1: *> \brief \b DGELQT
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGEQRT + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelqt.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelqt.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelqt.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, LDT, M, N, MB
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
37: *> using the compact WY representation of Q.
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] M
44: *> \verbatim
45: *> M is INTEGER
46: *> The number of rows of the matrix A. M >= 0.
47: *> \endverbatim
48: *>
49: *> \param[in] N
50: *> \verbatim
51: *> N is INTEGER
52: *> The number of columns of the matrix A. N >= 0.
53: *> \endverbatim
54: *>
55: *> \param[in] MB
56: *> \verbatim
57: *> MB is INTEGER
58: *> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
59: *> \endverbatim
60: *>
61: *> \param[in,out] A
62: *> \verbatim
63: *> A is DOUBLE PRECISION array, dimension (LDA,N)
64: *> On entry, the M-by-N matrix A.
65: *> On exit, the elements on and below the diagonal of the array
66: *> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
67: *> lower triangular if M <= N); the elements above the diagonal
68: *> are the rows of V.
69: *> \endverbatim
70: *>
71: *> \param[in] LDA
72: *> \verbatim
73: *> LDA is INTEGER
74: *> The leading dimension of the array A. LDA >= max(1,M).
75: *> \endverbatim
76: *>
77: *> \param[out] T
78: *> \verbatim
79: *> T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
80: *> The upper triangular block reflectors stored in compact form
81: *> as a sequence of upper triangular blocks. See below
82: *> for further details.
83: *> \endverbatim
84: *>
85: *> \param[in] LDT
86: *> \verbatim
87: *> LDT is INTEGER
88: *> The leading dimension of the array T. LDT >= MB.
89: *> \endverbatim
90: *>
91: *> \param[out] WORK
92: *> \verbatim
93: *> WORK is DOUBLE PRECISION array, dimension (MB*N)
94: *> \endverbatim
95: *>
96: *> \param[out] INFO
97: *> \verbatim
98: *> INFO is INTEGER
99: *> = 0: successful exit
100: *> < 0: if INFO = -i, the i-th argument had an illegal value
101: *> \endverbatim
102: *
103: * Authors:
104: * ========
105: *
106: *> \author Univ. of Tennessee
107: *> \author Univ. of California Berkeley
108: *> \author Univ. of Colorado Denver
109: *> \author NAG Ltd.
110: *
111: *> \date November 2017
112: *
113: *> \ingroup doubleGEcomputational
114: *
115: *> \par Further Details:
116: * =====================
117: *>
118: *> \verbatim
119: *>
120: *> The matrix V stores the elementary reflectors H(i) in the i-th row
121: *> above the diagonal. For example, if M=5 and N=3, the matrix V is
122: *>
123: *> V = ( 1 v1 v1 v1 v1 )
124: *> ( 1 v2 v2 v2 )
125: *> ( 1 v3 v3 )
126: *>
127: *>
128: *> where the vi's represent the vectors which define H(i), which are returned
129: *> in the matrix A. The 1's along the diagonal of V are not stored in A.
130: *> Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
131: *> block is of order MB except for the last block, which is of order
132: *> IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
133: *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
134: *> for the last block) T's are stored in the MB-by-K matrix T as
135: *>
136: *> T = (T1 T2 ... TB).
137: *> \endverbatim
138: *>
139: * =====================================================================
140: SUBROUTINE DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
141: *
142: * -- LAPACK computational routine (version 3.8.0) --
143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145: * November 2017
146: *
147: * .. Scalar Arguments ..
148: INTEGER INFO, LDA, LDT, M, N, MB
149: * ..
150: * .. Array Arguments ..
151: DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * ..
157: * .. Local Scalars ..
158: INTEGER I, IB, IINFO, K
159: * ..
160: * .. External Subroutines ..
161: EXTERNAL DGEQRT2, DGELQT3, DGEQRT3, DLARFB, XERBLA
162: * ..
163: * .. Executable Statements ..
164: *
165: * Test the input arguments
166: *
167: INFO = 0
168: IF( M.LT.0 ) THEN
169: INFO = -1
170: ELSE IF( N.LT.0 ) THEN
171: INFO = -2
172: ELSE IF( MB.LT.1 .OR. ( MB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
173: INFO = -3
174: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
175: INFO = -5
176: ELSE IF( LDT.LT.MB ) THEN
177: INFO = -7
178: END IF
179: IF( INFO.NE.0 ) THEN
180: CALL XERBLA( 'DGELQT', -INFO )
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
186: K = MIN( M, N )
187: IF( K.EQ.0 ) RETURN
188: *
189: * Blocked loop of length K
190: *
191: DO I = 1, K, MB
192: IB = MIN( K-I+1, MB )
193: *
194: * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
195: *
196: CALL DGELQT3( IB, N-I+1, A(I,I), LDA, T(1,I), LDT, IINFO )
197: IF( I+IB.LE.M ) THEN
198: *
199: * Update by applying H**T to A(I:M,I+IB:N) from the right
200: *
201: CALL DLARFB( 'R', 'N', 'F', 'R', M-I-IB+1, N-I+1, IB,
202: $ A( I, I ), LDA, T( 1, I ), LDT,
203: $ A( I+IB, I ), LDA, WORK , M-I-IB+1 )
204: END IF
205: END DO
206: RETURN
207: *
208: * End of DGELQT
209: *
210: END
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