LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zung2l.f
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1*> \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (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/zung2l.f">
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zung2l.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZUNG2L( 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*16 A( LDA, * ), TAU( * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
37*> which is defined as the last n columns of a product of k elementary
38*> reflectors of order m
39*>
40*> Q = H(k) . . . H(2) H(1)
41*>
42*> as returned by ZGEQLF.
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*16 array, dimension (LDA,N)
70*> On entry, the (n-k+i)-th column must contain the vector which
71*> defines the elementary reflector H(i), for i = 1,2,...,k, as
72*> returned by ZGEQLF in the last 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*16 array, dimension (K)
86*> TAU(i) must contain the scalar factor of the elementary
87*> reflector H(i), as returned by ZGEQLF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*> WORK is COMPLEX*16 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 ung2l
111*
112* =====================================================================
113 SUBROUTINE zung2l( 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*16 A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 COMPLEX*16 ONE, ZERO
130 parameter( one = ( 1.0d+0, 0.0d+0 ),
131 \$ zero = ( 0.0d+0, 0.0d+0 ) )
132* ..
133* .. Local Scalars ..
134 INTEGER I, II, J, L
135* ..
136* .. External Subroutines ..
137 EXTERNAL xerbla, zlarf, zscal
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( 'ZUNG2L', -info )
158 RETURN
159 END IF
160*
161* Quick return if possible
162*
163 IF( n.LE.0 )
164 \$ RETURN
165*
166* Initialise columns 1:n-k to columns of the unit matrix
167*
168 DO 20 j = 1, n - k
169 DO 10 l = 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 a( m-n+j, j ) = one
173 20 CONTINUE
174*
175 DO 40 i = 1, k
176 ii = n - k + i
177*
178* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
179*
180 a( m-n+ii, ii ) = one
181 CALL zlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
182 \$ lda, work )
183 CALL zscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
184 a( m-n+ii, ii ) = one - tau( i )
185*
186* Set A(m-k+i+1:m,n-k+i) to zero
187*
188 DO 30 l = m - n + ii + 1, m
189 a( l, ii ) = zero
190 30 CONTINUE
191 40 CONTINUE
192 RETURN
193*
194* End of ZUNG2L
195*
196 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zlarf(side, m, n, v, incv, tau, c, ldc, work)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition zlarf.f:128
subroutine zscal(n, za, zx, incx)
ZSCAL
Definition zscal.f:78
subroutine zung2l(m, n, k, a, lda, tau, work, info)
ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (un...
Definition zung2l.f:114