from maxima import find_maxima

find_maxima([1, 2, 3, 2, 4, 1])

%run test_maxima.py

find_maxima([1, 2, 1, 2, 3])

find_maxima([1, 1, 1])

import numpy as np

a = np.random.randn(100, 200)
b = np.random.randn(100, 200)
c = np.zeros_like(a)

%%timeit
assert a.shape == b.shape
N = a.shape[0]
M = a.shape[1]
for i in range(N):
    for j in range(M):
        c[i, j] = a[i, j] + b[i, j]

%%timeit
c = a + b

from IPython.display import HTML
HTML('<iframe src="http://en.m.wikipedia.org/wiki/Kepler%27s_equation" width="800" height="400"></iframe>')

%matplotlib inline

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

%%prun -s cumtime
def kepler(E, e, M):
    """Kepler's equation."""
    return E - e * np.sin(E) - M

fig, axes = plt.subplots(figsize=(6, 6))

N = 10000
M_domain = np.linspace(0, 2 * np.pi, N)
for ecc in 0.0167, 0.249, 0.432, 0.775, 0.967:
    E_domain = np.zeros_like(M_domain)
    ii = 0
    for M in M_domain:
        sol = optimize.root(kepler, E_domain[ii], args=(ecc, M))
        E_domain[ii] = sol.x
        ii += 1

    axes.plot(M_domain, E_domain)

axes.set_xlim(0, 2 * np.pi)
axes.set_ylim(0, 2 * np.pi)
axes.set_xlabel("$M$", fontsize=15)
axes.set_ylabel("$E$", fontsize=15)
axes.set_aspect(1)
axes.grid(True)
axes.legend(["Earth", "Pluto", "Comet Holmes", "28P/Neujmin", "Halley's Comet"], loc=2)
axes.set_title("Kepler's equation solutions")