LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zhegst()

 subroutine zhegst ( integer itype, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info )

ZHEGST

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Purpose:
``` ZHEGST 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 = 'U': Upper triangle of A is stored and B is factored as U**H*U; = 'L': Lower triangle of A is stored and B is factored as L*L**H.``` [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 zhegst.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
145 parameter( one = 1.0d+0 )
146 COMPLEX*16 CONE, HALF
147 parameter( cone = ( 1.0d+0, 0.0d+0 ),
148 \$ half = ( 0.5d+0, 0.0d+0 ) )
149* ..
150* .. Local Scalars ..
151 LOGICAL UPPER
152 INTEGER K, KB, NB
153* ..
154* .. External Subroutines ..
155 EXTERNAL xerbla, zhegs2, zhemm, zher2k, ztrmm, ztrsm
156* ..
157* .. Intrinsic Functions ..
158 INTRINSIC max, min
159* ..
160* .. External Functions ..
161 LOGICAL LSAME
162 INTEGER ILAENV
163 EXTERNAL lsame, ilaenv
164* ..
165* .. Executable Statements ..
166*
167* Test the input parameters.
168*
169 info = 0
170 upper = lsame( uplo, 'U' )
171 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
172 info = -1
173 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174 info = -2
175 ELSE IF( n.LT.0 ) THEN
176 info = -3
177 ELSE IF( lda.LT.max( 1, n ) ) THEN
178 info = -5
179 ELSE IF( ldb.LT.max( 1, n ) ) THEN
180 info = -7
181 END IF
182 IF( info.NE.0 ) THEN
183 CALL xerbla( 'ZHEGST', -info )
184 RETURN
185 END IF
186*
187* Quick return if possible
188*
189 IF( n.EQ.0 )
190 \$ RETURN
191*
192* Determine the block size for this environment.
193*
194 nb = ilaenv( 1, 'ZHEGST', uplo, n, -1, -1, -1 )
195*
196 IF( nb.LE.1 .OR. nb.GE.n ) THEN
197*
198* Use unblocked code
199*
200 CALL zhegs2( itype, uplo, n, a, lda, b, ldb, info )
201 ELSE
202*
203* Use blocked code
204*
205 IF( itype.EQ.1 ) THEN
206 IF( upper ) THEN
207*
208* Compute inv(U**H)*A*inv(U)
209*
210 DO 10 k = 1, n, nb
211 kb = min( n-k+1, nb )
212*
213* Update the upper triangle of A(k:n,k:n)
214*
215 CALL zhegs2( itype, uplo, kb, a( k, k ), lda,
216 \$ b( k, k ), ldb, info )
217 IF( k+kb.LE.n ) THEN
218 CALL ztrsm( 'Left', uplo, 'Conjugate transpose',
219 \$ 'Non-unit', kb, n-k-kb+1, cone,
220 \$ b( k, k ), ldb, a( k, k+kb ), lda )
221 CALL zhemm( 'Left', uplo, kb, n-k-kb+1, -half,
222 \$ a( k, k ), lda, b( k, k+kb ), ldb,
223 \$ cone, a( k, k+kb ), lda )
224 CALL zher2k( uplo, 'Conjugate transpose', n-k-kb+1,
225 \$ kb, -cone, a( k, k+kb ), lda,
226 \$ b( k, k+kb ), ldb, one,
227 \$ a( k+kb, k+kb ), lda )
228 CALL zhemm( 'Left', uplo, kb, n-k-kb+1, -half,
229 \$ a( k, k ), lda, b( k, k+kb ), ldb,
230 \$ cone, a( k, k+kb ), lda )
231 CALL ztrsm( 'Right', uplo, 'No transpose',
232 \$ 'Non-unit', kb, n-k-kb+1, cone,
233 \$ b( k+kb, k+kb ), ldb, a( k, k+kb ),
234 \$ lda )
235 END IF
236 10 CONTINUE
237 ELSE
238*
239* Compute inv(L)*A*inv(L**H)
240*
241 DO 20 k = 1, n, nb
242 kb = min( n-k+1, nb )
243*
244* Update the lower triangle of A(k:n,k:n)
245*
246 CALL zhegs2( itype, uplo, kb, a( k, k ), lda,
247 \$ b( k, k ), ldb, info )
