1*> \brief \b ZUNGTR
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 ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          UPLO
25*       INTEGER            INFO, LDA, LWORK, N
26*       ..
27*       .. Array Arguments ..
28*       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> ZUNGTR generates a complex unitary matrix Q which is defined as the
38*> product of n-1 elementary reflectors of order N, as returned by
39*> ZHETRD:
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 triangle of A contains elementary reflectors
53*>                 from ZHETRD;
54*>          = 'L': Lower triangle of A contains elementary reflectors
55*>                 from ZHETRD.
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,out] A
65*> \verbatim
66*>          A is COMPLEX*16 array, dimension (LDA,N)
67*>          On entry, the vectors which define the elementary reflectors,
68*>          as returned by ZHETRD.
69*>          On exit, the N-by-N unitary matrix Q.
70*> \endverbatim
71*>
72*> \param[in] LDA
73*> \verbatim
74*>          LDA is INTEGER
75*>          The leading dimension of the array A. LDA >= N.
76*> \endverbatim
77*>
78*> \param[in] TAU
79*> \verbatim
80*>          TAU is COMPLEX*16 array, dimension (N-1)
81*>          TAU(i) must contain the scalar factor of the elementary
82*>          reflector H(i), as returned by ZHETRD.
83*> \endverbatim
84*>
85*> \param[out] WORK
86*> \verbatim
87*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
88*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
89*> \endverbatim
90*>
91*> \param[in] LWORK
92*> \verbatim
93*>          LWORK is INTEGER
94*>          The dimension of the array WORK. LWORK >= N-1.
95*>          For optimum performance LWORK >= (N-1)*NB, where NB is
96*>          the optimal blocksize.
97*>
98*>          If LWORK = -1, then a workspace query is assumed; the routine
99*>          only calculates the optimal size of the WORK array, returns
100*>          this value as the first entry of the WORK array, and no error
101*>          message related to LWORK is issued by XERBLA.
102*> \endverbatim
103*>
104*> \param[out] INFO
105*> \verbatim
106*>          INFO is INTEGER
107*>          = 0:  successful exit
108*>          < 0:  if INFO = -i, the i-th argument had an illegal value
109*> \endverbatim
110*
111*  Authors:
112*  ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \date November 2011
120*
121*> \ingroup complex16OTHERcomputational
122*
123*  =====================================================================
124      SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
125*
126*  -- LAPACK computational routine (version 3.4.0) --
127*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
128*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*     November 2011
130*
131*     .. Scalar Arguments ..
132      CHARACTER          UPLO
133      INTEGER            INFO, LDA, LWORK, N
134*     ..
135*     .. Array Arguments ..
136      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
137*     ..
138*
139*  =====================================================================
140*
141*     .. Parameters ..
142      COMPLEX*16         ZERO, ONE
143      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
144     $                   ONE = ( 1.0D+0, 0.0D+0 ) )
145*     ..
146*     .. Local Scalars ..
147      LOGICAL            LQUERY, UPPER
148      INTEGER            I, IINFO, J, LWKOPT, NB
149*     ..
150*     .. External Functions ..
151      LOGICAL            LSAME
152      INTEGER            ILAENV
153      EXTERNAL           LSAME, ILAENV
154*     ..
155*     .. External Subroutines ..
156      EXTERNAL           XERBLA, ZUNGQL, ZUNGQR
157*     ..
158*     .. Intrinsic Functions ..
159      INTRINSIC          MAX
160*     ..
161*     .. Executable Statements ..
162*
163*     Test the input arguments
164*
165      INFO = 0
166      LQUERY = ( LWORK.EQ.-1 )
167      UPPER = LSAME( UPLO, 'U' )
168      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
169         INFO = -1
170      ELSE IF( N.LT.0 ) THEN
171         INFO = -2
172      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
173         INFO = -4
174      ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
175         INFO = -7
176      END IF
177*
178      IF( INFO.EQ.0 ) THEN
179         IF( UPPER ) THEN
180            NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
181         ELSE
182            NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
183         END IF
184         LWKOPT = MAX( 1, N-1 )*NB
185         WORK( 1 ) = LWKOPT
186      END IF
187*
188      IF( INFO.NE.0 ) THEN
189         CALL XERBLA( 'ZUNGTR', -INFO )
190         RETURN
191      ELSE IF( LQUERY ) THEN
192         RETURN
193      END IF
194*
195*     Quick return if possible
196*
197      IF( N.EQ.0 ) THEN
198         WORK( 1 ) = 1
199         RETURN
200      END IF
201*
202      IF( UPPER ) THEN
203*
204*        Q was determined by a call to ZHETRD with UPLO = 'U'
205*
206*        Shift the vectors which define the elementary reflectors one
207*        column to the left, and set the last row and column of Q to
208*        those of the unit matrix
209*
210         DO 20 J = 1, N - 1
211            DO 10 I = 1, J - 1
212               A( I, J ) = A( I, J+1 )
213   10       CONTINUE
214            A( N, J ) = ZERO
215   20    CONTINUE
216         DO 30 I = 1, N - 1
217            A( I, N ) = ZERO
218   30    CONTINUE
219         A( N, N ) = ONE
220*
221*        Generate Q(1:n-1,1:n-1)
222*
223         CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
224*
225      ELSE
226*
227*        Q was determined by a call to ZHETRD with UPLO = 'L'.
228*
229*        Shift the vectors which define the elementary reflectors one
230*        column to the right, and set the first row and column of Q to
231*        those of the unit matrix
232*
233         DO 50 J = N, 2, -1
234            A( 1, J ) = ZERO
235            DO 40 I = J + 1, N
236               A( I, J ) = A( I, J-1 )
237   40       CONTINUE
238   50    CONTINUE
239         A( 1, 1 ) = ONE
240         DO 60 I = 2, N
241            A( I, 1 ) = ZERO
242   60    CONTINUE
243         IF( N.GT.1 ) THEN
244*
245*           Generate Q(2:n,2:n)
246*
247            CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
248     $                   LWORK, IINFO )
249         END IF
250      END IF
251      WORK( 1 ) = LWKOPT
252      RETURN
253*
254*     End of ZUNGTR
255*
256      END
257