*> \brief \b ZGERQS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Compute a minimum-norm solution *> min || A*X - B || *> using the RQ factorization *> A = R*Q *> computed by ZGERQF. *> \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 COMPLEX*16 array, dimension (LDA,N) *> Details of the RQ factorization of the original matrix A as *> returned by ZGERQF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= M. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (M) *> Details of the orthogonal matrix Q. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the right hand side vectors for the linear system. *> On exit, the solution vectors X. Each solution vector *> is contained in rows 1:N of a column of B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 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. * *> \date December 2016 * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, $ INFO ) * * -- 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 INFO, LDA, LDB, LWORK, M, N, NRHS * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMRQ * .. * .. 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( 'ZGERQS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) $ RETURN * * Solve R*X = B(n-m+1:n,:) * CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS, $ CONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB ) * * Set B(1:n-m,:) to zero * CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B, LDB ) * * B := Q' * B * CALL ZUNMRQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, $ TAU, B, LDB, WORK, LWORK, INFO ) * RETURN * * End of ZGERQS * END