LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zung2r.f
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1 *> \brief \b ZUNG2R
2 *
3 * =========== DOCUMENTATION ===========
4 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUNG2R( 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 *> ZUNG2R 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 ZGEQRF.
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 i-th column must contain the vector which
71 *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72 *> returned by ZGEQRF 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*16 array, dimension (K)
86 *> TAU(i) must contain the scalar factor of the elementary
87 *> reflector H(i), as returned by ZGEQRF.
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 *> \date November 2011
111 *
112 *> \ingroup complex16OTHERcomputational
113 *
114 * =====================================================================
115  SUBROUTINE zung2r( M, N, K, A, LDA, TAU, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.4.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * November 2011
121 *
122 * .. Scalar Arguments ..
123  INTEGER INFO, K, LDA, M, N
124 * ..
125 * .. Array Arguments ..
126  COMPLEX*16 A( lda, * ), TAU( * ), WORK( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  COMPLEX*16 ONE, ZERO
133  parameter ( one = ( 1.0d+0, 0.0d+0 ),
134  \$ zero = ( 0.0d+0, 0.0d+0 ) )
135 * ..
136 * .. Local Scalars ..
137  INTEGER I, J, L
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL xerbla, zlarf, zscal
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input arguments
148 *
149  info = 0
150  IF( m.LT.0 ) THEN
151  info = -1
152  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
153  info = -2
154  ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
155  info = -3
156  ELSE IF( lda.LT.max( 1, m ) ) THEN
157  info = -5
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'ZUNG2R', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( n.LE.0 )
167  \$ RETURN
168 *
169 * Initialise columns k+1:n to columns of the unit matrix
170 *
171  DO 20 j = k + 1, n
172  DO 10 l = 1, m
173  a( l, j ) = zero
174  10 CONTINUE
175  a( j, j ) = one
176  20 CONTINUE
177 *
178  DO 40 i = k, 1, -1
179 *
180 * Apply H(i) to A(i:m,i:n) from the left
181 *
182  IF( i.LT.n ) THEN
183  a( i, i ) = one
184  CALL zlarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
185  \$ a( i, i+1 ), lda, work )
186  END IF
187  IF( i.LT.m )
188  \$ CALL zscal( m-i, -tau( i ), a( i+1, i ), 1 )
189  a( i, i ) = one - tau( i )
190 *
191 * Set A(1:i-1,i) to zero
192 *
193  DO 30 l = 1, i - 1
194  a( l, i ) = zero
195  30 CONTINUE
196  40 CONTINUE
197  RETURN
198 *
199 * End of ZUNG2R
200 *
201  END
subroutine zung2r(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNG2R
Definition: zung2r.f:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:130
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:54