## 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
• f08bbQR factorization of real general triangular-pentagonal matrix
• nag_lapack_dtpqrt
• f08bc – Applies the orthogonal transformation determined by f08bb
• nag_lapack_dtpmqrt
• f08beQR factorization, with column pivoting, of real general rectangular matrix
• nag_lapack_dgeqpf
• f08bfQR 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
• f08bpQR factorization of complex triangular-pentagonal matrix
• nag_lapack_ztpqrt
• f08bq – Applies the unitary transformation determined by f08bp
• nag_lapack_ztpmqrt
• f08bsQR factorization, with column pivoting, of complex general rectangular matrix
• nag_lapack_zgeqpf
• f08btQR 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
• f08ceQL 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
• f08chRQ 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
• f08csQL 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
• f08cvRQ 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