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

 subroutine ssygst ( integer ITYPE, character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, integer INFO )

SSYGST

Purpose:
``` SSYGST reduces a real symmetric-definite generalized eigenproblem
to standard form.

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

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**T or L**T*A*L.

B must have been previously factorized as U**T*U or L*L**T by SPOTRF.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T*A*L.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored and B is factored as U**T*U; = 'L': Lower triangle of A is stored and B is factored as L*L**T.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] A ``` A is REAL array, dimension (LDA,N) On entry, the symmetric 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] B ``` B is REAL array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by SPOTRF.``` [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 126 of file ssygst.f.

127*
128* -- LAPACK computational routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 CHARACTER UPLO
134 INTEGER INFO, ITYPE, LDA, LDB, N
135* ..
136* .. Array Arguments ..
137 REAL A( LDA, * ), B( LDB, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ONE, HALF
144 parameter( one = 1.0, half = 0.5 )
145* ..
146* .. Local Scalars ..
147 LOGICAL UPPER
148 INTEGER K, KB, NB
149* ..
150* .. External Subroutines ..
151 EXTERNAL ssygs2, ssymm, ssyr2k, strmm, strsm, xerbla
152* ..
153* .. Intrinsic Functions ..
154 INTRINSIC max, min
155* ..
156* .. External Functions ..
157 LOGICAL LSAME
158 INTEGER ILAENV
159 EXTERNAL lsame, ilaenv
160* ..
161* .. Executable Statements ..
162*
163* Test the input parameters.
164*
165 info = 0
166 upper = lsame( uplo, 'U' )
167 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
168 info = -1
169 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
170 info = -2
171 ELSE IF( n.LT.0 ) THEN
172 info = -3
173 ELSE IF( lda.LT.max( 1, n ) ) THEN
174 info = -5
175 ELSE IF( ldb.LT.max( 1, n ) ) THEN
176 info = -7
177 END IF
178 IF( info.NE.0 ) THEN
179 CALL xerbla( 'SSYGST', -info )
180 RETURN
181 END IF
182*
183* Quick return if possible
184*
185 IF( n.EQ.0 )
186 \$ RETURN
187*
188* Determine the block size for this environment.
189*
190 nb = ilaenv( 1, 'SSYGST', uplo, n, -1, -1, -1 )
191*
192 IF( nb.LE.1 .OR. nb.GE.n ) THEN
193*
194* Use unblocked code
195*
196 CALL ssygs2( itype, uplo, n, a, lda, b, ldb, info )
197 ELSE
198*
199* Use blocked code
200*
201 IF( itype.EQ.1 ) THEN
202 IF( upper ) THEN
203*
204* Compute inv(U**T)*A*inv(U)
205*
206 DO 10 k = 1, n, nb
207 kb = min( n-k+1, nb )
208*
209* Update the upper triangle of A(k:n,k:n)
210*
211 CALL ssygs2( itype, uplo, kb, a( k, k ), lda,
212 \$ b( k, k ), ldb, info )
213 IF( k+kb.LE.n ) THEN
214 CALL strsm( 'Left', uplo, 'Transpose', 'Non-unit',
215 \$ kb, n-k-kb+1, one, b( k, k ), ldb,
216 \$ a( k, k+kb ), lda )
217 CALL ssymm( 'Left', uplo, kb, n-k-kb+1, -half,
218 \$ a( k, k ), lda, b( k, k+kb ), ldb, one,
219 \$ a( k, k+kb ), lda )
220 CALL ssyr2k( uplo, 'Transpose', n-k-kb+1, kb, -one,
221 \$ a( k, k+kb ), lda, b( k, k+kb ), ldb,
222 \$ one, a( k+kb, k+kb ), lda )
223 CALL ssymm( 'Left', uplo, kb, n-k-kb+1, -half,
224 \$ a( k, k ), lda, b( k, k+kb ), ldb, one,
225 \$ a( k, k+kb ), lda )
