# Coverage for pygeodesy/fstats.py : 99%

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''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import isodd, _xinstanceof, _xsubclassof, _zip from pygeodesy.errors import _xError from pygeodesy.fmath import hypot2, sqrt from pygeodesy.fsums import _2float, Fmt, Fsum from pygeodesy.interns import NN, _iadd_, _invalid_, _other_, _SPACE_, \ _0_0, _1_5, _2_0, _3_0, _4_0, _6_0 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import _Named, _NotImplemented, notOverloaded, \ property_RO # from pygeodesy.props import property_RO # from .named # from pygeodesy.streprs import Fmt # from .fsums # from math import sqrt # pow from .fmath __all__ = _ALL_LAZY.fstats __version__ = '22.06.15' _Float = Fsum, float _Scalar = _Float + (int,) # XXX basics._Ints is ABCMeta try: _Scalar += (long,) except NameError: # Python 3+ pass def _2Floats(xs, ys=False): '''(INTERNAL) Yield each value as C{float} or L{Fsum}. ''' for i, x in enumerate(xs): yield x if isinstance(x, _Float) else (_2float(index=i, ys=x) if ys else _2float(index=i, xs=x)) def _sampled(n, sample): '''(INTERNAL) Return the sample or the entire count. ''' return (n - 1) if sample and n > 0 else n class _FstatsNamed(_Named): '''(INTERNAL) Base class. ''' _n = 0 def __add__(self, other): '''Sum of this and a scalar, an L{Fsum} or an other instance. ''' f = self.fcopy(name=self.__add__.__name__) # PYCHOK expected f += other return f def __float__(self): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self) def __int__(self): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self) def __len__(self): '''Return the I{total} number of accumulated values (C{int}). ''' return self._n def __neg__(self): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self) def __radd__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __str__(self): return Fmt.SQUARE(self.named3, len(self)) def fcopy(self, deep=False, name=NN): '''Copy this instance, C{shallow} or B{C{deep}}. ''' n = name or self.fcopy.__name__ f = _Named.copy(self, deep=deep, name=n) return self._copy(f, self) # PYCHOK expected copy = fcopy class _FstatsBase(_FstatsNamed): '''(INTERNAL) Base running stats class. ''' _Ms = () def _copy(self, c, s): '''(INTERNAL) Copy C{B{c} = B{s}}. ''' _xinstanceof(self.__class__, c=c, s=s) c._Ms = tuple(M.fcopy() for M in s._Ms) # deep=False c._n = s._n return c def fadd(self, xs, sample=False): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, xs, sample=sample) def fadd_(self, *xs, **sample): '''Accumulate and return the current count. @see: Method C{fadd}. ''' return self.fadd(xs, **sample) def fmean(self, xs=None): '''Accumulate and return the current mean. @kwarg xs: Iterable with additional values (C{Scalar}s). @return: Current, running mean (C{float}). @see: Method C{fadd}. ''' if xs: self.fadd(xs) return self._M1.fsum() def fmean_(self, *xs): '''Accumulate and return the current mean. @see: Method C{fmean}. ''' return self.fmean(xs) def fstdev(self, xs=None, sample=False): '''Accumulate and return the current standard deviation. @kwarg xs: Iterable with additional values (C{Scalar}). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) standard deviation (C{float}). @see: Method C{fadd}. ''' v = self.fvariance(xs, sample=sample) return sqrt(v) if v > 0 else _0_0 def fstdev_(self, *xs, **sample): '''Accumulate and return the current standard deviation. @see: Method C{fstdev}. ''' return self.fstdev(xs, **sample) def fvariance(self, xs=None, sample=False): '''Accumulate and return the current variance. @kwarg xs: Iterable with additional values (C{Scalar}s). