SRC/sppequ.f(3)

NAME
SRC/sppequ.f

SYNOPSIS

  Functions/Subroutines
subroutine sppequ (uplo, n, ap, s, scond, amax, info)
SPPEQU

Function/Subroutine Documentation

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

SPPEQU

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
    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 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.
    !>

    S

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

    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.
    !>

    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.
    !>

    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.

Definition at line 115 of file sppequ.f.

Author

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