Annotation of rpl/lapack/lapack/dtpqrt.f, revision 1.10
1.1 bertrand 1: *> \brief \b DTPQRT
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.7 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
8: *> \htmlonly
1.7 bertrand 9: *> Download DTPQRT + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpqrt.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpqrt.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpqrt.f">
1.1 bertrand 15: *> [TXT]</a>
1.7 bertrand 16: *> \endhtmlonly
1.1 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
22: * INFO )
1.7 bertrand 23: *
1.1 bertrand 24: * .. Scalar Arguments ..
25: * INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
29: * ..
1.7 bertrand 30: *
1.1 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
1.7 bertrand 37: *> DTPQRT computes a blocked QR 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
1.1 bertrand 40: *> WY representation for Q.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] M
47: *> \verbatim
48: *> M is INTEGER
1.7 bertrand 49: *> The number of rows of the matrix B.
1.1 bertrand 50: *> M >= 0.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> The number of columns of the matrix B, and the order of the
57: *> triangular matrix A.
58: *> N >= 0.
59: *> \endverbatim
60: *>
61: *> \param[in] L
62: *> \verbatim
63: *> L is INTEGER
64: *> The number of rows of the upper trapezoidal part of B.
65: *> MIN(M,N) >= L >= 0. See Further Details.
66: *> \endverbatim
67: *>
68: *> \param[in] NB
69: *> \verbatim
70: *> NB is INTEGER
71: *> The block size to be used in the blocked QR. N >= NB >= 1.
72: *> \endverbatim
73: *>
74: *> \param[in,out] A
75: *> \verbatim
76: *> A is DOUBLE PRECISION array, dimension (LDA,N)
77: *> On entry, the upper triangular N-by-N matrix A.
78: *> On exit, the elements on and above the diagonal of the array
79: *> contain the upper triangular matrix R.
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)
1.7 bertrand 91: *> On entry, the pentagonal M-by-N matrix B. The first M-L rows
1.1 bertrand 92: *> are rectangular, and the last L rows are upper 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 upper triangular block reflectors stored in compact form
106: *> as a sequence of upper triangular blocks. See Further Details.
107: *> \endverbatim
1.7 bertrand 108: *>
1.1 bertrand 109: *> \param[in] LDT
110: *> \verbatim
111: *> LDT is INTEGER
112: *> The leading dimension of the array T. LDT >= NB.
113: *> \endverbatim
114: *>
115: *> \param[out] WORK
116: *> \verbatim
117: *> WORK is DOUBLE PRECISION array, dimension (NB*N)
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: *
1.7 bertrand 130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
1.1 bertrand 134: *
135: *> \ingroup doubleOTHERcomputational
136: *
137: *> \par Further Details:
138: * =====================
139: *>
140: *> \verbatim
141: *>
1.7 bertrand 142: *> The input matrix C is a (N+M)-by-N matrix
1.1 bertrand 143: *>
144: *> C = [ A ]
1.7 bertrand 145: *> [ B ]
1.1 bertrand 146: *>
147: *> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
148: *> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
149: *> upper trapezoidal matrix B2:
150: *>
151: *> B = [ B1 ] <- (M-L)-by-N rectangular
152: *> [ B2 ] <- L-by-N upper trapezoidal.
153: *>
154: *> The upper trapezoidal matrix B2 consists of the first L rows of a
1.7 bertrand 155: *> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
156: *> B is rectangular M-by-N; if M=L=N, B is upper triangular.
1.1 bertrand 157: *>
158: *> The matrix W stores the elementary reflectors H(i) in the i-th column
159: *> below the diagonal (of A) in the (N+M)-by-N input matrix C
160: *>
161: *> C = [ A ] <- upper triangular N-by-N
162: *> [ B ] <- M-by-N pentagonal
163: *>
164: *> so that W can be represented as
165: *>
166: *> W = [ 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
1.7 bertrand 170: *> we call V above. Note that V has the same form as B; that is,
1.1 bertrand 171: *>
172: *> V = [ V1 ] <- (M-L)-by-N rectangular
173: *> [ V2 ] <- L-by-N upper trapezoidal.
174: *>
1.7 bertrand 175: *> The columns of V represent the vectors which define the H(i)'s.
1.1 bertrand 176: *>
177: *> The number of blocks is B = ceiling(N/NB), where each
1.7 bertrand 178: *> block is of order NB except for the last block, which is of order
1.1 bertrand 179: *> IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block
1.7 bertrand 180: *> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
1.1 bertrand 181: *> for the last block) T's are stored in the NB-by-N matrix T as
182: *>
183: *> T = [T1 T2 ... TB].
184: *> \endverbatim
185: *>
186: * =====================================================================
187: SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
188: $ INFO )
189: *
1.10 ! 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, NB
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, MB, IINFO
206: * ..
207: * .. External Subroutines ..
208: EXTERNAL DTPQRT2, 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
1.4 bertrand 219: ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
1.1 bertrand 220: INFO = -3
1.4 bertrand 221: ELSE IF( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
1.1 bertrand 222: INFO = -4
223: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
224: INFO = -6
225: ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
226: INFO = -8
227: ELSE IF( LDT.LT.NB ) THEN
228: INFO = -10
229: END IF
230: IF( INFO.NE.0 ) THEN
231: CALL XERBLA( 'DTPQRT', -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, N, NB
1.7 bertrand 240: *
1.1 bertrand 241: * Compute the QR factorization of the current block
242: *
243: IB = MIN( N-I+1, NB )
244: MB = MIN( M-L+I+IB-1, M )
245: IF( I.GE.L ) THEN
246: LB = 0
247: ELSE
248: LB = MB-M+L-I+1
249: END IF
250: *
1.7 bertrand 251: CALL DTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB,
1.1 bertrand 252: $ T(1, I ), LDT, IINFO )
253: *
254: * Update by applying H**T to B(:,I+IB:N) from the left
255: *
256: IF( I+IB.LE.N ) THEN
257: CALL DTPRFB( 'L', 'T', 'F', 'C', MB, N-I-IB+1, IB, LB,
1.7 bertrand 258: $ B( 1, I ), LDB, T( 1, I ), LDT,
259: $ A( I, I+IB ), LDA, B( 1, I+IB ), LDB,
1.1 bertrand 260: $ WORK, IB )
261: END IF
262: END DO
263: RETURN
1.7 bertrand 264: *
1.1 bertrand 265: * End of DTPQRT
266: *
267: END
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