factorization of complex general rectangular matrix
• nag_lapack_zgeqrf – f08as
• f08at – Form all or part of unitary Q from QR factorization determined by f08as, f08bs, f08bt
• nag_lapack_zungqr – f08at
• f08au – Apply unitary transformation determined by f08as, f08bs, f08bt
• nag_lapack_zunmqr – f08au
• f08av – LQ factorization of complex general rectangular matrix
• nag_lapack_zgelqf – f08av
• f08aw – Form all or part of unitary Q from LQ factorization determined by f08av
• nag_lapack_zunglq – f08aw
• f08ax – Apply unitary transformation determined by f08av
• nag_lapack_zunmlq – f08ax
• f08ba – Computes the minimum-norm solution to a real linear least squares problem
• nag_lapack_dgelsy – f08ba
• f08be – QR factorization of real general rectangular matrix with column pivoting
• nag_lapack_dgeqpf – f08be
• f08bf – QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
• nag_lapack_dgeqp3 – f08bf
• f08bh – Reduces a real upper trapezoidal matrix to upper triangular form
• nag_lapack_dtzrzf – f08bh
• f08bk – Apply orthogonal transformation determined by f08bh
• nag_lapack_dormrz – f08bk
• f08bn – Computes the minimum-norm solution to a complex linear least squares problem
• nag_lapack_zgelsy – f08bn
• f08bs – QR factorization of complex general rectangular matrix with column pivoting
• nag_lapack_zgeqpf – f08bs
• f08bt – QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
• nag_lapack_zgeqp3 – f08bt
• f08bv – Reduces a complex upper trapezoidal matrix to upper triangular form
• nag_lapack_ztzrzf – f08bv
• f08bx – Apply unitary transformation determined by f08bv
• nag_lapack_zunmrz – f08bx
• f08ce – QL factorization of real general rectangular matrix
• nag_lapack_dgeqlf – f08ce
• f08cf – Form all or part of orthogonal Q from QL factorization determined by f08ce
• nag_lapack_dorgql – f08cf
• f08cg – Apply orthogonal transformation determined by f08ce
• nag_lapack_dormql – f08cg
• f08ch – RQ factorization of real general rectangular matrix
• nag_lapack_dgerqf – f08ch
• f08cj – Form all or part of orthogonal Q from RQ factorization determined by f08ch
• nag_lapack_dorgrq – f08cj
• f08ck – Apply orthogonal transformation determined by f08ch
• nag_lapack_dormrq – f08ck
• f08cs – QL factorization of complex general rectangular matrix
• nag_lapack_zgeqlf – f08cs
• f08ct – Form all or part of orthogonal Q from QL factorization determined by f08cs
• nag_lapack_zungql – f08ct
• f08cu – Apply unitary transformation determined by f08cs
• nag_lapack_zunmql – f08cu
• f08cv – RQ factorization of complex general rectangular matrix
• nag_lapack_zgerqf – f08cv
• f08cw – Form all or part of orthogonal Q from RQ factorization determined by f08cv
• nag_lapack_zungrq – f08cw
• f08cx – Apply unitary transformation determined by f08cv
• nag_lapack_zunmrq – f08cx
• f08fa – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
• nag_lapack_dsyev – f08fa
• f08fb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
• nag_lapack_dsyevx – f08fb
• f08fc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
• nag_lapack_dsyevd – f08fc
• f08fd – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
• nag_lapack_dsyevr – f08fd
• f08fe – Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
• nag_lapack_dsytrd – f08fe
• f08ff – Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fe
• nag_lapack_dorgtr – f08ff
• f08fg – Apply orthogonal transformation determined by f08fe
• nag_lapack_dormtr – f08fg
• 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 – f08fl
• f08fn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
• nag_lapack_zheev – f08fn
• f08fp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
• nag_lapack_zheevx – f08fp
• f08fq – Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
• nag_lapack_zheevd – f08fq
• f08fr – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
• nag_lapack_zheevr – f08fr
• f08fs – Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
• nag_lapack_zhetrd – f08fs
• f08ft – Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fs
• nag_lapack_zungtr – f08ft
• f08fu – Apply unitary transformation matrix determined by f08fs
• nag_lapack_zunmtr – f08fu
• f08ga – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
• nag_lapack_dspev – f08ga
• f08gb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
• nag_lapack_dspevx – f08gb
• f08gc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
• nag_lapack_dspevd – f08gc
• f08ge – Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
• nag_lapack_dsptrd – f08ge
• f08gf – Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08ge
• nag_lapack_dopgtr – f08gf
• f08gg – Apply orthogonal transformation determined by f08ge
• nag_lapack_dopmtr – f08gg
