LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cung2r.f
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1*> \brief \b CUNG2R
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/cung2r.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cung2r.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cung2r.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, K, 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*> CUNG2R generates an m by n complex matrix Q with orthonormal columns,
37*> which is defined as the first n columns of a product of k elementary
38*> reflectors of order m
39*>
40*> Q = H(1) H(2) . . . H(k)
41*>
42*> as returned by CGEQRF.
43*> \endverbatim
44*
45* Arguments:
46* ==========
47*
48*> \param[in] M
49*> \verbatim
50*> M is INTEGER
51*> The number of rows of the matrix Q. M >= 0.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*> N is INTEGER
57*> The number of columns of the matrix Q. M >= N >= 0.
58*> \endverbatim
59*>
60*> \param[in] K
61*> \verbatim
62*> K is INTEGER
63*> The number of elementary reflectors whose product defines the
64*> matrix Q. N >= K >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*> A is COMPLEX array, dimension (LDA,N)
70*> On entry, the i-th column must contain the vector which
71*> defines the elementary reflector H(i), for i = 1,2,...,k, as
72*> returned by CGEQRF in the first k columns of its array
73*> argument A.
74*> On exit, the m by n matrix Q.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*> LDA is INTEGER
80*> The first dimension of the array A. LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[in] TAU
84*> \verbatim
85*> TAU is COMPLEX array, dimension (K)
86*> TAU(i) must contain the scalar factor of the elementary
87*> reflector H(i), as returned by CGEQRF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*> WORK is COMPLEX array, dimension (N)
93*> \endverbatim
94*>
95*> \param[out] INFO
96*> \verbatim
97*> INFO is INTEGER
98*> = 0: successful exit
99*> < 0: if INFO = -i, the i-th argument has an illegal value
100*> \endverbatim
101*
102* Authors:
103* ========
104*
105*> \author Univ. of Tennessee
106*> \author Univ. of California Berkeley
107*> \author Univ. of Colorado Denver
108*> \author NAG Ltd.
109*
110*> \ingroup ung2r
111*
112* =====================================================================
113 SUBROUTINE cung2r( M, N, K, A, LDA, TAU, WORK, INFO )
114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 INTEGER INFO, K, LDA, M, N
121* ..
122* .. Array Arguments ..
123 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 COMPLEX ONE, ZERO
130 parameter( one = ( 1.0e+0, 0.0e+0 ),
131 \$ zero = ( 0.0e+0, 0.0e+0 ) )
132* ..
133* .. Local Scalars ..
134 INTEGER I, J, L
135* ..
136* .. External Subroutines ..
137 EXTERNAL clarf, cscal, xerbla
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC max
141* ..
142* .. Executable Statements ..
143*
144* Test the input arguments
145*
146 info = 0
147 IF( m.LT.0 ) THEN
148 info = -1
149 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
150 info = -2
151 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
152 info = -3
153 ELSE IF( lda.LT.max( 1, m ) ) THEN
154 info = -5
155 END IF
156 IF( info.NE.0 ) THEN
157 CALL xerbla( 'CUNG2R', -info )
158 RETURN
159 END IF
160*
161* Quick return if possible
162*
163 IF( n.LE.0 )
164 \$ RETURN
165*
166* Initialise columns k+1:n to columns of the unit matrix
167*
168 DO 20 j = k + 1, n
169 DO 10 l = 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 a( j, j ) = one
173 20 CONTINUE
174*
175 DO 40 i = k, 1, -1
176*
177* Apply H(i) to A(i:m,i:n) from the left
178*
179 IF( i.LT.n ) THEN
180 a( i, i ) = one
181 CALL clarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
182 \$ a( i, i+1 ), lda, work )
183 END IF
184 IF( i.LT.m )
185 \$ CALL cscal( m-i, -tau( i ), a( i+1, i ), 1 )
186 a( i, i ) = one - tau( i )
187*
188* Set A(1:i-1,i) to zero
189*
190 DO 30 l = 1, i - 1
191 a( l, i ) = zero
192 30 CONTINUE
193 40 CONTINUE
194 RETURN
195*
196* End of CUNG2R
197*
198 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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 cscal(n, ca, cx, incx)
CSCAL
Definition cscal.f:78
subroutine cung2r(m, n, k, a, lda, tau, work, info)
CUNG2R
Definition cung2r.f:114