LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zupgtr.f
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1 *> \brief \b ZUPGTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDQ, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZUPGTR generates a complex unitary matrix Q which is defined as the
38 *> product of n-1 elementary reflectors H(i) of order n, as returned by
39 *> ZHPTRD using packed storage:
40 *>
41 *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
42 *>
43 *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] UPLO
50 *> \verbatim
51 *> UPLO is CHARACTER*1
52 *> = 'U': Upper triangular packed storage used in previous
53 *> call to ZHPTRD;
54 *> = 'L': Lower triangular packed storage used in previous
55 *> call to ZHPTRD.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The order of the matrix Q. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] AP
65 *> \verbatim
66 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
67 *> The vectors which define the elementary reflectors, as
68 *> returned by ZHPTRD.
69 *> \endverbatim
70 *>
71 *> \param[in] TAU
72 *> \verbatim
73 *> TAU is COMPLEX*16 array, dimension (N-1)
74 *> TAU(i) must contain the scalar factor of the elementary
75 *> reflector H(i), as returned by ZHPTRD.
76 *> \endverbatim
77 *>
78 *> \param[out] Q
79 *> \verbatim
80 *> Q is COMPLEX*16 array, dimension (LDQ,N)
81 *> The N-by-N unitary matrix Q.
82 *> \endverbatim
83 *>
84 *> \param[in] LDQ
85 *> \verbatim
86 *> LDQ is INTEGER
87 *> The leading dimension of the array Q. LDQ >= max(1,N).
88 *> \endverbatim
89 *>
90 *> \param[out] WORK
91 *> \verbatim
92 *> WORK is COMPLEX*16 array, dimension (N-1)
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 had 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 complex16OTHERcomputational
111 *
112 * =====================================================================
113  SUBROUTINE zupgtr( UPLO, N, AP, TAU, Q, LDQ, 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  CHARACTER UPLO
121  INTEGER INFO, LDQ, N
122 * ..
123 * .. Array Arguments ..
124  COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  COMPLEX*16 CZERO, CONE
131  parameter( czero = ( 0.0d+0, 0.0d+0 ),
132  $ cone = ( 1.0d+0, 0.0d+0 ) )
133 * ..
134 * .. Local Scalars ..
135  LOGICAL UPPER
136  INTEGER I, IINFO, IJ, J
137 * ..
138 * .. External Functions ..
139  LOGICAL LSAME
140  EXTERNAL lsame
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL xerbla, zung2l, zung2r
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC max
147 * ..
148 * .. Executable Statements ..
149 *
150 * Test the input arguments
151 *
152  info = 0
153  upper = lsame( uplo, 'U' )
154  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
155  info = -1
156  ELSE IF( n.LT.0 ) THEN
157  info = -2
158  ELSE IF( ldq.LT.max( 1, n ) ) THEN
159  info = -6
160  END IF
161  IF( info.NE.0 ) THEN
162  CALL xerbla( 'ZUPGTR', -info )
163  RETURN
164  END IF
165 *
166 * Quick return if possible
167 *
168  IF( n.EQ.0 )
169  $ RETURN
170 *
171  IF( upper ) THEN
172 *
173 * Q was determined by a call to ZHPTRD with UPLO = 'U'
174 *
175 * Unpack the vectors which define the elementary reflectors and
176 * set the last row and column of Q equal to those of the unit
177 * matrix
178 *
179  ij = 2
180  DO 20 j = 1, n - 1
181  DO 10 i = 1, j - 1
182  q( i, j ) = ap( ij )
183  ij = ij + 1
184  10 CONTINUE
185  ij = ij + 2
186  q( n, j ) = czero
187  20 CONTINUE
188  DO 30 i = 1, n - 1
189  q( i, n ) = czero
190  30 CONTINUE
191  q( n, n ) = cone
192 *
193 * Generate Q(1:n-1,1:n-1)
194 *
195  CALL zung2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
196 *
197  ELSE
198 *
199 * Q was determined by a call to ZHPTRD with UPLO = 'L'.
200 *
201 * Unpack the vectors which define the elementary reflectors and
202 * set the first row and column of Q equal to those of the unit
203 * matrix
204 *
205  q( 1, 1 ) = cone
206  DO 40 i = 2, n
207  q( i, 1 ) = czero
208  40 CONTINUE
209  ij = 3
210  DO 60 j = 2, n
211  q( 1, j ) = czero
212  DO 50 i = j + 1, n
213  q( i, j ) = ap( ij )
214  ij = ij + 1
215  50 CONTINUE
216  ij = ij + 2
217  60 CONTINUE
218  IF( n.GT.1 ) THEN
219 *
220 * Generate Q(2:n,2:n)
221 *
222  CALL zung2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
223  $ iinfo )
224  END IF
225  END IF
226  RETURN
227 *
228 * End of ZUPGTR
229 *
230  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zung2r(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNG2R
Definition: zung2r.f:114
subroutine zupgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
ZUPGTR
Definition: zupgtr.f:114
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