LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
stplqt.f
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1 * Definition:
2 * ===========
3 *
4 * SUBROUTINE STPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
5 * INFO )
6 *
7 * .. Scalar Arguments ..
8 * INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
9 * ..
10 * .. Array Arguments ..
11 * REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
12 * ..
13 *
14 *
15 *> \par Purpose:
16 * =============
17 *>
18 *> \verbatim
19 *>
20 *> STPLQT computes a blocked LQ factorization of a real
21 *> "triangular-pentagonal" matrix C, which is composed of a
22 *> triangular block A and pentagonal block B, using the compact
23 *> WY representation for Q.
24 *> \endverbatim
25 *
26 * Arguments:
27 * ==========
28 *
29 *> \param[in] M
30 *> \verbatim
31 *> M is INTEGER
32 *> The number of rows of the matrix B, and the order of the
33 *> triangular matrix A.
34 *> M >= 0.
35 *> \endverbatim
36 *>
37 *> \param[in] N
38 *> \verbatim
39 *> N is INTEGER
40 *> The number of columns of the matrix B.
41 *> N >= 0.
42 *> \endverbatim
43 *>
44 *> \param[in] L
45 *> \verbatim
46 *> L is INTEGER
47 *> The number of rows of the lower trapezoidal part of B.
48 *> MIN(M,N) >= L >= 0. See Further Details.
49 *> \endverbatim
50 *>
51 *> \param[in] MB
52 *> \verbatim
53 *> MB is INTEGER
54 *> The block size to be used in the blocked QR. M >= MB >= 1.
55 *> \endverbatim
56 *>
57 *> \param[in,out] A
58 *> \verbatim
59 *> A is REAL array, dimension (LDA,N)
60 *> On entry, the lower triangular N-by-N matrix A.
61 *> On exit, the elements on and below the diagonal of the array
62 *> contain the lower triangular matrix L.
63 *> \endverbatim
64 *>
65 *> \param[in] LDA
66 *> \verbatim
67 *> LDA is INTEGER
68 *> The leading dimension of the array A. LDA >= max(1,N).
69 *> \endverbatim
70 *>
71 *> \param[in,out] B
72 *> \verbatim
73 *> B is REAL array, dimension (LDB,N)
74 *> On entry, the pentagonal M-by-N matrix B. The first N-L columns
75 *> are rectangular, and the last L columns are lower trapezoidal.
76 *> On exit, B contains the pentagonal matrix V. See Further Details.
77 *> \endverbatim
78 *>
79 *> \param[in] LDB
80 *> \verbatim
81 *> LDB is INTEGER
82 *> The leading dimension of the array B. LDB >= max(1,M).
83 *> \endverbatim
84 *>
85 *> \param[out] T
86 *> \verbatim
87 *> T is REAL array, dimension (LDT,N)
88 *> The lower triangular block reflectors stored in compact form
89 *> as a sequence of upper triangular blocks. See Further Details.
90 *> \endverbatim
91 *>
92 *> \param[in] LDT
93 *> \verbatim
94 *> LDT is INTEGER
95 *> The leading dimension of the array T. LDT >= MB.
96 *> \endverbatim
97 *>
98 *> \param[out] WORK
99 *> \verbatim
100 *> WORK is REAL array, dimension (MB*M)
101 *> \endverbatim
102 *>
103 *> \param[out] INFO
104 *> \verbatim
105 *> INFO is INTEGER
106 *> = 0: successful exit
107 *> < 0: if INFO = -i, the i-th argument had an illegal value
108 *> \endverbatim
109 *
110 * Authors:
111 * ========
112 *
113 *> \author Univ. of Tennessee
114 *> \author Univ. of California Berkeley
115 *> \author Univ. of Colorado Denver
116 *> \author NAG Ltd.
