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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgghrd.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgghrd.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgghrd.f

SYNOPSIS

Functions/Subroutines


subroutine SGGHRD (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
SGGHRD

Function/Subroutine Documentation

subroutine SGGHRD (character compq, character compz, integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldq, * ) q, integer ldq, real, dimension( ldz, * ) z, integer ldz, integer info)

SGGHRD

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.  The form of the
!> generalized eigenvalue problem is
!>    A*x = lambda*B*x,
!> and B is typically made upper triangular by computing its QR
!> factorization and moving the orthogonal matrix Q to the left side
!> of the equation.
!>
!> This subroutine simultaneously reduces A to a Hessenberg matrix H:
!>    Q**T*A*Z = H
!> and transforms B to another upper triangular matrix T:
!>    Q**T*B*Z = T
!> in order to reduce the problem to its standard form
!>    H*y = lambda*T*y
!> where y = Z**T*x.
!>
!> 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**T = (Q1*Q) * H * (Z1*Z)**T
!>
!>      Q1 * B * Z1**T = (Q1*Q) * T * (Z1*Z)**T
!>
!> If Q1 is the orthogonal matrix from the QR factorization of B in the
!> original equation A*x = lambda*B*x, then SGGHRD reduces the original
!> problem to generalized Hessenberg form.
!> 

Parameters

COMPQ

!>          COMPQ is 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

!>          COMPZ is 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

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!> 

ILO

!>          ILO is INTEGER
!> 

IHI

!>          IHI is INTEGER
!>
!>          ILO and IHI mark the rows and columns of A which are to be
!>          reduced.  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

!>          A is 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

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

B

!>          B is REAL array, dimension (LDB, N)
!>          On entry, the N-by-N upper triangular matrix B.
!>          On exit, the upper triangular matrix T = Q**T B Z.  The
!>          elements below the diagonal are set to zero.
!> 

LDB

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

Q

!>          Q is REAL array, dimension (LDQ, N)
!>          On entry, if COMPQ = 'V', the orthogonal matrix Q1,
!>          typically from the QR factorization of B.
!>          On exit, if COMPQ='I', the orthogonal matrix Q, and if
!>          COMPQ = 'V', the product Q1*Q.
!>          Not referenced if COMPQ='N'.
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q.
!>          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
!> 

Z

!>          Z is REAL array, dimension (LDZ, N)
!>          On entry, if COMPZ = 'V', the orthogonal matrix Z1.
!>          On exit, if COMPZ='I', the orthogonal matrix Z, and if
!>          COMPZ = 'V', the product Z1*Z.
!>          Not referenced if COMPZ='N'.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z.
!>          LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.)
!> 

Definition at line 205 of file sgghrd.f.

Author

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Version 3.12.0 LAPACK