Viewing file:  RandomArray.py (13.93 KB) -rw-r--r--
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import ranlib
import Numeric
import LinearAlgebra
import sys
import math
from types import *
# Extended RandomArray to provide more distributions:
# normal, beta, chi square, F, multivariate normal,
# exponential, binomial, multinomial
# Lee Barford, Dec. 1999.
class ArgumentError(Exception):
pass
def seed(x=0,y=0):
"""seed(x, y), set the seed using the integers x, y;
Set a random one from clock if y == 0
"""
if type (x) != IntType or type (y) != IntType :
raise ArgumentError, "seed requires integer arguments."
if y == 0:
import time
t = time.time()
ndigits = int(math.log10(t))
base = 10**(ndigits/2)
x = int(t/base)
y = 1 + int(t%base)
ranlib.set_seeds(x,y)
seed()
def get_seed():
"Return the current seed pair"
return ranlib.get_seeds()
def _build_random_array(fun, args, shape=[]):
# Build an array by applying function fun to
# the arguments in args, creating an array with
# the specified shape.
# Allows an integer shape n as a shorthand for (n,).
if isinstance(shape, IntType):
shape = [shape]
if len(shape) != 0:
n = Numeric.multiply.reduce(shape)
s = apply(fun, args + (n,))
s.shape = shape
return s
else:
n = 1
s = apply(fun, args + (n,))
return s[0]
def random(shape=[]):
"random(n) or random([n, m, ...]) returns array of random numbers"
return _build_random_array(ranlib.sample, (), shape)
def uniform(minimum, maximum, shape=[]):
"""uniform(minimum, maximum, shape=[]) returns array of given shape of random reals
in given range"""
return minimum + (maximum-minimum)*random(shape)
def randint(minimum, maximum=None, shape=[]):
"""randint(min, max, shape=[]) = random integers >=min, < max
If max not given, random integers >= 0, <min"""
if not isinstance(minimum, IntType):
raise ArgumentError, "randint requires first argument integer"
if maximum is None:
maximum = minimum
minimum = 0
if not isinstance(maximum, IntType):
raise ArgumentError, "randint requires second argument integer"
a = ((maximum-minimum)* random(shape))
if isinstance(a, Numeric.ArrayType):
return minimum + a.astype(Numeric.Int)
else:
return minimum + int(a)
def random_integers(maximum, minimum=1, shape=[]):
"""random_integers(max, min=1, shape=[]) = random integers in range min-max inclusive"""
return randint(minimum, maximum+1, shape)
def permutation(n):
"permutation(n) = a permutation of indices range(n)"
return Numeric.argsort(random(n))
def standard_normal(shape=[]):
"""standard_normal(n) or standard_normal([n, m, ...]) returns array of
random numbers normally distributed with mean 0 and standard
deviation 1"""
return _build_random_array(ranlib.standard_normal, (), shape)
def normal(mean, std, shape=[]):
"""normal(mean, std, n) or normal(mean, std, [n, m, ...]) returns
array of random numbers randomly distributed with specified mean and
standard deviation"""
s = standard_normal(shape)
return s * std + mean
def multivariate_normal(mean, cov, shape=[]):
"""multivariate_normal(mean, cov) or multivariate_normal(mean, cov, [m, n, ...])
returns an array containing multivariate normally distributed random numbers
with specified mean and covariance.
mean must be a 1 dimensional array. cov must be a square two dimensional
array with the same number of rows and columns as mean has elements.
The first form returns a single 1-D array containing a multivariate
normal.
The second form returns an array of shape (m, n, ..., cov.shape[0]).
In this case, output[i,j,...,:] is a 1-D array containing a multivariate
normal."""
# Check preconditions on arguments
mean = Numeric.array(mean)
cov = Numeric.array(cov)
if len(mean.shape) != 1:
raise ArgumentError, "mean must be 1 dimensional."
if (len(cov.shape) != 2) or (cov.shape[0] != cov.shape[1]):
raise ArgumentError, "cov must be 2 dimensional and square."
if mean.shape[0] != cov.shape[0]:
raise ArgumentError, "mean and cov must have same length."