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) variance (C{float}). @see: Method C{fadd}. ''' n = self.fadd(xs, sample=sample) return float(self._M2 / float(n)) if n > 0 else _0_0 def fvariance_(self, *xs, **sample): '''Accumulate and return the current variance. @see: Method C{fvariance}. ''' return self.fvariance(xs, **sample) def _iadd_other(self, other): '''(INTERNAL) Add Scalar or Scalars. ''' if isinstance(other, _Scalar): self.fadd_(other) else: try: if not isinstance(other, (list, tuple)): raise TypeError(_SPACE_(_invalid_, _other_)) self.fadd(other) except Exception as x: raise _xError(x, _SPACE_(self, _iadd_, repr(other))) @property_RO def _M1(self): '''(INTERNAL) get the 1st Moment accumulator.''' return self._Ms[0] @property_RO def _M2(self): '''(INTERNAL) get the 2nd Moment accumulator.''' return self._Ms[1] class Fcook(_FstatsBase): '''U{Cook<https://www.JohnDCook.com/blog/skewness_kurtosis>}'s C{RunningStats} computing the running mean, median and (sample) kurtosis, skewness, variance, standard deviation and Jarque-Bera normality. @see: L{Fwelford} and U{Higher-order statistics<https:// WikiPedia.org/wiki/Algorithms_for_calculating_variance>}. ''' def __init__(self, xs=None, name=NN): '''New L{Fcook} stats accumulator. @kwarg xs: Iterable with initial values (C{Scalar}s). @kwarg name: Optional name (C{str}). @see: Method L{Fcook.fadd}. ''' self._Ms = tuple(Fsum() for _ in range(4)) # 1st, 2nd ... Moment if name: self.name = name if xs: self.fadd(xs) def __iadd__(self, other): '''Add B{C{other}} to this L{Fcook} instance. @arg other: An L{Fcook} instance or C{Scalar}s, meaning one or more C{scalar} or L{Fsum} instances. @return: This instance, updated (L{Fcook}). @raise TypeError: Invalid B{C{other}} type. @raise ValueError: Invalid B{C{other}}. @see: Method L{Fcook.fadd}. ''' if isinstance(other, Fcook): nb = len(other) if nb > 0: na = len(self) if na > 0: A1, A2, A3, A4 = self._Ms B1, B2, B3, B4 = other._Ms n = na + nb n_ = float(n) D = A1 - B1 # b1 - a1 Dn = D / n_ Dn2 = Dn**2 # d**2 / n**2 nab = na * nb Dn3 = Dn2 * (D * nab) na2 = na**2 nb2 = nb**2 A4 += B4 A4 += (B3 * na - (A3 * nb)) * (Dn * _4_0) A4 += (B2 * na2 + (A2 * nb2)) * (Dn2 * _6_0) A4 += (Dn * Dn3) * (na2 - nab + nb2) # d**4 / n**3 A3 += B3 A3 += (A2 * na - (B2 * nb)) * (Dn * _3_0) A3 += Dn3 * (na - nb) A2 += B2 A2 += Dn2 * (nab / n_) B1n = B1 * nb # if other is self A1 *= na A1 += B1n A1 *= 1 / n_ # /= chokes PyChecker # self._Ms = A1, A2, A3, A4 self._n = n else: self._copy(self, other) else: self._iadd_other(other) return self def fadd(self, xs, sample=False): '''Accumulate and return the current count. @arg xs: Iterable with additional values (C{Scalar}s, meaning C{scalar} or L{Fsum} instances). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) count (C{int}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: Non-scalar B{C{xs}} value. @raise ValueError: Invalid or non-finite B{C{xs}} value. @see: U{online_kurtosis<https://WikiPedia.org/wiki/ Algorithms_for_calculating_variance>}. ''' n = self._n if xs: M1, M2, M3, M4 = self._Ms for x in _2Floats(xs): n1 = n n += 1 D = x - M1 Dn = D / n if Dn: Dn2 = Dn**2 if n1 > 1: T1 = D * (Dn * n1) T2 = T1 * (Dn * (n1 - 1)) T3 = T1 * (Dn2 * (n**2 - 3 * n1)) elif