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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/EIG/sgrqts.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/EIG/sgrqts.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/EIG/sgrqts.f

SYNOPSIS

Functions/Subroutines


subroutine SGRQTS (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)
SGRQTS

Function/Subroutine Documentation

subroutine SGRQTS (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) taua, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, real, dimension( ldb, * ) z, real, dimension( ldb, * ) t, real, dimension( ldb, * ) bwk, integer ldb, real, dimension( * ) taub, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)

SGRQTS

Purpose:

!>
!> SGRQTS tests SGGRQF, which computes the GRQ factorization of an
!> M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
!>

Parameters

M 

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

P

!>          P is INTEGER
!>          The number of rows of the matrix B.  P >= 0.
!>

N

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

A

!>          A is REAL array, dimension (LDA,N)
!>          The M-by-N matrix A.
!>

AF

!>          AF is REAL array, dimension (LDA,N)
!>          Details of the GRQ factorization of A and B, as returned
!>          by SGGRQF, see SGGRQF for further details.
!>

Q

!>          Q is REAL array, dimension (LDA,N)
!>          The N-by-N orthogonal matrix Q.
!>

R

!>          R is REAL array, dimension (LDA,MAX(M,N))
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A, AF, R and Q.
!>          LDA >= max(M,N).
!>

TAUA

!>          TAUA is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by SGGQRC.
!>

B

!>          B is REAL array, dimension (LDB,N)
!>          On entry, the P-by-N matrix A.
!>

BF

!>          BF is REAL array, dimension (LDB,N)
!>          Details of the GQR factorization of A and B, as returned
!>          by SGGRQF, see SGGRQF for further details.
!>

Z

!>          Z is REAL array, dimension (LDB,P)
!>          The P-by-P orthogonal matrix Z.
!>

T

!>          T is REAL array, dimension (LDB,max(P,N))
!>

BWK

!>          BWK is REAL array, dimension (LDB,N)
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the arrays B, BF, Z and T.
!>          LDB >= max(P,N).
!>

TAUB

!>          TAUB is REAL array, dimension (min(P,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by SGGRQF.
!>

WORK

!>          WORK is REAL array, dimension (LWORK)
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK, LWORK >= max(M,P,N)**2.
!>

RWORK

!>          RWORK is REAL array, dimension (M)
!>

RESULT

!>          RESULT is REAL array, dimension (4)
!>          The test ratios:
!>            RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
!>            RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
!>            RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
!>            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 175 of file sgrqts.f.

Author

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Version 3.12.0 LAPACK