#!/usr/bin/env python

import numpy as np

x = np.array([[1,2],[3,4]], dtype=np.float64)

y = np.array([[5,6],[7,8]], dtype=np.float64)

# Elementwise sum; both produce the array

# [[ 6.0 8.0]

# [10.0 12.0]]

print x + y

print np.add(x, y)

# Elementwise difference; both produce the array

# [[-4.0 -4.0]

# [-4.0 -4.0]]

print x - y

print np.subtract(x, y)

# Elementwise product; both produce the array

# [[ 5.0 12.0]

# [21.0 32.0]]

print x * y

print np.multiply(x, y)

# Elementwise division; both produce the array

# [[ 0.2 0.33333333]

# [ 0.42857143 0.5 ]]

print x / y

print np.divide(x, y)

# Elementwise square root; produces the array

# [[ 1. 1.41421356]

# [ 1.73205081 2. ]]

print np.sqrt(x)

x = np.array([[1,2],[3,4]])

y = np.array([[5,6],[7,8]])

v = np.array([9,10])

w = np.array([11, 12])

# Inner product of vectors; both produce 219

print v.dot(w)

print np.dot(v, w)

# Matrix / vector product; both produce the rank 1 array [29 67]

print x.dot(v)

print np.dot(x, v)

# Matrix / matrix product; both produce the rank 2 array

# [[19 22]

# [43 50]]

print x.dot(y)

print np.dot(x, y)

x = np.array([[1,2],[3,4]])

print np.sum(x) # Compute sum of all elements; prints "10"

print np.sum(x, axis=0) # Compute sum of each column; prints "[4 6]"

print np.sum(x, axis=1) # Compute sum of each row; prints "[3 7]"

x = np.array([[1,2], [3,4]])

print x # Prints "[[1 2]

# [3 4]]"

print x.T # Prints "[[1 3]

# [2 4]]"

# Note that taking the transpose of a rank 1 array does nothing:

v = np.array([1,2,3])

print v # Prints "[1 2 3]"

print v.T # Prints "[1 2 3]"

# We will add the vector v to each row of the matrix x,

# storing the result in the matrix y

x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])

v = np.array([1, 0, 1])

y = np.empty_like(x) # Create an empty matrix with the same shape as x

# Add the vector v to each row of the matrix x with an explicit loop

for i in range(4):

y[i, :] = x[i, :] + v

# Now y is the following

# [[ 2 2 4]

# [ 5 5 7]

# [ 8 8 10]

# [11 11 13]]

print y

# We will add the vector v to each row of the matrix x,

# storing the result in the matrix y

x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])

v = np.array([1, 0, 1])

vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other

print vv # Prints "[[1 0 1]

# [1 0 1]

# [1 0 1]

# [1 0 1]]"

y = x + vv # Add x and vv elementwise

print y # Prints "[[ 2 2 4

# [ 5 5 7]

# [ 8 8 10]

# [11 11 13]]"

# We will add the vector v to each row of the matrix x,

# storing the result in the matrix y

x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])

v = np.array([1, 0, 1])

y = x + v # Add v to each row of x using broadcasting

print y # Prints "[[ 2 2 4]

# [ 5 5 7]

# [ 8 8 10]

# [11 11 13]]"

# Compute outer product of vectors

v = np.array([1,2,3]) # v has shape (3,)

w = np.array([4,5]) # w has shape (2,)

# To compute an outer product, we first reshape v to be a column

# vector of shape (3, 1); we can then broadcast it against w to yield

# an output of shape (3, 2), which is the outer product of v and w:

# [[ 4 5]

# [ 8 10]

# [12 15]]

print np.reshape(v, (3, 1)) * w

# Add a vector to each row of a matrix

x = np.array([[1,2,3], [4,5,6]])

# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),

# giving the following matrix:

# [[2 4 6]

# [5 7 9]]

print x + v

# Add a vector to each column of a matrix

# x has shape (2, 3) and w has shape (2,).

# If we transpose x then it has shape (3, 2) and can be broadcast

# against w to yield a result of shape (3, 2); transposing this result

# yields the final result of shape (2, 3) which is the matrix x with

# the vector w added to each column. Gives the following matrix:

# [[ 5 6 7]

# [ 9 10 11]]

print (x.T + w).T

# Another solution is to reshape w to be a row vector of shape (2, 1);

# we can then broadcast it directly against x to produce the same

# output.

print x + np.reshape(w, (2, 1))

# Multiply a matrix by a constant:

# x has shape (2, 3). Numpy treats scalars as arrays of shape ();

# these can be broadcast together to shape (2, 3), producing the

# following array:

# [[ 2 4 6]

# [ 8 10 12]]

print x * 2