• f08gn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
• nag_lapack_zhpev – f08gn
• f08gp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
• nag_lapack_zhpevx – f08gp
• f08gq – Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
• nag_lapack_zhpevd – f08gq
• f08gs – Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
• nag_lapack_zhptrd – f08gs
• f08gt – Generate unitary transformation matrix from reduction to tridiagonal form determined by f08gs
• nag_lapack_zupgtr – f08gt
• f08gu – Apply unitary transformation matrix determined by f08gs
• nag_lapack_zupmtr – f08gu
• f08ha – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
• nag_lapack_dsbev – f08ha
• f08hb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
• nag_lapack_dsbevx – f08hb
• f08hc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer)
• nag_lapack_dsbevd – f08hc
• f08he – Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
• nag_lapack_dsbtrd – f08he
• f08hn – Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
• nag_lapack_zhbev – f08hn
• f08hp – Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
• nag_lapack_zhbevx – f08hp
• f08hq – Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
• nag_lapack_zhbevd – f08hq
• f08hs – Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
• nag_lapack_zhbtrd – f08hs
• f08ja – Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
• nag_lapack_dstev – f08ja
• f08jb – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
• nag_lapack_dstevx – f08jb
• f08jc – Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
• nag_lapack_dstevd – f08jc
• f08jd – Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
• nag_lapack_dstevr – f08jd
• f08je – All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
• nag_lapack_dsteqr – f08je
• f08jf – All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
• nag_lapack_dsterf – f08jf
• f08jg – Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
• nag_lapack_dpteqr – f08jg
• 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 – f08jh
• f08jj – Selected eigenvalues of real symmetric tridiagonal matrix by bisection
• nag_lapack_dstebz – f08jj
• f08jk – Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
• nag_lapack_dstein – f08jk
• 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 – f08jl
• f08js – All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
• nag_lapack_zsteqr – f08js
• f08ju – Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
• nag_lapack_zpteqr – f08ju
• 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 – f08jv
• f08jx – Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
• nag_lapack_zstein – f08jx
• 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 – f08jy
• f08ka – Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
• nag_lapack_dgelss – f08ka
• f08kb – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
• nag_lapack_dgesvd – f08kb
• f08kc – Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
• nag_lapack_dgelsd – f08kc
• 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 – f08kd
• f08ke – Orthogonal reduction of real general rectangular matrix to bidiagonal form
• nag_lapack_dgebrd – f08ke
• f08kf – Generate orthogonal transformation matrices from reduction to bidiagonal form determined by f08ke
• nag_lapack_dorgbr – f08kf
• f08kg – Apply orthogonal transformations from reduction to bidiagonal form determined by f08ke
• nag_lapack_dormbr – f08kg
• f08kh – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
• nag_lapack_dgejsv – f08kh
• f08kj – Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
• nag_lapack_dgesvj – f08kj
• f08kn – Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
• nag_lapack_zgelss – f08kn
• f08kp – Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
• nag_lapack_zgesvd – f08kp
• f08kq – Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
• nag_lapack_zgelsd – f08kq
• 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 – f08kr
• f08ks – Unitary reduction of complex general rectangular matrix to bidiagonal form
• nag_lapack_zgebrd – f08ks
• f08kt – Generate unitary transformation matrices from reduction to bidiagonal form determined by f08ks
• nag_lapack_zungbr – f08kt
• f08ku – Apply unitary transformations from reduction to bidiagonal form determined by f08ks
• nag_lapack_zunmbr – f08ku
• f08le – Reduction of real rectangular band matrix to upper bidiagonal form
• nag_lapack_dgbbrd – f08le
• f08ls – Reduction of complex rectangular band matrix to upper bidiagonal form
• nag_lapack_zgbbrd – f08ls
• f08md – Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
• nag_lapack_dbdsdc – f08md
• f08me – SVD of real bidiagonal matrix reduced from real general matrix
• nag_lapack_dbdsqr – f08me
