zppequ.f(3)

NAME
zppequ.f -

SYNOPSIS

  Functions/Subroutines

subroutine zppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
ZPPEQU

Function/Subroutine Documentation

  subroutine zppequ (characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)

ZPPEQU

Purpose:

     ZPPEQU computes row and column scalings intended to equilibrate a
     Hermitian 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:
    UPLO

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

    N

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

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              The upper or lower triangle of the Hermitian 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.

    S

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

    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.

    AMAX

              AMAX is DOUBLE PRECISION
              Absolute value of largest matrix element.  If AMAX is very
              close to overflow or very close to underflow, the matrix
              should be scaled.

    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.

Date:
    November 2011

Definition at line 118 of file zppequ.f.

Author

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