117 *
118 *> \date December 2016
119 *
120 *> \ingroup doubleOTHERcomputational
121 *
122 *> \par Further Details:
123 * =====================
124 *>
125 *> \verbatim
126 *>
127 *> The input matrix C is a M-by-(M+N) matrix
128 *>
129 *> C = [ A ] [ B ]
130 *>
131 *>
132 *> where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
133 *> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
134 *> upper trapezoidal matrix B2:
135 *> [ B ] = [ B1 ] [ B2 ]
136 *> [ B1 ] <- M-by-(N-L) rectangular
137 *> [ B2 ] <- M-by-L upper trapezoidal.
138 *>
139 *> The lower trapezoidal matrix B2 consists of the first L columns of a
140 *> N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
141 *> B is rectangular M-by-N; if M=L=N, B is lower triangular.
142 *>
143 *> The matrix W stores the elementary reflectors H(i) in the i-th row
144 *> above the diagonal (of A) in the M-by-(M+N) input matrix C
145 *> [ C ] = [ A ] [ B ]
146 *> [ A ] <- lower triangular N-by-N
147 *> [ B ] <- M-by-N pentagonal
148 *>
149 *> so that W can be represented as
150 *> [ W ] = [ I ] [ V ]
151 *> [ I ] <- identity, N-by-N
152 *> [ V ] <- M-by-N, same form as B.
153 *>
154 *> Thus, all of information needed for W is contained on exit in B, which
155 *> we call V above. Note that V has the same form as B; that is,
156 *> [ V ] = [ V1 ] [ V2 ]
157 *> [ V1 ] <- M-by-(N-L) rectangular
158 *> [ V2 ] <- M-by-L lower trapezoidal.
159 *>
160 *> The rows of V represent the vectors which define the H(i)'s.
161 *>
162 *> The number of blocks is B = ceiling(M/MB), where each
163 *> block is of order MB except for the last block, which is of order
164 *> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
165 *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
166 *> for the last block) T's are stored in the MB-by-N matrix T as
167 *>
168 *> T = [T1 T2 ... TB].
169 *> \endverbatim
170 *>
171 * =====================================================================
172  SUBROUTINE stplqt( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
173  \$ INFO )
174 *
175 * -- LAPACK computational routine (version 3.7.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * December 2016
179 *
180 * .. Scalar Arguments ..
181  INTEGER info, lda, ldb, ldt, n, m, l, mb
182 * ..
183 * .. Array Arguments ..
184  REAL a( lda, * ), b( ldb, * ), t( ldt, * ), work( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * ..
190 * .. Local Scalars ..
191  INTEGER i, ib, lb, nb, iinfo
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL stplqt2, stprfb, xerbla
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input arguments
199 *
200  info = 0
201  IF( m.LT.0 ) THEN
202  info = -1
203  ELSE IF( n.LT.0 ) THEN
204  info = -2
205  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
206  info = -3
207  ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
208  info = -4
209  ELSE IF( lda.LT.max( 1, m ) ) THEN
210  info = -6
211  ELSE IF( ldb.LT.max( 1, m ) ) THEN
212  info = -8
213  ELSE IF( ldt.LT.mb ) THEN
214  info = -10
215  END IF
216  IF( info.NE.0 ) THEN
217  CALL xerbla( 'STPLQT', -info )
218  RETURN
219  END IF
220 *
221 * Quick return if possible
222 *
223  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
224 *
225  DO i = 1, m, mb
226 *
227 * Compute the QR factorization of the current block
228 *
229  ib = min( m-i+1, mb )
230  nb = min( n-l+i+ib-1, n )
231  IF( i.GE.l ) THEN
232  lb = 0
233  ELSE
234  lb = nb-n+l-i+1
235  END IF
236 *
237  CALL stplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
238  \$ t(1, i ), ldt, iinfo )
239 *
240 * Update by applying H**T to B(I+IB:M,:) from the right
241 *
242  IF( i+ib.LE.m ) THEN
243  CALL stprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
244  \$ b( i, 1 ), ldb, t( 1, i ), ldt,
245  \$ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
246  \$ work, m-i-ib+1)
247  END IF
248  END DO
249  RETURN
250 *
251 * End of STPLQT
252 *
253  END
subroutine stplqt(M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
STPLQT
Definition: stplqt.f:191
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Definition: stplqt2.f:179
subroutine stprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
STPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: stprfb.f:253