LAPACK  3.9.1
LAPACK: Linear Algebra PACKage
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 *
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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 complexOTHERcomputational
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)
XERBLA
Definition: xerbla.f:60
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
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 cung2r(M, N, K, A, LDA, TAU, WORK, INFO)
CUNG2R
Definition: cung2r.f:114