import random as rd
import numpy as np

%timeit a = [rd.random() for x in range(1000)]

%timeit a = [np.random.random() for x in range(1000)]

%timeit a = np.random.random(1000)

%%time
# This is a terrible way to do this
fib = [0, 1]
for i in range(10**5):
    fib.append(fib[-1] + fib[-2])

from scipy.special import jn
x = linspace(0, 4*pi)
for i in range(6):
    plot(x, jn(i, x))

import random as rd
N = 4

lol = [[rd.random() for c in range(N)] for r in range(N)]
# OR
lol = []
for r in range(N):
    row = []
    for c in range(N):
        row.append(rd.random())
    lol.append(row)
lol

lol[:,0]

lol[:][0]

[x[0] for x in lol]

import numpy as np

npm = np.random.random((N, N))
npm

npm[:,0]

npm.sum(0)

import numpy
import scipy.ndimage
import Image

class Life(object):

    def __init__(self, n, p=0.5, mode='wrap'):
        self.n = n
        self.mode = mode
        self.array = numpy.uint8(numpy.random.random((n, n)) < p)
        self.weights = numpy.array([[1,1,1],
                                    [1,10,1],
                                    [1,1,1]], dtype=numpy.uint8)

    def step(self):
        con = scipy.ndimage.filters.convolve(self.array,
                                             self.weights,
                                             mode=self.mode)

        boolean = (con==3) | (con==12) | (con==13)
        self.array = numpy.int8(boolean)
        
    def run(self, N):
        for _ in range(N):
            self.step()
        
    def draw(self, scale):
        im = Image.fromarray(numpy.uint8(self.array)*255)
        z = int(scale*self.n)
        return im.resize((z,z))

l = Life(50)
imshow(l.draw(15))

l.run(10)
imshow(l.draw(15))

from scipy import stats
import numpy as np

x = np.random.random(10)
y = np.random.random(10)
slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)

print "r-squared:", r_value**2

from scipy import stats
import numpy as np

x = np.random.random(10)
y = np.random.random(10)
slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)

print "r-squared:", r_value**2

import matplotlib.pyplot as plt

sizes = 1000* np.random.random(10)
colors = np.random.random(10)

fit_x = np.linspace(0,1,100)
fit_y = slope * xx + intercept

plt.scatter(x,y, sizes, colors, alpha=0.5)
plt.plot(fit_x, fit_y, '--r')

plt.title("Fit line to random junk", fontsize=16)
plt.show()

import sympy
sympy.init_printing(use_latex=True) ##or use_unicode=True in a console
x, y = sympy.symbols('x y')

sympy.diff(sympy.exp(x**2), x)

my_deriv = sympy.Derivative(sympy.exp(x**2), x, x)
my_deriv

my_deriv.doit()

sympy.Integral(sympy.exp(-x**2 - y**2), x, y)

from sympy import oo
sympy.integrate(sympy.exp(-x**2 - y**2), (x, -oo, oo), (y, -oo, oo))

sympy.solve([x*y - 7, x + y - 6], [x, y])