LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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cgelqt.f
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1*> \brief \b CGELQT
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE CGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
7*
8* .. Scalar Arguments ..
9* INTEGER INFO, LDA, LDT, M, N, MB
10* ..
11* .. Array Arguments ..
12* COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
13* ..
14*
15*
16*> \par Purpose:
17* =============
18*>
19*> \verbatim
20*>
21*> CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A
22*> using the compact WY representation of Q.
23*> \endverbatim
24*
25* Arguments:
26* ==========
27*
28*> \param[in] M
29*> \verbatim
30*> M is INTEGER
31*> The number of rows of the matrix A. M >= 0.
32*> \endverbatim
33*>
34*> \param[in] N
35*> \verbatim
36*> N is INTEGER
37*> The number of columns of the matrix A. N >= 0.
38*> \endverbatim
39*>
40*> \param[in] MB
41*> \verbatim
42*> MB is INTEGER
43*> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
44*> \endverbatim
45*>
46*> \param[in,out] A
47*> \verbatim
48*> A is COMPLEX array, dimension (LDA,N)
49*> On entry, the M-by-N matrix A.
50*> On exit, the elements on and below the diagonal of the array
51*> contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
52*> lower triangular if M <= N); the elements above the diagonal
53*> are the rows of V.
54*> \endverbatim
55*>
56*> \param[in] LDA
57*> \verbatim
58*> LDA is INTEGER
59*> The leading dimension of the array A. LDA >= max(1,M).
60*> \endverbatim
61*>
62*> \param[out] T
63*> \verbatim
64*> T is COMPLEX array, dimension (LDT,MIN(M,N))
65*> The upper triangular block reflectors stored in compact form
66*> as a sequence of upper triangular blocks. See below
67*> for further details.
68*> \endverbatim
69*>
70*> \param[in] LDT
71*> \verbatim
72*> LDT is INTEGER
73*> The leading dimension of the array T. LDT >= MB.
74*> \endverbatim
75*>
76*> \param[out] WORK
77*> \verbatim
78*> WORK is COMPLEX array, dimension (MB*N)
79*> \endverbatim
80*>
81*> \param[out] INFO
82*> \verbatim
83*> INFO is INTEGER
84*> = 0: successful exit
85*> < 0: if INFO = -i, the i-th argument had an illegal value
86*> \endverbatim
87*
88* Authors:
89* ========
90*
91*> \author Univ. of Tennessee
92*> \author Univ. of California Berkeley
93*> \author Univ. of Colorado Denver
94*> \author NAG Ltd.
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 cgelqt( M, N, MB, A, LDA, T, LDT, WORK, INFO )
124*
125* -- LAPACK computational routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 INTEGER INFO, LDA, LDT, M, N, MB
131* ..
132* .. Array Arguments ..
133 COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
134* ..
135*
136* =====================================================================
137*
138* ..
139* .. Local Scalars ..
140 INTEGER I, IB, IINFO, K
141* ..
142* .. External Subroutines ..
143 EXTERNAL cgelqt3, clarfb, xerbla
144* ..
145* .. Executable Statements ..
146*
147* Test the input arguments
148*
149 info = 0
150 IF( m.LT.0 ) THEN
151 info = -1
152 ELSE IF( n.LT.0 ) THEN
153 info = -2
154 ELSE IF( mb.LT.1 .OR. (mb.GT.min(m,n) .AND. min(m,n).GT.0 ))THEN
155 info = -3
156 ELSE IF( lda.LT.max( 1, m ) ) THEN
157 info = -5
158 ELSE IF( ldt.LT.mb ) THEN
159 info = -7
160 END IF
161 IF( info.NE.0 ) THEN
162 CALL xerbla( 'CGELQT', -info )
163 RETURN
164 END IF
165*
166* Quick return if possible
167*
168 k = min( m, n )
169 IF( k.EQ.0 ) RETURN
170*
171* Blocked loop of length K
172*
173 DO i = 1, k, mb
174 ib = min( k-i+1, mb )
175*
176* Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
177*
178 CALL cgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
179 IF( i+ib.LE.m ) THEN
180*
181* Update by applying H**T to A(I:M,I+IB:N) from the right
182*
183 CALL clarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
184 \$ a( i, i ), lda, t( 1, i ), ldt,
185 \$ a( i+ib, i ), lda, work , m-i-ib+1 )
186 END IF
187 END DO
188 RETURN
189*
190* End of CGELQT
191*
192 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: clarfb.f:197
subroutine cgelqt(M, N, MB, A, LDA, T, LDT, WORK, INFO)
CGELQT
Definition: cgelqt.f:124
recursive subroutine cgelqt3(M, N, A, LDA, T, LDT, INFO)
CGELQT3
Definition: cgelqt3.f:116