Loading...
Searching...
No Matches

## csycon_3()

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 )

CSYCON_3

Download CSYCON_3 + dependencies [TGZ] [ZIP] [TXT]

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

  [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 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.
      !>

  [in]

  LDA

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

  [in]

  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.
      !>

  [in]

  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.
      !>

  [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 COMPLEX array, dimension (2*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
      !>
      !>