> On Thu, Feb 16, 2012 at 1:36 AM, Daniel Fetchinson
> <
[hidden email]> wrote:
>>>> Hi folks, often times in science one expresses a value (say
>>>> 1.03789291) and its error (say 0.00089) in a short way by parentheses
>>>> like so: 1.0379(9)
>>>>
>>>> One can vary things a bit, but let's take the simplest case when we
>>>> only keep 1 digit of the error (and round it of course) and round the
>>>> value correspondingly. I've been searching around for a simple
>>>> function that would take 2 float arguments and would return a string
>>>> but didn't find anything although something tells me it's been done a
>>>> gazillion times.
>>>>
>>>> What would be the simplest such function?
>>>
>>> Well, this basically works:
>>>
>>>>>> def format_error(value, error):
>>> ... precision = int(math.floor(math.log(error, 10)))
>>> ... format = "%%.%df(%%d)" % max(-precision, 0)
>>> ... return format % (round(value, -precision),
>>> ... int(round(error / 10 ** precision)))
>>> ...
>>>>>> format_error(1.03789291, 0.00089)
>>> '1.0379(9)'
>>>
>>> Note that "math.floor(math.log(error, 10))" may return the wrong
>>> decimal precision due to binary floating point rounding error, which
>>> could produce some strange results:
>>>
>>>>>> format_error(10378929, 1000)
>>> '10378900(10)'
>>>
>>> So you'll probably want to use decimals instead:
>>>
>>> def format_error(value, error):
>>> value = decimal.Decimal(value)
>>> error = decimal.Decimal(error)
>>> value_scale = value.log10().to_integral(decimal.ROUND_FLOOR)
>>> error_scale = error.log10().to_integral(decimal.ROUND_FLOOR)
>>> precision = value_scale - error_scale
>>> if error_scale > 0:
>>> format = "%%.%dE" % max(precision, 0)
>>> else:
>>> format = "%%.%dG" % (max(precision, 0) + 1)
>>> value_str = format % value.quantize(decimal.Decimal("10") **
>>> error_scale)
>>> error_str = '(%d)' % error.scaleb(-error_scale).to_integral()
>>> if 'E' in value_str:
>>> index = value_str.index('E')
>>> return value_str[:index] + error_str + value_str[index:]
>>> else:
>>> return value_str + error_str
>>>
>>>>>> format_error(1.03789291, 0.00089)
>>> '1.0379(9)'
>>>>>> format_error(103789291, 1000)
>>> '1.03789(1)E+08'
>>>
>>> I haven't tested this thoroughly, so use at your own risk. :-)
>>
>> Thanks a lot, this indeed mostly works, except for cases when the
>> error needs to be rounded up and becomes two digits:
>>
>>>>> format_error( '1.34883', '0.0098' )
>> '1.349(10)'
>>
>> But in this case I'd like to see 1.35(1)
>
> A small adjustment to the scale fixes that. Also tidied up the string
> formatting part:
>
> import decimal
>
> def format_error(value, error):
> value = decimal.Decimal(value)
> error = decimal.Decimal(error)
> error_scale = error.adjusted()
> error_scale += error.scaleb(-error_scale).to_integral().adjusted()
> value_str = str(value.quantize(decimal.Decimal("1E%d" % error_scale)))
> error_str = '(%d)' % error.scaleb(-error_scale).to_integral()
> if 'E' in value_str:
> index = value_str.index('E')
> return value_str[:index] + error_str + value_str[index:]
> else:
> return value_str + error_str
>
> Cheers,
> Ian
Locked
