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# Backward compatible module for RandomArray
__all__ = ['ArgumentError','F','beta','binomial','chi_square', 'exponential',
'gamma', 'get_seed', 'mean_var_test', 'multinomial',
'multivariate_normal', 'negative_binomial', 'noncentral_F',
'noncentral_chi_square', 'normal', 'permutation', 'poisson',
'randint', 'random', 'random_integers', 'seed', 'standard_normal',
'uniform']
ArgumentError = ValueError
import numpy.random.mtrand as mt
import numpy as np
def seed(x=0, y=0):
if (x == 0 or y == 0):
mt.seed()
else:
mt.seed((x,y))
def get_seed():
raise NotImplementedError, \
"If you want to save the state of the random number generator.\n"\
"Then you should use obj = numpy.random.get_state() followed by.\n"\
"numpy.random.set_state(obj)."
def random(shape=[]):
"random(n) or random([n, m, ...]) returns array of random numbers"
if shape == []:
shape = None
return mt.random_sample(shape)
def uniform(minimum, maximum, shape=[]):
"""uniform(minimum, maximum, shape=[]) returns array of given shape of random reals
in given range"""
if shape == []:
shape = None
return mt.uniform(minimum, maximum, 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, int):
raise ArgumentError, "randint requires first argument integer"
if maximum is None:
maximum = minimum
minimum = 0
if not isinstance(maximum, int):
raise ArgumentError, "randint requires second argument integer"
a = ((maximum-minimum)* random(shape))
if isinstance(a, np.ndarray):
return minimum + a.astype(np.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 mt.permutation(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"""
if shape == []:
shape = None
return mt.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"""
if shape == []:
shape = None
return mt.normal(mean, std, shape)
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."""
if shape == []:
shape = None
return mt.multivariate_normal(mean, cov, shape)
def exponential(mean, shape=[]):
"""exponential(mean, n) or exponential(mean, [n, m, ...]) returns array
of random numbers exponentially distributed with specified mean"""
if shape == []:
shape = None
return mt.exponential(mean, shape)
def beta(a, b, shape=[]):
"""beta(a, b) or beta(a, b, [n, m, ...]) returns array of beta distributed random numbers."""
if shape == []:
shape = None
return mt.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."""
if shape == []:
shape = None
return mt.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."""
if shape == []:
shape = None
return mt.f(dfn, dfd, shape)
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."""
if shape == []:
shape = None
return mt.noncentral_f(dfn, dfd, nconc, shape)
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."""
if shape == []:
shape = None
return mt.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."""
if shape == []:
shape = None
return mt.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."""
if shape == []:
shape = None
return mt.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."""
if shape == []:
shape = None
return mt.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.-np.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."""
if shape == []:
shape = None
return mt.multinomial(trials, probs, shape)
def poisson(mean, shape=[]):
"""poisson(mean) or poisson(mean, [n, m, ...]) returns array of poisson
distributed random integers with specified mean."""
if shape == []:
shape = None
return mt.poisson(mean, shape)
def mean_var_test(x, type, mean, var, skew=[]):
n = len(x) * 1.0
x_mean = np.sum(x,axis=0)/n
x_minus_mean = x - x_mean
x_var = np.sum(x_minus_mean*x_minus_mean,axis=0)/(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 = (np.sum(x_minus_mean*x_minus_mean*x_minus_mean,axis=0)/9998.)/x_var**(3./2.)
print "Skewness of those random numbers (should be about ", skew, "):", x_skew
def test():
obj = mt.get_state()
mt.set_state(obj)
obj2 = mt.get_state()
if (obj2[1] - obj[1]).any():
raise SystemExit, "Failed seed test."
print "First random number is", random()
print "Average of 10000 random numbers is", np.sum(random(10000),axis=0)/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", np.sum(x,axis=0)/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 np.minimum.reduce(y) <= 0.5 or np.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(np.array([10,20]), np.array(([1,2],[2,4])))
print "\nA multivariate normal", x
if x.shape != (2,): raise SystemExit, "multivariate_normal returned wrong shape"
x = multivariate_normal(np.array([10,20]), np.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(np.array([-100,0,100]), np.array([[3,2,1],[2,2,1],[1,1,1]]), 10000)
x_mean = np.sum(x,axis=0)/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 np.dot(np.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*np.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 = ", np.sum(x,axis=0)/8.
if __name__ == '__main__':
test()
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