*> \brief \b DGELQS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Compute a minimum-norm solution *> min || A*X - B || *> using the LQ factorization *> A = L*Q *> computed by DGELQF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= M >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of columns of B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> Details of the LQ factorization of the original matrix A as *> returned by DGELQF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= M. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (M) *> Details of the orthogonal matrix Q. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the m-by-nrhs right hand side matrix B. *> On exit, the n-by-nrhs solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK must be at least NRHS, *> and should be at least NRHS*NB, where NB is the block size *> for this environment. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, $ INFO ) * * -- 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 INFO, LDA, LDB, LWORK, M, N, NRHS * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. External Subroutines .. EXTERNAL DLASET, DORMLQ, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) $ THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGELQS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) $ RETURN * * Solve L*X = B(1:m,:) * CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, $ ONE, A, LDA, B, LDB ) * * Set B(m+1:n,:) to zero * IF( M.LT.N ) $ CALL DLASET( 'Full', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB ) * * B := Q' * B * CALL DORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB, $ WORK, LWORK, INFO ) * RETURN * * End of DGELQS * END