# Compute shape of output
if isinstance(shape, IntType): shape = [shape]
final_shape = list(shape[:])
final_shape.append(mean.shape[0])
# Create a matrix of independent standard normally distributed random
# numbers. The matrix has rows with the same length as mean and as
# many rows are necessary to form a matrix of shape final_shape.
x = ranlib.standard_normal(Numeric.multiply.reduce(final_shape))
x.shape = (Numeric.multiply.reduce(final_shape[0:len(final_shape)-1]),
mean.shape[0])
# Transform matrix of standard normals into matrix where each row
# contains multivariate normals with the desired covariance.
# Compute A such that matrixmultiply(transpose(A),A) == cov.
# Then the matrix products of the rows of x and A has the desired
# covariance. Note that sqrt(s)*v where (u,s,v) is the singular value
# decomposition of cov is such an A.
(u,s,v) = LinearAlgebra.singular_value_decomposition(cov)
x = Numeric.matrixmultiply(x*Numeric.sqrt(s),v)
# The rows of x now have the correct covariance but mean 0. Add
# mean to each row. Then each row will have mean mean.
Numeric.add(mean,x,x)
x.shape = final_shape
return x
def exponential(mean, shape=[]):
"""exponential(mean, n) or exponential(mean, [n, m, ...]) returns array
of random numbers exponentially distributed with specified mean"""
# If U is a random number uniformly distributed on [0,1], then
# -ln(U) is exponentially distributed with mean 1, and so
# -ln(U)*M is exponentially distributed with mean M.
x = random(shape)
Numeric.log(x, x)
Numeric.subtract(0.0, x, x)
Numeric.multiply(mean, x, x)
return x
def beta(a, b, shape=[]):
"""beta(a, b) or beta(a, b, [n, m, ...]) returns array of beta distributed random numbers."""
return _build_random_array(ranlib.beta, (a, b), shape)
def gamma(a, r, shape=[]):
"""gamma(a, r) or gamma(a, r, [n, m, ...]) returns array of gamma distributed random numbers."""
return _build_random_array(ranlib.gamma, (a, r), shape)
def F(dfn, dfd, shape=[]):
"""F(dfn, dfd) or F(dfn, dfd, [n, m, ...]) returns array of F distributed random numbers with dfn degrees of freedom in the numerator and dfd degrees of freedom in the denominator."""
return ( chi_square(dfn, shape) / dfn) / ( chi_square(dfd, shape) / dfd)
def noncentral_F(dfn, dfd, nconc, shape=[]):
"""noncentral_F(dfn, dfd, nonc) or noncentral_F(dfn, dfd, nonc, [n, m, ...]) returns array of noncentral F distributed random numbers with dfn degrees of freedom in the numerator and dfd degrees of freedom in the denominator, and noncentrality parameter nconc."""
return ( noncentral_chi_square(dfn, nconc, shape) / dfn ) / ( chi_square(dfd, shape) / dfd )
def chi_square(df, shape=[]):
"""chi_square(df) or chi_square(df, [n, m, ...]) returns array of chi squared distributed random numbers with df degrees of freedom."""
return _build_random_array(ranlib.chisquare, (df,), shape)
def noncentral_chi_square(df, nconc, shape=[]):
"""noncentral_chi_square(df, nconc) or chi_square(df, nconc, [n, m, ...]) returns array of noncentral chi squared distributed random numbers with df degrees of freedom and noncentrality parameter."""
return _build_random_array(ranlib.noncentral_chisquare, (df, nconc), shape)
def binomial(trials, p, shape=[]):
"""binomial(trials, p) or binomial(trials, p, [n, m, ...]) returns array of binomially distributed random integers.
trials is the number of trials in the binomial distribution.
p is the probability of an event in each trial of the binomial distribution."""
return _build_random_array(ranlib.binomial, (trials, p), shape)
def negative_binomial(trials, p, shape=[]):
"""negative_binomial(trials, p) or negative_binomial(trials, p, [n, m, ...]) returns
array of negative binomially distributed random integers.
trials is the number of trials in the negative binomial distribution.
p is the probability of an event in each trial of the negative binomial distribution."""
return _build_random_array(ranlib.negative_binomial, (trials, p), shape)
def multinomial(trials, probs, shape=[]):
"""multinomial(trials, probs) or multinomial(trials, probs, [n, m, ...]) returns
array of multinomial distributed integer vectors.
trials is the number of trials in each multinomial distribution.
probs is a one dimensional array. There are len(prob)+1 events.
prob[i] is the probability of the i-th event, 0<=i<len(prob).
The probability of event len(prob) is 1.-Numeric.sum(prob).
The first form returns a single 1-D array containing one multinomially
distributed vector.
The second form returns an array of shape (m, n, ..., len(probs)).
In this case, output[i,j,...,:] is a 1-D array containing a multinomially
distributed integer 1-D array."""
# Check preconditions on arguments
probs = Numeric.array(probs)
if len(probs.shape) != 1:
raise ArgumentError, "probs must be 1 dimensional."
