Coverage for local/lib/python2.7/site-packages/sage/stats/distributions/discrete_gaussian_polynomial.py : 94%

# -*- coding: utf-8 -*- 

r""" 

Discrete Gaussian Samplers for `\ZZ[x]` 

This class realizes oracles which returns polynomials in `\ZZ[x]` 

where each coefficient is sampled independently with a probability 

proportional to `\exp(-(x-c)²/(2σ²))`. 

AUTHORS: 

- Martin Albrecht, Robert Fitzpatrick, Daniel Cabracas, Florian Göpfert, 

Michael Schneider: initial version 

EXAMPLES:: 

sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler 

sage: sigma = 3.0; n=1000 

sage: l = [DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 64, sigma)() for _ in range(n)] 

sage: l = [vector(f).norm().n() for f in l] 

sage: mean(l), sqrt(64)*sigma 

(23.83..., 24.0...) 

""" 

#****************************************************************************** 

# 

# DGS - Discrete Gaussian Samplers 

# 

# Copyright (c) 2014, Martin Albrecht <martinralbrecht+dgs@googlemail.com> 

# All rights reserved. 

# 

# Redistribution and use in source and binary forms, with or without 

# modification, are permitted provided that the following conditions are met: 

# 

# 1. Redistributions of source code must retain the above copyright notice, this 

# list of conditions and the following disclaimer. 

# 2. Redistributions in binary form must reproduce the above copyright notice, 

# this list of conditions and the following disclaimer in the documentation 

# and/or other materials provided with the distribution. 

# 

# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 

# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 

# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 

# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE 

# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 

# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR 

# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 

# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, 

# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 

# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 

# 

# The views and conclusions contained in the software and documentation are 

# those of the authors and should not be interpreted as representing official 

# policies, either expressed or implied, of the FreeBSD Project. 

#*****************************************************************************/ 

from __future__ import absolute_import 

from sage.rings.all import RealField, RR, ZZ 

from .discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler 

from sage.structure.sage_object import SageObject 

class DiscreteGaussianDistributionPolynomialSampler(SageObject): 

r""" 

Discrete Gaussian sampler for polynomials. 

EXAMPLES:: 

sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler 

sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)() 

3*x^7 + 3*x^6 - 3*x^5 - x^4 - 5*x^2 + 3 

sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0) 

sage: [gs() for _ in range(3)] 

[4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1] 

.. automethod:: __init__ 

.. automethod:: __call__ 

""" 

def __init__(self, P, n, sigma): 

r""" 

Construct a sampler for univariate polynomials of degree ``n-1`` 

where coefficients are drawn independently with standard deviation 

``sigma``. 

INPUT: 

- ``P`` - a univariate polynomial ring over the Integers 

- ``n`` - number of coefficients to be sampled 

- ``sigma`` - coefficients `x` are accepted with probability 

proportional to `\exp(-x²/(2σ²))`. If an object of type 

:class:`sage.stats.distributions.discrete_gaussian_integer.DiscreteGaussianDistributionIntegerSampler` 

is passed, then this sampler is used to sample coefficients. 

EXAMPLES:: 

sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler 

sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)() 

3*x^7 + 3*x^6 - 3*x^5 - x^4 - 5*x^2 + 3 

sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0) 

sage: [gs() for _ in range(3)] 

[4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1] 

""" 

if isinstance(sigma, DiscreteGaussianDistributionIntegerSampler): 

self.D = sigma 

else: 

self.D = DiscreteGaussianDistributionIntegerSampler(RR(sigma)) 

self.n = ZZ(n) 

self.P = P 

def __call__(self): 

""" 

Return a new sample. 

EXAMPLES:: 

sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler 

sage: sampler = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 12.0) 

sage: sampler() 

8*x^7 - 11*x^5 - 19*x^4 + 6*x^3 - 34*x^2 - 21*x + 9 

""" 

coeffs = [self.D() for _ in range(self.n)] 

return self.P(coeffs) 

def _repr_(self): 

""" 

EXAMPLES:: 

sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler 

sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0) 

Discrete Gaussian sampler for polynomials of degree < 8 with σ=3.000000 in each component 

""" 

# beware of unicode character in ascii string ! 

return "Discrete Gaussian sampler for polynomials of degree < %d with σ=%f in each component" % (self.n, self.D.sigma)