1*> \brief \b ZGELQS 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 ZGELQS( 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*16 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 ZGELQF. 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*16 array, dimension (LDA,N) 59*> Details of the LQ factorization of the original matrix A as 60*> returned by ZGELQF. 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*16 array, dimension (M) 72*> Details of the orthogonal matrix Q. 73*> \endverbatim 74*> 75*> \param[in,out] B 76*> \verbatim 77*> B is COMPLEX*16 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*16 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*> \ingroup complex16_lin 117* 118* ===================================================================== 119 SUBROUTINE ZGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 120 $ INFO ) 121* 122* -- LAPACK test routine -- 123* -- LAPACK is a software package provided by Univ. of Tennessee, -- 124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 125* 126* .. Scalar Arguments .. 127 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 128* .. 129* .. Array Arguments .. 130 COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ), 131 $ WORK( LWORK ) 132* .. 133* 134* ===================================================================== 135* 136* .. Parameters .. 137 COMPLEX*16 CZERO, CONE 138 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 139 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 140* .. 141* .. External Subroutines .. 142 EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMLQ 143* .. 144* .. Intrinsic Functions .. 145 INTRINSIC MAX 146* .. 147* .. Executable Statements .. 148* 149* Test the input parameters. 150* 151 INFO = 0 152 IF( M.LT.0 ) THEN 153 INFO = -1 154 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 155 INFO = -2 156 ELSE IF( NRHS.LT.0 ) THEN 157 INFO = -3 158 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 159 INFO = -5 160 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 161 INFO = -8 162 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 163 $ THEN 164 INFO = -10 165 END IF 166 IF( INFO.NE.0 ) THEN 167 CALL XERBLA( 'ZGELQS', -INFO ) 168 RETURN 169 END IF 170* 171* Quick return if possible 172* 173 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 174 $ RETURN 175* 176* Solve L*X = B(1:m,:) 177* 178 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, 179 $ CONE, A, LDA, B, LDB ) 180* 181* Set B(m+1:n,:) to zero 182* 183 IF( M.LT.N ) 184 $ CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), 185 $ LDB ) 186* 187* B := Q' * B 188* 189 CALL ZUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, 190 $ TAU, B, LDB, WORK, LWORK, INFO ) 191* 192 RETURN 193* 194* End of ZGELQS 195* 196 END 197