LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
sgelqt.f
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1 * Definition:
2 * ===========
3 *
4 * SUBROUTINE SGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
5 *
6 * .. Scalar Arguments ..
7 * INTEGER INFO, LDA, LDT, M, N, MB
8 * ..
9 * .. Array Arguments ..
10 * REAL A( LDA, * ), T( LDT, * ), WORK( * )
11 * ..
12 *
13 *
14 *> \par Purpose:
15 * =============
16 *>
17 *> \verbatim
18 *>
19 *> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
20 *> using the compact WY representation of Q.
21 *> \endverbatim
22 *
23 * Arguments:
24 * ==========
25 *
26 *> \param[in] M
27 *> \verbatim
28 *> M is INTEGER
29 *> The number of rows of the matrix A. M >= 0.
30 *> \endverbatim
31 *>
32 *> \param[in] N
33 *> \verbatim
34 *> N is INTEGER
35 *> The number of columns of the matrix A. N >= 0.
36 *> \endverbatim
37 *>
38 *> \param[in] MB
39 *> \verbatim
40 *> MB is INTEGER
41 *> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
42 *> \endverbatim
43 *>
44 *> \param[in,out] A
45 *> \verbatim
46 *> A is REAL array, dimension (LDA,N)
47 *> On entry, the M-by-N matrix A.
48 *> On exit, the elements on and below the diagonal of the array
49 *> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
50 *> lower triangular if M <= N); the elements above the diagonal
51 *> are the rows of V.
52 *> \endverbatim
53 *>
54 *> \param[in] LDA
55 *> \verbatim
56 *> LDA is INTEGER
57 *> The leading dimension of the array A. LDA >= max(1,M).
58 *> \endverbatim
59 *>
60 *> \param[out] T
61 *> \verbatim
62 *> T is REAL array, dimension (LDT,MIN(M,N))
63 *> The upper triangular block reflectors stored in compact form
64 *> as a sequence of upper triangular blocks. See below
65 *> for further details.
66 *> \endverbatim
67 *>
68 *> \param[in] LDT
69 *> \verbatim
70 *> LDT is INTEGER
71 *> The leading dimension of the array T. LDT >= MB.
72 *> \endverbatim
73 *>
74 *> \param[out] WORK
75 *> \verbatim
76 *> WORK is REAL array, dimension (MB*N)
77 *> \endverbatim
78 *>
79 *> \param[out] INFO
80 *> \verbatim
81 *> INFO is INTEGER
82 *> = 0: successful exit
83 *> < 0: if INFO = -i, the i-th argument had an illegal value
84 *> \endverbatim
85 *
86 * Authors:
87 * ========
88 *
89 *> \author Univ. of Tennessee
90 *> \author Univ. of California Berkeley
91 *> \author Univ. of Colorado Denver
92 *> \author NAG Ltd.
93 *
94 *> \date November 2017
95 *
96 *> \ingroup doubleGEcomputational
97 *
98 *> \par Further Details:
99 * =====================
100 *>
101 *> \verbatim
102 *>
103 *> The matrix V stores the elementary reflectors H(i) in the i-th row
104 *> above the diagonal. For example, if M=5 and N=3, the matrix V is
105 *>
106 *> V = ( 1 v1 v1 v1 v1 )
107 *> ( 1 v2 v2 v2 )
108 *> ( 1 v3 v3 )
109 *>
110 *>
111 *> where the vi's represent the vectors which define H(i), which are returned
112 *> in the matrix A. The 1's along the diagonal of V are not stored in A.
113 *> Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
114 *> block is of order MB except for the last block, which is of order
115 *> IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
116 *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
117 *> for the last block) T's are stored in the MB-by-K matrix T as
118 *>
119 *> T = (T1 T2 ... TB).
120 *> \endverbatim
121 *>
122 * =====================================================================
123  SUBROUTINE sgelqt( M, N, MB, A, LDA, T, LDT, WORK, INFO )
124 *
125 * -- LAPACK computational routine (version 3.8.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * November 2017
129 *
130 * .. Scalar Arguments ..
131  INTEGER INFO, LDA, LDT, M, N, MB
132 * ..
133 * .. Array Arguments ..
134  REAL A( lda, * ), T( ldt, * ), WORK( * )
135 * ..
136 *
137 * =====================================================================
138 *
139 * ..
140 * .. Local Scalars ..
141  INTEGER I, IB, IINFO, K
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL sgeqrt2, sgeqrt3, sgelqt3, slarfb, xerbla
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input arguments
149 *
150  info = 0
151  IF( m.LT.0 ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( mb.LT.1 .OR. ( mb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
156  info = -3
157  ELSE IF( lda.LT.max( 1, m ) ) THEN
158  info = -5
159  ELSE IF( ldt.LT.mb ) THEN
160  info = -7
161  END IF
162  IF( info.NE.0 ) THEN
163  CALL xerbla( 'SGELQT', -info )
164  RETURN
165  END IF
166 *
167 * Quick return if possible
168 *
169  k = min( m, n )
170  IF( k.EQ.0 ) RETURN
171 *
172 * Blocked loop of length K
173 *
174  DO i = 1, k, mb
175  ib = min( k-i+1, mb )
176 *
177 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
178 *
179  CALL sgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
180  IF( i+ib.LE.m ) THEN
181 *
182 * Update by applying H**T to A(I:M,I+IB:N) from the right
183 *
184  CALL slarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
185  \$ a( i, i ), lda, t( 1, i ), ldt,
186  \$ a( i+ib, i ), lda, work , m-i-ib+1 )
187  END IF
188  END DO
189  RETURN
190 *
191 * End of SGELQT
192 *
193  END
subroutine sgeqrt2(M, N, A, LDA, T, LDT, INFO)
SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY represen...
Definition: sgeqrt2.f:129
subroutine sgelqt(M, N, MB, A, LDA, T, LDT, WORK, INFO)
Definition: sgelqt.f:124
subroutine slarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: slarfb.f:197
recursive subroutine sgelqt3(M, N, A, LDA, T, LDT, INFO)
Definition: sgelqt3.f:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
recursive subroutine sgeqrt3(M, N, A, LDA, T, LDT, INFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact...
Definition: sgeqrt3.f:134