Speed#

This benchmark focuses on comparing the speed of pyMultiFit’s statistical distribution generations compared to the well-established SciPy library. The focus is on ensuring that pyMultiFit provides reliably faster generation that closely match or are better than SciPy running time.

What is Tested?#

  • Probability Density Function (PDF): Evaluates the time taken to compute the PDF for a set of input values.

  • Cumulative Distribution Function (CDF): Measures the performance of computing cumulative probabilities.

Benchmark setup#

To test accuracy:

  • Both pyMultiFit and SciPy are run on the same input data, using distributions like Gaussian, Beta, and Laplace.

  • Results are compared using metrics such as absolute error, relative error, and visual plots.

  • A range of parameter values and edge cases are included to evaluate robustness and consistency.#%% md

Summary#

A summary of the speed benchmarks is given in the next notebook.

Testing#

[1]:

import numpy as np
import pandas as pd
import scipy.stats as ss

import pymultifit.distributions as p_dist
from functions import cdf_pdf_plots

[2]:

np.random.seed(43)
n_points_list = np.logspace(0.3, 6, num=50, dtype=int)

norm(loc=0, scale=1)#

[3]:

custom_dist = p_dist.GaussianDistribution.from_scipy_params()
scipy_dist = ss.norm()

m_norm1, s_norm1, = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Gaussian N(0, 1)")
../_images/benchmarks__bm_speed_5_0.png
../_images/benchmarks__bm_speed_5_1.png

norm(loc=3, scale=0.1)#

[4]:

custom_dist = p_dist.GaussianDistribution.from_scipy_params(loc=3, scale=0.1)
scipy_dist = ss.norm(loc=3, scale=0.1)

m_norm2, s_norm2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Gaussian N(3, 0.1)")
../_images/benchmarks__bm_speed_7_0.png
../_images/benchmarks__bm_speed_7_1.png

laplace(loc=0, scale=1)#

[5]:

custom_dist = p_dist.LaplaceDistribution.from_scipy_params()
scipy_dist = ss.laplace()

m_laplace1, s_laplace1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Laplace L(0, 1)")
../_images/benchmarks__bm_speed_9_0.png
../_images/benchmarks__bm_speed_9_1.png

laplace(loc=-3, scale=3)#

[6]:

custom_dist = p_dist.LaplaceDistribution.from_scipy_params(loc=-3, scale=3)
scipy_dist = ss.laplace(loc=-3, scale=3)

m_laplace2, s_laplace2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Laplace L(-3, 3)")
../_images/benchmarks__bm_speed_11_0.png
../_images/benchmarks__bm_speed_11_1.png

skewnorm(a=1, loc=0, scale=1)#

[7]:

custom_dist = p_dist.SkewNormalDistribution.from_scipy_params(a=1)
scipy_dist = ss.skewnorm(a=1)

m_skewnorm1, s_skewnorm1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "SkewNorm S(1, 0, 1)")
../_images/benchmarks__bm_speed_13_0.png
../_images/benchmarks__bm_speed_13_1.png

skewnorm(a=3, loc=-3, scale=0.5)#

[8]:

custom_dist = p_dist.SkewNormalDistribution.from_scipy_params(a=3, loc=-3, scale=0.5)
scipy_dist = ss.skewnorm(a=3, loc=-3, scale=0.5)

m_skewnorm2, s_skewnorm2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "SkewNorm S(3, -3, 0.5)")
../_images/benchmarks__bm_speed_15_0.png
../_images/benchmarks__bm_speed_15_1.png

lognorm(s=1, loc=0, scale=1)#

[9]:

custom_dist = p_dist.LogNormalDistribution.from_scipy_params(s=1, loc=0, scale=1)
scipy_dist = ss.lognorm(s=1, loc=0, scale=1)

m_lognorm1, s_lognorm1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "LogNorm L(1, 0, 1)")
../_images/benchmarks__bm_speed_17_0.png
../_images/benchmarks__bm_speed_17_1.png

