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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zqrt02.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zqrt02.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/TESTING/LIN/zqrt02.f

SYNOPSIS

Functions/Subroutines


subroutine ZQRT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZQRT02

Function/Subroutine Documentation

subroutine ZQRT02 (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)

ZQRT02

Purpose:

!>
!> ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with
!> orthonormal columns that is defined as the product of k elementary
!> reflectors.
!>
!> Given the QR factorization of an m-by-n matrix A, ZQRT02 generates
!> the orthogonal matrix Q defined by the factorization of the first k
!> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
!> and checks that the columns 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.
!>          M >= N >= 0.
!> 

K

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

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by ZQRT01.
!> 

AF

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

Q

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

R

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

LDA

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

TAU

!>          TAU is COMPLEX*16 array, dimension (N)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the QR 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 - Q'*A ) / ( M * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file zqrt02.f.

Author

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Version 3.12.0 LAPACK