 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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