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.

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).

N

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

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.

LDA

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

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.

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.

ANORM

          ANORM is REAL
          The 1-norm of the original matrix A.

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.

WORK

          WORK is REAL array, dimension (2*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

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

Univ. of Tennessee

Univ. of California Berkeley

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NAG Ltd.

December 2016