LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ssycon_3()

subroutine ssycon_3 ( character  UPLO,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  E,
integer, dimension( * )  IPIV,
real  ANORM,
real  RCOND,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SSYCON_3

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Purpose:
 SSYCON_3 estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric matrix A using the factorization
 computed by DSYTRF_RK or DSYTRF_BK:

    A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

 where U (or L) is unit upper (or lower) triangular matrix,
 U**T (or L**T) is the transpose of U (or L), P is a permutation
 matrix, P**T is the transpose of P, and D is symmetric and block
 diagonal with 1-by-1 and 2-by-2 diagonal blocks.

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
 This routine uses BLAS3 solver SSYTRS_3.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are
          stored as an upper or lower triangular matrix:
          = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
          = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          Diagonal of the block diagonal matrix D and factors U or L
          as computed by SSYTRF_RK and SSYTRF_BK:
            a) ONLY diagonal elements of the symmetric block diagonal
               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
               (superdiagonal (or subdiagonal) elements of D
                should be provided on entry in array E), and
            b) If UPLO = 'U': factor U in the superdiagonal part of A.
               If UPLO = 'L': factor L in the subdiagonal part of A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]E
          E is REAL array, dimension (N)
          On entry, contains the superdiagonal (or subdiagonal)
          elements of the symmetric block diagonal matrix D
          with 1-by-1 or 2-by-2 diagonal blocks, where
          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

          NOTE: For 1-by-1 diagonal block D(k), where
          1 <= k <= N, the element E(k) is not referenced in both
          UPLO = 'U' or UPLO = 'L' cases.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF_RK or SSYTRF_BK.
[in]ANORM
          ANORM is REAL
          The 1-norm of the original matrix A.
[out]RCOND
          RCOND is REAL
          The reciprocal of the condition number of the matrix A,
          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
          estimate of the 1-norm of inv(A) computed in this routine.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]IWORK
          IWORK is INTEGER array, dimension (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.
Contributors:
  June 2017,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 169 of file ssycon_3.f.

171 *
172 * -- LAPACK computational routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER UPLO
178  INTEGER INFO, LDA, N
179  REAL ANORM, RCOND
180 * ..
181 * .. Array Arguments ..
182  INTEGER IPIV( * ), IWORK( * )
183  REAL A( LDA, * ), E( * ), WORK( * )
184 * ..
185 *
186 * =====================================================================
187 *
188 * .. Parameters ..
189  REAL ONE, ZERO
190  parameter( one = 1.0e+0, zero = 0.0e+0 )
191 * ..
192 * .. Local Scalars ..
193  LOGICAL UPPER
194  INTEGER I, KASE
195  REAL AINVNM
196 * ..
197 * .. Local Arrays ..
198  INTEGER ISAVE( 3 )
199 * ..
200 * .. External Functions ..
201  LOGICAL LSAME
202  EXTERNAL lsame
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL slacn2, ssytrs_3, xerbla
206 * ..
207 * .. Intrinsic Functions ..
208  INTRINSIC max
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input parameters.
213 *
214  info = 0
215  upper = lsame( uplo, 'U' )
216  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
217  info = -1
218  ELSE IF( n.LT.0 ) THEN
219  info = -2
220  ELSE IF( lda.LT.max( 1, n ) ) THEN
221  info = -4
222  ELSE IF( anorm.LT.zero ) THEN
223  info = -7
224  END IF
225  IF( info.NE.0 ) THEN
226  CALL xerbla( 'SSYCON_3', -info )
227  RETURN
228  END IF
229 *
230 * Quick return if possible
231 *
232  rcond = zero
233  IF( n.EQ.0 ) THEN
234  rcond = one
235  RETURN
236  ELSE IF( anorm.LE.zero ) THEN
237  RETURN
238  END IF
239 *
240 * Check that the diagonal matrix D is nonsingular.
241 *
242  IF( upper ) THEN
243 *
244 * Upper triangular storage: examine D from bottom to top
245 *
246  DO i = n, 1, -1
247  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
248  $ RETURN
249  END DO
250  ELSE
251 *
252 * Lower triangular storage: examine D from top to bottom.
253 *
254  DO i = 1, n
255  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
256  $ RETURN
257  END DO
258  END IF
259 *
260 * Estimate the 1-norm of the inverse.
261 *
262  kase = 0
263  30 CONTINUE
264  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
265  IF( kase.NE.0 ) THEN
266 *
267 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
268 *
269  CALL ssytrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
270  GO TO 30
271  END IF
272 *
273 * Compute the estimate of the reciprocal condition number.
274 *
275  IF( ainvnm.NE.zero )
276  $ rcond = ( one / ainvnm ) / anorm
277 *
278  RETURN
279 *
280 * End of SSYCON_3
281 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine ssytrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
SSYTRS_3
Definition: ssytrs_3.f:165
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