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## sppequ()

subroutine sppequ | ( | character | uplo,
|  | integer | n,
|  | real, dimension( * ) | ap,
|  | real, dimension( * ) | s,
|  | real | scond,
|  | real | amax,
|  | integer | info )

SPPEQU

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

Purpose:

      !>
      !> SPPEQU computes row and column scalings intended to equilibrate a
      !> symmetric positive definite matrix A in packed storage 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]

  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]

  AP

      !>          AP is REAL array, dimension (N*(N+1)/2)
      !>          The upper or lower triangle of the symmetric matrix A, packed
      !>          columnwise in a linear array.  The j-th column of A is stored
      !>          in the array AP as follows:
      !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
      !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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.