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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