diff options
| -rw-r--r-- | Lib/statistics.py | 45 |
1 files changed, 27 insertions, 18 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index 6e6d62c..5a3de81 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -206,16 +206,17 @@ def _sum(data): def _ss(data, c=None): - """Return sum of square deviations of sequence data. + """Return the exact mean and sum of square deviations of sequence data. + + Calculations are done in a single pass, allowing the input to be an iterator. + + If given *c* is used the mean; otherwise, it is calculated from the data. + Use the *c* argument with care, as it can lead to garbage results. - If ``c`` is None, the mean is calculated in one pass, and the deviations - from the mean are calculated in a second pass. Otherwise, deviations are - calculated from ``c`` as given. Use the second case with care, as it can - lead to garbage results. """ if c is not None: - T, total, count = _sum((d := x - c) * d for x in data) - return (T, total, count) + T, ssd, count = _sum((d := x - c) * d for x in data) + return (T, ssd, c, count) count = 0 types = set() types_add = types.add @@ -228,20 +229,21 @@ def _ss(data, c=None): sx_partials[d] += n sxx_partials[d] += n * n if not count: - total = Fraction(0) + ssd = c = Fraction(0) elif None in sx_partials: # The sum will be a NAN or INF. We can ignore all the finite # partials, and just look at this special one. - total = sx_partials[None] + ssd = c = sx_partials[None] assert not _isfinite(total) else: sx = sum(Fraction(n, d) for d, n in sx_partials.items()) sxx = sum(Fraction(n, d*d) for d, n in sxx_partials.items()) # This formula has poor numeric properties for floats, # but with fractions it is exact. - total = (count * sxx - sx * sx) / count + ssd = (count * sxx - sx * sx) / count + c = sx / count T = reduce(_coerce, types, int) # or raise TypeError - return (T, total, count) + return (T, ssd, c, count) def _isfinite(x): @@ -854,7 +856,7 @@ def variance(data, xbar=None): Fraction(67, 108) """ - T, ss, n = _ss(data, xbar) + T, ss, c, n = _ss(data, xbar) if n < 2: raise StatisticsError('variance requires at least two data points') return _convert(ss / (n - 1), T) @@ -895,7 +897,7 @@ def pvariance(data, mu=None): Fraction(13, 72) """ - T, ss, n = _ss(data, mu) + T, ss, c, n = _ss(data, mu) if n < 1: raise StatisticsError('pvariance requires at least one data point') return _convert(ss / n, T) @@ -910,7 +912,7 @@ def stdev(data, xbar=None): 1.0810874155219827 """ - T, ss, n = _ss(data, xbar) + T, ss, c, n = _ss(data, xbar) if n < 2: raise StatisticsError('stdev requires at least two data points') mss = ss / (n - 1) @@ -928,7 +930,7 @@ def pstdev(data, mu=None): 0.986893273527251 """ - T, ss, n = _ss(data, mu) + T, ss, c, n = _ss(data, mu) if n < 1: raise StatisticsError('pstdev requires at least one data point') mss = ss / n @@ -937,6 +939,15 @@ def pstdev(data, mu=None): return _float_sqrt_of_frac(mss.numerator, mss.denominator) +def _mean_stdev(data): + """In one pass, compute the mean and sample standard deviation as floats.""" + T, ss, xbar, n = _ss(data) + if n < 2: + raise StatisticsError('stdev requires at least two data points') + mss = ss / (n - 1) + return float(xbar), _float_sqrt_of_frac(mss.numerator, mss.denominator) + + # === Statistics for relations between two inputs === # See https://en.wikipedia.org/wiki/Covariance @@ -1171,9 +1182,7 @@ class NormalDist: @classmethod def from_samples(cls, data): "Make a normal distribution instance from sample data." - if not isinstance(data, (list, tuple)): - data = list(data) - return cls(mean(data), stdev(data)) + return cls(*_mean_stdev(data)) def samples(self, n, *, seed=None): "Generate *n* samples for a given mean and standard deviation." |