subroutine dqrt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQRT01

Purpose:

 DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n
 matrix A, and partially tests DORGQR which forms the m-by-m
 orthogonal matrix Q.

 DQRT01 compares R with Q'*A, and checks that Q is orthogonal.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQRF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	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.

Date

November 2011

Definition at line 128 of file dqrt01.f.

*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            lda, lwork, m, n
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( lda, * ), af( lda, * ), q( lda, * ),
     $                   r( lda, * ), result( * ), rwork( * ), tau( * ),
     $                   work( lwork )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter                ( zero = 0.0d+0, one = 1.0d+0 )
      DOUBLE PRECISION   rogue
      parameter                ( rogue = -1.0d+10 )
*     ..
*     .. Local Scalars ..
      INTEGER            info, minmn
      DOUBLE PRECISION   anorm, eps, resid
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   dlamch, dlange, dlansy
      EXTERNAL           dlamch, dlange, dlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dgeqrf, dlacpy, dlaset, dorgqr, dsyrk
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, max, min
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       srnamt
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Executable Statements ..
*
      minmn = min( m, n )
      eps = dlamch( 'Epsilon' )
*
*     Copy the matrix A to the array AF.
*
      CALL dlacpy( 'Full', m, n, a, lda, af, lda )
*
*     Factorize the matrix A in the array AF.
*
      srnamt = 'DGEQRF'
      CALL dgeqrf( m, n, af, lda, tau, work, lwork, info )
*
*     Copy details of Q
*
      CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
      CALL dlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
*
*     Generate the m-by-m matrix Q
*
      srnamt = 'DORGQR'
      CALL dorgqr( m, m, minmn, q, lda, tau, work, lwork, info )
*
*     Copy R
*
      CALL dlaset( 'Full', m, n, zero, zero, r, lda )
      CALL dlacpy( 'Upper', m, n, af, lda, r, lda )
*
*     Compute R - Q'*A
*
      CALL dgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
     $            lda, one, r, lda )
*
*     Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
      anorm = dlange( '1', m, n, a, lda, rwork )
      resid = dlange( '1', m, n, r, lda, rwork )
      IF( anorm.GT.zero ) THEN
         result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
      ELSE
         result( 1 ) = zero
      END IF
*
*     Compute I - Q'*Q
*
      CALL dlaset( 'Full', m, m, zero, one, r, lda )
      CALL dsyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, r,
     $            lda )
*
*     Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
      resid = dlansy( '1', 'Upper', m, r, lda, rwork )
*
      result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
*
      RETURN
*
*     End of DQRT01
*

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