C Library, Mark 7 : f08 Chapter Contents

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

f08 – Least-squares and Eigenvalue Problems (LAPACK)