lognorm(s=3, loc=-5, scale=0.5)#

[10]:

custom_dist = p_dist.LogNormalDistribution.from_scipy_params(s=3, loc=-5, scale=0.5)
scipy_dist = ss.lognorm(s=3, loc=-5, scale=0.5)

m_lognorm2, s_lognorm2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "LogNorm L(3, -5, 0.5)")
../_images/benchmarks__bm_speed_19_0.png
../_images/benchmarks__bm_speed_19_1.png

beta(a=1, b=1)#

[11]:

custom_dist = p_dist.BetaDistribution.from_scipy_params(a=1, b=1)
scipy_dist = ss.beta(a=1, b=1)

m_beta1, s_beta1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Beta B(1, 1)")
../_images/benchmarks__bm_speed_21_0.png
../_images/benchmarks__bm_speed_21_1.png

beta(a=5, b=80, loc=-3, scale=5)#

[12]:

custom_dist = p_dist.BetaDistribution.from_scipy_params(a=5, b=80, loc=-3, scale=5.6)
scipy_dist = ss.beta(a=5, b=80, loc=-3, scale=5.6)

m_beta2, s_beta2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Beta B(5, 80, -3, 5.6)")
../_images/benchmarks__bm_speed_23_0.png
../_images/benchmarks__bm_speed_23_1.png

arcsine()#

[13]:

custom_dist = p_dist.ArcSineDistribution.from_scipy_params()
scipy_dist = ss.arcsine()

m_asin1, s_asin1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "ArcSine AS()")
../_images/benchmarks__bm_speed_25_0.png
../_images/benchmarks__bm_speed_25_1.png

arcsine(loc=3, scale=2.2)#

[14]:

custom_dist = p_dist.ArcSineDistribution.from_scipy_params(loc=3, scale=2.2)
scipy_dist = ss.arcsine(loc=3, scale=2.2)

m_asin2, s_asin2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "AcrSine AS(3, 2.2)")
../_images/benchmarks__bm_speed_27_0.png
../_images/benchmarks__bm_speed_27_1.png

gamma(a=1, loc=0, scale=1)#

[16]:

custom_dist = p_dist.GammaDistribution.from_scipy_params(a=1, loc=0, scale=1)
scipy_dist = ss.gamma(a=1, loc=0, scale=1)

m_gamma1, s_gamma1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Gamma G(1, 0, 1)")
../_images/benchmarks__bm_speed_29_0.png
../_images/benchmarks__bm_speed_29_1.png

gamma(a=1.27, loc=-3, scale=1.5)#

[17]:

custom_dist = p_dist.GammaDistribution.from_scipy_params(a=1.27, loc=-3, scale=1.5)
scipy_dist = ss.gamma(a=1.27, loc=-3, scale=1.5)

m_gamma2, s_gamma2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Gamma G(1.27, -3, 1.5)")
../_images/benchmarks__bm_speed_31_0.png
../_images/benchmarks__bm_speed_31_1.png

\(\chi^2\)(dof=1)#

[18]:

custom_dist = p_dist.ChiSquareDistribution.from_scipy_params(df=1)
scipy_dist = ss.chi2(df=1)

m_chi21, s_chi21 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Chi2 (1)")
../_images/benchmarks__bm_speed_33_0.png
../_images/benchmarks__bm_speed_33_1.png

\(\chi^2\)(dof=2, loc=-2.3, scale=0.3)#

[19]:

custom_dist = p_dist.ChiSquareDistribution.from_scipy_params(df=2, loc=-2.3, scale=0.3)
scipy_dist = ss.chi2(df=2, loc=-2.3, scale=0.3)

m_chi22, s_chi22 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Chi2 (2, -2.3, 0.3")
../_images/benchmarks__bm_speed_35_0.png
../_images/benchmarks__bm_speed_35_1.png

