SRC/spoequb.f(3)

NAME
SRC/spoequb.f

SYNOPSIS

  Functions/Subroutines
subroutine spoequb (n, a, lda, s, scond, amax, info)
SPOEQUB

Function/Subroutine Documentation

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

SPOEQUB

Purpose:

     SPOEQUB 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.
     This routine differs from SPOEQU by restricting the scaling factors
     to a power of the radix.  Barring over- and underflow, scaling by
     these factors introduces no additional rounding errors.  However, the
     scaled diagonal entries are no longer approximately 1 but lie
     between sqrt(radix) and 1/sqrt(radix).

Parameters
    N

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

    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.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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 117 of file spoequb.f.

Author

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