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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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