LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zgelqt.f
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1 *> \brief \b ZGELQT
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZGELQT( 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 * COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZGELQT computes a blocked LQ factorization of a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 June 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 zgelqt( M, N, MB, A, LDA, T, LDT, WORK, INFO )
141 *
142 * -- LAPACK computational routine (version 3.7.1) --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 * June 2017
146 *
147 * .. Scalar Arguments ..
148  INTEGER INFO, LDA, LDT, M, N, MB
149 * ..
150 * .. Array Arguments ..
151  COMPLEX*16 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 zgelqt3, zlarfb, 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( 'ZGELQT', -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 zgelqt3( 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 zlarfb( '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 ZGELQT
209 *
210  END
subroutine zgelqt(M, N, MB, A, LDA, T, LDT, WORK, INFO)
ZGELQT
Definition: zgelqt.f:141
recursive subroutine zgelqt3(M, N, A, LDA, T, LDT, INFO)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact...
Definition: zgelqt3.f:133
subroutine zlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: zlarfb.f:197
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62