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SUBROUTINE DQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* DQRT02 tests DORGQR, which generates an m-by-n matrix Q with
* orthonornmal columns that is defined as the product of k elementary
* reflectors.
*
* Given the QR factorization of an m-by-n matrix A, DQRT02 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.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix Q to be generated. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix Q to be generated.
* M >= N >= 0.
*
* K (input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. N >= K >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The m-by-n matrix A which was factorized by DQRT01.
*
* AF (input) DOUBLE PRECISION array, dimension (LDA,N)
* Details of the QR factorization of A, as returned by DGEQRF.
* See DGEQRF for further details.
*
* Q (workspace) DOUBLE PRECISION array, dimension (LDA,N)
*
* R (workspace) DOUBLE PRECISION array, dimension (LDA,N)
*
* LDA (input) INTEGER
* The leading dimension of the arrays A, AF, Q and R. LDA >= M.
*
* TAU (input) DOUBLE PRECISION array, dimension (N)
* The scalar factors of the elementary reflectors corresponding
* to the QR factorization in AF.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (M)
*
* RESULT (output) 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 )
*
* =====================================================================
*
* .. 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
DOUBLE PRECISION ANORM, EPS, RESID
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY, DLASET, DORGQR, DSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX
* ..
* .. Scalars in Common ..
CHARACTER*6 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'Epsilon' )
*
* Copy the first k columns of the factorization to the array Q
*
CALL DLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
CALL DLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
*
* Generate the first n columns of the matrix Q
*
SRNAMT = 'DORGQR'
CALL DORGQR( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO )
*
* Copy R(1:n,1:k)
*
CALL DLASET( 'Full', N, K, ZERO, ZERO, R, LDA )
CALL DLACPY( 'Upper', N, K, AF, LDA, R, LDA )
*
* Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
*
CALL DGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA, A,
$ LDA, ONE, R, LDA )
*
* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
ANORM = DLANGE( '1', M, K, A, LDA, RWORK )
RESID = DLANGE( '1', N, K, 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', N, N, ZERO, ONE, R, LDA )
CALL DSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, R,
$ LDA )
*
* Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
RESID = DLANSY( '1', 'Upper', N, R, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS
*
RETURN
*
* End of DQRT02
*
END
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