LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zungr2.f
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1 *> \brief \b ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUNGR2( 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 *> ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
37 *> which is defined as the last m rows of a product of k elementary
38 *> reflectors of order n
39 *>
40 *> Q = H(1)**H H(2)**H . . . H(k)**H
41 *>
42 *> as returned by ZGERQF.
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*16 array, dimension (LDA,N)
70 *> On entry, the (m-k+i)-th row must contain the vector which
71 *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72 *> returned by ZGERQF in the last k rows of its array argument
73 *> 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 ZGERQF.
88 *> \endverbatim
89 *>
90 *> \param[out] WORK
91 *> \verbatim
92 *> WORK is COMPLEX*16 array, dimension (M)
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 September 2012
111 *
112 *> \ingroup complex16OTHERcomputational
113 *
114 * =====================================================================
115  SUBROUTINE zungr2( M, N, K, A, LDA, TAU, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.4.2) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * September 2012
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, II, J, L
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL xerbla, zlacgv, zlarf, zscal
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC dconjg, 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.m ) THEN
153  info = -2
154  ELSE IF( k.LT.0 .OR. k.GT.m ) 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( 'ZUNGR2', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( m.LE.0 )
167  \$ RETURN
168 *
169  IF( k.LT.m ) THEN
170 *
171 * Initialise rows 1:m-k to rows of the unit matrix
172 *
173  DO 20 j = 1, n
174  DO 10 l = 1, m - k
175  a( l, j ) = zero
176  10 CONTINUE
177  IF( j.GT.n-m .AND. j.LE.n-k )
178  \$ a( m-n+j, j ) = one
179  20 CONTINUE
180  END IF
181 *
182  DO 40 i = 1, k
183  ii = m - k + i
184 *
185 * Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
186 *
187  CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
188  a( ii, n-m+ii ) = one
189  CALL zlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda,
190  \$ dconjg( tau( i ) ), a, lda, work )
191  CALL zscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
192  CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
193  a( ii, n-m+ii ) = one - dconjg( tau( i ) )
194 *
195 * Set A(m-k+i,n-k+i+1:n) to zero
196 *
197  DO 30 l = n - m + ii + 1, n
198  a( ii, l ) = zero
199  30 CONTINUE
200  40 CONTINUE
201  RETURN
202 *
203 * End of ZUNGR2
204 *
205  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zungr2(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (u...
Definition: zungr2.f:116
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
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76