LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zgeqrt.f
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1*> \brief \b ZGEQRT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqrt.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqrt.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqrt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, LDA, LDT, M, N, NB
25* ..
26* .. Array Arguments ..
27* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> ZGEQRT computes a blocked QR 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] NB
56*> \verbatim
57*> NB is INTEGER
58*> The block size to be used in the blocked QR. MIN(M,N) >= NB >= 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 above the diagonal of the array
66*> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
67*> upper triangular if M >= N); the elements below the diagonal
68*> are the columns 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 >= NB.
89*> \endverbatim
90*>
91*> \param[out] WORK
92*> \verbatim
93*> WORK is COMPLEX*16 array, dimension (NB*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*> \ingroup geqrt
112*
113*> \par Further Details:
114* =====================
115*>
116*> \verbatim
117*>
118*> The matrix V stores the elementary reflectors H(i) in the i-th column
119*> below the diagonal. For example, if M=5 and N=3, the matrix V is
120*>
121*> V = ( 1 )
122*> ( v1 1 )
123*> ( v1 v2 1 )
124*> ( v1 v2 v3 )
125*> ( v1 v2 v3 )
126*>
127*> where the vi's represent the vectors which define H(i), which are returned
128*> in the matrix A. The 1's along the diagonal of V are not stored in A.
129*>
130*> Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each
131*> block is of order NB except for the last block, which is of order
132*> IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block
133*> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
134*> for the last block) T's are stored in the NB-by-K matrix T as
135*>
136*> T = (T1 T2 ... TB).
137*> \endverbatim
138*>
139* =====================================================================
140 SUBROUTINE zgeqrt( M, N, NB, A, LDA, T, LDT, WORK, INFO )
141*
142* -- LAPACK computational routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146* .. Scalar Arguments ..
147 INTEGER INFO, LDA, LDT, M, N, NB
148* ..
149* .. Array Arguments ..
150 COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
151* ..
152*
153* =====================================================================
154*
155* ..
156* .. Local Scalars ..
157 INTEGER I, IB, IINFO, K
158 LOGICAL USE_RECURSIVE_QR
159 parameter( use_recursive_qr=.true. )
160* ..
161* .. External Subroutines ..
162 EXTERNAL zgeqrt2, zgeqrt3, zlarfb, xerbla
163* ..
164* .. Executable Statements ..
165*
166* Test the input arguments
167*
168 info = 0
169 IF( m.LT.0 ) THEN
170 info = -1
171 ELSE IF( n.LT.0 ) THEN
172 info = -2
173 ELSE IF( nb.LT.1 .OR. ( nb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
174 info = -3
175 ELSE IF( lda.LT.max( 1, m ) ) THEN
176 info = -5
177 ELSE IF( ldt.LT.nb ) THEN
178 info = -7
179 END IF
180 IF( info.NE.0 ) THEN
181 CALL xerbla( 'ZGEQRT', -info )
182 RETURN
183 END IF
184*
185* Quick return if possible
186*
187 k = min( m, n )
188 IF( k.EQ.0 ) RETURN
189*
190* Blocked loop of length K
191*
192 DO i = 1, k, nb
193 ib = min( k-i+1, nb )
194*
195* Compute the QR factorization of the current block A(I:M,I:I+IB-1)
196*
197 IF( use_recursive_qr ) THEN
198 CALL zgeqrt3( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
199 ELSE
200 CALL zgeqrt2( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
201 END IF
202 IF( i+ib.LE.n ) THEN
203*
204* Update by applying H**H to A(I:M,I+IB:N) from the left
205*
206 CALL zlarfb( 'L', 'C', 'F', 'C', m-i+1, n-i-ib+1, ib,
207 \$ a( i, i ), lda, t( 1, i ), ldt,
208 \$ a( i, i+ib ), lda, work , n-i-ib+1 )
209 END IF
210 END DO
211 RETURN
212*
213* End of ZGEQRT
214*
215 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zgeqrt2(m, n, a, lda, t, ldt, info)
ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY represen...
Definition zgeqrt2.f:127
recursive subroutine zgeqrt3(m, n, a, lda, t, ldt, info)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact...
Definition zgeqrt3.f:132
subroutine zgeqrt(m, n, nb, a, lda, t, ldt, work, info)
ZGEQRT
Definition zgeqrt.f:141
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