211 lines
5.4 KiB
Fortran
211 lines
5.4 KiB
Fortran
*> \brief \b SQPT01
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
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* WORK, LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER JPVT( * )
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* REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
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* $ WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SQPT01 tests the QR-factorization with pivoting of a matrix A. The
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*> array AF contains the (possibly partial) QR-factorization of A, where
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*> the upper triangle of AF(1:k,1:k) is a partial triangular factor,
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*> the entries below the diagonal in the first k columns are the
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*> Householder vectors, and the rest of AF contains a partially updated
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*> matrix.
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*>
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*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrices A and AF.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrices A and AF.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of columns of AF that have been reduced
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*> to upper triangular form.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA, N)
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*> The original matrix A.
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is REAL array, dimension (LDA,N)
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*> The (possibly partial) output of SGEQPF. The upper triangle
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*> of AF(1:k,1:k) is a partial triangular factor, the entries
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*> below the diagonal in the first k columns are the Householder
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*> vectors, and the rest of AF contains a partially updated
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*> matrix.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the arrays A and AF.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (K)
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*> Details of the Householder transformations as returned by
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*> SGEQPF.
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*> \endverbatim
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*>
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*> \param[in] JPVT
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*> \verbatim
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*> JPVT is INTEGER array, dimension (N)
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*> Pivot information as returned by SGEQPF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK >= M*N+N.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
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$ WORK, LWORK )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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INTEGER JPVT( * )
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REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
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$ WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J
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REAL NORMA
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* ..
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* .. Local Arrays ..
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REAL RWORK( 1 )
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SCOPY, SORMQR, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, REAL
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* ..
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* .. Executable Statements ..
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*
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SQPT01 = ZERO
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*
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* Test if there is enough workspace
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*
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IF( LWORK.LT.M*N+N ) THEN
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CALL XERBLA( 'SQPT01', 10 )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK )
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*
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DO 30 J = 1, K
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DO 10 I = 1, MIN( J, M )
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WORK( ( J-1 )*M+I ) = AF( I, J )
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10 CONTINUE
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DO 20 I = J + 1, M
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WORK( ( J-1 )*M+I ) = ZERO
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20 CONTINUE
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30 CONTINUE
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DO 40 J = K + 1, N
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CALL SCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
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40 CONTINUE
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*
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CALL SORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
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$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
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*
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DO 50 J = 1, N
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*
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* Compare i-th column of QR and jpvt(i)-th column of A
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*
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CALL SAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ),
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$ 1 )
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50 CONTINUE
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*
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SQPT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
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$ ( REAL( MAX( M, N ) )*SLAMCH( 'Epsilon' ) )
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IF( NORMA.NE.ZERO )
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$ SQPT01 = SQPT01 / NORMA
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*
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RETURN
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*
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* End of SQPT01
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*
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END
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