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RedHat 9 (Linux i386) - man page for sgghrd (redhat section l)

SGGHRD(l)					)					SGGHRD(l)

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	  COMPQ, COMPZ

	   INTEGER	  IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N

	   REAL 	  A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

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

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

ARGUMENTS
       COMPQ   (input) CHARACTER*1
	       = 'N': do not compute Q;
	       =  'I':	Q  is  initialized  to	the  unit  matrix, and the orthogonal matrix Q is
	       returned; = 'V': Q must contain an orthogonal matrix Q1 on entry, and the  product
	       Q1*Q is returned.

       COMPZ   (input) CHARACTER*1
	       = 'N': do not compute Z;
	       =  'I':	Z  is  initialized  to	the  unit  matrix, and the orthogonal matrix Z is
	       returned; = 'V': Z must contain an orthogonal matrix Z1 on entry, and the  product
	       Z1*Z is returned.

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

       ILO     (input) INTEGER
	       IHI	(input)  INTEGER 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.

       A       (input/output) REAL array, dimension (LDA, N)
	       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) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       B       (input/output) REAL array, dimension (LDB, N)
	       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) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

       Q       (input/output) REAL array, dimension (LDQ, N)
	       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) INTEGER
	       The leading dimension of the array Q.  LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 oth-
	       erwise.

       Z       (input/output) REAL array, dimension (LDZ, N)
	       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) INTEGER
	       The leading dimension of the array Z.  LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 oth-
	       erwise.

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
       This  routine  reduces A to Hessenberg and B to triangular form by an unblocked reduction,
       as described in _Matrix_Computations_, by Golub and Van Loan (Johns Hopkins Press.)

LAPACK version 3.0			   15 June 2000 				SGGHRD(l)


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