1*> \brief \b DTPLQT
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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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