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""" | |
License: BSD | |
Author: Mathieu Blondel | |
Implements three algorithms for projecting a vector onto the simplex: sort, pivot and bisection. | |
For details and references, see the following paper: | |
Large-scale Multiclass Support Vector Machine Training via Euclidean Projection onto the Simplex | |
Mathieu Blondel, Akinori Fujino, and Naonori Ueda. |
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# Author: Mathieu Blondel | |
# License: BSD 3 clause | |
import numpy as np | |
def projection_simplex(V, z=1, axis=None): | |
""" | |
Projection of x onto the simplex, scaled by z: | |
P(x; z) = argmin_{y >= 0, sum(y) = z} ||y - x||^2 |
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# Authors: Mathieu Blondel, Vlad Niculae | |
# License: BSD 3 clause | |
import numpy as np | |
def _gen_pairs(gen, max_iter, max_inner, random_state, verbose): | |
rng = np.random.RandomState(random_state) | |
# if tuple, interpret as randn |
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#!/usr/bin/env python | |
""" | |
Find the solution for the second order differential equation | |
u'' = -u | |
with u(0) = 10 and u'(0) = -5 | |
using the Euler and the Runge-Kutta methods. |
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# (C) Mathieu Blondel, November 2013 | |
# License: BSD 3 clause | |
import numpy as np | |
def ranking_precision_score(y_true, y_score, k=10): | |
"""Precision at rank k | |
Parameters |
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# Mathieu Blondel, September 2010 | |
# License: BSD 3 clause | |
import numpy as np | |
from numpy import linalg | |
import cvxopt | |
import cvxopt.solvers | |
def linear_kernel(x1, x2): | |
return np.dot(x1, x2) |
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% (C) Mathieu Blondel, July 2010 | |
\documentclass[a4paper,10pt]{article} | |
\usepackage[english]{babel} | |
\usepackage[T1]{fontenc} | |
\usepackage[ansinew]{inputenc} | |
\usepackage{lmodern} | |
\usepackage{amsmath} |
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# Mathieu Blondel, February 2012 | |
# License: BSD 3 clause | |
# Port to Python of examples in chapter 5 of | |
# "Introductory Statistics with R" by Peter Dalgaard | |
import numpy as np | |
from scipy.stats import ttest_1samp, wilcoxon, ttest_ind, mannwhitneyu | |
# daily intake of energy in kJ for 11 women |
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# Mathieu Blondel, October 2010 | |
# License: BSD 3 clause | |
import numpy as np | |
from numpy import linalg | |
def linear_kernel(x1, x2): | |
return np.dot(x1, x2) | |
def polynomial_kernel(x, y, p=3): |
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from random import random | |
""" | |
Find pi by the Monte-Carlo method. | |
area of a circle = pi r^2 | |
area of a square = (2r)^2 = 4 r^2 | |
Perform random uniform sampling between -1 and 1. | |
The proportion of points in the unit circle is: |
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