Source code for smpl.stat.stat

import numpy as np
import uncertainties as unc
import uncertainties.unumpy as unp
from smpl import doc
import scipy
import math
import statistics as stat
import pandas as pd


unv = unp.nominal_values
usd = unp.std_devs


def R2(y, f):
    """
    R2 - Coefficient of determination

    In the best case, the modeled values exactly match the observed values, which results in R2 = 1. 
    A baseline model, which always predicts the mean of y, will have R2 = 0. 
    Models that have worse predictions than this baseline will have a negative R2. 

    References
    ----------

    https://en.wikipedia.org/wiki/Coefficient_of_determination
    """
    r = y - f
    mean = np.sum(r)/len(r)
    SSres = np.sum((r)**2)
    SStot = np.sum((r-mean)**2)
    Rsq = 1 - SSres/SStot
    return Rsq


def Chi2(y, f, sigmas=None):
    """
    Chi2 - Goodness of Fit

    In general, if Chi-squared/Nd is of order 1.0, then the fit is reasonably good. 
    Coversely,  if Chi-squared/Nd >> 1.0, then the fit is a poor one.

    References
    ----------

    https://www.phys.hawaii.edu/~varner/PHYS305-Spr12/DataFitting.html
    """
    r = y - f
    if sigmas is not None:
        chisq = np.sum((r/sigmas)**2)
    else:
        chisq = np.sum((r)**2)

    return chisq


def unv_lambda(f):
    """Returns a function which applies :func:`unv` on the result of ``f``."""
    return lambda *a: unv(f(*a))


def poisson_dist(N):
    """Return ``N`` with added poissonian uncertainties."""
    return unp.uarray(N, np.sqrt(N))


def no_dist(N):
    """Return ``N`` with no uncertainties."""
    return unp.uarray(N, 0)


def normalize(ydata):
    """Return normalized ``ydata``."""
    return (ydata-np.amin(ydata))/(np.amax(ydata)-np.amin(ydata))


def novar_mean(n):
    """Return mean of ``n`` with only the uncertainties of ``n`` and no variance."""
    return np.sum(n)/len(n)


def mean(n):
    """Return mean of ``n`` with combined error of variance and unvertainties of ``n``."""
    # find the mean value and add uncertainties
    if isinstance(n, pd.core.series.Series):
        n = n.to_numpy()
    k = np.mean(n)
    err = stat.variance(unv(n))
    return unc.ufloat(unv(k), math.sqrt(usd(k)**2 + err))


def noisy(x, mean=0, std=1):
    """Add gaussian noise to ``x``."""
    return x+np.random.normal(mean, std, len(x))


def normal(x, mean=0, std=1):
    return np.random.normal(mean, std, len(x))


@doc.insert_eq()
def fft(y):
    """
    $F(y)$
    """
    N = len(y)
    fft = scipy.fftpack.fft(y)
    return 2 * abs(fft[:N//2]) / N