LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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