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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zrqt02.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zrqt02.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zrqt02.f

SYNOPSIS

Functions/Subroutines


subroutine ZRQT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZRQT02

Function/Subroutine Documentation

subroutine ZRQT02 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZRQT02

Purpose:

!>
!> ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with
!> orthonormal rows that is defined as the product of k elementary
!> reflectors.
!>
!> Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates
!> the orthogonal matrix Q defined by the factorization of the last k
!> rows of A; it compares R(m-k+1:m,n-m+1:n) with
!> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
!> orthonormal.
!> 

Parameters

M

!>          M is INTEGER
!>          The number of rows of the matrix Q to be generated.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix Q to be generated.
!>          N >= M >= 0.
!> 

K

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q. M >= K >= 0.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by ZRQT01.
!> 

AF

!>          AF is COMPLEX*16 array, dimension (LDA,N)
!>          Details of the RQ factorization of A, as returned by ZGERQF.
!>          See ZGERQF for further details.
!> 

Q

!>          Q is COMPLEX*16 array, dimension (LDA,N)
!> 

R

!>          R is COMPLEX*16 array, dimension (LDA,M)
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
!> 

TAU

!>          TAU is COMPLEX*16 array, dimension (M)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the RQ factorization in AF.
!> 

WORK

!>          WORK is COMPLEX*16 array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!> 

RWORK

!>          RWORK is DOUBLE PRECISION array, dimension (M)
!> 

RESULT

!>          RESULT is DOUBLE PRECISION array, dimension (2)
!>          The test ratios:
!>          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file zrqt02.f.

Author

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Version 3.12.0 LAPACK