%pylab inline
%run talktools

import scipy.special as spec
x = linspace(0, 20, 200)
for n in range(0,13,3):
    plot(x, spec.jn(n, x), label=r'$J_{%i}(x)$' % n)
grid()
legend()
title('Bessel Functions are neat');

@interactive(x=(1, 10))
def f(x):
    print 'X is:', x

from sklearn import datasets

digits = datasets.load_digits()
n = len(digits.images)

@interactive(i=(0,n-1))
def view_image(i):
    print 'Classif. Label:', digits.target[i]
    plt.matshow(digits.images[i], cmap=cm.gray_r)
    plt.show()

Image('fig/logo.png')

Video('fig/animation.m4v')  # Credit: Chris Kees, Army ERDC; created with Proteus.

plot_audio('voice.wav')
Audio('voice.wav')

Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx')

from sympy import symbols, Eq, factor, init_printing, expand
init_printing(use_latex=True)
x, y = symbols("x y")

eq = ((x+y)**3 * (x+1))
display(Eq(eq, expand(eq)))

@interactive(n=(1,10))
def _(n):
    eq = ((x+y)**n * (x+1))
    display(Eq(eq, expand(eq)))

X = np.array([0,1,2,3,4])
Y = np.array([3,5,4,6,7])
# Now, load R support
%load_ext rmagic

%%R -i X,Y -o XYcoef
XYlm = lm(Y~X)
XYcoef = coef(XYlm)
print(summary(XYlm))
par(mfrow=c(2,2))
plot(XYlm)

%load_ext julia.magic
%julia @pyimport matplotlib.pyplot as plt
%julia @pyimport numpy as np

%%julia
# Note how we mix numpy and julia:
x = linspace(0,2*pi,1000); # use the julia linspace
y = sin(3*x + 4*np.cos(2*x)); # use the numpy cosine and julia sine
plt.plot(x, y, color="red", linewidth=2.0, linestyle="--")

jfib = %julia jfib(n, fib) = n < 2 ? n : fib(n-1, jfib) + fib(n-2, jfib)
    
def pyfib(n, fib):
    if n < 2:
         return n
    return fib(n-1, pyfib) + fib(n-2, pyfib)

pyfib(20, jfib)   # Credit: Steven Johnson, MIT.

%load_ext fortranmagic

%%fortran
subroutine f1(x, y, n)
    real, intent(in), dimension(n) :: x
    real, intent(out), dimension(n) :: y
    !intent(hide) :: n
    y = sin(x**2)
end subroutine f1

x = np.linspace(0, 2*pi, 300)
plot(x, f1(x));

website('nbviewer.ipython.org')

website('http://www.nature.com/ismej/journal/v7/n3/full/ismej2012123a.html', 'Paper:')

website('http://qiime.org/home_static/nih-cloud-apr2012', 'Companion Website:')

website('http://jakevdp.github.io/blog/2013/12/05/static-interactive-widgets',
        'Pythonic Perambulations')

YouTubeVideo('tlontoyWX70',start='800', width=600, height=400)

website('camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers', 
        'Probabilistic programming...')

website('http://cs109.org/homework/homework.php', 'CS 109 Homeworks')

website('http://nbviewer.ipython.org/gist/jackparmer/7729584', 'Rosling Countries',
        width=900, height=600)

YouTubeVideo('UUjTAq8cCcs', width=600, height=500)