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*> \ingroup doubleOTHERcomputational
136*
137*> \par Further Details:
138*  =====================
139*>
140*> \verbatim
141*>
142*>  The input matrix C is a M-by-(M+N) matrix
143*>
144*>               C = [ A ] [ B ]
145*>
146*>
147*>  where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
148*>  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
149*>  upper trapezoidal matrix B2:
150*>          [ B ] = [ B1 ] [ B2 ]
151*>                   [ B1 ]  <- M-by-(N-L) rectangular
152*>                   [ B2 ]  <-     M-by-L upper trapezoidal.
153*>
154*>  The lower trapezoidal matrix B2 consists of the first L columns of a
155*>  N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
156*>  B is rectangular M-by-N; if M=L=N, B is lower triangular.
157*>
158*>  The matrix W stores the elementary reflectors H(i) in the i-th row
159*>  above the diagonal (of A) in the M-by-(M+N) input matrix C
160*>            [ C ] = [ A ] [ B ]
161*>                   [ A ]  <- lower triangular N-by-N
162*>                   [ B ]  <- M-by-N pentagonal
163*>
164*>  so that W can be represented as
165*>            [ W ] = [ I ] [ V ]
166*>                   [ I ]  <- identity, N-by-N
167*>                   [ V ]  <- M-by-N, same form as B.
168*>
169*>  Thus, all of information needed for W is contained on exit in B, which
170*>  we call V above.  Note that V has the same form as B; that is,
171*>            [ V ] = [ V1 ] [ V2 ]
172*>                   [ V1 ] <- M-by-(N-L) rectangular
173*>                   [ V2 ] <-     M-by-L lower trapezoidal.
174*>
175*>  The rows of V represent the vectors which define the H(i)'s.
176*>
177*>  The number of blocks is B = ceiling(M/MB), where each
178*>  block is of order MB except for the last block, which is of order
179*>  IB = M - (M-1)*MB.  For each of the B blocks, a upper triangular block
180*>  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
181*>  for the last block) T's are stored in the MB-by-N matrix T as
182*>
183*>               T = [T1 T2 ... TB].
184*> \endverbatim
185*>
186*  =====================================================================
187      SUBROUTINE DTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
188     $                   INFO )
189*
190*  -- LAPACK computational routine --
191*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
192*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193*
194*     .. Scalar Arguments ..
195      INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
196*     ..
197*     .. Array Arguments ..
198      DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
199*     ..
200*
201* =====================================================================
202*
203*     ..
204*     .. Local Scalars ..
205      INTEGER    I, IB, LB, NB, IINFO
206*     ..
207*     .. External Subroutines ..
208      EXTERNAL   DTPLQT2, DTPRFB, XERBLA
209*     ..
210*     .. Executable Statements ..
211*
212*     Test the input arguments
213*
214      INFO = 0
215      IF( M.LT.0 ) THEN
216         INFO = -1
217      ELSE IF( N.LT.0 ) THEN
218         INFO = -2
219      ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
220         INFO = -3
221      ELSE IF( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) THEN
222         INFO = -4
223      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
224         INFO = -6
225      ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
226         INFO = -8
227      ELSE IF( LDT.LT.MB ) THEN
228         INFO = -10
229      END IF
230      IF( INFO.NE.0 ) THEN
231         CALL XERBLA( 'DTPLQT', -INFO )
232         RETURN
233      END IF
234*
235*     Quick return if possible
236*
237      IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
238*
239      DO I = 1, M, MB
240*
241*     Compute the QR factorization of the current block
242*
243         IB = MIN( M-I+1, MB )
244         NB = MIN( N-L+I+IB-1, N )
245         IF( I.GE.L ) THEN
246            LB = 0
247         ELSE
248            LB = NB-N+L-I+1
249         END IF
250*
251         CALL DTPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB,
252     $                 T(1, I ), LDT, IINFO )
253*
254*     Update by applying H**T to B(I+IB:M,:) from the right
255*
256         IF( I+IB.LE.M ) THEN
257            CALL DTPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB,
258     $                    B( I, 1 ), LDB, T( 1, I ), LDT,
259     $                    A( I+IB, I ), LDA, B( I+IB, 1 ), LDB,
260     $                    WORK, M-I-IB+1)
261         END IF
262      END DO
263      RETURN
264*
265*     End of DTPLQT
266*
267      END
268