LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
dtplqt.f
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1 *> \brief \b DTPLQT
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \date December 2016
136 *
137 *> \ingroup doubleOTHERcomputational
138 *
139 *> \par Further Details:
140 * =====================
141 *>
142 *> \verbatim
143 *>
144 *> The input matrix C is a M-by-(M+N) matrix
145 *>
146 *> C = [ A ] [ B ]
147 *>
148 *>
149 *> where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
150 *> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
151 *> upper trapezoidal matrix B2:
152 *> [ B ] = [ B1 ] [ B2 ]
153 *> [ B1 ] <- M-by-(N-L) rectangular
154 *> [ B2 ] <- M-by-L upper trapezoidal.
155 *>
156 *> The lower trapezoidal matrix B2 consists of the first L columns of a
157 *> N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
158 *> B is rectangular M-by-N; if M=L=N, B is lower triangular.
159 *>
160 *> The matrix W stores the elementary reflectors H(i) in the i-th row
161 *> above the diagonal (of A) in the M-by-(M+N) input matrix C
162 *> [ C ] = [ A ] [ B ]
163 *> [ A ] <- lower triangular N-by-N
164 *> [ B ] <- M-by-N pentagonal
165 *>
166 *> so that W can be represented as
167 *> [ W ] = [ I ] [ V ]
168 *> [ I ] <- identity, N-by-N
169 *> [ V ] <- M-by-N, same form as B.
170 *>
171 *> Thus, all of information needed for W is contained on exit in B, which
172 *> we call V above. Note that V has the same form as B; that is,
173 *> [ V ] = [ V1 ] [ V2 ]
174 *> [ V1 ] <- M-by-(N-L) rectangular
175 *> [ V2 ] <- M-by-L lower trapezoidal.
176 *>
177 *> The rows of V represent the vectors which define the H(i)'s.
178 *>
179 *> The number of blocks is B = ceiling(M/MB), where each
180 *> block is of order MB except for the last block, which is of order
181 *> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
182 *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
183 *> for the last block) T's are stored in the MB-by-N matrix T as
184 *>
185 *> T = [T1 T2 ... TB].
186 *> \endverbatim
187 *>
188 * =====================================================================
189  SUBROUTINE dtplqt( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
190  \$ INFO )
191 *
192 * -- LAPACK computational routine (version 3.7.0) --
193 * -- LAPACK is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * December 2016
196 *
197 * .. Scalar Arguments ..
198  INTEGER info, lda, ldb, ldt, n, m, l, mb
199 * ..
200 * .. Array Arguments ..
201  DOUBLE PRECISION a( lda, * ), b( ldb, * ), t( ldt, * ), work( * )
202 * ..
203 *
204 * =====================================================================
205 *
206 * ..
207 * .. Local Scalars ..
208  INTEGER i, ib, lb, nb, iinfo
209 * ..
210 * .. External Subroutines ..
211  EXTERNAL dtplqt2, dtprfb, xerbla
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input arguments
216 *
217  info = 0
218  IF( m.LT.0 ) THEN
219  info = -1
220  ELSE IF( n.LT.0 ) THEN
221  info = -2
222  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
223  info = -3
224  ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
225  info = -4
226  ELSE IF( lda.LT.max( 1, m ) ) THEN
227  info = -6
228  ELSE IF( ldb.LT.max( 1, m ) ) THEN
229  info = -8
230  ELSE IF( ldt.LT.mb ) THEN
231  info = -10
232  END IF
233  IF( info.NE.0 ) THEN
234  CALL xerbla( 'DTPLQT', -info )
235  RETURN
236  END IF
237 *
238 * Quick return if possible
239 *
240  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
241 *
242  DO i = 1, m, mb
243 *
244 * Compute the QR factorization of the current block
245 *
246  ib = min( m-i+1, mb )
247  nb = min( n-l+i+ib-1, n )
248  IF( i.GE.l ) THEN
249  lb = 0
250  ELSE
251  lb = nb-n+l-i+1
252  END IF
253 *
254  CALL dtplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
255  \$ t(1, i ), ldt, iinfo )
256 *
257 * Update by applying H**T to B(I+IB:M,:) from the right
258 *
259  IF( i+ib.LE.m ) THEN
260  CALL dtprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
261  \$ b( i, 1 ), ldb, t( 1, i ), ldt,
262  \$ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
263  \$ work, m-i-ib+1)
264  END IF
265  END DO
266  RETURN
267 *
268 * End of DTPLQT
269 *
270  END
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:253
subroutine dtplqt(M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPLQT
Definition: dtplqt.f:191
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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Definition: dtplqt2.f:179
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62