Truncation error

[Meghna Karkera]

Thanks, the problem was I solved a covariance matrix manually, but my
fellow mate using the covariance syntax. That's why there was difference in
Matlab and python results. But now when I use the covariance syntax in
python, matlab and python gives the same results.

On Sat, Oct 10, 2020, 21:37 Peter J. Holzer <hjp-python at hjp.at> wrote:

> On 2020-10-07 07:53:55 +0200, Marco Sulla wrote:
> > If you want to avoid float problems, you can use Decimal:
>
> Decimal doesn't avoid floating point problems, because it is a floating
> point format. For example:
>
>     Python 3.8.5 (default, Jul 28 2020, 12:59:40)
>     [GCC 9.3.0] on linux
>     Type "help", "copyright", "credits" or "license" for more information.
>     >>> from decimal import *
>     >>> a = Decimal(3)
>     >>> a
>     Decimal('3')
>     >>> b = Decimal(1E50)
>     >>> b
>     Decimal('100000000000000007629769841091887003294964970946560')
>     >>> c = Decimal(2)
>     >>> a + b - c - b
>     Decimal('8112996705035029053440')
>     >>> b - b + a - c
>     Decimal('1')
>     >>> a + (b - b) - c
>     Decimal('1')
>     >>> a + b - b - c
>     Decimal('8112996705035029053438')
>     >>>
>
> Mathematically, all four expressions should have the result 1, but with
> floating point numbers they don't because intermediate results are
> rounded.
>
> For comparison, here are the results with float:
>
>     >>> a + b - c - b
>     0.0
>     >>> b - b + a - c
>     1.0
>     >>> a + (b - b) - c
>     1.0
>     >>> a + b - b - c
>     -2.0
>     >>>
>
> One could argue that these are at least closer to the truth, although I
> think that's just luck,
>
> Decimal does have two advantages over float:
>
> a) It's precision is configurable and even by default higher. So on
>    average, the error is smaller (but still not zero).
>
> b) It uses decimal numbers like we learned in school. So it will make
>    the same errors as we make when we use pencil and paper, which is
>    less confusing to laypersons than the seemingly arbitrary errors from
>    converting from decimal to binary and back.
>
>
> The disadvantages are of course higher memory consumption and lower
> speed. Also, I'm very confident that the engineers at Intel and AMD knew
> what they were doing when they designed the FP units of their
> processors. I'm slightly less confident about the authors of the Decimal
> module. And I'm much less confident that the average Python programmer
> can implement a matrix multiplication with Decimal which is as
> numerically stable as what Matlab or Pandas provide using IEEE-754
> arithmetic.
>
>         hp
>
> PS: I recently read an interesting article on the Android calculator.
>     That goes to extreme lengths to avoid unexpected rounding errors.
>     It is also very slow, but still faster than a human can look, so it
>     doesn't matter.
>
> --
>    _  | Peter J. Holzer    | Story must make more sense than reality.
> |_|_) |                    |
> | |   | hjp at hjp.at         |    -- Charles Stross, "Creative writing
> __/   | http://www.hjp.at/ |       challenge!"
> --
> https://mail.python.org/mailman/listinfo/python-list
>