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dgegs.f(3) LAPACK dgegs.f(3)

NAME

dgegs.f -

SYNOPSIS

Functions/Subroutines


subroutine dgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO)
DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

subroutine dgegs (characterJOBVSL, characterJOBVSR, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )ALPHAR, double precision, dimension( * )ALPHAI, double precision, dimension( * )BETA, double precision, dimension( ldvsl, * )VSL, integerLDVSL, double precision, dimension( ldvsr, * )VSR, integerLDVSR, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:


This routine is deprecated and has been replaced by routine DGGES.
DGEGS computes the eigenvalues, real Schur form, and, optionally,
left and or/right Schur vectors of a real matrix pair (A,B).
Given two square matrices A and B, the generalized real Schur
factorization has the form
A = Q*S*Z**T, B = Q*T*Z**T
where Q and Z are orthogonal matrices, T is upper triangular, and S
is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
of eigenvalues of (A,B). The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver routine
DGEGV should be used instead. See DGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).

Parameters:

JOBVSL


JOBVSL is CHARACTER*1
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors (returned in VSL).

JOBVSR


JOBVSR is CHARACTER*1
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors (returned in VSR).

N


N is INTEGER
The order of the matrices A, B, VSL, and VSR. N >= 0.

A


A is DOUBLE PRECISION array, dimension (LDA, N)
On entry, the matrix A.
On exit, the upper quasi-triangular matrix S from the
generalized real Schur factorization.

LDA


LDA is INTEGER
The leading dimension of A. LDA >= max(1,N).

B


B is DOUBLE PRECISION array, dimension (LDB, N)
On entry, the matrix B.
On exit, the upper triangular matrix T from the generalized
real Schur factorization.

LDB


LDB is INTEGER
The leading dimension of B. LDB >= max(1,N).

ALPHAR


ALPHAR is DOUBLE PRECISION array, dimension (N)
The real parts of each scalar alpha defining an eigenvalue
of GNEP.

ALPHAI


ALPHAI is DOUBLE PRECISION array, dimension (N)
The imaginary parts of each scalar alpha defining an
eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th
eigenvalue is real; if positive, then the j-th and (j+1)-st
eigenvalues are a complex conjugate pair, with
ALPHAI(j+1) = -ALPHAI(j).

BETA


BETA is DOUBLE PRECISION array, dimension (N)
The scalars beta that define the eigenvalues of GNEP.
Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
beta = BETA(j) represent the j-th eigenvalue of the matrix
pair (A,B), in one of the forms lambda = alpha/beta or
mu = beta/alpha. Since either lambda or mu may overflow,
they should not, in general, be computed.

VSL


VSL is DOUBLE PRECISION array, dimension (LDVSL,N)
If JOBVSL = 'V', the matrix of left Schur vectors Q.
Not referenced if JOBVSL = 'N'.

LDVSL


LDVSL is INTEGER
The leading dimension of the matrix VSL. LDVSL >=1, and
if JOBVSL = 'V', LDVSL >= N.

VSR


VSR is DOUBLE PRECISION array, dimension (LDVSR,N)
If JOBVSR = 'V', the matrix of right Schur vectors Z.
Not referenced if JOBVSR = 'N'.

LDVSR


LDVSR is INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = 'V', LDVSR >= N.

WORK


WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK


LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,4*N).
For good performance, LWORK must generally be larger.
To compute the optimal value of LWORK, call ILAENV to get
blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute:
NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR
The optimal LWORK is 2*N + N*(NB+1).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. (A,B) are not in Schur
form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
be correct for j=INFO+1,...,N.
> N: errors that usually indicate LAPACK problems:
=N+1: error return from DGGBAL
=N+2: error return from DGEQRF
=N+3: error return from DORMQR
=N+4: error return from DORGQR
=N+5: error return from DGGHRD
=N+6: error return from DHGEQZ (other than failed
iteration)
=N+7: error return from DGGBAK (computing VSL)
=N+8: error return from DGGBAK (computing VSR)
=N+9: error return from DLASCL (various places)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 226 of file dgegs.f.

Author

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Tue Sep 25 2012 Version 3.4.2