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*> \brief \b SQLT02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
* $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQLT02 tests SORGQL, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> reflectors.
*>
*> Given the QL factorization of an m-by-n matrix A, SQLT02 generates
*> the orthogonal matrix Q defined by the factorization of the last k
*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
*> orthonormal.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix Q to be generated. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix Q to be generated.
*> M >= N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines the
*> matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> The m-by-n matrix A which was factorized by SQLT01.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is REAL array, dimension (LDA,N)
*> Details of the QL factorization of A, as returned by SGEQLF.
*> See SGEQLF for further details.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] L
*> \verbatim
*> L is REAL array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A, AF, Q and L. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (N)
*> The scalar factors of the elementary reflectors corresponding
*> to the QL factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (2)
*> The test ratios:
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
REAL ROGUE
PARAMETER ( ROGUE = -1.0E+10 )
* ..
* .. Local Scalars ..
INTEGER INFO
REAL ANORM, EPS, RESID
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLACPY, SLASET, SORGQL, SSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL
* ..
* .. Scalars in Common ..
CHARACTER*32 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
RETURN
END IF
*
EPS = SLAMCH( 'Epsilon' )
*
* Copy the last k columns of the factorization to the array Q
*
CALL SLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
IF( K.LT.M )
$ CALL SLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA,
$ Q( 1, N-K+1 ), LDA )
IF( K.GT.1 )
$ CALL SLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA,
$ Q( M-K+1, N-K+2 ), LDA )
*
* Generate the last n columns of the matrix Q
*
SRNAMT = 'SORGQL'
CALL SORGQL( M, N, K, Q, LDA, TAU( N-K+1 ), WORK, LWORK, INFO )
*
* Copy L(m-n+1:m,n-k+1:n)
*
CALL SLASET( 'Full', N, K, ZERO, ZERO, L( M-N+1, N-K+1 ), LDA )
CALL SLACPY( 'Lower', K, K, AF( M-K+1, N-K+1 ), LDA,
$ L( M-K+1, N-K+1 ), LDA )
*
* Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
*
CALL SGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA,
$ A( 1, N-K+1 ), LDA, ONE, L( M-N+1, N-K+1 ), LDA )
*
* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
*
ANORM = SLANGE( '1', M, K, A( 1, N-K+1 ), LDA, RWORK )
RESID = SLANGE( '1', N, K, L( M-N+1, N-K+1 ), LDA, RWORK )
IF( ANORM.GT.ZERO ) THEN
RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, M ) ) ) / ANORM ) / EPS
ELSE
RESULT( 1 ) = ZERO
END IF
*
* Compute I - Q'*Q
*
CALL SLASET( 'Full', N, N, ZERO, ONE, L, LDA )
CALL SSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, L,
$ LDA )
*
* Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
RESID = SLANSY( '1', 'Upper', N, L, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS
*
RETURN
*
* End of SQLT02
*
END
|