• f08ms – SVD of real bidiagonal matrix reduced from complex general matrix
• nag_lapack_zbdsqr – f08ms
• f08na – Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
• nag_lapack_dgeev – f08na
• 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 – f08nb
• f08ne – Orthogonal reduction of real general matrix to upper Hessenberg form
• nag_lapack_dgehrd – f08ne
• f08nf – Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08ne
• nag_lapack_dorghr – f08nf
• f08ng – Apply orthogonal transformation matrix from reduction to Hessenberg form determined by f08ne
• nag_lapack_dormhr – f08ng
• f08nh – Balance real general matrix
• nag_lapack_dgebal – f08nh
• f08nj – Transform eigenvectors of real balanced matrix to those of original matrix supplied to f08nh
• nag_lapack_dgebak – f08nj
• f08nn – Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
• nag_lapack_zgeev – f08nn
• 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 – f08np
• f08ns – Unitary reduction of complex general matrix to upper Hessenberg form
• nag_lapack_zgehrd – f08ns
• f08nt – Generate unitary transformation matrix from reduction to Hessenberg form determined by f08ns
• nag_lapack_zunghr – f08nt
• f08nu – Apply unitary transformation matrix from reduction to Hessenberg form determined by f08ns
• nag_lapack_zunmhr – f08nu
• f08nv – Balance complex general matrix
• nag_lapack_zgebal – f08nv
• f08nw – Transform eigenvectors of complex balanced matrix to those of original matrix supplied to f08nv
• nag_lapack_zgebak – f08nw
• f08pa – Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
• nag_lapack_dgees – f08pa
• 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 – f08pb
• f08pe – Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
• nag_lapack_dhseqr – f08pe
• f08pk – Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
• nag_lapack_dhsein – f08pk
• f08pn – Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
• nag_lapack_zgees – f08pn
• f08pp – Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
• nag_lapack_zgeesx – f08pp
• f08ps – Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
• nag_lapack_zhseqr – f08ps
• f08px – Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
• nag_lapack_zhsein – f08px
• f08qf – Reorder Schur factorization of real matrix using orthogonal similarity transformation
• nag_lapack_dtrexc – f08qf
• f08qg – Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
• nag_lapack_dtrsen – f08qg
• f08qh – Solve real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
• nag_lapack_dtrsyl – f08qh
• f08qk – Left and right eigenvectors of real upper quasi-triangular matrix
• nag_lapack_dtrevc – f08qk
• f08ql – Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
• nag_lapack_dtrsna – f08ql
• f08qt – Reorder Schur factorization of complex matrix using unitary similarity transformation
• nag_lapack_ztrexc – f08qt
• f08qu – Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
• nag_lapack_ztrsen – f08qu
• f08qv – Solve complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
• nag_lapack_ztrsyl – f08qv
• f08qx – Left and right eigenvectors of complex upper triangular matrix
• nag_lapack_ztrevc – f08qx
• f08qy – Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
• nag_lapack_ztrsna – f08qy
• f08sa – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
• nag_lapack_dsygv – f08sa
• f08sb – Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
• nag_lapack_dsygvx – f08sb
• f08sc – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
• nag_lapack_dsygvd – f08sc
• f08se – Reduction to standard form of real symmetric-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x or BAx= lambda x, B factorized by f07fd
• nag_lapack_dsygst – f08se
• f08sn – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
• nag_lapack_zhegv – f08sn
• f08sp – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
• nag_lapack_zhegvx – f08sp
• f08sq – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
• nag_lapack_zhegvd – f08sq
• f08ss – Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x or BAx= lambda x, B factorized by f07fr
• nag_lapack_zhegst – f08ss
• f08ta – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
• nag_lapack_dspgv – f08ta
• f08tb – Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
• nag_lapack_dspgvx – f08tb
• f08tc – Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
• nag_lapack_dspgvd – f08tc
• f08te – 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 f07gd
• nag_lapack_dspgst – f08te
• f08tn – Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
• nag_lapack_zhpgv – f08tn
• f08tp – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
• nag_lapack_zhpgvx – f08tp
• f08tq – Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
