LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cgerqs.f
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00001 *> \brief \b CGERQS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE CGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
00012 *                          INFO )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       COMPLEX            A( LDA, * ), B( LDB, * ), TAU( * ),
00019 *      $                   WORK( LWORK )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> Compute a minimum-norm solution
00029 *>     min || A*X - B ||
00030 *> using the RQ factorization
00031 *>     A = R*Q
00032 *> computed by CGERQF.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] M
00039 *> \verbatim
00040 *>          M is INTEGER
00041 *>          The number of rows of the matrix A.  M >= 0.
00042 *> \endverbatim
00043 *>
00044 *> \param[in] N
00045 *> \verbatim
00046 *>          N is INTEGER
00047 *>          The number of columns of the matrix A.  N >= M >= 0.
00048 *> \endverbatim
00049 *>
00050 *> \param[in] NRHS
00051 *> \verbatim
00052 *>          NRHS is INTEGER
00053 *>          The number of columns of B.  NRHS >= 0.
00054 *> \endverbatim
00055 *>
00056 *> \param[in] A
00057 *> \verbatim
00058 *>          A is COMPLEX array, dimension (LDA,N)
00059 *>          Details of the RQ factorization of the original matrix A as
00060 *>          returned by CGERQF.
00061 *> \endverbatim
00062 *>
00063 *> \param[in] LDA
00064 *> \verbatim
00065 *>          LDA is INTEGER
00066 *>          The leading dimension of the array A.  LDA >= M.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] TAU
00070 *> \verbatim
00071 *>          TAU is COMPLEX array, dimension (M)
00072 *>          Details of the orthogonal matrix Q.
00073 *> \endverbatim
00074 *>
00075 *> \param[in,out] B
00076 *> \verbatim
00077 *>          B is COMPLEX array, dimension (LDB,NRHS)
00078 *>          On entry, the right hand side vectors for the linear system.
00079 *>          On exit, the solution vectors X.  Each solution vector
00080 *>          is contained in rows 1:N of a column of B.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDB
00084 *> \verbatim
00085 *>          LDB is INTEGER
00086 *>          The leading dimension of the array B. LDB >= max(1,N).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is COMPLEX array, dimension (LWORK)
00092 *> \endverbatim
00093 *>
00094 *> \param[in] LWORK
00095 *> \verbatim
00096 *>          LWORK is INTEGER
00097 *>          The length of the array WORK.  LWORK must be at least NRHS,
00098 *>          and should be at least NRHS*NB, where NB is the block size
00099 *>          for this environment.
00100 *> \endverbatim
00101 *>
00102 *> \param[out] INFO
00103 *> \verbatim
00104 *>          INFO is INTEGER
00105 *>          = 0: successful exit
00106 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00107 *> \endverbatim
00108 *
00109 *  Authors:
00110 *  ========
00111 *
00112 *> \author Univ. of Tennessee 
00113 *> \author Univ. of California Berkeley 
00114 *> \author Univ. of Colorado Denver 
00115 *> \author NAG Ltd. 
00116 *
00117 *> \date November 2011
00118 *
00119 *> \ingroup complex_lin
00120 *
00121 *  =====================================================================
00122       SUBROUTINE CGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
00123      $                   INFO )
00124 *
00125 *  -- LAPACK test routine (version 3.4.0) --
00126 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00127 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00128 *     November 2011
00129 *
00130 *     .. Scalar Arguments ..
00131       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
00132 *     ..
00133 *     .. Array Arguments ..
00134       COMPLEX            A( LDA, * ), B( LDB, * ), TAU( * ),
00135      $                   WORK( LWORK )
00136 *     ..
00137 *
00138 *  =====================================================================
00139 *
00140 *     .. Parameters ..
00141       COMPLEX            CZERO, CONE
00142       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00143      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00144 *     ..
00145 *     .. External Subroutines ..
00146       EXTERNAL           CLASET, CTRSM, CUNMRQ, XERBLA
00147 *     ..
00148 *     .. Intrinsic Functions ..
00149       INTRINSIC          MAX
00150 *     ..
00151 *     .. Executable Statements ..
00152 *
00153 *     Test the input parameters.
00154 *
00155       INFO = 0
00156       IF( M.LT.0 ) THEN
00157          INFO = -1
00158       ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
00159          INFO = -2
00160       ELSE IF( NRHS.LT.0 ) THEN
00161          INFO = -3
00162       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00163          INFO = -5
00164       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00165          INFO = -8
00166       ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
00167      $          THEN
00168          INFO = -10
00169       END IF
00170       IF( INFO.NE.0 ) THEN
00171          CALL XERBLA( 'CGERQS', -INFO )
00172          RETURN
00173       END IF
00174 *
00175 *     Quick return if possible
00176 *
00177       IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
00178      $   RETURN
00179 *
00180 *     Solve R*X = B(n-m+1:n,:)
00181 *
00182       CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
00183      $            CONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
00184 *
00185 *     Set B(1:n-m,:) to zero
00186 *
00187       CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B, LDB )
00188 *
00189 *     B := Q' * B
00190 *
00191       CALL CUNMRQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
00192      $             TAU, B, LDB, WORK, LWORK, INFO )
00193 *
00194       RETURN
00195 *
00196 *     End of CGERQS
00197 *
00198       END
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