dqrt03()

subroutine dqrt03	(	integer	m,
		integer	n,
		integer	k,
		double precision, dimension( lda, * )	af,
		double precision, dimension( lda, * )	c,
		double precision, dimension( lda, * )	cc,
		double precision, dimension( lda, * )	q,
		integer	lda,
		double precision, dimension( * )	tau,
		double precision, dimension( lwork )	work,
		integer	lwork,
		double precision, dimension( * )	rwork,
		double precision, dimension( * )	result
	)

DQRT03

Purpose:

 DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 DQRT03 compares the results of a call to DORMQR with the results of
 forming Q explicitly by a call to DORGQR and then performing matrix
 multiplication by a call to DGEMM.

Parameters

[in]	M	M is INTEGER The order of the orthogonal matrix Q. M >= 0.
[in]	N	N is INTEGER The number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returned by DGEQRF. See DGEQRF for further details.
[out]	C	C is DOUBLE PRECISION array, dimension (LDA,N)
[out]	CC	CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an m-by-m orthogonal matrix Q. RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file dqrt03.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
     $                   Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
     $                   WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d0 )
      DOUBLE PRECISION   ROGUE
      parameter( rogue = -1.0d+10 )
*     ..
*     .. Local Scalars ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, ISIDE, ITRANS, J, MC, NC
      DOUBLE PRECISION   CNORM, EPS, RESID
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           lsame, dlamch, dlange
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dlacpy, dlarnv, dlaset, dorgqr, dormqr
*     ..
*     .. Local Arrays ..
      INTEGER            ISEED( 4 )
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, max
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Data statements ..
      DATA               iseed / 1988, 1989, 1990, 1991 /
*     ..
*     .. Executable Statements ..
*
      eps = dlamch( 'Epsilon' )
*
*     Copy the first k columns of the factorization to the array Q
*
      CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
      CALL dlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
*
*     Generate the m-by-m matrix Q
*
      srnamt = 'DORGQR'
      CALL dorgqr( m, m, k, q, lda, tau, work, lwork, info )
*
      DO 30 iside = 1, 2
         IF( iside.EQ.1 ) THEN
            side = 'L'
            mc = m
            nc = n
         ELSE
            side = 'R'
            mc = n
            nc = m
         END IF
*
*        Generate MC by NC matrix C
*
         DO 10 j = 1, nc
            CALL dlarnv( 2, iseed, mc, c( 1, j ) )
   10    CONTINUE
         cnorm = dlange( '1', mc, nc, c, lda, rwork )
         IF( cnorm.EQ.0.0d0 )
     $      cnorm = one
*
         DO 20 itrans = 1, 2
            IF( itrans.EQ.1 ) THEN
               trans = 'N'
            ELSE
               trans = 'T'
            END IF
*
*           Copy C
*
            CALL dlacpy( 'Full', mc, nc, c, lda, cc, lda )
*
*           Apply Q or Q' to C
*
            srnamt = 'DORMQR'
            CALL dormqr( side, trans, mc, nc, k, af, lda, tau, cc, lda,
     $                   work, lwork, info )
*
*           Form explicit product and subtract
*
            IF( lsame( side, 'L' ) ) THEN
               CALL dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
     $                     lda, c, lda, one, cc, lda )
            ELSE
               CALL dgemm( 'No transpose', trans, mc, nc, nc, -one, c,
     $                     lda, q, lda, one, cc, lda )
            END IF
*
*           Compute error in the difference
*
            resid = dlange( '1', mc, nc, cc, lda, rwork )
            result( ( iside-1 )*2+itrans ) = resid /
     $         ( dble( max( 1, m ) )*cnorm*eps )
*
   20    CONTINUE
   30 CONTINUE
*
      RETURN
*
*     End of DQRT03
*

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