LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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stplqt.f
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1*> \brief \b STPLQT
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/stplqt.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stplqt.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stplqt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE STPLQT( 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* REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> STPLQT 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 REAL array, dimension (LDA,M)
77*> On entry, the lower triangular M-by-M 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,M).
86*> \endverbatim
87*>
88*> \param[in,out] B
89*> \verbatim
90*> B is REAL 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 REAL 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 REAL 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 tplqt
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 M-by-M 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 lower trapezoidal.
153*>
154*> The lower trapezoidal matrix B2 consists of the first L columns of a
155*> M-by-M 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 M-by-M
162*> [ B ] <- M-by-N pentagonal
163*>
164*> so that W can be represented as
165*> [ W ] = [ I ] [ V ]
166*> [ I ] <- identity, M-by-M
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 stplqt( 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 REAL 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 stplqt2, stprfb, 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( 'STPLQT', -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 stplqt2( 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 stprfb( '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 STPLQT
266*
267 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine stplqt2(m, n, l, a, lda, b, ldb, t, ldt, info)
STPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix,...
Definition stplqt2.f:177
subroutine stplqt(m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
STPLQT
Definition stplqt.f:189
subroutine stprfb(side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of ...
Definition stprfb.f:251