sgeequb.f - Man Page

subroutine sgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
SGEEQUB

SGEEQUB  

Purpose:

 SGEEQUB computes row and column scalings intended to equilibrate an
 M-by-N matrix A and reduce its condition number.  R returns the row
 scale factors and C the column scale factors, chosen to try to make
 the largest element in each row and column of the matrix B with
 elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
 the radix.

 R(i) and C(j) are restricted to be a power of the radix between
 SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
 of these scaling factors is not guaranteed to reduce the condition
 number of A but works well in practice.

 This routine differs from SGEEQU 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 entries' magnitudes are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix).

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

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

A

          A is REAL array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

R

          R is REAL array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A.

C

          C is REAL array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A.

ROWCND

          ROWCND is REAL
          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
          AMAX is neither too large nor too small, it is not worth
          scaling by R.

COLCND

          COLCND is REAL
          If INFO = 0, COLCND contains the ratio of the smallest
          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
          worth scaling by C.

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,  and i is
                <= M:  the i-th row of A is exactly zero
                >  M:  the (i-M)-th column of A is exactly zero

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file sgeequb.f.