LAPACK  3.10.0
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).

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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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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