chgeqz

NAME

chgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right

SYNOPSIS 

  SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, 
 *      ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO)
  CHARACTER * 1 JOB, COMPQ, COMPZ
  COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), Q(LDQ,*), Z(LDZ,*), WORK(*)
  INTEGER N, ILO, IHI, LDA, LDB, LDQ, LDZ, LWORK, INFO
  REAL RWORK(*)
 
  SUBROUTINE CHGEQZ_64( JOB, COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, 
 *      LDB, ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO)
  CHARACTER * 1 JOB, COMPQ, COMPZ
  COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), Q(LDQ,*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, ILO, IHI, LDA, LDB, LDQ, LDZ, LWORK, INFO
  REAL RWORK(*)

F95 INTERFACE 

  SUBROUTINE HGEQZ( JOB, COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, 
 *       [LDB], ALPHA, BETA, Q, [LDQ], Z, [LDZ], [WORK], [LWORK], [RWORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOB, COMPQ, COMPZ
  COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
  COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
  INTEGER :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, LWORK, INFO
  REAL, DIMENSION(:) :: RWORK
 
  SUBROUTINE HGEQZ_64( JOB, COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, 
 *       [LDB], ALPHA, BETA, Q, [LDQ], Z, [LDZ], [WORK], [LWORK], [RWORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOB, COMPQ, COMPZ
  COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
  COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
  INTEGER(8) :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, LWORK, INFO
  REAL, DIMENSION(:) :: RWORK

C INTERFACE

#include <sunperf.h>

void chgeqz(char job, char compq, char compz, int n, int ilo, int ihi, complex *a, int lda, complex *b, int ldb, complex *alpha, complex *beta, complex *q, int ldq, complex *z, int ldz, int *info);

void chgeqz_64(char job, char compq, char compz, long n, long ilo, long ihi, complex *a, long lda, complex *b, long ldb, complex *alpha, complex *beta, complex *q, long ldq, complex *z, long ldz, long *info);

PURPOSE

chgeqz implements a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation A are then ALPHA(1),...,ALPHA(N), and of B are BETA(1),...,BETA(N).

If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the unitary transformations used to reduce (A,B) are accumulated into the arrays Q and Z s.t.:

(in) A(in) Z(in)* = Q(out) A(out) Z(out)* (in) B(in) Z(in)* = Q(out) B(out) Z(out)*

Ref: C.B. Moler & G.W. Stewart, ``An Algorithm for Generalized Matrixigenvalue Problems'', SIAM J. Numer. Anal., 10(1973),p. 241--256.

ARGUMENTS

* JOB (input)
* COMPQ (input)
* COMPZ (input)
* N (input)
The order of the matrices A, B, Q, and Z. N >= 0.

* ILO (input)
It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

* IHI (input)
It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

* A (input)
On entry, the N-by-N upper Hessenberg matrix A. Elements below the subdiagonal must be zero. If JOB='S', then on exit A and B will have been simultaneously reduced to upper triangular form. If JOB='E', then on exit A will have been destroyed.

* LDA (input)
The leading dimension of the array A. LDA >= max( 1, N ).

* B (input)
On entry, the N-by-N upper triangular matrix B. Elements below the diagonal must be zero. If JOB='S', then on exit A and B will have been simultaneously reduced to upper triangular form. If JOB='E', then on exit B will have been destroyed.

* LDB (input)
The leading dimension of the array B. LDB >= max( 1, N ).

* ALPHA (output)
The diagonal elements of A when the pair (A,B) has been reduced to Schur form. ALPHA(i)/BETA(i) i=1,...,N are the generalized eigenvalues.

* BETA (output)
The diagonal elements of B when the pair (A,B) has been reduced to Schur form. ALPHA(i)/BETA(i) i=1,...,N are the generalized eigenvalues. A and B are normalized so that BETA(1),...,BETA(N) are non-negative real numbers.

* Q (input/output)
If COMPQ='N', then Q will not be referenced. If COMPQ='V' or 'I', then the conjugate transpose of the unitary transformations which are applied to A and B on the left will be applied to the array Q on the right.

* LDQ (input)
The leading dimension of the array Q. LDQ >= 1. If COMPQ='V' or 'I', then LDQ >= N.

* Z (input/output)
If COMPZ='N', then Z will not be referenced. If COMPZ='V' or 'I', then the unitary transformations which are applied to A and B on the right will be applied to the array Z on the right.

* LDZ (input)
The leading dimension of the array Z. LDZ >= 1. If COMPZ='V' or 'I', then LDZ >= N.

* WORK (workspace)
On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.

* LWORK (input)
The dimension of the array WORK. LWORK >= max(1,N).

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.

* RWORK (workspace)
dimension(N)

* INFO (output)