1*> \brief \b DGELQT 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DGELQT + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelqt.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelqt.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelqt.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) 22* 23* .. Scalar Arguments .. 24* INTEGER INFO, LDA, LDT, M, N, MB 25* .. 26* .. Array Arguments .. 27* DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * ) 28* .. 29* 30* 31*> \par Purpose: 32* ============= 33*> 34*> \verbatim 35*> 36*> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A 37*> using the compact WY representation of Q. 38*> \endverbatim 39* 40* Arguments: 41* ========== 42* 43*> \param[in] M 44*> \verbatim 45*> M is INTEGER 46*> The number of rows of the matrix A. M >= 0. 47*> \endverbatim 48*> 49*> \param[in] N 50*> \verbatim 51*> N is INTEGER 52*> The number of columns of the matrix A. N >= 0. 53*> \endverbatim 54*> 55*> \param[in] MB 56*> \verbatim 57*> MB is INTEGER 58*> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 59*> \endverbatim 60*> 61*> \param[in,out] A 62*> \verbatim 63*> A is DOUBLE PRECISION array, dimension (LDA,N) 64*> On entry, the M-by-N matrix A. 65*> On exit, the elements on and below the diagonal of the array 66*> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is 67*> lower triangular if M <= N); the elements above the diagonal 68*> are the rows of V. 69*> \endverbatim 70*> 71*> \param[in] LDA 72*> \verbatim 73*> LDA is INTEGER 74*> The leading dimension of the array A. LDA >= max(1,M). 75*> \endverbatim 76*> 77*> \param[out] T 78*> \verbatim 79*> T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) 80*> The upper triangular block reflectors stored in compact form 81*> as a sequence of upper triangular blocks. See below 82*> for further details. 83*> \endverbatim 84*> 85*> \param[in] LDT 86*> \verbatim 87*> LDT is INTEGER 88*> The leading dimension of the array T. LDT >= MB. 89*> \endverbatim 90*> 91*> \param[out] WORK 92*> \verbatim 93*> WORK is DOUBLE PRECISION array, dimension (MB*N) 94*> \endverbatim 95*> 96*> \param[out] INFO 97*> \verbatim 98*> INFO is INTEGER 99*> = 0: successful exit 100*> < 0: if INFO = -i, the i-th argument had an illegal value 101*> \endverbatim 102* 103* Authors: 104* ======== 105* 106*> \author Univ. of Tennessee 107*> \author Univ. of California Berkeley 108*> \author Univ. of Colorado Denver 109*> \author NAG Ltd. 110* 111*> \ingroup doubleGEcomputational 112* 113*> \par Further Details: 114* ===================== 115*> 116*> \verbatim 117*> 118*> The matrix V stores the elementary reflectors H(i) in the i-th row 119*> above the diagonal. For example, if M=5 and N=3, the matrix V is 120*> 121*> V = ( 1 v1 v1 v1 v1 ) 122*> ( 1 v2 v2 v2 ) 123*> ( 1 v3 v3 ) 124*> 125*> 126*> where the vi's represent the vectors which define H(i), which are returned 127*> in the matrix A. The 1's along the diagonal of V are not stored in A. 128*> Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each 129*> block is of order MB except for the last block, which is of order 130*> IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block 131*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB 132*> for the last block) T's are stored in the MB-by-K matrix T as 133*> 134*> T = (T1 T2 ... TB). 135*> \endverbatim 136*> 137* ===================================================================== 138 SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) 139* 140* -- LAPACK computational routine -- 141* -- LAPACK is a software package provided by Univ. of Tennessee, -- 142* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 143* 144* .. Scalar Arguments .. 145 INTEGER INFO, LDA, LDT, M, N, MB 146* .. 147* .. Array Arguments .. 148 DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * ) 149* .. 150* 151* ===================================================================== 152* 153* .. 154* .. Local Scalars .. 155 INTEGER I, IB, IINFO, K 156* .. 157* .. External Subroutines .. 158 EXTERNAL DGELQT3, DLARFB, XERBLA 159* .. 160* .. Executable Statements .. 161* 162* Test the input arguments 163* 164 INFO = 0 165 IF( M.LT.0 ) THEN 166 INFO = -1 167 ELSE IF( N.LT.0 ) THEN 168 INFO = -2 169 ELSE IF( MB.LT.1 .OR. ( MB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN 170 INFO = -3 171 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 172 INFO = -5 173 ELSE IF( LDT.LT.MB ) THEN 174 INFO = -7 175 END IF 176 IF( INFO.NE.0 ) THEN 177 CALL XERBLA( 'DGELQT', -INFO ) 178 RETURN 179 END IF 180* 181* Quick return if possible 182* 183 K = MIN( M, N ) 184 IF( K.EQ.0 ) RETURN 185* 186* Blocked loop of length K 187* 188 DO I = 1, K, MB 189 IB = MIN( K-I+1, MB ) 190* 191* Compute the LQ factorization of the current block A(I:M,I:I+IB-1) 192* 193 CALL DGELQT3( IB, N-I+1, A(I,I), LDA, T(1,I), LDT, IINFO ) 194 IF( I+IB.LE.M ) THEN 195* 196* Update by applying H**T to A(I:M,I+IB:N) from the right 197* 198 CALL DLARFB( 'R', 'N', 'F', 'R', M-I-IB+1, N-I+1, IB, 199 $ A( I, I ), LDA, T( 1, I ), LDT, 200 $ A( I+IB, I ), LDA, WORK , M-I-IB+1 ) 201 END IF 202 END DO 203 RETURN 204* 205* End of DGELQT 206* 207 END 208