# import some things
%pylab --no-import-all inline
import numpy as np
import pylab as pl
from scipy import linalg

s = "Hello World!"
print s

%run my_script.py

my_str = 'Hello World!'
print my_str
print my_str[0]

print my_str.replace('World', 'Why N\' How')
print my_str.upper()

my_list = [1, 2, 3, 'test']   # Notice: [] creates a list
print my_list

my_list.append('test2')
print my_list
my_list.insert(1, 0)
print my_list


print my_list
print my_list[0]   # first element
print my_list[-1]  # last element
print my_list[-2]  # second last element


print my_list
print my_list[2:5]  # Notice: index 5 is not included

print my_list[:3]   # first 3 elements
print my_list[-3:]  # last 3 elements
print my_list[::2]  # every 2nd element
print my_list[::-1] # list with order reversed

phone = {'joe': 554, 'bob': 308}  # using {} creates a dict
print phone  # Notice: no order

print phone['joe']

phone[0] = 101
print phone
print phone.keys()    # list with the keys
print phone.values()  # list with the values

a = 10
if a == 1:
    print 1
    print 22
elif a == 2:
    print 2
else:
    print 'a lot'

for word in ['cool', 'powerful', 'readable']:
    print 'Python is %s !!!' % word

def disk_area(radius):
    area = 3.14 * radius * radius
    return area

print disk_area(1.0)
print disk_area(2.0)

import copy

def foo(a):
    a.append(1) 

b = [0]
foo(b)
print b  # a has been modified !!!

import numpy as np  # import numpy so we can use it
a = np.array([0, 1, 2, 3], dtype=np.float)  # create array
print a

print a.ndim   # number of dimensions, in Matlab `ndims(a)`
print a.shape  # shape, in Matlab `size(a)`
print a.dtype  # the data type of the array

# 2-D array
b = np.array([[0, 1, 2], [3, 4, 5]]) # 2 x 3 array
print b
print b.dtype  # Notice: here the data type is int64
print b.shape

# 3-D
c = np.array([[[1], [2]], [[3], [4]]])
print c.shape  # in Matlab `size(c)`

a = np.ones((3, 3))
print a

b = np.zeros((2, 3))
print b

c = np.eye(3)
print c

a = np.diag(np.arange(3))
print a

print a[1, 1]
print a[:,1]  # takes the entire second row!

# slicing
a = np.arange(10)
print a
print a[::2] # every 2nd element
print a[-5:] # last 5 elements

a = np.arange(10)
print a
b = a[::2]
print b

b[0] = 100
print b
print a  # a was modified as well!

a = np.arange(10)
b = a[::2].copy()  # force a copy
b[0] = 100
print b
print a

a = np.arange(10)
np.save('test.npy', a)
a = 0
a = np.load('test.npy')
print a

a = np.triu(np.ones((2, 2)), 1)   # see help(np.triu)
print 'a:' + str(a)
b = np.diag([1, 2])
print 'b:' + str(b)
c = np.dot(a, b)  # same as a.dot(b)
print 'c:' + str(c)

print a * b  # element-wise multiplication

a_t = a.T
print a_t

print 'a.flags:\n' + str(a.flags)
print 'a_t.flags:\n' + str(a_t.flags)

from numpy import linalg  # OR
from scipy import linalg  # even better
A = np.triu(np.ones((3, 3)), 0)
print 'A:\n' + str(A)
B = linalg.inv(A)
C = np.dot(B, A)
print 'C:\n' + str(C)
x = linalg.solve(A, [1, 2, 3])  # linear system
U, s, V = linalg.svd(A)  # SVD
vals = linalg.eigvals(A)  # Eigenvalues

x = np.arange(5)
print x
print np.sum(x)  # or x.sum()
    

x = np.array([[1, 1], [2, 2]])
print np.sum(x, axis=0),   # columns (first dimension)
print np.sum(x, axis=1)   # rows (second dimension)

from scipy import stats
a = np.random.normal(0, 1, size=10)
b = np.random.normal(1, 1, size=10)
tval, pval = stats.ttest_ind(a, b)
print 'T=%0.4f, p=%0.4f' % (tval, pval)

import pylab as pl
t = np.linspace(0, 8 * np.pi, 1000)
pl.plot(t, np.sin(t))
pl.xlabel('$x$')
pl.ylabel('$sin(x)$')
pl.ylim([-1.1, 1.1])
pl.savefig('pylab_demo.pdf')  # natively save pdf, svg, etc.

image = np.random.rand(30, 30)
pl.imshow(image)
pl.gray()
pl.show()