248 IF( k+kb.LE.n ) THEN
249 CALL ztrsm( 'Right', uplo, 'Conjugate transpose',
250 \$ 'Non-unit', n-k-kb+1, kb, cone,
251 \$ b( k, k ), ldb, a( k+kb, k ), lda )
252 CALL zhemm( 'Right', uplo, n-k-kb+1, kb, -half,
253 \$ a( k, k ), lda, b( k+kb, k ), ldb,
254 \$ cone, a( k+kb, k ), lda )
255 CALL zher2k( uplo, 'No transpose', n-k-kb+1, kb,
256 \$ -cone, a( k+kb, k ), lda,
257 \$ b( k+kb, k ), ldb, one,
258 \$ a( k+kb, k+kb ), lda )
259 CALL zhemm( 'Right', uplo, n-k-kb+1, kb, -half,
260 \$ a( k, k ), lda, b( k+kb, k ), ldb,
261 \$ cone, a( k+kb, k ), lda )
262 CALL ztrsm( 'Left', uplo, 'No transpose',
263 \$ 'Non-unit', n-k-kb+1, kb, cone,
264 \$ b( k+kb, k+kb ), ldb, a( k+kb, k ),
265 \$ lda )
266 END IF
267 20 CONTINUE
268 END IF
269 ELSE
270 IF( upper ) THEN
271*
272* Compute U*A*U**H
273*
274 DO 30 k = 1, n, nb
275 kb = min( n-k+1, nb )
276*
277* Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
278*
279 CALL ztrmm( 'Left', uplo, 'No transpose', 'Non-unit',
280 \$ k-1, kb, cone, b, ldb, a( 1, k ), lda )
281 CALL zhemm( 'Right', uplo, k-1, kb, half, a( k, k ),
282 \$ lda, b( 1, k ), ldb, cone, a( 1, k ),
283 \$ lda )
284 CALL zher2k( uplo, 'No transpose', k-1, kb, cone,
285 \$ a( 1, k ), lda, b( 1, k ), ldb, one, a,
286 \$ lda )
287 CALL zhemm( 'Right', uplo, k-1, kb, half, a( k, k ),
288 \$ lda, b( 1, k ), ldb, cone, a( 1, k ),
289 \$ lda )
290 CALL ztrmm( 'Right', uplo, 'Conjugate transpose',
291 \$ 'Non-unit', k-1, kb, cone, b( k, k ), ldb,
292 \$ a( 1, k ), lda )
293 CALL zhegs2( itype, uplo, kb, a( k, k ), lda,
294 \$ b( k, k ), ldb, info )
295 30 CONTINUE
296 ELSE
297*
298* Compute L**H*A*L
299*
300 DO 40 k = 1, n, nb
301 kb = min( n-k+1, nb )
302*
303* Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
304*
305 CALL ztrmm( 'Right', uplo, 'No transpose', 'Non-unit',
306 \$ kb, k-1, cone, b, ldb, a( k, 1 ), lda )
307 CALL zhemm( 'Left', uplo, kb, k-1, half, a( k, k ),
308 \$ lda, b( k, 1 ), ldb, cone, a( k, 1 ),
309 \$ lda )
310 CALL zher2k( uplo, 'Conjugate transpose', k-1, kb,
311 \$ cone, a( k, 1 ), lda, b( k, 1 ), ldb,
312 \$ one, a, lda )
313 CALL zhemm( 'Left', uplo, kb, k-1, half, a( k, k ),
314 \$ lda, b( k, 1 ), ldb, cone, a( k, 1 ),
315 \$ lda )
316 CALL ztrmm( 'Left', uplo, 'Conjugate transpose',
317 \$ 'Non-unit', kb, k-1, cone, b( k, k ), ldb,
318 \$ a( k, 1 ), lda )
319 CALL zhegs2( itype, uplo, kb, a( k, k ), lda,
320 \$ b( k, k ), ldb, info )
321 40 CONTINUE
322 END IF
323 END IF
324 END IF
325 RETURN
326*
327* End of ZHEGST
328*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zhegs2(itype, uplo, n, a, lda, b, ldb, info)
ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorizatio...
Definition zhegs2.f:128
subroutine zhemm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZHEMM
Definition zhemm.f:191
subroutine zher2k(uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZHER2K
Definition zher2k.f:198
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ztrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRMM
Definition ztrmm.f:177
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180
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