SYCON_3 - 5.2 English - 68552

SYCON_3 estimates the reciprocal of the condition number of a real symmetric matrix A.

Purpose:

  SYCON_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:

• UPLO – [in]

  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).

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0.

• A – [in]

  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.

• LDA – [in]

  LDA is INTEGER

  The leading dimension of the array A. LDA >= fla_max(1,N).

• E – [in]

  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.

• IPIV – [in]

  IPIV is INTEGER array, dimension (N)

  Details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK.

• ANORM – [in]

  ANORM is REAL

  The 1-norm of the original matrix A.

• RCOND – [out]

  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.

• WORK – [out] WORK is REAL array, dimension (2*N)

• IWORK – [out] IWORK is INTEGER array, dimension (N)

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -i, the i-th argument had an illegal value