*> \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. * *> \ingroup single_lin * * ===================================================================== REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT, $ WORK, LWORK ) * * -- 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 .. 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