LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dtpqrt.f
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1*> \brief \b DTPQRT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpqrt.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpqrt.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpqrt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DTPQRT( 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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DTPQRT computes a blocked QR 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.
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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleOTHERcomputational
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 dtpqrt( 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 DOUBLE PRECISION 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 dtpqrt2, 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( 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( 'DTPQRT', -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 dtpqrt2( mb, ib, lb, a(i,i), lda, b( 1, i ), ldb,
252 \$ t(1, i ), ldt, iinfo )
253*
254* Update by applying H**T to B(:,I+IB:N) from the left
255*
256 IF( i+ib.LE.n ) THEN
257 CALL dtprfb( 'L', 'T', '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 DTPQRT
266*
267 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
DTPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of ...
Definition: dtprfb.f:251
subroutine dtpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
DTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix,...
Definition: dtpqrt2.f:173
subroutine dtpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPQRT
Definition: dtpqrt.f:189