srqt02.f - Man Page

subroutine srqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
SRQT02

SRQT02

Purpose:

 SRQT02 tests SORGRQ, 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, SRQT02 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 REAL array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by SRQT01.

AF

          AF is REAL array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by SGERQF.
          See SGERQF for further details.

Q

          Q is REAL array, dimension (LDA,N)

R

          R is REAL array, dimension (LDA,M)

LDA

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

TAU

          TAU is REAL array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL 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 srqt02.f.