# Compute shape of output
if type(shape) == type(0): shape = [shape]
final_shape = shape[:]
final_shape.append(probs.shape[0]+1)
x = ranlib.multinomial(trials, probs.astype(Numeric.Float32), Numeric.multiply.reduce(shape))
# Change its shape to the desire one
x.shape = final_shape
return x
def poisson(mean, shape=[]):
"""poisson(mean) or poisson(mean, [n, m, ...]) returns array of poisson
distributed random integers with specifed mean."""
return _build_random_array(ranlib.poisson, (mean,), shape)
def mean_var_test(x, type, mean, var, skew=[]):
n = len(x) * 1.0
x_mean = Numeric.sum(x)/n
x_minus_mean = x - x_mean
x_var = Numeric.sum(x_minus_mean*x_minus_mean)/(n-1.0)
print "\nAverage of ", len(x), type
print "(should be about ", mean, "):", x_mean
print "Variance of those random numbers (should be about ", var, "):", x_var
if skew != []:
x_skew = (Numeric.sum(x_minus_mean*x_minus_mean*x_minus_mean)/9998.)/x_var**(3./2.)
print "Skewness of those random numbers (should be about ", skew, "):", x_skew
def test():
x, y = get_seed()
print "Initial seed", x, y
seed(x, y)
x1, y1 = get_seed()
if x1 != x or y1 != y:
raise SystemExit, "Failed seed test."
print "First random number is", random()
print "Average of 10000 random numbers is", Numeric.sum(random(10000))/10000.
x = random([10,1000])
if len(x.shape) != 2 or x.shape[0] != 10 or x.shape[1] != 1000:
raise SystemExit, "random returned wrong shape"
x.shape = (10000,)
print "Average of 100 by 100 random numbers is", Numeric.sum(x)/10000.
y = uniform(0.5,0.6, (1000,10))
if len(y.shape) !=2 or y.shape[0] != 1000 or y.shape[1] != 10:
raise SystemExit, "uniform returned wrong shape"
y.shape = (10000,)
if Numeric.minimum.reduce(y) <= 0.5 or Numeric.maximum.reduce(y) >= 0.6:
raise SystemExit, "uniform returned out of desired range"
print "randint(1, 10, shape=[50])"
print randint(1, 10, shape=[50])
print "permutation(10)", permutation(10)
print "randint(3,9)", randint(3,9)
print "random_integers(10, shape=[20])"
print random_integers(10, shape=[20])
s = 3.0
x = normal(2.0, s, [10, 1000])
if len(x.shape) != 2 or x.shape[0] != 10 or x.shape[1] != 1000:
raise SystemExit, "standard_normal returned wrong shape"
x.shape = (10000,)
mean_var_test(x, "normally distributed numbers with mean 2 and variance %f"%(s**2,), 2, s**2, 0)
x = exponential(3, 10000)
mean_var_test(x, "random numbers exponentially distributed with mean %f"%(s,), s, s**2, 2)
x = multivariate_normal(Numeric.array([10,20]), Numeric.array(([1,2],[2,4])))
print "\nA multivariate normal", x
if x.shape != (2,): raise SystemExit, "multivariate_normal returned wrong shape"
x = multivariate_normal(Numeric.array([10,20]), Numeric.array([[1,2],[2,4]]), [4,3])
print "A 4x3x2 array containing multivariate normals"
print x
if x.shape != (4,3,2): raise SystemExit, "multivariate_normal returned wrong shape"
x = multivariate_normal(Numeric.array([-100,0,100]), Numeric.array([[3,2,1],[2,2,1],[1,1,1]]), 10000)
x_mean = Numeric.sum(x)/10000.
print "Average of 10000 multivariate normals with mean [-100,0,100]"
print x_mean
x_minus_mean = x - x_mean
print "Estimated covariance of 10000 multivariate normals with covariance [[3,2,1],[2,2,1],[1,1,1]]"
print Numeric.matrixmultiply(Numeric.transpose(x_minus_mean),x_minus_mean)/9999.
x = beta(5.0, 10.0, 10000)
mean_var_test(x, "beta(5.,10.) random numbers", 0.333, 0.014)
x = gamma(.01, 2., 10000)
mean_var_test(x, "gamma(.01,2.) random numbers", 2*100, 2*100*100)
x = chi_square(11., 10000)
mean_var_test(x, "chi squared random numbers with 11 degrees of freedom", 11, 22, 2*Numeric.sqrt(2./11.))
x = F(5., 10., 10000)
mean_var_test(x, "F random numbers with 5 and 10 degrees of freedom", 1.25, 1.35)
x = poisson(50., 10000)
mean_var_test(x, "poisson random numbers with mean 50", 50, 50, 0.14)
print "\nEach element is the result of 16 binomial trials with probability 0.5:"
print binomial(16, 0.5, 16)
print "\nEach element is the result of 16 negative binomial trials with probability 0.5:"
print negative_binomial(16, 0.5, [16,])
print "\nEach row is the result of 16 multinomial trials with probabilities [0.1, 0.5, 0.1 0.3]:"
x = multinomial(16, [0.1, 0.5, 0.1], 8)
print x
print "Mean = ", Numeric.sum(x)/8.
if __name__ == '__main__':
test()
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