Computes row and column scaling factors restricted to a power of radix to equilibrate a general matrix and reduce its condition number.
The routine computes row and column scalings intended to equilibrate an
Aand reduce its condition number. The output array
rreturns the row scale factors and the array
c- the column scale factors. These factors are chosen to try to make the largest element in each row and column of the matrix
have an absolute value of at most the radix.
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
abut works well in practice.
BIGNUMare parameters representing machine precision. You can use the
?lamchroutines to compute them. For example, compute single precision values of
SMLNUM = slamch ('s') BIGNUM = 1 / SMLNUM
This routine differs from
?geequby restricting the scaling factors to a power of the radix. Except for over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer equal to approximately 1 but lie between
- The number of rows of the matrixINTEGER.A;.m≥0
- The number of columns of the matrixINTEGER.A;.n≥0
- REALforsgeequbDOUBLE PRECISIONfordgeequbCOMPLEXforcgeequbDOUBLE COMPLEXforzgeequb.Array: size(.lda,*)Contains them-by-nmatrixAwhose equilibration factors are to be computed.The second dimension ofamust be at leastmax(1,.n)
- The leading dimension ofINTEGER.a;.lda≥max(1,m)
- REALfor single precision flavorsDOUBLE PRECISIONfor double precision flavors.Arrays:,r(m).c(n)