1*> \brief \b ZUNGHR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNGHR( 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*16         A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> ZUNGHR 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*> ZGEHRD:
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 ZGEHRD. 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*16 array, dimension (LDA,N)
70*>          On entry, the vectors which define the elementary reflectors,
71*>          as returned by ZGEHRD.
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*16 array, dimension (N-1)
84*>          TAU(i) must contain the scalar factor of the elementary
85*>          reflector H(i), as returned by ZGEHRD.
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*>          WORK is COMPLEX*16 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 complex16OTHERcomputational
123*
124*  =====================================================================
125      SUBROUTINE ZUNGHR( 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*16         A( LDA, * ), TAU( * ), WORK( * )
136*     ..
137*
138*  =====================================================================
139*
140*     .. Parameters ..
141      COMPLEX*16         ZERO, ONE
142      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
143     $                   ONE = ( 1.0D+0, 0.0D+0 ) )
144*     ..
145*     .. Local Scalars ..
146      LOGICAL            LQUERY
147      INTEGER            I, IINFO, J, LWKOPT, NB, NH
148*     ..
149*     .. External Subroutines ..
150      EXTERNAL           XERBLA, ZUNGQR
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, 'ZUNGQR', ' ', 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( 'ZUNGHR', -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 ZUNGQR( 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 ZUNGHR
237*
238      END
239