1*> \brief \b DORGL2 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DORGL2 + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgl2.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgl2.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) 22* 23* .. Scalar Arguments .. 24* INTEGER INFO, K, LDA, M, N 25* .. 26* .. Array Arguments .. 27* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 28* .. 29* 30* 31*> \par Purpose: 32* ============= 33*> 34*> \verbatim 35*> 36*> DORGL2 generates an m by n real matrix Q with orthonormal rows, 37*> which is defined as the first m rows of a product of k elementary 38*> reflectors of order n 39*> 40*> Q = H(k) . . . H(2) H(1) 41*> 42*> as returned by DGELQF. 43*> \endverbatim 44* 45* Arguments: 46* ========== 47* 48*> \param[in] M 49*> \verbatim 50*> M is INTEGER 51*> The number of rows of the matrix Q. M >= 0. 52*> \endverbatim 53*> 54*> \param[in] N 55*> \verbatim 56*> N is INTEGER 57*> The number of columns of the matrix Q. N >= M. 58*> \endverbatim 59*> 60*> \param[in] K 61*> \verbatim 62*> K is INTEGER 63*> The number of elementary reflectors whose product defines the 64*> matrix Q. M >= K >= 0. 65*> \endverbatim 66*> 67*> \param[in,out] A 68*> \verbatim 69*> A is DOUBLE PRECISION array, dimension (LDA,N) 70*> On entry, the i-th row must contain the vector which defines 71*> the elementary reflector H(i), for i = 1,2,...,k, as returned 72*> by DGELQF in the first k rows of its array argument A. 73*> On exit, the m-by-n matrix Q. 74*> \endverbatim 75*> 76*> \param[in] LDA 77*> \verbatim 78*> LDA is INTEGER 79*> The first dimension of the array A. LDA >= max(1,M). 80*> \endverbatim 81*> 82*> \param[in] TAU 83*> \verbatim 84*> TAU is DOUBLE PRECISION array, dimension (K) 85*> TAU(i) must contain the scalar factor of the elementary 86*> reflector H(i), as returned by DGELQF. 87*> \endverbatim 88*> 89*> \param[out] WORK 90*> \verbatim 91*> WORK is DOUBLE PRECISION array, dimension (M) 92*> \endverbatim 93*> 94*> \param[out] INFO 95*> \verbatim 96*> INFO is INTEGER 97*> = 0: successful exit 98*> < 0: if INFO = -i, the i-th argument has an illegal value 99*> \endverbatim 100* 101* Authors: 102* ======== 103* 104*> \author Univ. of Tennessee 105*> \author Univ. of California Berkeley 106*> \author Univ. of Colorado Denver 107*> \author NAG Ltd. 108* 109*> \date December 2016 110* 111*> \ingroup doubleOTHERcomputational 112* 113* ===================================================================== 114 SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) 115* 116* -- LAPACK computational routine (version 3.7.0) -- 117* -- LAPACK is a software package provided by Univ. of Tennessee, -- 118* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 119* December 2016 120* 121* .. Scalar Arguments .. 122 INTEGER INFO, K, LDA, M, N 123* .. 124* .. Array Arguments .. 125 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 126* .. 127* 128* ===================================================================== 129* 130* .. Parameters .. 131 DOUBLE PRECISION ONE, ZERO 132 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 133* .. 134* .. Local Scalars .. 135 INTEGER I, J, L 136* .. 137* .. External Subroutines .. 138 EXTERNAL DLARF, DSCAL, XERBLA 139* .. 140* .. Intrinsic Functions .. 141 INTRINSIC MAX 142* .. 143* .. Executable Statements .. 144* 145* Test the input arguments 146* 147 INFO = 0 148 IF( M.LT.0 ) THEN 149 INFO = -1 150 ELSE IF( N.LT.M ) THEN 151 INFO = -2 152 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 153 INFO = -3 154 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 155 INFO = -5 156 END IF 157 IF( INFO.NE.0 ) THEN 158 CALL XERBLA( 'DORGL2', -INFO ) 159 RETURN 160 END IF 161* 162* Quick return if possible 163* 164 IF( M.LE.0 ) 165 $ RETURN 166* 167 IF( K.LT.M ) THEN 168* 169* Initialise rows k+1:m to rows of the unit matrix 170* 171 DO 20 J = 1, N 172 DO 10 L = K + 1, M 173 A( L, J ) = ZERO 174 10 CONTINUE 175 IF( J.GT.K .AND. J.LE.M ) 176 $ A( J, J ) = ONE 177 20 CONTINUE 178 END IF 179* 180 DO 40 I = K, 1, -1 181* 182* Apply H(i) to A(i:m,i:n) from the right 183* 184 IF( I.LT.N ) THEN 185 IF( I.LT.M ) THEN 186 A( I, I ) = ONE 187 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, 188 $ TAU( I ), A( I+1, I ), LDA, WORK ) 189 END IF 190 CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) 191 END IF 192 A( I, I ) = ONE - TAU( I ) 193* 194* Set A(i,1:i-1) to zero 195* 196 DO 30 L = 1, I - 1 197 A( I, L ) = ZERO 198 30 CONTINUE 199 40 CONTINUE 200 RETURN 201* 202* End of DORGL2 203* 204 END 205