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*> \date November 2011
123*
124*> \ingroup complexOTHERcomputational
125*
126*  =====================================================================
127      SUBROUTINE CUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
128*
129*  -- LAPACK computational routine (version 3.4.0) --
130*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
131*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*     November 2011
133*
134*     .. Scalar Arguments ..
135      INTEGER            IHI, ILO, INFO, LDA, LWORK, N
136*     ..
137*     .. Array Arguments ..
138      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
139*     ..
140*
141*  =====================================================================
142*
143*     .. Parameters ..
144      COMPLEX            ZERO, ONE
145      PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ),
146     $                   ONE = ( 1.0E+0, 0.0E+0 ) )
147*     ..
148*     .. Local Scalars ..
149      LOGICAL            LQUERY
150      INTEGER            I, IINFO, J, LWKOPT, NB, NH
151*     ..
152*     .. External Subroutines ..
153      EXTERNAL           CUNGQR, XERBLA
154*     ..
155*     .. External Functions ..
156      INTEGER            ILAENV
157      EXTERNAL           ILAENV
158*     ..
159*     .. Intrinsic Functions ..
160      INTRINSIC          MAX, MIN
161*     ..
162*     .. Executable Statements ..
163*
164*     Test the input arguments
165*
166      INFO = 0
167      NH = IHI - ILO
168      LQUERY = ( LWORK.EQ.-1 )
169      IF( N.LT.0 ) THEN
170         INFO = -1
171      ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
172         INFO = -2
173      ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
174         INFO = -3
175      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
176         INFO = -5
177      ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
178         INFO = -8
179      END IF
180*
181      IF( INFO.EQ.0 ) THEN
182         NB = ILAENV( 1, 'CUNGQR', ' ', NH, NH, NH, -1 )
183         LWKOPT = MAX( 1, NH )*NB
184         WORK( 1 ) = LWKOPT
185      END IF
186*
187      IF( INFO.NE.0 ) THEN
188         CALL XERBLA( 'CUNGHR', -INFO )
189         RETURN
190      ELSE IF( LQUERY ) THEN
191         RETURN
192      END IF
193*
194*     Quick return if possible
195*
196      IF( N.EQ.0 ) THEN
197         WORK( 1 ) = 1
198         RETURN
199      END IF
200*
201*     Shift the vectors which define the elementary reflectors one
202*     column to the right, and set the first ilo and the last n-ihi
203*     rows and columns to those of the unit matrix
204*
205      DO 40 J = IHI, ILO + 1, -1
206         DO 10 I = 1, J - 1
207            A( I, J ) = ZERO
208   10    CONTINUE
209         DO 20 I = J + 1, IHI
210            A( I, J ) = A( I, J-1 )
211   20    CONTINUE
212         DO 30 I = IHI + 1, N
213            A( I, J ) = ZERO
214   30    CONTINUE
215   40 CONTINUE
216      DO 60 J = 1, ILO
217         DO 50 I = 1, N
218            A( I, J ) = ZERO
219   50    CONTINUE
220         A( J, J ) = ONE
221   60 CONTINUE
222      DO 80 J = IHI + 1, N
223         DO 70 I = 1, N
224            A( I, J ) = ZERO
225   70    CONTINUE
226         A( J, J ) = ONE
227   80 CONTINUE
228*
229      IF( NH.GT.0 ) THEN
230*
231*        Generate Q(ilo+1:ihi,ilo+1:ihi)
232*
233         CALL CUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
234     $                WORK, LWORK, IINFO )
235      END IF
236      WORK( 1 ) = LWKOPT
237      RETURN
238*
239*     End of CUNGHR
240*
241      END
242c $Id$
243