LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cunghr.f
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1 *> \brief \b CUNGHR
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 CUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER IHI, ILO, INFO, LDA, LWORK, N
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CUNGHR generates a complex unitary matrix Q which is defined as the
37 *> product of IHI-ILO elementary reflectors of order N, as returned by
38 *> CGEHRD:
39 *>
40 *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
41 *> \endverbatim
42 *
43 * Arguments:
44 * ==========
45 *
46 *> \param[in] N
47 *> \verbatim
48 *> N is INTEGER
49 *> The order of the matrix Q. N >= 0.
50 *> \endverbatim
51 *>
52 *> \param[in] ILO
53 *> \verbatim
54 *> ILO is INTEGER
55 *> \endverbatim
56 *>
57 *> \param[in] IHI
58 *> \verbatim
59 *> IHI is INTEGER
60 *>
61 *> ILO and IHI must have the same values as in the previous call
62 *> of CGEHRD. Q is equal to the unit matrix except in the
63 *> submatrix Q(ilo+1:ihi,ilo+1:ihi).
64 *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
65 *> \endverbatim
66 *>
67 *> \param[in,out] A
68 *> \verbatim
69 *> A is COMPLEX array, dimension (LDA,N)
70 *> On entry, the vectors which define the elementary reflectors,
71 *> as returned by CGEHRD.
72 *> On exit, the N-by-N unitary matrix Q.
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of the array A. LDA >= max(1,N).
79 *> \endverbatim
80 *>
81 *> \param[in] TAU
82 *> \verbatim
83 *> TAU is COMPLEX array, dimension (N-1)
84 *> TAU(i) must contain the scalar factor of the elementary
85 *> reflector H(i), as returned by CGEHRD.
86 *> \endverbatim
87 *>
88 *> \param[out] WORK
89 *> \verbatim
90 *> WORK is COMPLEX array, dimension (MAX(1,LWORK))
91 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
92 *> \endverbatim
93 *>
94 *> \param[in] LWORK
95 *> \verbatim
96 *> LWORK is INTEGER
97 *> The dimension of the array WORK. LWORK >= IHI-ILO.
98 *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
99 *> the optimal blocksize.
100 *>
101 *> If LWORK = -1, then a workspace query is assumed; the routine
102 *> only calculates the optimal size of the WORK array, returns
103 *> this value as the first entry of the WORK array, and no error
104 *> message related to LWORK is issued by XERBLA.
105 *> \endverbatim
106 *>
107 *> \param[out] INFO
108 *> \verbatim
109 *> INFO is INTEGER
110 *> = 0: successful exit
111 *> < 0: if INFO = -i, the i-th argument had an illegal value
112 *> \endverbatim
113 *
114 * Authors:
115 * ========
116 *
117 *> \author Univ. of Tennessee
118 *> \author Univ. of California Berkeley
119 *> \author Univ. of Colorado Denver
120 *> \author NAG Ltd.
121 *
122 *> \ingroup complexOTHERcomputational
123 *
124 * =====================================================================
125  SUBROUTINE cunghr( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
126 *
127 * -- LAPACK computational routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  INTEGER IHI, ILO, INFO, LDA, LWORK, N
133 * ..
134 * .. Array Arguments ..
135  COMPLEX A( LDA, * ), TAU( * ), WORK( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  COMPLEX ZERO, ONE
142  parameter( zero = ( 0.0e+0, 0.0e+0 ),
143  $ one = ( 1.0e+0, 0.0e+0 ) )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL LQUERY
147  INTEGER I, IINFO, J, LWKOPT, NB, NH
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL cungqr, xerbla
151 * ..
152 * .. External Functions ..
153  INTEGER ILAENV
154  EXTERNAL ilaenv
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC max, min
158 * ..
159 * .. Executable Statements ..
160 *
161 * Test the input arguments
162 *
163  info = 0
164  nh = ihi - ilo
165  lquery = ( lwork.EQ.-1 )
166  IF( n.LT.0 ) THEN
167  info = -1
168  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
169  info = -2
170  ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
171  info = -3
172  ELSE IF( lda.LT.max( 1, n ) ) THEN
173  info = -5
174  ELSE IF( lwork.LT.max( 1, nh ) .AND. .NOT.lquery ) THEN
175  info = -8
176  END IF
177 *
178  IF( info.EQ.0 ) THEN
179  nb = ilaenv( 1, 'CUNGQR', ' ', nh, nh, nh, -1 )
180  lwkopt = max( 1, nh )*nb
181  work( 1 ) = lwkopt
182  END IF
183 *
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'CUNGHR', -info )
186  RETURN
187  ELSE IF( lquery ) THEN
188  RETURN
189  END IF
190 *
191 * Quick return if possible
192 *
193  IF( n.EQ.0 ) THEN
194  work( 1 ) = 1
195  RETURN
196  END IF
197 *
198 * Shift the vectors which define the elementary reflectors one
199 * column to the right, and set the first ilo and the last n-ihi
200 * rows and columns to those of the unit matrix
201 *
202  DO 40 j = ihi, ilo + 1, -1
203  DO 10 i = 1, j - 1
204  a( i, j ) = zero
205  10 CONTINUE
206  DO 20 i = j + 1, ihi
207  a( i, j ) = a( i, j-1 )
208  20 CONTINUE
209  DO 30 i = ihi + 1, n
210  a( i, j ) = zero
211  30 CONTINUE
212  40 CONTINUE
213  DO 60 j = 1, ilo
214  DO 50 i = 1, n
215  a( i, j ) = zero
216  50 CONTINUE
217  a( j, j ) = one
218  60 CONTINUE
219  DO 80 j = ihi + 1, n
220  DO 70 i = 1, n
221  a( i, j ) = zero
222  70 CONTINUE
223  a( j, j ) = one
224  80 CONTINUE
225 *
226  IF( nh.GT.0 ) THEN
227 *
228 * Generate Q(ilo+1:ihi,ilo+1:ihi)
229 *
230  CALL cungqr( nh, nh, nh, a( ilo+1, ilo+1 ), lda, tau( ilo ),
231  $ work, lwork, iinfo )
232  END IF
233  work( 1 ) = lwkopt
234  RETURN
235 *
236 * End of CUNGHR
237 *
238  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cunghr(N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
CUNGHR
Definition: cunghr.f:126
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:128