mblondel

"""
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.

mblondel

# 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

mblondel

# 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

mblondel

#!/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.

mblondel

# (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

mblondel

# 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)

mblondel

% (C) Mathieu Blondel, July 2010

\documentclass[a4paper,10pt]{article}

\usepackage[english]{babel}
\usepackage[T1]{fontenc}
\usepackage[ansinew]{inputenc}

\usepackage{lmodern}
\usepackage{amsmath}

mblondel

# 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

mblondel

# 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):

mblondel

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: