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*> \ingroup doubleOTHERcomputational 110* 111* ===================================================================== 112 SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) 113* 114* -- LAPACK computational routine -- 115* -- LAPACK is a software package provided by Univ. of Tennessee, -- 116* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 117* 118* .. Scalar Arguments .. 119 INTEGER INFO, K, LDA, M, N 120* .. 121* .. Array Arguments .. 122 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 123* .. 124* 125* ===================================================================== 126* 127* .. Parameters .. 128 DOUBLE PRECISION ONE, ZERO 129 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 130* .. 131* .. Local Scalars .. 132 INTEGER I, J, L 133* .. 134* .. External Subroutines .. 135 EXTERNAL DLARF, DSCAL, XERBLA 136* .. 137* .. Intrinsic Functions .. 138 INTRINSIC MAX 139* .. 140* .. Executable Statements .. 141* 142* Test the input arguments 143* 144 INFO = 0 145 IF( M.LT.0 ) THEN 146 INFO = -1 147 ELSE IF( N.LT.M ) THEN 148 INFO = -2 149 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 150 INFO = -3 151 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 152 INFO = -5 153 END IF 154 IF( INFO.NE.0 ) THEN 155 CALL XERBLA( 'DORGL2', -INFO ) 156 RETURN 157 END IF 158* 159* Quick return if possible 160* 161 IF( M.LE.0 ) 162 $ RETURN 163* 164 IF( K.LT.M ) THEN 165* 166* Initialise rows k+1:m to rows of the unit matrix 167* 168 DO 20 J = 1, N 169 DO 10 L = K + 1, M 170 A( L, J ) = ZERO 171 10 CONTINUE 172 IF( J.GT.K .AND. J.LE.M ) 173 $ A( J, J ) = ONE 174 20 CONTINUE 175 END IF 176* 177 DO 40 I = K, 1, -1 178* 179* Apply H(i) to A(i:m,i:n) from the right 180* 181 IF( I.LT.N ) THEN 182 IF( I.LT.M ) THEN 183 A( I, I ) = ONE 184 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, 185 $ TAU( I ), A( I+1, I ), LDA, WORK ) 186 END IF 187 CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) 188 END IF 189 A( I, I ) = ONE - TAU( I ) 190* 191* Set A(i,1:i-1) to zero 192* 193 DO 30 L = 1, I - 1 194 A( I, L ) = ZERO 195 30 CONTINUE 196 40 CONTINUE 197 RETURN 198* 199* End of DORGL2 200* 201 END 202