问题
The intent is to show the result of several observations without unnecessary digits i.e., to display a value with the number of significant digits that is consistent with a given uncertainty.
For example, if computed mean=123.45
and err=0.0012345
then the
expected output may look like 123450 ± 1.2 (× 10-3) where
the following rules are used:
- the error always has one or two significant digits. Two if the first
digit is
1
(ignoring the leading zeros) - the mean value is rounded to drop uncertain digits except for the last one ("stop the mean at the same decade as that of the first significant (non-zero) digit in the SEM"). Trailing zeros are added to display the precision corresponding to the error if necessary.
How it might be used in Python:
import statistics
mean = statistics.mean(measurements)
err = statistics.stdev(measurements, mean) / len(measurements) ** 0.5
print("{} ± {} (×10<sup>{}</sup>)".format(*round_to_uncertainty(mean, err)))
The question is how to implement the round_to_uncertainty(value,
uncertainty)
function expressing the rules 1 and 2 above.
Note: the terms error, uncertainty are used loosely in the question. See the Guide to the Expression of Uncertainty in Measurement (GUM). Here's a related question for R.
回答1:
decimal module could be used to manipulate the decimal representation of the numbers conveniently:
from decimal import Decimal
def round_to_uncertainty(value, uncertainty):
# round the uncertainty to 1-2 significant digits
u = Decimal(uncertainty).normalize()
exponent = u.adjusted() # find position of the most significant digit
precision = (u.as_tuple().digits[0] == 1) # is the first digit 1?
u = u.scaleb(-exponent).quantize(Decimal(10)**-precision)
# round the value to remove excess digits
return round(Decimal(value).scaleb(-exponent).quantize(u)), u, exponent
Example:
for mean, err in [
(123.45, 0.0012345), # 123450 ± 1.2 (×10<sup>-3</sup>)
(8165.666, 338.9741), # 82 ± 3 (×10<sup>2</sup>)
]:
print("{} ± {} (×10<sup>{}</sup>)".format(*round_to_uncertainty(mean, err)))
The input 123.45
, 0.0012345
is reported as 123450 ± 1.2
(×10-3). And 8165.666
, 338.9741
translates to 82 ± 3 (×102) according to the rules from the current question.
来源:https://stackoverflow.com/questions/53976847/report-uncertainty-given-a-mean-and-the-standard-error-show-only-significant-f