n1 > 0: # n1 == 1, n == 2 T1 = D * Dn T2 = _0_0 T3 = T1 * Dn2 else: T1 = T2 = T3 = _0_0 M4 += T3 M4 -= M3 * (Dn * _4_0) M4 += M2 * (Dn2 * _6_0) M3 += T2 M3 -= M2 * (Dn * _3_0) M2 += T1 M1 += Dn # self._Ms = M1, M2, M3, M4 self._n = n return _sampled(n, sample) def fjb(self, xs=None, sample=True, excess=True): '''Accumulate and compute the current U{Jarque-Bera <https://WikiPedia.org/wiki/Jarque–Bera_test>} normality. @kwarg xs: Iterable with additional values (C{Scalar}s). @kwarg sample: Return the I{sample} value (C{bool}), default. @kwarg excess: Return the I{excess} kurtosis (C{bool}), default. @return: Current, running (sample) Jarque-Bera normality (C{float}). @see: Method L{Fcook.fadd}. ''' n = self.fadd(xs, sample=sample) k = self.fkurtosis(sample=sample, excess=excess) / _2_0 s = self.fskewness(sample=sample) return n * hypot2(k, s) / _6_0 def fjb_(self, *xs, **sample_excess): '''Accumulate and compute the current U{Jarque-Bera <https://WikiPedia.org/wiki/Jarque–Bera_test>} normality. @see: Method L{Fcook.fjb}. ''' return self.fjb(xs, **sample_excess) def fkurtosis(self, xs=None, sample=False, excess=True): '''Accumulate and return the current kurtosis. @kwarg xs: Iterable with additional values (C{Scalar}s). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @kwarg excess: Return the I{excess} kurtosis (C{bool}), default. @return: Current, running (sample) kurtosis or I{excess} kurtosis (C{float}). @see: U{Kurtosis Formula<https://www.Macroption.com/kurtosis-formula>} and U{Mantalos<https://www.researchgate.net/publication/ 227440210_Three_different_measures_of_sample_skewness_and_kurtosis_and_their_effects_on_the_JarqueBera_test_for_normality>}. @see: Method L{Fcook.fadd}. ''' k, n = _0_0, self.fadd(xs, sample=sample) if n > 0: _, M2, _, M4 = self._Ms m2 = float(M2 * M2) if m2: K, x = (M4 * (n / m2)), _3_0 if sample and 2 < n < len(self): d = float((n - 1) * (n - 2)) K *= (n + 1) * (n + 2) / d x *= n**2 / d if excess: K -= x k = K.fsum() return k def fkurtosis_(self, *xs, **sample_excess): '''Accumulate and return the current kurtosis. @see: Method L{Fcook.fkurtosis}. ''' return self.fkurtosis(xs, **sample_excess) def fmedian(self, xs=None): '''Accumulate and return the current median. @kwarg xs: Iterable with additional values (C{Scalar}s). @return: Current, running median (C{float}). @see: U{Pearson's Skewness Coefficients<https://MathWorld.Wolfram.com/ PearsonsSkewnessCoefficients.html>}, U{Skewness & Kurtosis Simplified https://TowardsDataScience.com/skewness-kurtosis-simplified-1338e094fc85>} and method L{Fcook.fadd}. ''' # skewness = 3 * (mean - median) / stdev, i.e. # median = mean - skewness * stdef / 3 m = float(self._M1) if xs is None else self.fmean(xs) return m - self.fskewness() * self.fstdev() / _3_0 def fmedian_(self, *xs): '''Accumulate and return the current median. @see: Method L{Fcook.fmedian}. ''' return self.fmedian(xs) def fskewness(self, xs=None, sample=False): '''Accumulate and return the current skewness. @kwarg xs: Iterable with additional values (C{Scalar}s). