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*> \brief \b SQPT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
* WORK, LWORK )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* INTEGER JPVT( * )
* REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> the upper triangle of AF(1:k,1:k) is a partial triangular factor,
*> the entries below the diagonal in the first k columns are the
*> Householder vectors, and the rest of AF contains a partially updated
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of columns of AF that have been reduced
*> to upper triangular form.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA, N)
*> The original matrix A.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is REAL array, dimension (LDA,N)
*> The (possibly partial) output of SGEQPF. The upper triangle
*> of AF(1:k,1:k) is a partial triangular factor, the entries
*> below the diagonal in the first k columns are the Householder
*> vectors, and the rest of AF contains a partially updated
*> matrix.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A and AF.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (K)
*> Details of the Householder transformations as returned by
*> SGEQPF.
*> \endverbatim
*>
*> \param[in] JPVT
*> \verbatim
*> JPVT is INTEGER array, dimension (N)
*> Pivot information as returned by SGEQPF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*N+N.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
$ WORK, LWORK )
*
* -- 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 K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
INTEGER JPVT( * )
REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
REAL NORMA
* ..
* .. Local Arrays ..
REAL RWORK( 1 )
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SAXPY, SCOPY, SORMQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
SQPT01 = ZERO
*
* Test if there is enough workspace
*
IF( LWORK.LT.M*N+N ) THEN
CALL XERBLA( 'SQPT01', 10 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
DO 30 J = 1, K
DO 10 I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
DO 20 I = J + 1, M
WORK( ( J-1 )*M+I ) = ZERO
20 CONTINUE
30 CONTINUE
DO 40 J = K + 1, N
CALL SCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
40 CONTINUE
*
CALL SORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
DO 50 J = 1, N
*
* Compare i-th column of QR and jpvt(i)-th column of A
*
CALL SAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ),
$ 1 )
50 CONTINUE
*
SQPT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
$ ( REAL( MAX( M, N ) )*SLAMCH( 'Epsilon' ) )
IF( NORMA.NE.ZERO )
$ SQPT01 = SQPT01 / NORMA
*
RETURN
*
* End of SQPT01
*
END
|
