 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ssygs2()

 subroutine ssygs2 ( integer ITYPE, character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, integer INFO )

SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

Purpose:
``` SSYGS2 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 Specifies whether the upper or lower triangular part of the symmetric 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 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 ssygs2.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
149  REAL AKK, BKK, CT
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL saxpy, sscal, ssyr2, strmv, strsv, xerbla
153 * ..
154 * .. Intrinsic Functions ..
155  INTRINSIC max
156 * ..
157 * .. External Functions ..
158  LOGICAL LSAME
159  EXTERNAL lsame
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( 'SSYGS2', -info )
180  RETURN
181  END IF
182 *
183  IF( itype.EQ.1 ) THEN
184  IF( upper ) THEN
185 *
186 * Compute inv(U**T)*A*inv(U)
187 *
188  DO 10 k = 1, n
189 *
190 * Update the upper triangle of A(k:n,k:n)
191 *
192  akk = a( k, k )
193  bkk = b( k, k )
194  akk = akk / bkk**2
195  a( k, k ) = akk
196  IF( k.LT.n ) THEN
197  CALL sscal( n-k, one / bkk, a( k, k+1 ), lda )
198  ct = -half*akk
199  CALL saxpy( n-k, ct, b( k, k+1 ), ldb, a( k, k+1 ),
200  \$ lda )
201  CALL ssyr2( uplo, n-k, -one, a( k, k+1 ), lda,
202  \$ b( k, k+1 ), ldb, a( k+1, k+1 ), lda )
203  CALL saxpy( n-k, ct, b( k, k+1 ), ldb, a( k, k+1 ),
204  \$ lda )
205  CALL strsv( uplo, 'Transpose', 'Non-unit', n-k,
206  \$ b( k+1, k+1 ), ldb, a( k, k+1 ), lda )
207  END IF
208  10 CONTINUE
209  ELSE
210 *
211 * Compute inv(L)*A*inv(L**T)
212 *
213  DO 20 k = 1, n
214 *
215 * Update the lower triangle of A(k:n,k:n)
216 *
217  akk = a( k, k )
218  bkk = b( k, k )
219  akk = akk / bkk**2
220  a( k, k ) = akk
221  IF( k.LT.n ) THEN
222  CALL sscal( n-k, one / bkk, a( k+1, k ), 1 )
223  ct = -half*akk
224  CALL saxpy( n-k, ct, b( k+1, k ), 1, a( k+1, k ), 1 )
225  CALL ssyr2( uplo, n-k, -one, a( k+1, k ), 1,
226  \$ b( k+1, k ), 1, a( k+1, k+1 ), lda )
227  CALL saxpy( n-k, ct, b( k+1, k ), 1, a( k+1, k ), 1 )
228  CALL strsv( uplo, 'No transpose', 'Non-unit', n-k,
229  \$ b( k+1, k+1 ), ldb, a( k+1, k ), 1 )
230  END IF
231  20 CONTINUE
232  END IF
233  ELSE
234  IF( upper ) THEN
235 *
236 * Compute U*A*U**T
237 *
238  DO 30 k = 1, n
239 *
240 * Update the upper triangle of A(1:k,1:k)
241 *
242  akk = a( k, k )
243  bkk = b( k, k )
244  CALL strmv( uplo, 'No transpose', 'Non-unit', k-1, b,
245  \$ ldb, a( 1, k ), 1 )
246  ct = half*akk
247  CALL saxpy( k-1, ct, b( 1, k ), 1, a( 1, k ), 1 )
248  CALL ssyr2( uplo, k-1, one, a( 1, k ), 1, b( 1, k ), 1,
249  \$ a, lda )
250  CALL saxpy( k-1, ct, b( 1, k ), 1, a( 1, k ), 1 )
251  CALL sscal( k-1, bkk, a( 1, k ), 1 )
252  a( k, k ) = akk*bkk**2
253  30 CONTINUE
254  ELSE
255 *
256 * Compute L**T *A*L
257 *
258  DO 40 k = 1, n
259 *
260 * Update the lower triangle of A(1:k,1:k)
261 *
262  akk = a( k, k )
263  bkk = b( k, k )
264  CALL strmv( uplo, 'Transpose', 'Non-unit', k-1, b, ldb,
265  \$ a( k, 1 ), lda )
266  ct = half*akk
267  CALL saxpy( k-1, ct, b( k, 1 ), ldb, a( k, 1 ), lda )
268  CALL ssyr2( uplo, k-1, one, a( k, 1 ), lda, b( k, 1 ),
269  \$ ldb, a, lda )
270  CALL saxpy( k-1, ct, b( k, 1 ), ldb, a( k, 1 ), lda )
271  CALL sscal( k-1, bkk, a( k, 1 ), lda )
272  a( k, k ) = akk*bkk**2
273  40 CONTINUE
274  END IF
275  END IF
276  RETURN
277 *
278 * End of SSYGS2
279 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine strsv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRSV
Definition: strsv.f:149
subroutine ssyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SSYR2
Definition: ssyr2.f:147
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