LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cupgtr()

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

CUPGTR

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Purpose:
 CUPGTR 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
 CHPTRD 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 CHPTRD;
          = 'L': Lower triangular packed storage used in previous
                 call to CHPTRD.
[in]N
          N is INTEGER
          The order of the matrix Q. N >= 0.
[in]AP
          AP is COMPLEX array, dimension (N*(N+1)/2)
          The vectors which define the elementary reflectors, as
          returned by CHPTRD.
[in]TAU
          TAU is COMPLEX array, dimension (N-1)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CHPTRD.
[out]Q
          Q is COMPLEX 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 array, dimension (N-1)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 113 of file cupgtr.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 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  COMPLEX CZERO, CONE
131  parameter( czero = ( 0.0e+0, 0.0e+0 ),
132  $ cone = ( 1.0e+0, 0.0e+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 cung2l, cung2r, xerbla
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( 'CUPGTR', -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 CHPTRD 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 cung2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
196 *
197  ELSE
198 *
199 * Q was determined by a call to CHPTRD 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 cung2r( 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 CUPGTR
229 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cung2l(M, N, K, A, LDA, TAU, WORK, INFO)
CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (un...
Definition: cung2l.f:114
subroutine cung2r(M, N, K, A, LDA, TAU, WORK, INFO)
CUNG2R
Definition: cung2r.f:114
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