cgegs(3P) Sun Performance Library cgegs(3P)NAMEcgegs - routine is deprecated and has been replaced by routine CGGES
SYNOPSIS
SUBROUTINE CGEGS(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL,
LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVSL, JOBVSR
COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*),
VSR(LDVSR,*), WORK(*)
INTEGER N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO
REAL WORK2(*)
SUBROUTINE CGEGS_64(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVSL, JOBVSR
COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*),
VSR(LDVSR,*), WORK(*)
INTEGER*8 N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO
REAL WORK2(*)
F95 INTERFACE
SUBROUTINE GEGS(JOBVSL, JOBVSR, [N], A, [LDA], B, [LDB], ALPHA, BETA,
VSL, [LDVSL], VSR, [LDVSR], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBVSL, JOBVSR
COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
INTEGER :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO
REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEGS_64(JOBVSL, JOBVSR, [N], A, [LDA], B, [LDB], ALPHA,
BETA, VSL, [LDVSL], VSR, [LDVSR], [WORK], [LDWORK], [WORK2],
[INFO])
CHARACTER(LEN=1) :: JOBVSL, JOBVSR
COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
INTEGER(8) :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO
REAL, DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void cgegs(char jobvsl, char jobvsr, int n, complex *a, int lda, com‐
plex *b, int ldb, complex *alpha, complex *beta, complex
*vsl, int ldvsl, complex *vsr, int ldvsr, int *info);
void cgegs_64(char jobvsl, char jobvsr, long n, complex *a, long lda,
complex *b, long ldb, complex *alpha, complex *beta, complex
*vsl, long ldvsl, complex *vsr, long ldvsr, long *info);
PURPOSEcgegs routine is deprecated and has been replaced by routine CGGES.
CGEGS computes for a pair of N-by-N complex nonsymmetric matrices A, B:
the generalized eigenvalues (alpha, beta), the complex Schur form (A,
B), and optionally left and/or right Schur vectors (VSL and VSR).
(If only the generalized eigenvalues are needed, use the driver CGEGV
instead.)
A generalized eigenvalue for a pair of matrices (A,B) is, roughly
speaking, a scalar w or a ratio alpha/beta = w, such that A - w*B is
singular. It is usually represented as the pair (alpha,beta), as there
is a reasonable interpretation for beta=0, and even for both being
zero. A good beginning reference is the book, "Matrix Computations",
by G. Golub & C. van Loan (Johns Hopkins U. Press)
The (generalized) Schur form of a pair of matrices is the result of
multiplying both matrices on the left by one unitary matrix and both on
the right by another unitary matrix, these two unitary matrices being
chosen so as to bring the pair of matrices into upper triangular form
with the diagonal elements of B being non-negative real numbers (this
is also called complex Schur form.)
The left and right Schur vectors are the columns of VSL and VSR,
respectively, where VSL and VSR are the unitary matrices
which reduce A and B to Schur form:
Schur form of (A,B) = ( (VSL)**H A (VSR), (VSL)**H B (VSR) )
ARGUMENTS
JOBVSL (input)
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
JOBVSR (input)
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
N (input) The order of the matrices A, B, VSL, and VSR. N >= 0.
A (input/output)
On entry, the first of the pair of matrices whose generalized
eigenvalues and (optionally) Schur vectors are to be com‐
puted. On exit, the generalized Schur form of A.
LDA (input)
The leading dimension of A. LDA >= max(1,N).
B (input/output)
On entry, the second of the pair of matrices whose general‐
ized eigenvalues and (optionally) Schur vectors are to be
computed. On exit, the generalized Schur form of B.
LDB (input)
The leading dimension of B. LDB >= max(1,N).
ALPHA (output)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the general‐
ized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),
j=1,...,N are the diagonals of the complex Schur form (A,B)
output by CGEGS. The BETA(j) will be non-negative real.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user
should avoid naively computing the ratio alpha/beta. How‐
ever, ALPHA will be always less than and usually comparable
with norm(A) in magnitude, and BETA always less than and usu‐
ally comparable with norm(B).
BETA (output)
See the description of ALPHA.
VSL (output)
If JOBVSL = 'V', VSL will contain the left Schur vectors.
(See "Purpose", above.) Not referenced if JOBVSL = 'N'.
LDVSL (input)
The leading dimension of the matrix VSL. LDVSL >= 1, and if
JOBVSL = 'V', LDVSL >= N.
VSR (output)
If JOBVSR = 'V', VSR will contain the right Schur vectors.
(See "Purpose", above.) Not referenced if JOBVSR = 'N'.
LDVSR (input)
The leading dimension of the matrix VSR. LDVSR >= 1, and if
JOBVSR = 'V', LDVSR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,2*N). For
good performance, LDWORK must generally be larger. To com‐
pute the optimal value of LDWORK, call ILAENV to get block‐
sizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: NB as
the MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; the
optimal LDWORK is N*(NB+1).
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(3*N)
INFO (output)
= 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 ALPHA(j) and BETA(j) should be correct for
j=INFO+1,...,N. > N: errors that usually indicate LAPACK
problems:
=N+1: error return from CGGBAL
=N+2: error return from CGEQRF
=N+3: error return from CUNMQR
=N+4: error return from CUNGQR
=N+5: error return from CGGHRD
=N+6: error return from CHGEQZ (other than failed iteration)
=N+7: error return from CGGBAK (computing VSL)
=N+8: error return from CGGBAK (computing VSR)
=N+9: error return from CLASCL (various places)
6 Mar 2009 cgegs(3P)
