LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ctplqt.f
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1 *> \brief \b CTPLQT
2 *
3 * Definition:
4 * ===========
5 *
6 * SUBROUTINE CTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
7 * INFO )
8 *
9 * .. Scalar Arguments ..
10 * INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
11 * ..
12 * .. Array Arguments ..
13 * COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
14 * ..
15 *
16 *
17 *> \par Purpose:
18 * =============
19 *>
20 *> \verbatim
21 *>
22 *> CTPLQT computes a blocked LQ factorization of a complex
23 *> "triangular-pentagonal" matrix C, which is composed of a
24 *> triangular block A and pentagonal block B, using the compact
25 *> WY representation for Q.
26 *> \endverbatim
27 *
28 * Arguments:
29 * ==========
30 *
31 *> \param[in] M
32 *> \verbatim
33 *> M is INTEGER
34 *> The number of rows of the matrix B, and the order of the
35 *> triangular matrix A.
36 *> M >= 0.
37 *> \endverbatim
38 *>
39 *> \param[in] N
40 *> \verbatim
41 *> N is INTEGER
42 *> The number of columns of the matrix B.
43 *> N >= 0.
44 *> \endverbatim
45 *>
46 *> \param[in] L
47 *> \verbatim
48 *> L is INTEGER
49 *> The number of rows of the lower trapezoidal part of B.
50 *> MIN(M,N) >= L >= 0. See Further Details.
51 *> \endverbatim
52 *>
53 *> \param[in] MB
54 *> \verbatim
55 *> MB is INTEGER
56 *> The block size to be used in the blocked QR. M >= MB >= 1.
57 *> \endverbatim
58 *>
59 *> \param[in,out] A
60 *> \verbatim
61 *> A is COMPLEX array, dimension (LDA,M)
62 *> On entry, the lower triangular M-by-M matrix A.
63 *> On exit, the elements on and below the diagonal of the array
64 *> contain the lower triangular matrix L.
65 *> \endverbatim
66 *>
67 *> \param[in] LDA
68 *> \verbatim
69 *> LDA is INTEGER
70 *> The leading dimension of the array A. LDA >= max(1,M).
71 *> \endverbatim
72 *>
73 *> \param[in,out] B
74 *> \verbatim
75 *> B is COMPLEX array, dimension (LDB,N)
76 *> On entry, the pentagonal M-by-N matrix B. The first N-L columns
77 *> are rectangular, and the last L columns are lower trapezoidal.
78 *> On exit, B contains the pentagonal matrix V. See Further Details.
79 *> \endverbatim
80 *>
81 *> \param[in] LDB
82 *> \verbatim
83 *> LDB is INTEGER
84 *> The leading dimension of the array B. LDB >= max(1,M).
85 *> \endverbatim
86 *>
87 *> \param[out] T
88 *> \verbatim
89 *> T is COMPLEX array, dimension (LDT,N)
90 *> The lower triangular block reflectors stored in compact form
91 *> as a sequence of upper triangular blocks. See Further Details.
92 *> \endverbatim
93 *>
94 *> \param[in] LDT
95 *> \verbatim
96 *> LDT is INTEGER
97 *> The leading dimension of the array T. LDT >= MB.
98 *> \endverbatim
99 *>
100 *> \param[out] WORK
101 *> \verbatim
102 *> WORK is COMPLEX array, dimension (MB*M)
103 *> \endverbatim
104 *>
105 *> \param[out] INFO
106 *> \verbatim
107 *> INFO is INTEGER
108 *> = 0: successful exit
109 *> < 0: if INFO = -i, the i-th argument had an illegal value
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
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 M-by-M 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 lower trapezoidal.
138 *>
139 *> The lower trapezoidal matrix B2 consists of the first L columns of a
140 *> M-by-M 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 M-by-M
147 *> [ B ] <- M-by-N pentagonal
148 *>
149 *> so that W can be represented as
150 *> [ W ] = [ I ] [ V ]
151 *> [ I ] <- identity, M-by-M
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 ctplqt( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
173  $ INFO )
174 *
175 * -- LAPACK computational routine --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 *
179 * .. Scalar Arguments ..
180  INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
181 * ..
182 * .. Array Arguments ..
183  COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
184 * ..
185 *
186 * =====================================================================
187 *
188 * ..
189 * .. Local Scalars ..
190  INTEGER I, IB, LB, NB, IINFO
191 * ..
192 * .. External Subroutines ..
193  EXTERNAL ctplqt2, ctprfb, xerbla
194 * ..
195 * .. Executable Statements ..
196 *
197 * Test the input arguments
198 *
199  info = 0
200  IF( m.LT.0 ) THEN
201  info = -1
202  ELSE IF( n.LT.0 ) THEN
203  info = -2
204  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
205  info = -3
206  ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
207  info = -4
208  ELSE IF( lda.LT.max( 1, m ) ) THEN
209  info = -6
210  ELSE IF( ldb.LT.max( 1, m ) ) THEN
211  info = -8
212  ELSE IF( ldt.LT.mb ) THEN
213  info = -10
214  END IF
215  IF( info.NE.0 ) THEN
216  CALL xerbla( 'CTPLQT', -info )
217  RETURN
218  END IF
219 *
220 * Quick return if possible
221 *
222  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
223 *
224  DO i = 1, m, mb
225 *
226 * Compute the QR factorization of the current block
227 *
228  ib = min( m-i+1, mb )
229  nb = min( n-l+i+ib-1, n )
230  IF( i.GE.l ) THEN
231  lb = 0
232  ELSE
233  lb = nb-n+l-i+1
234  END IF
235 *
236  CALL ctplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
237  $ t(1, i ), ldt, iinfo )
238 *
239 * Update by applying H**T to B(I+IB:M,:) from the right
240 *
241  IF( i+ib.LE.m ) THEN
242  CALL ctprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
243  $ b( i, 1 ), ldb, t( 1, i ), ldt,
244  $ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
245  $ work, m-i-ib+1)
246  END IF
247  END DO
248  RETURN
249 *
250 * End of CTPLQT
251 *
252  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ctprfb.f:251
subroutine ctplqt(M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPLQT
Definition: ctplqt.f:174
subroutine ctplqt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
CTPLQT2
Definition: ctplqt2.f:162