mblondel

# Mathieu Blondel, 2022
# BSD license

import numpy as np
from scipy.ndimage import convolve1d
from sklearn.metrics.pairwise import euclidean_distances


def smoothed_conjugate_conv(f, x, eps=1.0):
  """

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

# Author: Mathieu Blondel
# License: BSD 3 clause

import numpy as np
from sklearn.isotonic import isotonic_regression


def projection_simplex(x, z=1):
    """
    Compute argmin_{p : p >= 0 and \sum_i p_i = z} ||p - x||

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

# Author: Mathieu Blondel
# License: BSD 3 clause

import numpy as np
from scipy.optimize import linprog


def dual_lp(a, b, C, verbose=0):
    """Solves the dual optimal transport problem:

mblondel

"""
Efficient implementation of FISTA.
"""

# Author: Mathieu Blondel
# License: BSD 3 clause

import numpy as np

mblondel

# -*- coding: utf-8 -*-

# Copyright (C) 2010 Mathieu Blondel
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,

mblondel

import numpy as np

rng = np.random.RandomState(0)

print "Trace"
A = rng.rand(3, 3)
print np.trace(A)
print np.einsum("ii", A)
print

mblondel

"""
Multiclass SVMs (Crammer-Singer formulation).

A pure Python re-implementation of:

Large-scale Multiclass Support Vector Machine Training via Euclidean Projection onto the Simplex.
Mathieu Blondel, Akinori Fujino, and Naonori Ueda.
ICPR 2014.
http://www.mblondel.org/publications/mblondel-icpr2014.pdf
"""

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.