LAPACK 3.12.1
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*> Download STPLQT + dependencies
9*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stplqt.f">
10*> [TGZ]</a>
11*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stplqt.f">
12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stplqt.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* SUBROUTINE STPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
20* INFO )
21*
22* .. Scalar Arguments ..
23* INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
24* ..
25* .. Array Arguments ..
26* REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
27* ..
28*
29*
30*> \par Purpose:
31* =============
32*>
33*> \verbatim
34*>
35*> STPLQT computes a blocked LQ factorization of a real
36*> "triangular-pentagonal" matrix C, which is composed of a
37*> triangular block A and pentagonal block B, using the compact
38*> WY representation for Q.
39*> \endverbatim
40*
41* Arguments:
42* ==========
43*
44*> \param[in] M
45*> \verbatim
46*> M is INTEGER
47*> The number of rows of the matrix B, and the order of the
48*> triangular matrix A.
49*> M >= 0.
50*> \endverbatim
51*>
52*> \param[in] N
53*> \verbatim
54*> N is INTEGER
55*> The number of columns of the matrix B.
56*> N >= 0.
57*> \endverbatim
58*>
59*> \param[in] L
60*> \verbatim
61*> L is INTEGER
62*> The number of rows of the lower trapezoidal part of B.
63*> MIN(M,N) >= L >= 0. See Further Details.
64*> \endverbatim
65*>
66*> \param[in] MB
67*> \verbatim
68*> MB is INTEGER
69*> The block size to be used in the blocked QR. M >= MB >= 1.
70*> \endverbatim
71*>
72*> \param[in,out] A
73*> \verbatim
74*> A is REAL array, dimension (LDA,M)
75*> On entry, the lower triangular M-by-M matrix A.
76*> On exit, the elements on and below the diagonal of the array
77*> contain the lower triangular matrix L.
78*> \endverbatim
79*>
80*> \param[in] LDA
81*> \verbatim
82*> LDA is INTEGER
83*> The leading dimension of the array A. LDA >= max(1,M).
84*> \endverbatim
85*>
86*> \param[in,out] B
87*> \verbatim
88*> B is REAL array, dimension (LDB,N)
89*> On entry, the pentagonal M-by-N matrix B. The first N-L columns
90*> are rectangular, and the last L columns are lower trapezoidal.
91*> On exit, B contains the pentagonal matrix V. See Further Details.
92*> \endverbatim
93*>
94*> \param[in] LDB
95*> \verbatim
96*> LDB is INTEGER
97*> The leading dimension of the array B. LDB >= max(1,M).
98*> \endverbatim
99*>
100*> \param[out] T
101*> \verbatim
102*> T is REAL array, dimension (LDT,N)
103*> The lower triangular block reflectors stored in compact form
104*> as a sequence of upper triangular blocks. See Further Details.
105*> \endverbatim
106*>
107*> \param[in] LDT
108*> \verbatim
109*> LDT is INTEGER
110*> The leading dimension of the array T. LDT >= MB.
111*> \endverbatim
112*>
113*> \param[out] WORK
114*> \verbatim
115*> WORK is REAL array, dimension (MB*M)
116*> \endverbatim
117*>
118*> \param[out] INFO
119*> \verbatim
120*> INFO is INTEGER
121*> = 0: successful exit
122*> < 0: if INFO = -i, the i-th argument had an illegal value
123*> \endverbatim
124*
125* Authors:
126* ========
127*
128*> \author Univ. of Tennessee
129*> \author Univ. of California Berkeley
130*> \author Univ. of Colorado Denver
131*> \author NAG Ltd.
132*
133*> \ingroup tplqt
134*
135*> \par Further Details:
136* =====================
137*>
138*> \verbatim
139*>
140*> The input matrix C is a M-by-(M+N) matrix
141*>
142*> C = [ A ] [ B ]
143*>
144*>
145*> where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
146*> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
147*> upper trapezoidal matrix B2:
148*> [ B ] = [ B1 ] [ B2 ]
149*> [ B1 ] <- M-by-(N-L) rectangular
150*> [ B2 ] <- M-by-L lower trapezoidal.
151*>
152*> The lower trapezoidal matrix B2 consists of the first L columns of a
153*> M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
154*> B is rectangular M-by-N; if M=L=N, B is lower triangular.
155*>
156*> The matrix W stores the elementary reflectors H(i) in the i-th row
157*> above the diagonal (of A) in the M-by-(M+N) input matrix C
158*> [ C ] = [ A ] [ B ]
159*> [ A ] <- lower triangular M-by-M
160*> [ B ] <- M-by-N pentagonal
161*>
162*> so that W can be represented as
163*> [ W ] = [ I ] [ V ]
164*> [ I ] <- identity, M-by-M
165*> [ V ] <- M-by-N, same form as B.
166*>
167*> Thus, all of information needed for W is contained on exit in B, which
168*> we call V above. Note that V has the same form as B; that is,
169*> [ V ] = [ V1 ] [ V2 ]
170*> [ V1 ] <- M-by-(N-L) rectangular
171*> [ V2 ] <- M-by-L lower trapezoidal.
172*>
173*> The rows of V represent the vectors which define the H(i)'s.
174*>
175*> The number of blocks is B = ceiling(M/MB), where each
176*> block is of order MB except for the last block, which is of order
177*> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
178*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
179*> for the last block) T's are stored in the MB-by-N matrix T as
180*>
181*> T = [T1 T2 ... TB].
182*> \endverbatim
183*>
184* =====================================================================
185 SUBROUTINE stplqt( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
186 $ INFO )
187*
188* -- LAPACK computational routine --
189* -- LAPACK is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192* .. Scalar Arguments ..
193 INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
194* ..
195* .. Array Arguments ..
196 REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
197* ..
198*
199* =====================================================================
200*
201* ..
202* .. Local Scalars ..
203 INTEGER I, IB, LB, NB, IINFO
204* ..
205* .. External Subroutines ..
206 EXTERNAL stplqt2, stprfb, xerbla
207* ..
208* .. Executable Statements ..
209*
210* Test the input arguments
211*
212 info = 0
213 IF( m.LT.0 ) THEN
214 info = -1
215 ELSE IF( n.LT.0 ) THEN
216 info = -2
217 ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
218 info = -3
219 ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
220 info = -4
221 ELSE IF( lda.LT.max( 1, m ) ) THEN
222 info = -6
223 ELSE IF( ldb.LT.max( 1, m ) ) THEN
224 info = -8
225 ELSE IF( ldt.LT.mb ) THEN
226 info = -10
227 END IF
228 IF( info.NE.0 ) THEN
229 CALL xerbla( 'STPLQT', -info )
230 RETURN
231 END IF
232*
233* Quick return if possible
234*
235 IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
236*
237 DO i = 1, m, mb
238*
239* Compute the QR factorization of the current block
240*
241 ib = min( m-i+1, mb )
242 nb = min( n-l+i+ib-1, n )
243 IF( i.GE.l ) THEN
244 lb = 0
245 ELSE
246 lb = nb-n+l-i+1
247 END IF
248*
249 CALL stplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
250 $ t(1, i ), ldt, iinfo )
251*
252* Update by applying H**T to B(I+IB:M,:) from the right
253*
254 IF( i+ib.LE.m ) THEN
255 CALL stprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
256 $ b( i, 1 ), ldb, t( 1, i ), ldt,
257 $ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
258 $ work, m-i-ib+1)
259 END IF
260 END DO
261 RETURN
262*
263* End of STPLQT
264*
265 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:175
subroutine stplqt(m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
STPLQT
Definition stplqt.f:187
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:249