LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
cungl2.f
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1 *> \brief \b CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CUNGL2( 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 *> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
37 *> which is defined as the first m rows of a product of k elementary
38 *> reflectors of order n
39 *>
40 *> Q = H(k)**H . . . H(2)**H H(1)**H
41 *>
42 *> as returned by CGELQF.
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. N >= M.
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. M >= 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 row must contain the vector which defines
71 *> the elementary reflector H(i), for i = 1,2,...,k, as returned
72 *> by CGELQF in the first k rows of its array argument A.
73 *> On exit, the m by n matrix Q.
74 *> \endverbatim
75 *>
76 *> \param[in] LDA
77 *> \verbatim
78 *> LDA is INTEGER
79 *> The first dimension of the array A. LDA >= max(1,M).
80 *> \endverbatim
81 *>
82 *> \param[in] TAU
83 *> \verbatim
84 *> TAU is COMPLEX array, dimension (K)
85 *> TAU(i) must contain the scalar factor of the elementary
86 *> reflector H(i), as returned by CGELQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is COMPLEX array, dimension (M)
92 *> \endverbatim
93 *>
94 *> \param[out] INFO
95 *> \verbatim
96 *> INFO is INTEGER
97 *> = 0: successful exit
98 *> < 0: if INFO = -i, the i-th argument has an illegal value
99 *> \endverbatim
100 *
101 * Authors:
102 * ========
103 *
104 *> \author Univ. of Tennessee
105 *> \author Univ. of California Berkeley
106 *> \author Univ. of Colorado Denver
107 *> \author NAG Ltd.
108 *
109 *> \date September 2012
110 *
111 *> \ingroup complexOTHERcomputational
112 *
113 * =====================================================================
114  SUBROUTINE cungl2( M, N, K, A, LDA, TAU, WORK, INFO )
115 *
116 * -- LAPACK computational routine (version 3.4.2) --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 * September 2012
120 *
121 * .. Scalar Arguments ..
122  INTEGER info, k, lda, m, n
123 * ..
124 * .. Array Arguments ..
125  COMPLEX a( lda, * ), tau( * ), work( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  COMPLEX one, zero
132  parameter( one = ( 1.0e+0, 0.0e+0 ),
133  \$ zero = ( 0.0e+0, 0.0e+0 ) )
134 * ..
135 * .. Local Scalars ..
136  INTEGER i, j, l
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL clacgv, clarf, cscal, xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC conjg, max
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input arguments
147 *
148  info = 0
149  IF( m.LT.0 ) THEN
150  info = -1
151  ELSE IF( n.LT.m ) THEN
152  info = -2
153  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
154  info = -3
155  ELSE IF( lda.LT.max( 1, m ) ) THEN
156  info = -5
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'CUNGL2', -info )
160  return
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( m.LE.0 )
166  \$ return
167 *
168  IF( k.LT.m ) THEN
169 *
170 * Initialise rows k+1:m to rows of the unit matrix
171 *
172  DO 20 j = 1, n
173  DO 10 l = k + 1, m
174  a( l, j ) = zero
175  10 continue
176  IF( j.GT.k .AND. j.LE.m )
177  \$ a( j, j ) = one
178  20 continue
179  END IF
180 *
181  DO 40 i = k, 1, -1
182 *
183 * Apply H(i)**H to A(i:m,i:n) from the right
184 *
185  IF( i.LT.n ) THEN
186  CALL clacgv( n-i, a( i, i+1 ), lda )
187  IF( i.LT.m ) THEN
188  a( i, i ) = one
189  CALL clarf( 'Right', m-i, n-i+1, a( i, i ), lda,
190  \$ conjg( tau( i ) ), a( i+1, i ), lda, work )
191  END IF
192  CALL cscal( n-i, -tau( i ), a( i, i+1 ), lda )
193  CALL clacgv( n-i, a( i, i+1 ), lda )
194  END IF
195  a( i, i ) = one - conjg( tau( i ) )
196 *
197 * Set A(i,1:i-1,i) to zero
198 *
199  DO 30 l = 1, i - 1
200  a( i, l ) = zero
201  30 continue
202  40 continue
203  return
204 *
205 * End of CUNGL2
206 *
207  END