Chapter Introduction (pdf version)
NAG C Library Manual

f08 – Least-squares and Eigenvalue Problems (LAPACK)

f08 Chapter Introduction
Routine
Name
Mark of
Introduction

Purpose
f08aec
Example Text
Example Data
7 nag_dgeqrf
QR factorization of real general rectangular matrix
f08afc
Example Text
Example Data
7 nag_dorgqr
Form all or part of orthogonal Q from QR 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
LQ factorization of real general rectangular matrix
f08ajc
Example Text
Example Data
7 nag_dorglq
Form all or part of orthogonal Q from LQ 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
QR factorization of complex general rectangular matrix
f08atc
Example Text
Example Data
7 nag_zungqr
Form all or part of unitary Q from QR 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
LQ factorization of complex general rectangular matrix
f08awc
Example Text
Example Data
7 nag_zunglq
Form all or part of unitary Q from LQ 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
QR factorization of real general rectangular matrix with column pivoting
f08bsc
Example Text
Example Data
7 nag_zgeqpf
QR 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 (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 (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 (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 (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 (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 (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 (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 QL or QR
f08jfc
Example Text
Example Data
7 nag_dsterf
All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
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 QL or QR
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 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
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 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
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 Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_dpotrf (f07fdc)
f08ssc
Example Text
Example Data
7 nag_zhegst
Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_zpotrf (f07frc)
f08tec
Example Text
Example Data
7 nag_dspgst
Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, 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 Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by nag_zpptrf (f07grc)
f08uec
Example Text
Example Data
7 nag_dsbgst
Reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, 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 Ax=λBx 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 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

Chapter Introduction (pdf version)
NAG C Library Manual

The Numerical Algorithms Group Ltd, Oxford, UK. 2005