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## spoequ()

subroutine spoequ | ( | integer | n,
|  | real, dimension( lda, * ) | a,
|  | integer | lda,
|  | real, dimension( * ) | s,
|  | real | scond,
|  | real | amax,
|  | integer | info )

SPOEQU

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

Purpose:

      !>
      !> SPOEQU computes row and column scalings intended to equilibrate a
      !> symmetric positive definite matrix A and reduce its condition number
      !> (with respect to the two-norm).  S contains the scale factors,
      !> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
      !> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
      !> choice of S puts the condition number of B within a factor N of the
      !> smallest possible condition number over all possible diagonal
      !> scalings.
      !>

Parameters

  [in]

  N

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

  [in]

  A

      !>          A is REAL array, dimension (LDA,N)
      !>          The N-by-N symmetric positive definite matrix whose scaling
      !>          factors are to be computed.  Only the diagonal elements of A
      !>          are referenced.
      !>

  [in]

  LDA

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

  [out]

  S

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

  [out]

  SCOND

      !>          SCOND is REAL
      !>          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 REAL
      !>          Absolute value of largest matrix element.  If AMAX is very
      !>          close to overflow or very close to underflow, the matrix
      !>          should be scaled.
      !>

  [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.