1*> \brief \b DTPLQT 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DTPQRT + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtplqt.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtplqt.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtplqt.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, 22* INFO ) 23* 24* .. Scalar Arguments .. 25* INTEGER INFO, LDA, LDB, LDT, N, M, L, MB 26* .. 27* .. Array Arguments .. 28* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> DTPLQT computes a blocked LQ factorization of a real 38*> "triangular-pentagonal" matrix C, which is composed of a 39*> triangular block A and pentagonal block B, using the compact 40*> WY representation for Q. 41*> \endverbatim 42* 43* Arguments: 44* ========== 45* 46*> \param[in] M 47*> \verbatim 48*> M is INTEGER 49*> The number of rows of the matrix B, and the order of the 50*> triangular matrix A. 51*> M >= 0. 52*> \endverbatim 53*> 54*> \param[in] N 55*> \verbatim 56*> N is INTEGER 57*> The number of columns of the matrix B. 58*> N >= 0. 59*> \endverbatim 60*> 61*> \param[in] L 62*> \verbatim 63*> L is INTEGER 64*> The number of rows of the lower trapezoidal part of B. 65*> MIN(M,N) >= L >= 0. See Further Details. 66*> \endverbatim 67*> 68*> \param[in] MB 69*> \verbatim 70*> MB is INTEGER 71*> The block size to be used in the blocked QR. M >= MB >= 1. 72*> \endverbatim 73*> 74*> \param[in,out] A 75*> \verbatim 76*> A is DOUBLE PRECISION array, dimension (LDA,N) 77*> On entry, the lower triangular N-by-N matrix A. 78*> On exit, the elements on and below the diagonal of the array 79*> contain the lower triangular matrix L. 80*> \endverbatim 81*> 82*> \param[in] LDA 83*> \verbatim 84*> LDA is INTEGER 85*> The leading dimension of the array A. LDA >= max(1,N). 86*> \endverbatim 87*> 88*> \param[in,out] B 89*> \verbatim 90*> B is DOUBLE PRECISION array, dimension (LDB,N) 91*> On entry, the pentagonal M-by-N matrix B. The first N-L columns 92*> are rectangular, and the last L columns are lower trapezoidal. 93*> On exit, B contains the pentagonal matrix V. See Further Details. 94*> \endverbatim 95*> 96*> \param[in] LDB 97*> \verbatim 98*> LDB is INTEGER 99*> The leading dimension of the array B. LDB >= max(1,M). 100*> \endverbatim 101*> 102*> \param[out] T 103*> \verbatim 104*> T is DOUBLE PRECISION array, dimension (LDT,N) 105*> The lower triangular block reflectors stored in compact form 106*> as a sequence of upper triangular blocks. See Further Details. 107*> \endverbatim 108*> 109*> \param[in] LDT 110*> \verbatim 111*> LDT is INTEGER 112*> The leading dimension of the array T. LDT >= MB. 113*> \endverbatim 114*> 115*> \param[out] WORK 116*> \verbatim 117*> WORK is DOUBLE PRECISION array, dimension (MB*M) 118*> \endverbatim 119*> 120*> \param[out] INFO 121*> \verbatim 122*> INFO is INTEGER 123*> = 0: successful exit 124*> < 0: if INFO = -i, the i-th argument had an illegal value 125*> \endverbatim 126* 127* Authors: 128* ======== 129* 130*> \author Univ. of Tennessee 131*> \author Univ. of California Berkeley 132*> \author Univ. of Colorado Denver 133*> \author NAG Ltd. 134* 135*> \date December 2016 136* 137*> \ingroup doubleOTHERcomputational 138* 139*> \par Further Details: 140* ===================== 141*> 142*> \verbatim 143*> 144*> The input matrix C is a M-by-(M+N) matrix 145*> 146*> C = [ A ] [ B ] 147*> 148*> 149*> where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal 150*> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L 151*> upper trapezoidal matrix B2: 152*> [ B ] = [ B1 ] [ B2 ] 153*> [ B1 ] <- M-by-(N-L) rectangular 154*> [ B2 ] <- M-by-L upper trapezoidal. 