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) skewness (C{float}). @see: U{Skewness Formula<https://www.Macroption.com/skewness-formula/>} and U{Mantalos<https://www.researchgate.net/publication/ 227440210_Three_different_measures_of_sample_skewness_and_kurtosis_and_their_effects_on_the_JarqueBera_test_for_normality>}. @see: Method L{Fcook.fadd}. ''' s, n = _0_0, self.fadd(xs, sample=sample) if n > 0: _, M2, M3, _ = self._Ms m2 = pow(float(M2), _1_5) if m2: S = M3 * (sqrt(float(n)) / m2) if sample and 1 < n < len(self): S *= (n + 1) / float(n - 1) s = S.fsum() return s def fskewness_(self, *xs, **sample): '''Accumulate and return the current skewness. @see: Method L{Fcook.fskewness}. ''' return self.fskewness(xs, **sample) def toFwelford(self, name=NN): '''Return an L{Fwelford} equivalent. ''' f = Fwelford(name=name or self.name) f._Ms = self._M1.fcopy(), self._M2.fcopy() # deep=False f._n = self._n return f class Fwelford(_FstatsBase): '''U{Welford<https://WikiPedia.org/wiki/Algorithms_for_calculating_variance>}'s accumulator computing the running mean, (sample) variance and standard deviation. @see: U{Cook<https://www.JohnDCook.com/blog/standard_deviation/>} and L{Fcook}. ''' def __init__(self, xs=None, name=NN): '''New L{Fwelford} stats accumulator. @kwarg xs: Iterable with initial values (C{Scalar}s). @kwarg name: Optional name (C{str}). @see: Method L{Fwelford.fadd}. ''' self._Ms = Fsum(), Fsum() # 1st and 2nd Moment if name: self.name = name if xs: self.fadd(xs) def __iadd__(self, other): '''Add B{C{other}} to this L{Fwelford} instance. @arg other: An L{Fwelford} or L{Fcook} instance or C{Scalar}s, meaning one or more C{scalar} or L{Fsum} instances. @return: This instance, updated (L{Fwelford}). @raise TypeError: Invalid B{C{other}} type. @raise ValueError: Invalid B{C{other}}. @see: Method L{Fwelford.fadd} and U{Parallel algorithm<https// WikiPedia.org/wiki/Algorithms_for_calculating_variance>}. ''' if isinstance(other, Fwelford): nb = len(other) if nb > 0: na = len(self) if na > 0: M, S = self._Ms M_, S_ = other._Ms n = na + nb n_ = float(n) D = M_ - M D *= D # D**2 D *= na * nb / n_ S += D S += S_ Mn = M_ * nb # if other is self M *= na M += Mn M *= 1 / n_ # /= chokes PyChecker # self._Ms = M, S self._n = n else: self._copy(self, other) elif isinstance(other, Fcook): self += other.toFwelford() else: self._iadd_other(other) return self def fadd(self, xs, sample=False): '''Accumulate and return the current count. @arg xs: Iterable with additional values (C{Scalar}s, meaning C{scalar} or L{Fsum} instances). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) count (C{int}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: Non-scalar B{C{xs}} value. @raise ValueError: Invalid or non-finite B{C{xs}} value. ''' n = self._n if xs: M, S = self._Ms for x in _2Floats(xs): n += 1 D = x - M M += D / n D *= x - M S += D # self._Ms = M, S self._n = n return _sampled(n, sample) class Flinear(_FstatsNamed): '''U{Cook<https://www.JohnDCook.com/blog/running_regression>}'s C{RunningRegression} computing the running slope, intercept and correlation of a linear regression. ''' def __init__(self, xs=None, ys=None, Fstats=Fwelford, name=NN): '''New L{Flinear} regression accumulator. @kwarg xs: Iterable with initial C{x} values (C{Scalar}s). @kwarg ys: Iterable with initial C{y} values (C{Scalar}s). @kwarg Fstats: Stats class for C{x} and C{y} values (L{Fcook} or L{Fwelford}). @kwarg name: Optional name (C{str}). @raise TypeError: Invalid B{C{Fs}}, not L{Fcook} or L{Fwelford}. @see: Method L{Flinear.fadd}. ''' _xsubclassof(Fcook, Fwelford, Fstats=Fstats) if name: self.name = name self._S = Fsum(name=name) self._X = Fstats(name=name) self._Y = Fstats(name=name) if xs and ys: self.fadd(xs, ys) def __iadd__(self, other): '''Add B{C{other}} to this