 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zupgtr()

 subroutine zupgtr ( character UPLO, integer N, complex*16, dimension( * ) AP, complex*16, dimension( * ) TAU, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( * ) WORK, integer INFO )

ZUPGTR

Purpose:
``` ZUPGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
ZHPTRD using packed storage:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to ZHPTRD; = 'L': Lower triangular packed storage used in previous call to ZHPTRD.``` [in] N ``` N is INTEGER The order of the matrix Q. N >= 0.``` [in] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by ZHPTRD.``` [in] TAU ``` TAU is COMPLEX*16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHPTRD.``` [out] Q ``` Q is COMPLEX*16 array, dimension (LDQ,N) The N-by-N unitary matrix Q.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).``` [out] WORK ` WORK is COMPLEX*16 array, dimension (N-1)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 113 of file zupgtr.f.

114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 CHARACTER UPLO
121 INTEGER INFO, LDQ, N
122* ..
123* .. Array Arguments ..
124 COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 COMPLEX*16 CZERO, CONE
131 parameter( czero = ( 0.0d+0, 0.0d+0 ),
132 \$ cone = ( 1.0d+0, 0.0d+0 ) )
133* ..
134* .. Local Scalars ..
135 LOGICAL UPPER
136 INTEGER I, IINFO, IJ, J
137* ..
138* .. External Functions ..
139 LOGICAL LSAME
140 EXTERNAL lsame
141* ..
142* .. External Subroutines ..
143 EXTERNAL xerbla, zung2l, zung2r
144* ..
145* .. Intrinsic Functions ..
146 INTRINSIC max
147* ..
148* .. Executable Statements ..
149*
150* Test the input arguments
151*
152 info = 0
153 upper = lsame( uplo, 'U' )
154 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
155 info = -1
156 ELSE IF( n.LT.0 ) THEN
157 info = -2
158 ELSE IF( ldq.LT.max( 1, n ) ) THEN
159 info = -6
160 END IF
161 IF( info.NE.0 ) THEN
162 CALL xerbla( 'ZUPGTR', -info )
163 RETURN
164 END IF
165*
166* Quick return if possible
167*
168 IF( n.EQ.0 )
169 \$ RETURN
170*
171 IF( upper ) THEN
172*
173* Q was determined by a call to ZHPTRD with UPLO = 'U'
174*
175* Unpack the vectors which define the elementary reflectors and
176* set the last row and column of Q equal to those of the unit
177* matrix
178*
179 ij = 2
180 DO 20 j = 1, n - 1
181 DO 10 i = 1, j - 1
182 q( i, j ) = ap( ij )
183 ij = ij + 1
184 10 CONTINUE
185 ij = ij + 2
186 q( n, j ) = czero
187 20 CONTINUE
188 DO 30 i = 1, n - 1
189 q( i, n ) = czero
190 30 CONTINUE
191 q( n, n ) = cone
192*
193* Generate Q(1:n-1,1:n-1)
194*
195 CALL zung2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
196*
197 ELSE
198*
199* Q was determined by a call to ZHPTRD with UPLO = 'L'.
200*
201* Unpack the vectors which define the elementary reflectors and
202* set the first row and column of Q equal to those of the unit
203* matrix
204*
205 q( 1, 1 ) = cone
206 DO 40 i = 2, n
207 q( i, 1 ) = czero
208 40 CONTINUE
209 ij = 3
210 DO 60 j = 2, n
211 q( 1, j ) = czero
212 DO 50 i = j + 1, n
213 q( i, j ) = ap( ij )
214 ij = ij + 1
215 50 CONTINUE
216 ij = ij + 2
217 60 CONTINUE
218 IF( n.GT.1 ) THEN
219*
220* Generate Q(2:n,2:n)
221*
222 CALL zung2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
223 \$ iinfo )
224 END IF
225 END IF
226 RETURN
227*
228* End of ZUPGTR
229*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zung2r(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNG2R
Definition: zung2r.f:114
subroutine zung2l(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (un...
Definition: zung2l.f:114
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