 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zhegs2()

 subroutine zhegs2 ( integer ITYPE, character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO )

ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).

Purpose:
``` ZHEGS2 reduces a complex Hermitian-definite generalized
eigenproblem to standard form.

If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.

B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); = 2 or 3: compute U*A*U**H or L**H *A*L.``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored, and how B has been factorized. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the transformed matrix, stored in the same format as A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by ZPOTRF. B is modified by the routine but restored on exit.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.```

Definition at line 127 of file zhegs2.f.

128*
129* -- LAPACK computational routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 CHARACTER UPLO
135 INTEGER INFO, ITYPE, LDA, LDB, N
136* ..
137* .. Array Arguments ..
138 COMPLEX*16 A( LDA, * ), B( LDB, * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 DOUBLE PRECISION ONE, HALF
145 parameter( one = 1.0d+0, half = 0.5d+0 )
146 COMPLEX*16 CONE
147 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
148* ..
149* .. Local Scalars ..
150 LOGICAL UPPER
151 INTEGER K
152 DOUBLE PRECISION AKK, BKK
153 COMPLEX*16 CT
154* ..
155* .. External Subroutines ..
156 EXTERNAL xerbla, zaxpy, zdscal, zher2, zlacgv, ztrmv,
157 \$ ztrsv
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC max
161* ..
162* .. External Functions ..
163 LOGICAL LSAME
164 EXTERNAL lsame
165* ..
166* .. Executable Statements ..
167*
168* Test the input parameters.
169*
170 info = 0
171 upper = lsame( uplo, 'U' )
172 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
173 info = -1
174 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175 info = -2
176 ELSE IF( n.LT.0 ) THEN
177 info = -3
178 ELSE IF( lda.LT.max( 1, n ) ) THEN
179 info = -5
180 ELSE IF( ldb.LT.max( 1, n ) ) THEN
181 info = -7
182 END IF
183 IF( info.NE.0 ) THEN
184 CALL xerbla( 'ZHEGS2', -info )
185 RETURN
186 END IF
187*
188 IF( itype.EQ.1 ) THEN
189 IF( upper ) THEN
190*
191* Compute inv(U**H)*A*inv(U)
192*
193 DO 10 k = 1, n
194*
195* Update the upper triangle of A(k:n,k:n)
196*
197 akk = dble( a( k, k ) )
198 bkk = dble( b( k, k ) )
199 akk = akk / bkk**2
200 a( k, k ) = akk
201 IF( k.LT.n ) THEN
202 CALL zdscal( n-k, one / bkk, a( k, k+1 ), lda )
203 ct = -half*akk
204 CALL zlacgv( n-k, a( k, k+1 ), lda )
205 CALL zlacgv( n-k, b( k, k+1 ), ldb )
206 CALL zaxpy( n-k, ct, b( k, k+1 ), ldb, a( k, k+1 ),
207 \$ lda )
208 CALL zher2( uplo, n-k, -cone, a( k, k+1 ), lda,
209 \$ b( k, k+1 ), ldb, a( k+1, k+1 ), lda )
210 CALL zaxpy( n-k, ct, b( k, k+1 ), ldb, a( k, k+1 ),
211 \$ lda )
212 CALL zlacgv( n-k, b( k, k+1 ), ldb )
213 CALL ztrsv( uplo, 'Conjugate transpose', 'Non-unit',
214 \$ n-k, b( k+1, k+1 ), ldb, a( k, k+1 ),
215 \$ lda )
216 CALL zlacgv( n-k, a( k, k+1 ), lda )
217 END IF
218 10 CONTINUE
219 ELSE
220*
221* Compute inv(L)*A*inv(L**H)
222*
223 DO 20 k = 1, n
224*
225* Update the lower triangle of A(k:n,k:n)
226*
227 akk = dble( a( k, k ) )
228 bkk = dble( b( k, k ) )
229 akk = akk / bkk**2
230 a( k, k ) = akk
231 IF( k.LT.n ) THEN
232 CALL zdscal( n-k, one / bkk, a( k+1, k ), 1 )
233 ct = -half*akk
234 CALL zaxpy( n-k, ct, b( k+1, k ), 1, a( k+1, k ), 1 )
235 CALL zher2( uplo, n-k, -cone, a( k+1, k ), 1,
236 \$ b( k+1, k ), 1, a( k+1, k+1 ), lda )
237 CALL zaxpy( n-k, ct, b( k+1, k ), 1, a( k+1, k ), 1 )
238 CALL ztrsv( uplo, 'No transpose', 'Non-unit', n-k,
239 \$ b( k+1, k+1 ), ldb, a( k+1, k ), 1 )
240 END IF
241 20 CONTINUE
242 END IF
243 ELSE
244 IF( upper ) THEN
245*
246* Compute U*A*U**H
247*
248 DO 30 k = 1, n
249*
250* Update the upper triangle of A(1:k,1:k)
251*
252 akk = dble( a( k, k ) )
253 bkk = dble( b( k, k ) )
254 CALL ztrmv( uplo, 'No transpose', 'Non-unit', k-1, b,
255 \$ ldb, a( 1, k ), 1 )
256 ct = half*akk
257 CALL zaxpy( k-1, ct, b( 1, k ), 1, a( 1, k ), 1 )
258 CALL zher2( uplo, k-1, cone, a( 1, k ), 1, b( 1, k ), 1,
259 \$ a, lda )
260 CALL zaxpy( k-1, ct, b( 1, k ), 1, a( 1, k ), 1 )
261 CALL zdscal( k-1, bkk, a( 1, k ), 1 )
262 a( k, k ) = akk*bkk**2
263 30 CONTINUE
264 ELSE
265*
266* Compute L**H *A*L
267*
268 DO 40 k = 1, n
269*
270* Update the lower triangle of A(1:k,1:k)
271*
272 akk = dble( a( k, k ) )
273 bkk = dble( b( k, k ) )
274 CALL zlacgv( k-1, a( k, 1 ), lda )
275 CALL ztrmv( uplo, 'Conjugate transpose', 'Non-unit', k-1,
276 \$ b, ldb, a( k, 1 ), lda )
277 ct = half*akk
278 CALL zlacgv( k-1, b( k, 1 ), ldb )
279 CALL zaxpy( k-1, ct, b( k, 1 ), ldb, a( k, 1 ), lda )
280 CALL zher2( uplo, k-1, cone, a( k, 1 ), lda, b( k, 1 ),
281 \$ ldb, a, lda )
282 CALL zaxpy( k-1, ct, b( k, 1 ), ldb, a( k, 1 ), lda )
283 CALL zlacgv( k-1, b( k, 1 ), ldb )
284 CALL zdscal( k-1, bkk, a( k, 1 ), lda )
285 CALL zlacgv( k-1, a( k, 1 ), lda )
286 a( k, k ) = akk*bkk**2
287 40 CONTINUE
288 END IF
289 END IF
290 RETURN
291*
292* End of ZHEGS2
293*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
subroutine ztrsv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRSV
Definition: ztrsv.f:149
subroutine zher2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZHER2
Definition: zher2.f:150
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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