# format a measurement result and its error in "scientific" way

Thu Feb 16 23:21:50 CET 2012

```On 2/16/12, Ian Kelly <ian.g.kelly at gmail.com> wrote:
> On Thu, Feb 16, 2012 at 1:36 AM, Daniel Fetchinson
>>>> 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)
>     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

Thanks, it's simpler indeed, but gives me an error for value=1.267, error=0.08:

Traceback (most recent call last):
File "/home/fetchinson/bin/format_error", line 26, in <module>
print format_error( sys.argv[1], sys.argv[2] )
File "/home/fetchinson/bin/format_error", line 9, in format_error
error_scale += error.scaleb( -error_scale ).to_integral(  ).adjusted(  )
File "/usr/lib64/python2.6/decimal.py", line 3398, in scaleb
ans = self._check_nans(other, context)
File "/usr/lib64/python2.6/decimal.py", line 699, in _check_nans
other_is_nan = other._isnan()
AttributeError: 'int' object has no attribute '_isnan'

Which version of python are you using?

Cheers,
Daniel

--
Psss, psss, put it down! - http://www.cafepress.com/putitdown

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