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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZGELQS 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 ZGELQS( 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*16 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 LQ factorization 00031 *> A = L*Q 00032 *> computed by ZGELQF. 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*16 array, dimension (LDA,N) 00059 *> Details of the LQ factorization of the original matrix A as 00060 *> returned by ZGELQF. 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*16 array, dimension (M) 00072 *> Details of the orthogonal matrix Q. 00073 *> \endverbatim 00074 *> 00075 *> \param[in,out] B 00076 *> \verbatim 00077 *> B is COMPLEX*16 array, dimension (LDB,NRHS) 00078 *> On entry, the m-by-nrhs right hand side matrix B. 00079 *> On exit, the n-by-nrhs solution matrix X. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] LDB 00083 *> \verbatim 00084 *> LDB is INTEGER 00085 *> The leading dimension of the array B. LDB >= N. 00086 *> \endverbatim 00087 *> 00088 *> \param[out] WORK 00089 *> \verbatim 00090 *> WORK is COMPLEX*16 array, dimension (LWORK) 00091 *> \endverbatim 00092 *> 00093 *> \param[in] LWORK 00094 *> \verbatim 00095 *> LWORK is INTEGER 00096 *> The length of the array WORK. LWORK must be at least NRHS, 00097 *> and should be at least NRHS*NB, where NB is the block size 00098 *> for this environment. 00099 *> \endverbatim 00100 *> 00101 *> \param[out] INFO 00102 *> \verbatim 00103 *> INFO is INTEGER 00104 *> = 0: successful exit 00105 *> < 0: if INFO = -i, the i-th argument had an illegal value 00106 *> \endverbatim 00107 * 00108 * Authors: 00109 * ======== 00110 * 00111 *> \author Univ. of Tennessee 00112 *> \author Univ. of California Berkeley 00113 *> \author Univ. of Colorado Denver 00114 *> \author NAG Ltd. 00115 * 00116 *> \date November 2011 00117 * 00118 *> \ingroup complex16_lin 00119 * 00120 * ===================================================================== 00121 SUBROUTINE ZGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 00122 $ INFO ) 00123 * 00124 * -- LAPACK test routine (version 3.4.0) -- 00125 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00127 * November 2011 00128 * 00129 * .. Scalar Arguments .. 00130 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 00131 * .. 00132 * .. Array Arguments .. 00133 COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ), 00134 $ WORK( LWORK ) 00135 * .. 00136 * 00137 * ===================================================================== 00138 * 00139 * .. Parameters .. 00140 COMPLEX*16 CZERO, CONE 00141 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 00142 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 00143 * .. 00144 * .. External Subroutines .. 00145 EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMLQ 00146 * .. 00147 * .. Intrinsic Functions .. 00148 INTRINSIC MAX 00149 * .. 00150 * .. Executable Statements .. 00151 * 00152 * Test the input parameters. 00153 * 00154 INFO = 0 00155 IF( M.LT.0 ) THEN 00156 INFO = -1 00157 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 00158 INFO = -2 00159 ELSE IF( NRHS.LT.0 ) THEN 00160 INFO = -3 00161 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00162 INFO = -5 00163 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00164 INFO = -8 00165 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 00166 $ THEN 00167 INFO = -10 00168 END IF 00169 IF( INFO.NE.0 ) THEN 00170 CALL XERBLA( 'ZGELQS', -INFO ) 00171 RETURN 00172 END IF 00173 * 00174 * Quick return if possible 00175 * 00176 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 00177 $ RETURN 00178 * 00179 * Solve L*X = B(1:m,:) 00180 * 00181 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, 00182 $ CONE, A, LDA, B, LDB ) 00183 * 00184 * Set B(m+1:n,:) to zero 00185 * 00186 IF( M.LT.N ) 00187 $ CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), 00188 $ LDB ) 00189 * 00190 * B := Q' * B 00191 * 00192 CALL ZUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, 00193 $ TAU, B, LDB, WORK, LWORK, INFO ) 00194 * 00195 RETURN 00196 * 00197 * End of ZGELQS 00198 * 00199 END