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## zheequb()

subroutine zheequb | ( | character | uplo,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( * ) | s,
|  | double precision | scond,
|  | double precision | amax,
|  | complex*16, dimension( * ) | work,
|  | integer | info )

ZHEEQUB

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

Purpose:

      !>
      !> ZHEEQUB computes row and column scalings intended to equilibrate a
      !> Hermitian matrix A (with respect to the Euclidean norm) and reduce
      !> its condition number. The scale factors S are computed by the BIN
      !> algorithm (see references) so that the scaled matrix B with elements
      !> B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
      !> the smallest possible condition number over all possible diagonal
      !> scalings.
      !>

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

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

  [in]

  A

      !>          A is COMPLEX*16 array, dimension (LDA,N)
      !>          The N-by-N Hermitian matrix whose scaling factors are to be
      !>          computed.
      !>

  [in]

  LDA

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

  [out]

  S

      !>          S is DOUBLE PRECISION array, dimension (N)
      !>          If INFO = 0, S contains the scale factors for A.
      !>

  [out]

  SCOND

      !>          SCOND is DOUBLE PRECISION
      !>          If INFO = 0, S contains the ratio of the smallest S(i) to
      !>          the largest S(i). If SCOND >= 0.1 and AMAX is neither too
      !>          large nor too small, it is not worth scaling by S.
      !>

  [out]

  AMAX

      !>          AMAX is DOUBLE PRECISION
      !>          Largest absolute value of any matrix element. If AMAX is
      !>          very close to overflow or very close to underflow, the
      !>          matrix should be scaled.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 array, dimension (2*N)
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

References:
  Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
  Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
  DOI 10.1023/B:NUMA.0000016606.32820.69
  Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679