sgghrd

NAME

sgghrd - reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular

SYNOPSIS 

  SUBROUTINE SGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, 
 *      LDQ, Z, LDZ, INFO)
  CHARACTER * 1 COMPQ, COMPZ
  INTEGER N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
  REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
 
  SUBROUTINE SGGHRD_64( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, 
 *      LDQ, Z, LDZ, INFO)
  CHARACTER * 1 COMPQ, COMPZ
  INTEGER*8 N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
  REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)

F95 INTERFACE 

  SUBROUTINE GGHRD( COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, [LDB], 
 *       Q, [LDQ], Z, [LDZ], [INFO])
  CHARACTER(LEN=1) :: COMPQ, COMPZ
  INTEGER :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
  REAL, DIMENSION(:,:) :: A, B, Q, Z
 
  SUBROUTINE GGHRD_64( COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, [LDB], 
 *       Q, [LDQ], Z, [LDZ], [INFO])
  CHARACTER(LEN=1) :: COMPQ, COMPZ
  INTEGER(8) :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
  REAL, DIMENSION(:,:) :: A, B, Q, Z

C INTERFACE

#include <sunperf.h>

void sgghrd(char compq, char compz, int n, int ilo, int ihi, float *a, int lda, float *b, int ldb, float *q, int ldq, float *z, int ldz, int *info);

void sgghrd_64(char compq, char compz, long n, long ilo, long ihi, float *a, long lda, float *b, long ldb, float *q, long ldq, float *z, long ldz, long *info);

PURPOSE

sgghrd reduces a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular: Q' * A * Z = H and Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular, and Q and Z are orthogonal, and ' means transpose.

The orthogonal matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so that

1 * A * Z1' = (Q1*Q) * H * (Z1*Z)' 1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'

ARGUMENTS

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

* ILO (input)
It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to SGGBAL; otherwise they should be set to 1 and N respectively. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

* IHI (input)
See the description of ILO.

* A (input/output)
On entry, the N-by-N general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the rest is set to zero.

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

* B (input/output)
On entry, the N-by-N upper triangular matrix B. On exit, the upper triangular matrix T = Q' B Z. The elements below the diagonal are set to zero.

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

* Q (input/output)
If COMPQ='N': Q is not referenced.

If COMPQ='I': on entry, Q need not be set, and on exit it contains the orthogonal matrix Q, where Q' is the product of the Givens transformations which are applied to A and B on the left. If COMPQ='V': on entry, Q must contain an orthogonal matrix Q1, and on exit this is overwritten by Q1*Q.

* LDQ (input)
The leading dimension of the array Q. LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.

* Z (input/output)
If COMPZ='N': Z is not referenced.

If COMPZ='I': on entry, Z need not be set, and on exit it contains the orthogonal matrix Z, which is the product of the Givens transformations which are applied to A and B on the right. If COMPZ='V': on entry, Z must contain an orthogonal matrix Z1, and on exit this is overwritten by Z1*Z.

* LDZ (input)
The leading dimension of the array Z. LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.

* INFO (output)