exponentialNoiseVariable.py

## -*-Pyth-*-
 # ###################################################################
 #  FiPy - a finite volume PDE solver in Python
 # 
 #  FILE: "exponentialNoiseVariable.py"
 #
 #  Author: Jonathan Guyer <guyer@nist.gov>
 #  Author: Daniel Wheeler <daniel.wheeler@nist.gov>
 #  Author: James Warren   <jwarren@nist.gov>
 #    mail: NIST
 #     www: http://www.ctcms.nist.gov/fipy/
 #  
 # ========================================================================
 # This document was prepared at the National Institute of Standards
 # and Technology by employees of the Federal Government in the course
 # of their official duties.  Pursuant to title 17 Section 105 of the
 # United States Code this document is not subject to copyright
 # protection and is in the public domain.  exponentialNoiseVariable.py
 # is an experimental work.  NIST assumes no responsibility whatsoever
 # for its use by other parties, and makes no guarantees, expressed
 # or implied, about its quality, reliability, or any other characteristic.
 # We would appreciate acknowledgement if the document is used.
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__docformat__ = 'restructuredtext'

from fipy.tools.numerix import random
from fipy.variables.noiseVariable import NoiseVariable

__all__ = ["ExponentialNoiseVariable"]

class ExponentialNoiseVariable(NoiseVariable):
    r"""
    Represents an exponential distribution of random numbers with the probability
    distribution
    
    .. math::
    
       \mu^{-1} e^{-\frac{x}{\mu}}
       
    with a mean parameter :math:`\mu`.

    Seed the random module for the sake of deterministic test results.

    >>> from fipy import numerix
    >>> numerix.random.seed(1)

    We generate noise on a uniform cartesian mesh
           
    >>> from fipy.variables.variable import Variable
    >>> mean = Variable()
    >>> from fipy.meshes import Grid2D
    >>> noise = ExponentialNoiseVariable(mesh = Grid2D(nx = 100, ny = 100), mean = mean)
           
    We histogram the root-volume-weighted noise distribution
    
    >>> from fipy.variables.histogramVariable import HistogramVariable
    >>> histogram = HistogramVariable(distribution = noise, dx = 0.1, nx = 100)
           
    and compare to a Gaussian distribution
    
    >>> from fipy.variables.cellVariable import CellVariable
    >>> expdist = CellVariable(mesh = histogram.mesh)
    >>> x = histogram.mesh.cellCenters[0]
    
    >>> if __name__ == '__main__':
    ...     from fipy import Viewer
    ...     viewer = Viewer(vars=noise, datamin=0, datamax=5)
    ...     histoplot = Viewer(vars=(histogram, expdist), 
    ...                        datamin=0, datamax=1.5)
    
    >>> from fipy.tools.numerix import arange, exp
    
    >>> for mu in arange(0.5,3,0.5):
    ...     mean.value = (mu)
    ...     expdist.value = ((1/mean)*exp(-x/mean))
    ...     if __name__ == '__main__':
    ...         import sys
    ...         print >>sys.stderr, "mean: %g" % mean
    ...         viewer.plot()
    ...         histoplot.plot()

    >>> print abs(noise.faceGrad.divergence.cellVolumeAverage) < 5e-15
    1

    .. image:: fipy/variables/exp.*
      :scale: 25
      :align: center
      :alt: random values with an exponential distribution
      
    .. image:: fipy/variables/exp-histogram.*
      :scale: 25
      :align: center
      :alt: histogram of random values with an exponential distribution

    """
    def __init__(self, mesh, mean=0.0, name = '', hasOld = 0):
        r"""
        :Parameters:
            - `mesh`: The mesh on which to define the noise.
            - `mean`: The mean of the distribution :math:`\mu`.
        """
        NoiseVariable.__init__(self, mesh = mesh, name = name, hasOld = hasOld)
        self.mean = self._requires(mean)
    
    def random(self):
        return random.exponential(scale = self.mean, 
                                  size = [self.mesh.globalNumberOfCells])

def _test(): 
    import fipy.tests.doctestPlus
    return fipy.tests.doctestPlus.testmod()
    
if __name__ == "__main__": 
    _test()