155*> 156*> The lower trapezoidal matrix B2 consists of the first L columns of a 157*> N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, 158*> B is rectangular M-by-N; if M=L=N, B is lower triangular. 159*> 160*> The matrix W stores the elementary reflectors H(i) in the i-th row 161*> above the diagonal (of A) in the M-by-(M+N) input matrix C 162*> [ C ] = [ A ] [ B ] 163*> [ A ] <- lower triangular N-by-N 164*> [ B ] <- M-by-N pentagonal 165*> 166*> so that W can be represented as 167*> [ W ] = [ I ] [ V ] 168*> [ I ] <- identity, N-by-N 169*> [ V ] <- M-by-N, same form as B. 170*> 171*> Thus, all of information needed for W is contained on exit in B, which 172*> we call V above. Note that V has the same form as B; that is, 173*> [ V ] = [ V1 ] [ V2 ] 174*> [ V1 ] <- M-by-(N-L) rectangular 175*> [ V2 ] <- M-by-L lower trapezoidal. 176*> 177*> The rows of V represent the vectors which define the H(i)'s. 178*> 179*> The number of blocks is B = ceiling(M/MB), where each 180*> block is of order MB except for the last block, which is of order 181*> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block 182*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB 183*> for the last block) T's are stored in the MB-by-N matrix T as 184*> 185*> T = [T1 T2 ... TB]. 186*> \endverbatim 187*> 188* ===================================================================== 189 SUBROUTINE DTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, 190 $ INFO ) 191* 192* -- LAPACK computational routine (version 3.7.0) -- 193* -- LAPACK is a software package provided by Univ. of Tennessee, -- 194* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 195* December 2016 196* 197* .. Scalar Arguments .. 198 INTEGER INFO, LDA, LDB, LDT, N, M, L, MB 199* .. 200* .. Array Arguments .. 201 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) 202* .. 203* 204* ===================================================================== 205* 206* .. 207* .. Local Scalars .. 208 INTEGER I, IB, LB, NB, IINFO 209* .. 210* .. External Subroutines .. 211 EXTERNAL DTPLQT2, DTPRFB, XERBLA 212* .. 213* .. Executable Statements .. 214* 215* Test the input arguments 216* 217 INFO = 0 218 IF( M.LT.0 ) THEN 219 INFO = -1 220 ELSE IF( N.LT.0 ) THEN 221 INFO = -2 222 ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN 223 INFO = -3 224 ELSE IF( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) THEN 225 INFO = -4 226 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 227 INFO = -6 228 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN 229 INFO = -8 230 ELSE IF( LDT.LT.MB ) THEN 231 INFO = -10 232 END IF 233 IF( INFO.NE.0 ) THEN 234 CALL XERBLA( 'DTPLQT', -INFO ) 235 RETURN 236 END IF 237* 238* Quick return if possible 239* 240 IF( M.EQ.0 .OR. N.EQ.0 ) RETURN 241* 242 DO I = 1, M, MB 243* 244* Compute the QR factorization of the current block 245* 246 IB = MIN( M-I+1, MB ) 247 NB = MIN( N-L+I+IB-1, N ) 248 IF( I.GE.L ) THEN 249 LB = 0 250 ELSE 251 LB = NB-N+L-I+1 252 END IF 253* 254 CALL DTPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB, 255 $ T(1, I ), LDT, IINFO ) 256* 257* Update by applying H**T to B(I+IB:M,:) from the right 258* 259 IF( I+IB.LE.M ) THEN 260 CALL DTPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB, 261 $ B( I, 1 ), LDB, T( 1, I ), LDT, 262 $ A( I+IB, I ), LDA, B( I+IB, 1 ), LDB, 263 $ WORK, M-I-IB+1) 264 END IF 265 END DO 266 RETURN 267* 268* End of DTPLQT 269* 270 END 271