cqrt03()

subroutine cqrt03	(	integer	m,
		integer	n,
		integer	k,
		complex, dimension( lda, * )	af,
		complex, dimension( lda, * )	c,
		complex, dimension( lda, * )	cc,
		complex, dimension( lda, * )	q,
		integer	lda,
		complex, dimension( * )	tau,
		complex, dimension( lwork )	work,
		integer	lwork,
		real, dimension( * )	rwork,
		real, dimension( * )	result
	)

CQRT03

Purpose:

 CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 CQRT03 compares the results of a call to CUNMQR with the results of
 forming Q explicitly by a call to CUNGQR and then performing matrix
 multiplication by a call to CGEMM.

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 COMPLEX array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returned by CGEQRF. See CGEQRF for further details.
[out]	C	C is COMPLEX array, dimension (LDA,N)
[out]	CC	CC is COMPLEX array, dimension (LDA,N)
[out]	Q	Q is COMPLEX array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is COMPLEX 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 REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 cqrt03.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 ..
      REAL               RESULT( * ), RWORK( * )
      COMPLEX            AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
     $                   Q( LDA, * ), TAU( * ), WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
      COMPLEX            ROGUE
      parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, ISIDE, ITRANS, J, MC, NC
      REAL               CNORM, EPS, RESID
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               CLANGE, SLAMCH
      EXTERNAL           lsame, clange, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemm, clacpy, clarnv, claset, cungqr, cunmqr
*     ..
*     .. Local Arrays ..
      INTEGER            ISEED( 4 )
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          cmplx, max, real
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Data statements ..
      DATA               iseed / 1988, 1989, 1990, 1991 /
*     ..
*     .. Executable Statements ..
*
      eps = slamch( 'Epsilon' )
*
*     Copy the first k columns of the factorization to the array Q
*
      CALL claset( 'Full', m, m, rogue, rogue, q, lda )
      CALL clacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
*
*     Generate the m-by-m matrix Q
*
      srnamt = 'CUNGQR'
      CALL cungqr( 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 clarnv( 2, iseed, mc, c( 1, j ) )
   10    CONTINUE
         cnorm = clange( '1', mc, nc, c, lda, rwork )
         IF( cnorm.EQ.zero )
     $      cnorm = one
*
         DO 20 itrans = 1, 2
            IF( itrans.EQ.1 ) THEN
               trans = 'N'
            ELSE
               trans = 'C'
            END IF
*
*           Copy C
*
            CALL clacpy( 'Full', mc, nc, c, lda, cc, lda )
*
*           Apply Q or Q' to C
*
            srnamt = 'CUNMQR'
            CALL cunmqr( side, trans, mc, nc, k, af, lda, tau, cc, lda,
     $                   work, lwork, info )
*
*           Form explicit product and subtract
*
            IF( lsame( side, 'L' ) ) THEN
               CALL cgemm( trans, 'No transpose', mc, nc, mc,
     $                     cmplx( -one ), q, lda, c, lda, cmplx( one ),
     $                     cc, lda )
            ELSE
               CALL cgemm( 'No transpose', trans, mc, nc, nc,
     $                     cmplx( -one ), c, lda, q, lda, cmplx( one ),
     $                     cc, lda )
            END IF
*
*           Compute error in the difference
*
            resid = clange( '1', mc, nc, cc, lda, rwork )
            result( ( iside-1 )*2+itrans ) = resid /
     $         ( real( max( 1, m ) )*cnorm*eps )
*
   20    CONTINUE
   30 CONTINUE
*
      RETURN
*
*     End of CQRT03
*

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