f08 – Least-squares and Eigenvalue Problems (LAPACK)

Routine Name	Mark of Introduction	Purpose
f08aec	7	nag_dgeqrf QR factorization of real general rectangular matrix
f08afc	7	nag_dorgqr Form all or part of orthogonal Q from QR factorization determined by f08aec or f08bec
f08agc	7	nag_dormqr Apply orthogonal transformation determined by f08aec or f08bec
f08ahc	7	nag_dgelqf LQ factorization of real general rectangular matrix
f08ajc	7	nag_dorglq Form all or part of orthogonal Q from LQ factorization determined by f08ahc
f08akc	7	nag_dormlq Apply orthogonal transformation determined by f08ahc
f08asc	7	nag_zgeqrf QR factorization of complex general rectangular matrix
f08atc	7	nag_zungqr Form all or part of unitary Q from QR factorization determined by f08asc or f08bsc
f08auc	7	nag_zunmqr Apply unitary transformation determined by f08asc or f08bsc
f08avc	7	nag_zgelqf LQ factorization of complex general rectangular matrix
f08awc	7	nag_zunglq Form all or part of unitary Q from LQ factorization determined by f08avc
f08axc	7	nag_zunmlq Apply unitary transformation determined by f08avc
f08bec	7	nag_dgeqpf QR factorization of real general rectangular matrix with column pivoting
f08bsc	7	nag_zgeqpf QR factorization of complex general rectangular matrix with column pivoting
f08fcc	7	nag_dsyevd All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
f08fec	7	nag_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc	7	nag_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec
f08fgc	7	nag_dormtr Apply orthogonal transformation determined by f08fec
f08fqc	7	nag_zheevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
f08fsc	7	nag_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc	7	nag_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc
f08fuc	7	nag_zunmtr Apply unitary transformation matrix determined by f08fsc
f08gcc	7	nag_dspevd All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
f08gec	7	nag_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc	7	nag_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec
f08ggc	7	nag_dopmtr Apply orthogonal transformation determined by f08gec
f08gqc	7	nag_zhpevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
f08gsc	7	nag_zhptrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc	7	nag_zupgtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08gsc
f08guc	7	nag_zupmtr Apply unitary transformation matrix determined by f08gsc
f08hcc	7	nag_dsbevd All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
f08hec	7	nag_dsbtrd Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hqc	7	nag_zhbevd All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
f08hsc	7	nag_zhbtrd Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jcc	7	nag_dstevd All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
f08jec	7	nag_dsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
f08jfc	7	nag_dsterf All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
f08jgc	7	nag_dpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
f08jjc	7	nag_dstebz Selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc	7	nag_dstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jsc	7	nag_zsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
f08juc	7	nag_zpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
f08jxc	7	nag_zstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08kec	7	nag_dgebrd Orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc	7	nag_dorgbr Generate orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec
f08kgc	7	nag_dormbr Apply orthogonal transformations from reduction to bidiagonal form determined by f08kec
f08ksc	7	nag_zgebrd Unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc	7	nag_zungbr Generate unitary transformation matrices from reduction to bidiagonal form determined by f08ksc
f08kuc	7	nag_zunmbr Apply unitary transformations from reduction to bidiagonal form determined by f08ksc
f08lec	7	nag_dgbbrd Reduction of real rectangular band matrix to upper bidiagonal form
f08lsc	7	nag_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form
f08mec	7	nag_dbdsqr SVD of real bidiagonal matrix reduced from real general matrix
f08msc	7	nag_zbdsqr SVD of real bidiagonal matrix reduced from complex general matrix
f08nec	7	nag_dgehrd Orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc	7	nag_dorghr Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08ngc	7	nag_dormhr Apply orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08nhc	7	nag_dgebal Balance real general matrix
f08njc	7	nag_dgebak Transform eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc
f08nsc	7	nag_zgehrd Unitary reduction of complex general matrix to upper Hessenberg form
f08ntc	7	nag_zunghr Generate unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nuc	7	nag_zunmhr Apply unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nvc	7	nag_zgebal Balance complex general matrix
f08nwc	7	nag_zgebak Transform eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvc
f08pec	7	nag_dhseqr Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkc	7	nag_dhsein Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08psc	7	nag_zhseqr Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxc	7	nag_zhsein Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qfc	7	nag_dtrexc Reorder Schur factorization of real matrix using orthogonal similarity transformation
f08qgc	7	nag_dtrsen Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qhc	7	nag_dtrsyl Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
f08qkc	7	nag_dtrevc Left and right eigenvectors of real upper quasi-triangular matrix
f08qlc	7	nag_dtrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc	7	nag_ztrexc Reorder Schur factorization of complex matrix using unitary similarity transformation
f08quc	7	nag_ztrsen Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qvc	7	nag_ztrsyl Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
f08qxc	7	nag_ztrevc Left and right eigenvectors of complex upper triangular matrix
f08qyc	7	nag_ztrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08sec	7	nag_dsygst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07fdc
f08ssc	7	nag_zhegst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07frc
f08tec	7	nag_dspgst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07gdc
f08tsc	7	nag_zhpgst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07grc
f08uec	7	nag_dsbgst Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
f08ufc	7	nag_dpbstf Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
f08usc	7	nag_zhbgst Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
f08utc	7	nag_zpbstf Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
f08wec	7	nag_dgghrd Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whc	7	nag_dggbal Balance a pair of real general matrices
f08wjc	7	nag_dggbak Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc
f08wsc	7	nag_zgghrd Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wvc	7	nag_zggbal Balance a pair of complex general matrices
f08wwc	7	nag_zggbak Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvc
f08xec	7	nag_dhgeqz Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
f08xsc	7	nag_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
f08ykc	7	nag_dtgevc Left and right eigenvectors of a pair of real upper quasi-triangular matrices
f08yxc	7	nag_ztgevc Left and right eigenvectors of a pair of complex upper triangular matrices

NAG C Library