1*> \brief \b CGELQS 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 12* INFO ) 13* 14* .. Scalar Arguments .. 15* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 16* .. 17* .. Array Arguments .. 18* COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ), 19* $ WORK( LWORK ) 20* .. 21* 22* 23*> \par Purpose: 24* ============= 25*> 26*> \verbatim 27*> 28*> Compute a minimum-norm solution 29*> min || A*X - B || 30*> using the LQ factorization 31*> A = L*Q 32*> computed by CGELQF. 33*> \endverbatim 34* 35* Arguments: 36* ========== 37* 38*> \param[in] M 39*> \verbatim 40*> M is INTEGER 41*> The number of rows of the matrix A. M >= 0. 42*> \endverbatim 43*> 44*> \param[in] N 45*> \verbatim 46*> N is INTEGER 47*> The number of columns of the matrix A. N >= M >= 0. 48*> \endverbatim 49*> 50*> \param[in] NRHS 51*> \verbatim 52*> NRHS is INTEGER 53*> The number of columns of B. NRHS >= 0. 54*> \endverbatim 55*> 56*> \param[in] A 57*> \verbatim 58*> A is COMPLEX array, dimension (LDA,N) 59*> Details of the LQ factorization of the original matrix A as 60*> returned by CGELQF. 61*> \endverbatim 62*> 63*> \param[in] LDA 64*> \verbatim 65*> LDA is INTEGER 66*> The leading dimension of the array A. LDA >= M. 67*> \endverbatim 68*> 69*> \param[in] TAU 70*> \verbatim 71*> TAU is COMPLEX array, dimension (M) 72*> Details of the orthogonal matrix Q. 73*> \endverbatim 74*> 75*> \param[in,out] B 76*> \verbatim 77*> B is COMPLEX array, dimension (LDB,NRHS) 78*> On entry, the m-by-nrhs right hand side matrix B. 79*> On exit, the n-by-nrhs solution matrix X. 80*> \endverbatim 81*> 82*> \param[in] LDB 83*> \verbatim 84*> LDB is INTEGER 85*> The leading dimension of the array B. LDB >= N. 86*> \endverbatim 87*> 88*> \param[out] WORK 89*> \verbatim 90*> WORK is COMPLEX array, dimension (LWORK) 91*> \endverbatim 92*> 93*> \param[in] LWORK 94*> \verbatim 95*> LWORK is INTEGER 96*> The length of the array WORK. LWORK must be at least NRHS, 97*> and should be at least NRHS*NB, where NB is the block size 98*> for this environment. 99*> \endverbatim 100*> 101*> \param[out] INFO 102*> \verbatim 103*> INFO is INTEGER 104*> = 0: successful exit 105*> < 0: if INFO = -i, the i-th argument had an illegal value 106*> \endverbatim 107* 108* Authors: 109* ======== 110* 111*> \author Univ. of Tennessee 112*> \author Univ. of California Berkeley 113*> \author Univ. of Colorado Denver 114*> \author NAG Ltd. 115* 116*> \date November 2011 117* 118*> \ingroup complex_lin 119* 120* ===================================================================== 121 SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 122 $ INFO ) 123* 124* -- LAPACK test routine (version 3.4.0) -- 125* -- LAPACK is a software package provided by Univ. of Tennessee, -- 126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 127* November 2011 128* 129* .. Scalar Arguments .. 130 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 131* .. 132* .. Array Arguments .. 133 COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ), 134 $ WORK( LWORK ) 135* .. 136* 137* ===================================================================== 138* 139* .. Parameters .. 140 COMPLEX CZERO, CONE 141 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), 142 $ CONE = ( 1.0E+0, 0.0E+0 ) ) 143* .. 144* .. External Subroutines .. 145 EXTERNAL CLASET, CTRSM, CUNMLQ, XERBLA 146* .. 147* .. Intrinsic Functions .. 148 INTRINSIC MAX 149* .. 150* .. Executable Statements .. 151* 152* Test the input parameters. 153* 154 INFO = 0 155 IF( M.LT.0 ) THEN 156 INFO = -1 157 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 158 INFO = -2 159 ELSE IF( NRHS.LT.0 ) THEN 160 INFO = -3 161 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 162 INFO = -5 163 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 164 INFO = -8 165 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 166 $ THEN 167 INFO = -10 168 END IF 169 IF( INFO.NE.0 ) THEN 170 CALL XERBLA( 'CGELQS', -INFO ) 171 RETURN 172 END IF 173* 174* Quick return if possible 175* 176 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 177 $ RETURN 178* 179* Solve L*X = B(1:m,:) 180* 181 CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, 182 $ CONE, A, LDA, B, LDB ) 183* 184* Set B(m+1:n,:) to zero 185* 186 IF( M.LT.N ) 187 $ CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), 188 $ LDB ) 189* 190* B := Q' * B 191* 192 CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, 193 $ TAU, B, LDB, WORK, LWORK, INFO ) 194* 195 RETURN 196* 197* End of CGELQS 198* 199 END 200