• nag_lapack_zhpgvd – f08tq
• f08ts – 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 f07gr
• nag_lapack_zhpgst – f08ts
• f08ua – Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
• nag_lapack_dsbgv – f08ua
• f08ub – Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
• nag_lapack_dsbgvx – f08ub
• f08uc – Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
• nag_lapack_dsbgvd – f08uc
• f08ue – 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
• nag_lapack_dsbgst – f08ue
• f08uf – Computes a split Cholesky factorization of real symmetric positive definite band matrix A
• nag_lapack_dpbstf – f08uf
• f08un – Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
• nag_lapack_zhbgv – f08un
• f08up – Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
• nag_lapack_zhbgvx – f08up
• f08uq – Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
• nag_lapack_zhbgvd – f08uq
• f08us – 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
• nag_lapack_zhbgst – f08us
• f08ut – Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
• nag_lapack_zpbstf – f08ut
• f08va – Computes the generalized singular value decomposition of a real matrix pair
• nag_lapack_dggsvd – f08va
• f08ve – Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
• nag_lapack_dggsvp – f08ve
• f08vn – Computes the generalized singular value decomposition of a complex matrix pair
• nag_lapack_zggsvd – f08vn
• f08vs – Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
• nag_lapack_zggsvp – f08vs
• f08wa – Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
• nag_lapack_dggev – f08wa
• 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 – f08wb
• f08we – Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
• nag_lapack_dgghrd – f08we
• f08wh – Balance a pair of real general matrices
• nag_lapack_dggbal – f08wh
• f08wj – Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08wh
• nag_lapack_dggbak – f08wj
• f08wn – Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
• nag_lapack_zggev – f08wn
• 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 – f08wp
• f08ws – Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
• nag_lapack_zgghrd – f08ws
• f08wv – Balance a pair of complex general matrices
• nag_lapack_zggbal – f08wv
• f08ww – Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wv
• nag_lapack_zggbak – f08ww
• 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 – f08xa
• 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 – f08xb
• f08xe – Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
• nag_lapack_dhgeqz – f08xe
• 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 – f08xn
• 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 – f08xp
• f08xs – Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
• nag_lapack_zhgeqz – f08xs
• f08ye – Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
• nag_lapack_dtgsja – f08ye
• f08yf – Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
• nag_lapack_dtgexc – f08yf
• 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 – f08yg
• f08yh – Solves the real-valued generalized Sylvester equation
• nag_lapack_dtgsyl – f08yh
• f08yk – Left and right eigenvectors of a pair of real upper quasi-triangular matrices
• nag_lapack_dtgevc – f08yk
• 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 – f08yl
• f08ys – Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
• nag_lapack_ztgsja – f08ys
• f08yt – Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
• nag_lapack_ztgexc – f08yt
• 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 – f08yu
• f08yv – Solves the complex generalized Sylvester equation
• nag_lapack_ztgsyl – f08yv
• f08yx – Left and right eigenvectors of a pair of complex upper triangular matrices
• nag_lapack_ztgevc – f08yx
• f08yy – Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
• nag_lapack_ztgsna – f08yy
• f08za – Solves the real linear equality-constrained least squares (LSE) problem
• nag_lapack_dgglse – f08za
• f08zb – Solves a real general Gauss–Markov linear model (GLM) problem
• nag_lapack_dggglm – f08zb
• f08ze – Computes a generalized QR factorization of a real matrix pair
• nag_lapack_dggqrf – f08ze
• f08zf – Computes a generalized RQ factorization of a real matrix pair
• nag_lapack_dggrqf – f08zf
• f08zn – Solves the complex linear equality-constrained least squares (LSE) problem
• nag_lapack_zgglse – f08zn
• f08zp – Solves a complex general Gauss–Markov linear model (GLM) problem
• nag_lapack_zggglm – f08zp
• f08zs – Computes a generalized QR factorization of a complex matrix pair
• nag_lapack_zggqrf – f08zs
• f08zt – Computes a generalized RQ factorization of a complex matrix pair
• nag_lapack_zggrqf – f08zt
 F07 F11