1*> \brief \b ZTPQRT
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
22*                          INFO )
23*
24*       .. Scalar Arguments ..
25*       INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
26*       ..
27*       .. Array Arguments ..
28*       COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> ZTPQRT computes a blocked QR factorization of a complex
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.
50*>          M >= 0.
51*> \endverbatim
52*>
53*> \param[in] N
54*> \verbatim
55*>          N is INTEGER
56*>          The number of columns of the matrix B, and the order of the
57*>          triangular matrix A.
58*>          N >= 0.
59*> \endverbatim
60*>
61*> \param[in] L
62*> \verbatim
63*>          L is INTEGER
64*>          The number of rows of the upper trapezoidal part of B.
65*>          MIN(M,N) >= L >= 0.  See Further Details.
66*> \endverbatim
67*>
68*> \param[in] NB
69*> \verbatim
70*>          NB is INTEGER
71*>          The block size to be used in the blocked QR.  N >= NB >= 1.
72*> \endverbatim
73*>
74*> \param[in,out] A
75*> \verbatim
76*>          A is COMPLEX*16 array, dimension (LDA,N)
77*>          On entry, the upper triangular N-by-N matrix A.
78*>          On exit, the elements on and above the diagonal of the array
79*>          contain the upper triangular matrix R.
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 COMPLEX*16 array, dimension (LDB,N)
91*>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
92*>          are rectangular, and the last L rows are upper 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 COMPLEX*16 array, dimension (LDT,N)
105*>          The upper 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 >= NB.
113*> \endverbatim
114*>
115*> \param[out] WORK
116*> \verbatim
117*>          WORK is COMPLEX*16 array, dimension (NB*N)
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 November 2013
136*
137*> \ingroup complex16OTHERcomputational
138*
139*> \par Further Details:
140*  =====================
141*>
142*> \verbatim
143*>
144*>  The input matrix C is a (N+M)-by-N matrix
145*>
146*>               C = [ A ]
147*>                   [ B ]
148*>
149*>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
150*>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
151*>  upper trapezoidal matrix B2:
152*>
153*>               B = [ B1 ]  <- (M-L)-by-N rectangular
154*>                   [ B2 ]  <-     L-by-N upper trapezoidal.
155*>
156*>  The upper trapezoidal matrix B2 consists of the first L rows of a
157*>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
158*>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
159*>
160*>  The matrix W stores the elementary reflectors H(i) in the i-th column
161*>  below the diagonal (of A) in the (N+M)-by-N input matrix C
162*>
163*>               C = [ A ]  <- upper triangular N-by-N
164*>                   [ B ]  <- M-by-N pentagonal
165*>
166*>  so that W can be represented as
167*>
168*>               W = [ 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*>
174*>               V = [ V1 ] <- (M-L)-by-N rectangular
175*>                   [ V2 ] <-     L-by-N upper trapezoidal.
176*>
177*>  The columns of V represent the vectors which define the H(i)'s.
178*>
179*>  The number of blocks is B = ceiling(N/NB), where each
180*>  block is of order NB except for the last block, which is of order
181*>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
182*>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
183*>  for the last block) T's are stored in the NB-by-N matrix T as
184*>
185*>               T = [T1 T2 ... TB].
186*> \endverbatim
187*>
188*  =====================================================================
189      SUBROUTINE ZTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
190     $                   INFO )
191*
192*  -- LAPACK computational routine (version 3.5.0) --
193*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
194*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195*     November 2013
196*
197*     .. Scalar Arguments ..
198      INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
199*     ..
200*     .. Array Arguments ..
201      COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
202*     ..
203*
204* =====================================================================
205*
206*     ..
207*     .. Local Scalars ..
208      INTEGER    I, IB, LB, MB, IINFO
209*     ..
210*     .. External Subroutines ..
211      EXTERNAL   ZTPQRT2, ZTPRFB, 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( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
225         INFO = -4
226      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
227         INFO = -6
228      ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
229         INFO = -8
230      ELSE IF( LDT.LT.NB ) THEN
231         INFO = -10
232      END IF
233      IF( INFO.NE.0 ) THEN
234         CALL XERBLA( 'ZTPQRT', -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, N, NB
243*
244*     Compute the QR factorization of the current block
245*
246         IB = MIN( N-I+1, NB )
247         MB = MIN( M-L+I+IB-1, M )
248         IF( I.GE.L ) THEN
249            LB = 0
250         ELSE
251            LB = MB-M+L-I+1
252         END IF
253*
254         CALL ZTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB,
255     $                 T(1, I ), LDT, IINFO )
256*
257*     Update by applying H**H to B(:,I+IB:N) from the left
258*
259         IF( I+IB.LE.N ) THEN
260            CALL ZTPRFB( 'L', 'C', 'F', 'C', MB, N-I-IB+1, IB, LB,
261     $                    B( 1, I ), LDB, T( 1, I ), LDT,
262     $                    A( I, I+IB ), LDA, B( 1, I+IB ), LDB,
263     $                    WORK, IB )
264         END IF
265      END DO
266      RETURN
267*
268*     End of ZTPQRT
269*
270      END
271