Numerics Py

7/30/2019 Numerics Py

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"""Numerical tools"""

import numpy

def ensure_numeric(A, typecode=None):"""Ensure that sequence is a numeric array.

Inputs:A: Sequence. If A is already a numeric array it will be returned

unalteredIf not, an attempt is made to convert it to a numericarray

A: Scalar. Return 0-dimensional array containing that value. Notethat a 0-dim array DOES NOT HAVE A LENGTH UNDER numpy.

A: String. Array of ASCII values (numpy can't handle this)

typecode: numeric type. If specified, use this in the conversion.If not, let numeric package decide.typecode will always be one of num.float, num.int, etc.

Note that numpy.array(A, dtype) will sometimes copy. Use 'copy=False' tocopy only when required.

This function is necessary as array(A) can cause memory overflow."""

if isinstance(A, basestring):msg = 'Sorry, cannot handle strings in ensure_numeric()'raise Exception(msg)

if typecode is None:if isinstance(A, numpy.ndarray):

return Aelse:

return numpy.array(A)

else:return numpy.array(A, dtype=typecode, copy=False)

def nanallclose(x, y, rtol=1.0e-5, atol=1.0e-8):"""Numpy allclose function which allows NaN

Inputx, y: Either scalars or numpy arrays

OutputTrue or False

Returns True if all non-nan elements pass."""

xn = numpy.isnan(x)yn = numpy.isnan(y)if numpy.any(xn != yn):

# Presence of NaNs is not the same in x and yreturn False

if numpy.all(xn):


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# Everything is NaN.# This will also take care of x and y being NaN scalarsreturn True

# Filter NaN's outif numpy.any(xn):

x = x[-xn]y = y[-yn]

# Compare non NaN's and returnreturn numpy.allclose(x, y, rtol=rtol, atol=atol)

def normal_cdf(x, mu=0, sigma=1):"""Cumulative Normal Distribution Function

Inputx: scalar or array of real numbersmu: Mean value. Default 0sigma: Standard deviation. Default 1

OutputAn approximation of the cdf of the normal

CDF of the normal distribution is defined as\frac12 [1 + erf(\frac{x - \mu}{\sigma \sqrt{2}})], x \in \R

Source: http://en.wikipedia.org/wiki/Normal_distribution"""

arg = (x - mu) / (sigma * numpy.sqrt(2))res = (1 + erf(arg)) / 2

return res

def lognormal_cdf(x, median=1, sigma=1):

"""Cumulative Log Normal Distribution Function

Inputx: scalar or array of real numbersmu: Median (exp(mean of log(x)). Default 1sigma: Log normal standard deviation. Default 1

OutputAn approximation of the cdf of the normal

CDF of the normal distribution is defined as\frac12 [1 + erf(\frac{x - \mu}{\sigma \sqrt{2}})], x \in \R

Source: http://en.wikipedia.org/wiki/Normal_distribution"""

return normal_cdf(numpy.log(x), mu=numpy.log(median), sigma=sigma)

def erf(z):"""Approximation to ERF

from:


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http://www.cs.princeton.edu/introcs/21function/ErrorFunction.java.htmlImplements the Gauss error function.erf(z) = 2 / sqrt(pi) * integral(exp(-t*t), t = 0..z)

Fractional error in math formula less than 1.2 * 10 ^ -7.although subject to catastrophic cancellation when z in very close to 0from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2

Source:http://stackoverflow.com/questions/457408/is-there-an-easily-available-implementation-of-erf-for-python"""

# Input checktry:

len(z)except:

scalar = Truez = [z]

else:scalar = False

z = numpy.array(z)

# Begin algorithmt = 1.0 / (1.0 + 0.5 * numpy.abs(z))

# Use Horner's methodans = 1 - t * numpy.exp(-z * z - 1.26551223 +

t * (1.00002368 +t * (0.37409196 +t * (0.09678418 +t * (-0.18628806 +t * (0.27886807 +t * (-1.13520398 +t * (1.48851587 +t * (-0.82215223 +

t * (0.17087277))))))))))

neg = (z < 0.0) # Mask for negative input valuesans[neg] = -ans[neg]

if scalar:return ans[0]

else:return ans

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