LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
cgeqr2.f
Go to the documentation of this file.
1*> \brief \b CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
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/cgeqr2.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqr2.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqr2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, LDA, M, N
25* ..
26* .. Array Arguments ..
27* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> CGEQR2 computes a QR factorization of a complex m-by-n matrix A:
37*>
38*> A = Q * ( R ),
39*> ( 0 )
40*>
41*> where:
42*>
43*> Q is a m-by-m orthogonal matrix;
44*> R is an upper-triangular n-by-n matrix;
45*> 0 is a (m-n)-by-n zero matrix, if m > n.
46*>
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] M
53*> \verbatim
54*> M is INTEGER
55*> The number of rows of the matrix A. M >= 0.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The number of columns of the matrix A. N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] A
65*> \verbatim
66*> A is COMPLEX array, dimension (LDA,N)
67*> On entry, the m by n matrix A.
68*> On exit, the elements on and above the diagonal of the array
69*> contain the min(m,n) by n upper trapezoidal matrix R (R is
70*> upper triangular if m >= n); the elements below the diagonal,
71*> with the array TAU, represent the unitary matrix Q as a
72*> product of elementary reflectors (see Further Details).
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*> LDA is INTEGER
78*> The leading dimension of the array A. LDA >= max(1,M).
79*> \endverbatim
80*>
81*> \param[out] TAU
82*> \verbatim
83*> TAU is COMPLEX array, dimension (min(M,N))
84*> The scalar factors of the elementary reflectors (see Further
85*> Details).
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*> WORK is COMPLEX array, dimension (N)
91*> \endverbatim
92*>
93*> \param[out] INFO
94*> \verbatim
95*> INFO is INTEGER
96*> = 0: successful exit
97*> < 0: if INFO = -i, the i-th argument had an illegal value
98*> \endverbatim
99*
100* Authors:
101* ========
102*
103*> \author Univ. of Tennessee
104*> \author Univ. of California Berkeley
105*> \author Univ. of Colorado Denver
106*> \author NAG Ltd.
107*
108*> \ingroup complexGEcomputational
109*
110*> \par Further Details:
111* =====================
112*>
113*> \verbatim
114*>
115*> The matrix Q is represented as a product of elementary reflectors
116*>
117*> Q = H(1) H(2) . . . H(k), where k = min(m,n).
118*>
119*> Each H(i) has the form
120*>
121*> H(i) = I - tau * v * v**H
122*>
123*> where tau is a complex scalar, and v is a complex vector with
124*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
125*> and tau in TAU(i).
126*> \endverbatim
127*>
128* =====================================================================
129 SUBROUTINE cgeqr2( M, N, A, LDA, TAU, WORK, INFO )
130*
131* -- LAPACK computational routine --
132* -- LAPACK is a software package provided by Univ. of Tennessee, --
133* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135* .. Scalar Arguments ..
136 INTEGER INFO, LDA, M, N
137* ..
138* .. Array Arguments ..
139 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 COMPLEX ONE
146 parameter( one = ( 1.0e+0, 0.0e+0 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER I, K
150 COMPLEX ALPHA
151* ..
152* .. External Subroutines ..
153 EXTERNAL clarf, clarfg, xerbla
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC conjg, max, min
157* ..
158* .. Executable Statements ..
159*
160* Test the input arguments
161*
162 info = 0
163 IF( m.LT.0 ) THEN
164 info = -1
165 ELSE IF( n.LT.0 ) THEN
166 info = -2
167 ELSE IF( lda.LT.max( 1, m ) ) THEN
168 info = -4
169 END IF
170 IF( info.NE.0 ) THEN
171 CALL xerbla( 'CGEQR2', -info )
172 RETURN
173 END IF
174*
175 k = min( m, n )
176*
177 DO 10 i = 1, k
178*
179* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
180*
181 CALL clarfg( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
182 \$ tau( i ) )
183 IF( i.LT.n ) THEN
184*
185* Apply H(i)**H to A(i:m,i+1:n) from the left
186*
187 alpha = a( i, i )
188 a( i, i ) = one
189 CALL clarf( 'Left', m-i+1, n-i, a( i, i ), 1,
190 \$ conjg( tau( i ) ), a( i, i+1 ), lda, work )
191 a( i, i ) = alpha
192 END IF
193 10 CONTINUE
194 RETURN
195*
196* End of CGEQR2
197*
198 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgeqr2(M, N, A, LDA, TAU, WORK, INFO)
CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
Definition: cgeqr2.f:130
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128
subroutine clarfg(N, ALPHA, X, INCX, TAU)
CLARFG generates an elementary reflector (Householder matrix).
Definition: clarfg.f:106