CoCalc -- outer_product.ipynb

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cocalc-examples / think-complexity-2ed / examples / outer_product.ipynb

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License: OTHER

Kernel: Python 3

In [3]:

import numpy as np

In [26]:

n = 4
m = 5

In [27]:

x = np.arange(n)
y = np.arange(m)
x, y

Out[27]:

(array([0, 1, 2, 3]), array([0, 1, 2, 3, 4]))

Version in the book

In [46]:

X, Y = np.meshgrid(x, y, indexing='ij')
X

Out[46]:

array([[0, 0, 0, 0, 0],
       [1, 1, 1, 1, 1],
       [2, 2, 2, 2, 2],
       [3, 3, 3, 3, 3]])

In [47]:

Out[47]:

array([[0, 1, 2, 3, 4],
       [0, 1, 2, 3, 4],
       [0, 1, 2, 3, 4],
       [0, 1, 2, 3, 4]])

In [48]:

np.hypot(X, Y)

Out[48]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

Using indices

In [40]:

X, Y = np.indices((n, m))

In [41]:

np.hypot(X, Y)

Out[41]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

In [45]:

np.hypot(*np.indices((n, m)))

Out[45]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

Using `fromfunction`

In [43]:

np.fromfunction(np.hypot, (n, m))

Out[43]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

Using broadcasting

In [31]:

X = x[:, None]
Y = y[None, :]
X

Out[31]:

array([[0],
       [1],
       [2],
       [3]])

In [32]:

Out[32]:

array([[0, 1, 2, 3, 4]])

In [33]:

X + Y

Out[33]:

array([[0, 1, 2, 3, 4],
       [1, 2, 3, 4, 5],
       [2, 3, 4, 5, 6],
       [3, 4, 5, 6, 7]])

In [34]:

np.sqrt(X**2 + Y**2)

Out[34]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

Using outer product

In [35]:

np.hypot.outer(x, y)

Out[35]:

array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],
       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],
       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],
       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ]])

In [ ]:

Version in the book

Using indices

Using `fromfunction`

Using broadcasting

Using outer product

Product

Resources

Company

Version in the book

Using indices

Using fromfunction

Using broadcasting

Using outer product

Using `fromfunction`