LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dtplqt.f
Go to the documentation of this file.
1 *> \brief \b DTPLQT
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DTPQRT + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtplqt.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtplqt.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtplqt.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DTPLQT( 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 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DTPLQT 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 DOUBLE PRECISION array, dimension (LDA,N)
77 *> On entry, the lower triangular N-by-N 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,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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleOTHERcomputational
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 N-by-N 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 upper trapezoidal.
153 *>
154 *> The lower trapezoidal matrix B2 consists of the first L columns of a
155 *> N-by-N 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 N-by-N
162 *> [ B ] <- M-by-N pentagonal
163 *>
164 *> so that W can be represented as
165 *> [ W ] = [ I ] [ V ]
166 *> [ 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 *> [ 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 dtplqt( 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  DOUBLE PRECISION 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 dtplqt2, 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( 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( 'DTPLQT', -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 dtplqt2( 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 dtprfb( '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 DTPLQT
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 or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: dtprfb.f:251
subroutine dtplqt(M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPLQT
Definition: dtplqt.f:189
subroutine dtplqt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
DTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix,...
Definition: dtplqt2.f:177