/
usr
/
lib64
/
python2.6
/
site-packages
/
numpy
/
oldnumeric
/
/usr/lib64/python2.6/site-packages/numpy/oldnumeric
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/usr/lib64/python2.6/site-packages/numpy/oldnumeric/random_array.py
(11454B)
# 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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