instance. @arg other: An L{Flinear} instance or C{Scalar} pairs, meaning C{scalar} or L{Fsum} instances. @return: This instance, updated (L{Flinear}). @raise TypeError: Invalid B{C{other}} or the B{C{other}} and these C{x} and C{y} accumulators are not compatible. @raise ValueError: Invalid or odd-length B{C{other}}. @see: Method L{Flinear.fadd_}. ''' if isinstance(other, Flinear): if len(other) > 0: if len(self) > 0: n = other._n S = other._S X = other._X Y = other._Y D = (X._M1 - self._X._M1) * \ (Y._M1 - self._Y._M1) * \ (n * self._n / float(n + self._n)) self._n += n self._S += S + D self._X += X self._Y += Y else: self._copy(self, other) else: try: if not isinstance(other, (list, tuple)): raise TypeError(_SPACE_(_invalid_, _other_)) elif isodd(len(other)): raise ValueError(Fmt.PAREN(isodd=Fmt.PAREN(len=_other_))) self.fadd_(*other) except Exception as x: raise _xError(x, _SPACE_(self, _iadd_, repr(other))) return self def _copy(self, c, s): '''(INTERNAL) Copy C{B{c} = B{s}}. ''' _xinstanceof(Flinear, c=c, s=s) c._n = s._n c._S = s._S.fcopy(deep=False) c._X = s._X.fcopy(deep=False) c._Y = s._Y.fcopy(deep=False) return c def fadd(self, xs, ys, sample=False): '''Accumulate and return the current count. @arg xs: Iterable with additional C{x} values (C{Scalar}s), meaning C{scalar} or L{Fsum} instances). @arg ys: Iterable with additional C{y} values (C{Scalar}s, meaning C{scalar} or L{Fsum} instances). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). @return: Current, running (sample) count (C{int}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: Non-scalar B{C{xs}} or B{C{ys}} value. @raise ValueError: Invalid or non-finite B{C{xs}} or B{C{ys}} value. ''' n = self._n if xs and ys: S = self._S X = self._X Y = self._Y for x, y in _zip(_2Floats(xs), _2Floats(ys, ys=True)): # strict=True n1 = n n += 1 if n1 > 0: S += (X._M1 - x) * (Y._M1 - y) * (n1 / float(n)) X += x Y += y self._n = n return _sampled(n, sample) def fadd_(self, *x_ys, **sample): '''Accumulate and return the current count. @arg x_ys: Individual, alternating C{x, y, x, y, ...} positional values (C{Scalar}s). @see: Method C{Flinear.fadd}. ''' return self.fadd(x_ys[0::2], x_ys[1::2], **sample) def fcorrelation(self, sample=False): '''Return the current, running (sample) correlation (C{float}). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). ''' return self._sampled(self.x.fstdev(sample=sample) * self.y.fstdev(sample=sample), sample) def fintercept(self, sample=False): '''Return the current, running (sample) intercept (C{float}). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). ''' return float(self.y._M1 - (self.x._M1 * self.fslope(sample=sample))) def fslope(self, sample=False): '''Return the current, running (sample) slope (C{float}). @kwarg sample: Return the I{sample} instead of the entire I{population} value (C{bool}). ''' return self._sampled(self.x.fvariance(sample=sample), sample) def _sampled(self, t, sample): '''(INTERNAL) Compute the sampled or entire population result. ''' t *= float(_sampled(self._n, sample)) return float(self._S / t) if t else _0_0 @property_RO def x(self): '''Get the C{x} accumulator (L{Fcook} or L{Fwelford}). ''' return self._X @property_RO def y(self): '''Get the C{y} accumulator (L{Fcook} or L{Fwelford}). ''' return self._Y __all__ += _ALL_DOCS(_FstatsBase, _FstatsNamed) # **) MIT License # # Copyright (C) 2021-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.