csycon_3.f(3)

NAME
csycon_3.f

SYNOPSIS

  Functions/Subroutines
subroutine csycon_3 (UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, INFO)
CSYCON_3

Function/Subroutine Documentation

  subroutine csycon_3 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) E, integer, dimension( * ) IPIV, real ANORM, real RCOND, complex, dimension( * ) WORK, integer INFO)

Purpose:

     CSYCON_3 estimates the reciprocal of the condition number (in the
     1-norm) of a complex symmetric matrix A using the factorization
     computed by CSYTRF_RK or CSYTRF_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 CSYTRS_3.

Parameters
    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 COMPLEX array, dimension (LDA,N)
              Diagonal of the block diagonal matrix D and factors U or L
              as computed by CSYTRF_RK and CSYTRF_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 COMPLEX 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 CSYTRF_RK or CSYTRF_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 COMPLEX array, dimension (2*N)

    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 164 of file csycon_3.f.

Author

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