LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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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*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunghr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunghr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunghr.f">
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 unghr
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 REAL SROUNDUP_LWORK
155 EXTERNAL ilaenv, sroundup_lwork
156* ..
157* .. Intrinsic Functions ..
158 INTRINSIC max, min
159* ..
160* .. Executable Statements ..
161*
162* Test the input arguments
163*
164 info = 0
165 nh = ihi - ilo
166 lquery = ( lwork.EQ.-1 )
167 IF( n.LT.0 ) THEN
168 info = -1
169 ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
170 info = -2
171 ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
172 info = -3
173 ELSE IF( lda.LT.max( 1, n ) ) THEN
174 info = -5
175 ELSE IF( lwork.LT.max( 1, nh ) .AND. .NOT.lquery ) THEN
176 info = -8
177 END IF
178*
179 IF( info.EQ.0 ) THEN
180 nb = ilaenv( 1, 'CUNGQR', ' ', nh, nh, nh, -1 )
181 lwkopt = max( 1, nh )*nb
182 work( 1 ) = sroundup_lwork(lwkopt)
183 END IF
184*
185 IF( info.NE.0 ) THEN
186 CALL xerbla( 'CUNGHR', -info )
187 RETURN
188 ELSE IF( lquery ) THEN
189 RETURN
190 END IF
191*
192* Quick return if possible
193*
194 IF( n.EQ.0 ) THEN
195 work( 1 ) = 1
196 RETURN
197 END IF
198*
199* Shift the vectors which define the elementary reflectors one
200* column to the right, and set the first ilo and the last n-ihi
201* rows and columns to those of the unit matrix
202*
203 DO 40 j = ihi, ilo + 1, -1
204 DO 10 i = 1, j - 1
205 a( i, j ) = zero
206 10 CONTINUE
207 DO 20 i = j + 1, ihi
208 a( i, j ) = a( i, j-1 )
209 20 CONTINUE
210 DO 30 i = ihi + 1, n
211 a( i, j ) = zero
212 30 CONTINUE
213 40 CONTINUE
214 DO 60 j = 1, ilo
215 DO 50 i = 1, n
216 a( i, j ) = zero
217 50 CONTINUE
218 a( j, j ) = one
219 60 CONTINUE
220 DO 80 j = ihi + 1, n
221 DO 70 i = 1, n
222 a( i, j ) = zero
223 70 CONTINUE
224 a( j, j ) = one
225 80 CONTINUE
226*
227 IF( nh.GT.0 ) THEN
228*
229* Generate Q(ilo+1:ihi,ilo+1:ihi)
230*
231 CALL cungqr( nh, nh, nh, a( ilo+1, ilo+1 ), lda, tau( ilo ),
232 \$ work, lwork, iinfo )
233 END IF
234 work( 1 ) = sroundup_lwork(lwkopt)
235 RETURN
236*
237* End of CUNGHR
238*
239 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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