\(\chi^2\)(dof=2.5, loc=-2.3, scale=0.3)#

[20]:

custom_dist = p_dist.ChiSquareDistribution.from_scipy_params(df=2.5, loc=-2.3, scale=0.3)
scipy_dist = ss.chi2(df=2.5, loc=-2.3, scale=0.3)

m_chi23, s_chi23 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Chi2 (2.5, -2.3, 0.3")
../_images/benchmarks__bm_speed_37_0.png
../_images/benchmarks__bm_speed_37_1.png

foldnorm(mean=2)#

[21]:

custom_dist = p_dist.FoldedNormalDistribution.from_scipy_params(c=2)
scipy_dist = ss.foldnorm(c=2)

m_fold1, s_fold1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "FoldNormal FN(2)")
../_images/benchmarks__bm_speed_39_0.png
../_images/benchmarks__bm_speed_39_1.png

foldnorm(mean=2, loc=1.4, scale=4)#

[22]:

custom_dist = p_dist.FoldedNormalDistribution.from_scipy_params(c=2, loc=1.4, scale=4)
scipy_dist = ss.foldnorm(c=2, loc=1.4, scale=4)

m_fold2, s_fold2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "FoldNormal FN(2, 1.4, 4)")
../_images/benchmarks__bm_speed_41_0.png
../_images/benchmarks__bm_speed_41_1.png

halfNormal(scale=2)#

[23]:

custom_dist = p_dist.HalfNormalDistribution.from_scipy_params(scale=2)
scipy_dist = ss.halfnorm(scale=2)

m_hnorm1, s_hnorm1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "HalfNormal HN(2)")
../_images/benchmarks__bm_speed_43_0.png
../_images/benchmarks__bm_speed_43_1.png

halfnorm(loc=-3, scale=1.3)#

[24]:

custom_dist = p_dist.HalfNormalDistribution.from_scipy_params(loc=-3, scale=1.3)
scipy_dist = ss.halfnorm(loc=-3, scale=1.3)

m_hnorm2, s_hnorm2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "HalfNormal HN(-3, 1.3)")
../_images/benchmarks__bm_speed_45_0.png
../_images/benchmarks__bm_speed_45_1.png

expon(scale=1.4)#

[25]:

custom_dist = p_dist.ExponentialDistribution.from_scipy_params(scale=1 / 1.4)
scipy_dist = ss.expon(scale=1 / 1.4)

m_exp1, s_exp1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Exponential Exp(1.4)")
../_images/benchmarks__bm_speed_47_0.png
../_images/benchmarks__bm_speed_47_1.png

expon(loc=-3, scale=1.4)#

[26]:

custom_dist = p_dist.ExponentialDistribution.from_scipy_params(loc=-3, scale=1 / 1.4)
scipy_dist = ss.expon(loc=-3, scale=1 / 1.4)

m_exp2, s_exp2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Exponential Exp(-3, 1.4)")
../_images/benchmarks__bm_speed_49_0.png
../_images/benchmarks__bm_speed_49_1.png

unif(0, 1)#

[27]:

custom_dist = p_dist.UniformDistribution.from_scipy_params()
scipy_dist = ss.uniform()

m_uni1, s_uni1 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Uniform Uni(0, 1)")
../_images/benchmarks__bm_speed_51_0.png
../_images/benchmarks__bm_speed_51_1.png

unif(-3, 2)#

[28]:

custom_dist = p_dist.UniformDistribution.from_scipy_params(loc=-3, scale=2)
scipy_dist = ss.uniform(loc=-3, scale=2)

m_uni2, s_uni2 = cdf_pdf_plots(custom_dist, scipy_dist, n_points_list, "Uniform Uni(3, 2)")
../_images/benchmarks__bm_speed_53_0.png
../_images/benchmarks__bm_speed_53_1.png

