table of contents
/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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