1*> \brief \b CTPQRT
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 CTPQRT( 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 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> CTPQRT 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 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 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 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 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*> \ingroup complexOTHERcomputational
136*
137*> \par Further Details:
138*  =====================
139*>
140*> \verbatim
141*>
142*>  The input matrix C is a (N+M)-by-N matrix
143*>
144*>               C = [ A ]
145*>                   [ B ]
146*>
147*>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
148*>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
149*>  upper trapezoidal matrix B2:
150*>
151*>               B = [ B1 ]  <- (M-L)-by-N rectangular
152*>                   [ B2 ]  <-     L-by-N upper trapezoidal.
153*>
154*>  The upper trapezoidal matrix B2 consists of the first L rows of a
155*>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
156*>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
157*>
158*>  The matrix W stores the elementary reflectors H(i) in the i-th column
159*>  below the diagonal (of A) in the (N+M)-by-N input matrix C
160*>
161*>               C = [ A ]  <- upper triangular N-by-N
162*>                   [ B ]  <- M-by-N pentagonal
163*>
164*>  so that W can be represented as
165*>
166*>               W = [ 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*>
172*>               V = [ V1 ] <- (M-L)-by-N rectangular
173*>                   [ V2 ] <-     L-by-N upper trapezoidal.
174*>
175*>  The columns of V represent the vectors which define the H(i)'s.
176*>
177*>  The number of blocks is B = ceiling(N/NB), where each
178*>  block is of order NB except for the last block, which is of order
179*>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
180*>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
181*>  for the last block) T's are stored in the NB-by-N matrix T as
182*>
183*>               T = [T1 T2 ... TB].
184*> \endverbatim
185*>
186*  =====================================================================
187      SUBROUTINE CTPQRT( M, N, L, NB, 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, NB
196*     ..
197*     .. Array Arguments ..
198      COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
199*     ..
200*
201* =====================================================================
202*
203*     ..
204*     .. Local Scalars ..
205      INTEGER    I, IB, LB, MB, IINFO
206*     ..
207*     .. External Subroutines ..
208      EXTERNAL   CTPQRT2, CTPRFB, 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( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
222         INFO = -4
223      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
224         INFO = -6
225      ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
226         INFO = -8
227      ELSE IF( LDT.LT.NB ) THEN
228         INFO = -10
229      END IF
230      IF( INFO.NE.0 ) THEN
231         CALL XERBLA( 'CTPQRT', -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, N, NB
240*
241*     Compute the QR factorization of the current block
242*
243         IB = MIN( N-I+1, NB )
244         MB = MIN( M-L+I+IB-1, M )
245         IF( I.GE.L ) THEN
246            LB = 0
247         ELSE
248            LB = MB-M+L-I+1
249         END IF
250*
251         CALL CTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB,
252     $                 T(1, I ), LDT, IINFO )
253*
254*     Update by applying H**H to B(:,I+IB:N) from the left
255*
256         IF( I+IB.LE.N ) THEN
257            CALL CTPRFB( 'L', 'C', 'F', 'C', MB, N-I-IB+1, IB, LB,
258     $                    B( 1, I ), LDB, T( 1, I ), LDT,
259     $                    A( I, I+IB ), LDA, B( 1, I+IB ), LDB,
260     $                    WORK, IB )
261         END IF
262      END DO
263      RETURN
264*
265*     End of CTPQRT
266*
267      END
268