Preparation for summary#

[29]:

pdf_df = pd.DataFrame([m_norm1[0],
                       m_laplace1[0],
                       m_skewnorm1[0],
                       m_lognorm1[0],
                       m_beta1[0],
                       m_asin1[0],
                       m_gamma1[0],
                       m_chi21[0],
                       m_fold1[0],
                       m_hnorm1[0],
                       m_exp1[0],
                       m_uni1[0]]).T
pdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

cdf_df = pd.DataFrame([m_norm1[1],
                       m_laplace1[1],
                       m_skewnorm1[1],
                       m_lognorm1[1],
                       m_beta1[1],
                       m_asin1[1],
                       m_gamma1[1],
                       m_chi21[1],
                       m_fold1[1],
                       m_hnorm1[1],
                       m_exp1[1],
                       m_uni1[1]]).T

cdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

pdf_df.to_csv('PDF_multifit_df.csv', index=False)
cdf_df.to_csv('CDF_multifit_df.csv', index=False)

[30]:

pdf_df = pd.DataFrame([s_norm1[0],
                       s_laplace1[0],
                       s_skewnorm1[0],
                       s_lognorm1[0],
                       s_beta1[0],
                       s_asin1[0],
                       s_gamma1[0],
                       s_chi21[0],
                       s_fold1[0],
                       s_hnorm1[0],
                       s_exp1[0],
                       s_uni1[0]]).T
pdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

cdf_df = pd.DataFrame([s_norm1[1],
                       s_laplace1[1],
                       s_skewnorm1[1],
                       s_lognorm1[1],
                       s_beta1[1],
                       s_asin1[1],
                       s_gamma1[1],
                       s_chi21[1],
                       s_fold1[1],
                       s_hnorm1[1],
                       s_exp1[1],
                       s_uni1[1]]).T

cdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

pdf_df.to_csv('PDF_scipy_df.csv', index=False)
cdf_df.to_csv('CDF_scipy_df.csv', index=False)

[31]:

pdf_df = pd.DataFrame([m_norm2[0],
                       m_laplace2[0],
                       m_skewnorm2[0],
                       m_lognorm2[0],
                       m_beta2[0],
                       m_asin2[0],
                       m_gamma2[0],
                       m_chi22[0],
                       m_fold2[0],
                       m_hnorm2[0],
                       m_exp2[0],
                       m_uni2[0]]).T

pdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

cdf_df = pd.DataFrame([m_norm2[1],
                       m_laplace2[1],
                       m_skewnorm2[1],
                       m_lognorm2[1],
                       m_beta2[1],
                       m_asin2[1],
                       m_gamma2[1],
                       m_chi22[1],
                       m_fold2[1],
                       m_hnorm2[1],
                       m_exp2[1],
                       m_uni2[1]]).T

cdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

pdf_df.to_csv('PDF_multifit_variable_df.csv', index=False)
cdf_df.to_csv('CDF_multifit_variable_df.csv', index=False)

[32]:

pdf_df = pd.DataFrame([s_norm2[0],
                       s_laplace2[0],
                       s_skewnorm2[0],
                       s_lognorm2[0],
                       s_beta2[0],
                       s_asin2[0],
                       s_gamma2[0],
                       s_chi22[0],
                       s_fold2[0],
                       s_hnorm2[0],
                       s_exp2[0],
                       s_uni2[0]]).T
pdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

cdf_df = pd.DataFrame([s_norm2[1],
                       s_laplace2[1],
                       s_skewnorm2[1],
                       s_lognorm2[1],
                       s_beta2[1],
                       s_asin2[1],
                       s_gamma2[1],
                       s_chi22[1],
                       s_fold2[1],
                       s_hnorm2[1],
                       s_exp2[1],
                       s_uni2[1]]).T

cdf_df.columns = ['norm', 'laplace', 'skewnorm', 'lognorm', 'beta', 'arcsine', 'gamma',
                  'chi2', 'foldnorm', 'halfnorm', 'exp', 'unif']

pdf_df.to_csv('PDF_scipy_variable_df.csv', index=False)
cdf_df.to_csv('CDF_scipy_variable_df.csv', index=False)