[Numpy-discussion] Different results from repeated calculation
Keith Goodman
kwgoodman at gmail.com
Mon Jan 29 14:00:35 CST 2007
On 1/29/07, Keith Goodman <kwgoodman at gmail.com> wrote:
> On 1/29/07, Keith Goodman <kwgoodman at gmail.com> wrote:
> > On 1/29/07, Keith Goodman <kwgoodman at gmail.com> wrote:
> > > On 1/29/07, Charles R Harris <charlesr.harris at gmail.com> wrote:
> > >
> > > > That's odd, the LSB bit of the double precision mantissa is only about
> > > > 2.2e-16, so you can't *get* differences as small as 8.4e-22 without about
> > > > 70 bit mantissa's. Hmmm, and extended double precision only has 63 bit
> > > > mantissa's. Are you sure you are computing the error correctly?
> > >
> > > That is odd.
> > >
> > > 8.4e-22 is just the output of the test script: abs(z - z0).max(). That
> > > abs is from python.
> >
> > By playing around with x and y I can get all sorts of values for abs(z
> > - z0).max(). I can get down to the e-23 range and to 2.2e-16. I've
> > also seen e-18 and e-22.
>
> Here is a setting for x and y that gives me a difference (using the
> unit test in this thread) of 4.54747e-13! That is huge---and a serious
> problem. I am sure I can get bigger.
>
> # x data
> x = M.zeros((3,3))
> x[0,0] = 9.0030140479499
> x[0,1] = 9.0026474226671
> x[0,2] = -9.0011270502873
> x[1,0] = 9.0228605377994
> x[1,1] = 9.0033715311274
> x[1,2] = -9.0082367491299
> x[2,0] = 9.0044783987583
> x[2,1] = 0.0027488028057
> x[2,2] = -9.0036113393360
>
> # y data
> y = M.zeros((3,1))
> y[0,0] =10.00088539878978
> y[1,0] = 0.00667193234012
> y[2,0] = 0.00032472712345
OK. I guess I should be looking at the fractional difference instead
of the absolute difference. The fractional difference is of order
e-16.
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