Annotation of rpl/lapack/lapack/ztplqt.f, revision 1.5
1.1 bertrand 1: *> \brief \b ZTPLQT
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
1.5 ! bertrand 9: *> Download ZTPLQT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztplqt.f">
1.1 bertrand 11: *> [TGZ]</a>
1.5 ! bertrand 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztplqt.f">
1.1 bertrand 13: *> [ZIP]</a>
1.5 ! bertrand 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztplqt.f">
1.1 bertrand 15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTPLQT( 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: * COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
1.5 ! bertrand 37: *> ZTPLQT computes a blocked LQ factorization of a complex
1.1 bertrand 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
1.3 bertrand 76: *> A is COMPLEX*16 array, dimension (LDA,M)
77: *> On entry, the lower triangular M-by-M matrix A.
1.1 bertrand 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
1.3 bertrand 85: *> The leading dimension of the array A. LDA >= max(1,M).
1.1 bertrand 86: *> \endverbatim
87: *>
88: *> \param[in,out] B
89: *> \verbatim
90: *> B is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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: *>
1.3 bertrand 147: *> where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
1.1 bertrand 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
1.3 bertrand 152: *> [ B2 ] <- M-by-L lower trapezoidal.
1.1 bertrand 153: *>
154: *> The lower trapezoidal matrix B2 consists of the first L columns of a
1.3 bertrand 155: *> M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
1.1 bertrand 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 ]
1.3 bertrand 161: *> [ A ] <- lower triangular M-by-M
1.1 bertrand 162: *> [ B ] <- M-by-N pentagonal
163: *>
164: *> so that W can be represented as
165: *> [ W ] = [ I ] [ V ]
1.3 bertrand 166: *> [ I ] <- identity, M-by-M
1.1 bertrand 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 ZTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
188: $ INFO )
189: *
1.5 ! bertrand 190: * -- LAPACK computational routine --
1.1 bertrand 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: COMPLEX*16 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 ZTPLQT2, ZTPRFB, 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( 'ZTPLQT', -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 ZTPLQT2( 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 ZTPRFB( '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 ZTPLQT
266: *
267: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to ztplqt.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack