%pylab inline
rcParams['figure.figsize'] = (10, 4) #wide graphs by default
from __future__ import print_function
from __future__ import division

random.random(4)

random.random( (4,4) )

mat = random.random((4,4))

sig = random.random(100)
plot(sig)

sig = (random.random(10000)*2) - 1
plot(sig)

mean(sig)

random.random(10000).mean()

random.random(100000).mean()

random.random(10000000).mean()

randint(1, 7, 10)

randint(1, 21, 10)

randint(1, 7, 10).mean()

randint(1, 7, 1000).mean()

die_throws = randint(1, 7, 1000)

from scipy.stats import mode
mode(die_throws)

1000/6

sig = array ([13, 18, 13, 14, 13, 16, 14, 21, 13])
sig.mean()

sig.median()

mean(sig), median(sig)

sort(sig)

mode(sig)

hist(sig);

mode(sig)

sig = r_[13, 18, 13, 14, 13, 16, 14, 21, 13, 18, 18, 18]
mode(sig)

normal()

sig = normal(size=100)
plot(sig)

mat = normal(size=(128,128))
subplot(121)
imshow(mat)
colorbar()
mat = random.random(size=(128,128))
subplot(122)
imshow(mat)
colorbar()

#from numpy.random import *

randint(1,7, 10)
die = randint(1,7, 10)
die
hist(die)

die = randint(1,7, 10)
hist(die);

hist(die, bins= (arange(7)+0.5))

die = randint(1,7, 100)
hist(die, bins= (arange(7)+0.5))

die = randint(1,7, 10000)
hist(die, bins= (arange(7)+0.5));

r = normal(size=10)
hist(r);

r = normal(size=100)
hist(r);

r = normal(0, 1, 10000)
hist(r);

hist(r, 31);

r = normal(0, 5, 10000)
hist(r, 31);

hist(r);

hist(r, 30);

r = normal(0, 5, 10000)
type(r)

hist(r, 31)
print(r.std(), r.var())

r = exponential(1, 10000)
hist(r, 30);

r = exponential(2, 10000)
hist(r, 30);

r = exponential(10, 10000)
hist(r, 30);

r = exponential(1, 10000)
hist(r, 30);

r = triangular(0,0, 5, 10000)
hist(r);

hist(r,30);

r = triangular(left=1, mode=3, right=9, size=10000)
hist(r);

hist(r,31);

r = gamma(1, 2, 10000)
hist(r,30);

r = gamma(5, 1, 10000)
hist(r,30);

r = gamma(50, 1, 10000)
hist(r,30);

r = poisson(0.5, 10000)
hist(r,30);

r = poisson(10, 10000)
hist(r,30);

binomial(1000, 1.0/6.0)

100.0/6

print(binomial(10000, 1.0/6.0))
r = binomial(10000, 1.0/6.0, 10000)

hist(r,30);

hist(sig);

from scipy import  stats
quantiles = linspace(-0.5,1.5, 100)
plot(quantiles, stats.uniform.pdf(quantiles))
ylim((0, 1.1))

quantiles = linspace(-4.5,4.5, 1024)
plot(quantiles, stats.norm.pdf(quantiles))
ylim((0, 1.1))

quantiles = arange(50)

plot(quantiles, stats.poisson.pmf(quantiles, 0.2), 'o-')
plot(quantiles, stats.poisson.pmf(quantiles, 5), 'o-')
plot(quantiles, stats.poisson.pmf(quantiles, 20), 'o-')
legend(['$\lambda$ = 0.2','$\lambda$ = 5','$\lambda$ = 20'])