226 CALL strsm( 'Right', uplo, 'No transpose',
227 \$ 'Non-unit', kb, n-k-kb+1, one,
228 \$ b( k+kb, k+kb ), ldb, a( k, k+kb ),
229 \$ lda )
230 END IF
231 10 CONTINUE
232 ELSE
233*
234* Compute inv(L)*A*inv(L**T)
235*
236 DO 20 k = 1, n, nb
237 kb = min( n-k+1, nb )
238*
239* Update the lower triangle of A(k:n,k:n)
240*
241 CALL ssygs2( itype, uplo, kb, a( k, k ), lda,
242 \$ b( k, k ), ldb, info )
243 IF( k+kb.LE.n ) THEN
244 CALL strsm( 'Right', uplo, 'Transpose', 'Non-unit',
245 \$ n-k-kb+1, kb, one, b( k, k ), ldb,
246 \$ a( k+kb, k ), lda )
247 CALL ssymm( 'Right', uplo, n-k-kb+1, kb, -half,
248 \$ a( k, k ), lda, b( k+kb, k ), ldb, one,
249 \$ a( k+kb, k ), lda )
250 CALL ssyr2k( uplo, 'No transpose', n-k-kb+1, kb,
251 \$ -one, a( k+kb, k ), lda, b( k+kb, k ),
252 \$ ldb, one, a( k+kb, k+kb ), lda )
253 CALL ssymm( 'Right', uplo, n-k-kb+1, kb, -half,
254 \$ a( k, k ), lda, b( k+kb, k ), ldb, one,
255 \$ a( k+kb, k ), lda )
256 CALL strsm( 'Left', uplo, 'No transpose',
257 \$ 'Non-unit', n-k-kb+1, kb, one,
258 \$ b( k+kb, k+kb ), ldb, a( k+kb, k ),
259 \$ lda )
260 END IF
261 20 CONTINUE
262 END IF
263 ELSE
264 IF( upper ) THEN
265*
266* Compute U*A*U**T
267*
268 DO 30 k = 1, n, nb
269 kb = min( n-k+1, nb )
270*
271* Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
272*
273 CALL strmm( 'Left', uplo, 'No transpose', 'Non-unit',
274 \$ k-1, kb, one, b, ldb, a( 1, k ), lda )
275 CALL ssymm( 'Right', uplo, k-1, kb, half, a( k, k ),
276 \$ lda, b( 1, k ), ldb, one, a( 1, k ), lda )
277 CALL ssyr2k( uplo, 'No transpose', k-1, kb, one,
278 \$ a( 1, k ), lda, b( 1, k ), ldb, one, a,
279 \$ lda )
280 CALL ssymm( 'Right', uplo, k-1, kb, half, a( k, k ),
281 \$ lda, b( 1, k ), ldb, one, a( 1, k ), lda )
282 CALL strmm( 'Right', uplo, 'Transpose', 'Non-unit',
283 \$ k-1, kb, one, b( k, k ), ldb, a( 1, k ),
284 \$ lda )
285 CALL ssygs2( itype, uplo, kb, a( k, k ), lda,
286 \$ b( k, k ), ldb, info )
287 30 CONTINUE
288 ELSE
289*
290* Compute L**T*A*L
291*
292 DO 40 k = 1, n, nb
293 kb = min( n-k+1, nb )
294*
295* Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
296*
297 CALL strmm( 'Right', uplo, 'No transpose', 'Non-unit',
298 \$ kb, k-1, one, b, ldb, a( k, 1 ), lda )
299 CALL ssymm( 'Left', uplo, kb, k-1, half, a( k, k ),
300 \$ lda, b( k, 1 ), ldb, one, a( k, 1 ), lda )
301 CALL ssyr2k( uplo, 'Transpose', k-1, kb, one,
302 \$ a( k, 1 ), lda, b( k, 1 ), ldb, one, a,
303 \$ lda )
304 CALL ssymm( 'Left', uplo, kb, k-1, half, a( k, k ),
305 \$ lda, b( k, 1 ), ldb, one, a( k, 1 ), lda )
306 CALL strmm( 'Left', uplo, 'Transpose', 'Non-unit', kb,
307 \$ k-1, one, b( k, k ), ldb, a( k, 1 ), lda )
308 CALL ssygs2( itype, uplo, kb, a( k, k ), lda,
309 \$ b( k, k ), ldb, info )
310 40 CONTINUE
311 END IF
312 END IF
313 END IF
314 RETURN
315*
316* End of SSYGST
317*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssygs2(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorizatio...
Definition: ssygs2.f:127
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:177
subroutine ssyr2k(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SSYR2K
Definition: ssyr2k.f:192
subroutine ssymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SSYMM
Definition: ssymm.f:189
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
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