NumPy Exercises 1

Udemy.com, PyDSML, Section 2 Numpy

https://www.udemy.com/python-for-data-science-and-machine-learning-bootcamp/learn/v4/overview
Answers by Jenifer Yoon
Date 3/27/2019

* Questions -- followed by my answers. *

Import NumPy as np

In [2]:
import numpy as np

Create an array of 10 zeros

In [3]:
np.zeros(10)
Out[3]:
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])

Create an array of 10 ones

In [4]:
np.ones(10)
Out[4]:
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

Create an array of 10 fives

In [5]:
np.ones(10)*5
Out[5]:
array([5., 5., 5., 5., 5., 5., 5., 5., 5., 5.])

Create an array of the integers from 10 to 50

In [6]:
np.arange(10, 51)
Out[6]:
array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
       27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
       44, 45, 46, 47, 48, 49, 50])

Create an array of all the even integers from 10 to 50

In [7]:
np.arange(10, 51, 2)
Out[7]:
array([10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42,
       44, 46, 48, 50])

Create a 3x3 matrix with values ranging from 0 to 8

In [8]:
mat = np.arange(0, 9)
mat.reshape(3, 3)
Out[8]:
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])

Create a 3x3 identity matrix

In [9]:
np.eye(3)
Out[9]:
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
In [10]:
np.eye(3, 3)
Out[10]:
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

Use NumPy to generate a random number between 0 and 1

In [16]:
np.random.rand(1)
# np.random.rand(d0, d1, d2, ...)  selects a random number from [0, 1) range.  Paramters are dimensions.]
Out[16]:
array([0.27345171])
In [17]:
help(np.random.rand)

Help on built-in function rand:

rand(...) method of mtrand.RandomState instance
    rand(d0, d1, ..., dn)
    
    Random values in a given shape.
    
    Create an array of the given shape and populate it with
    random samples from a uniform distribution
    over ``[0, 1)``.
    
    Parameters
    ----------
    d0, d1, ..., dn : int, optional
        The dimensions of the returned array, should all be positive.
        If no argument is given a single Python float is returned.
    
    Returns
    -------
    out : ndarray, shape ``(d0, d1, ..., dn)``
        Random values.
    
    See Also
    --------
    random
    
    Notes
    -----
    This is a convenience function. If you want an interface that
    takes a shape-tuple as the first argument, refer to
    np.random.random_sample .
    
    Examples
    --------
    >>> np.random.rand(3,2)
    array([[ 0.14022471,  0.96360618],  #random
           [ 0.37601032,  0.25528411],  #random
           [ 0.49313049,  0.94909878]]) #random

Use NumPy to generate an array of 25 random numbers sampled from a standard normal distribution

In [18]:
np.random.rand(25)
Out[18]:
array([0.52566673, 0.88139993, 0.24887143, 0.2956426 , 0.17621077,
       0.98663012, 0.43747115, 0.64025843, 0.02924842, 0.75702585,
       0.51010062, 0.09094537, 0.1174884 , 0.53385174, 0.64869243,
       0.37622658, 0.65330289, 0.41197009, 0.30165867, 0.63191869,
       0.39511783, 0.81510441, 0.75499403, 0.21194784, 0.94456316])
In [19]:
np.random.rand(25)
Out[19]:
array([0.7559873 , 0.08741562, 0.43933887, 0.13731684, 0.05901282,
       0.86639925, 0.48606921, 0.33415014, 0.23369125, 0.79805061,
       0.41485206, 0.6283579 , 0.84090133, 0.31386089, 0.13334902,
       0.38771005, 0.18281798, 0.79785461, 0.82618869, 0.90973119,
       0.28070039, 0.53574626, 0.56157786, 0.07180881, 0.8936017 ])

Create the following matrix:

In [35]:
Out[35]:
array([[ 0.01,  0.02,  0.03,  0.04,  0.05,  0.06,  0.07,  0.08,  0.09,  0.1 ],
       [ 0.11,  0.12,  0.13,  0.14,  0.15,  0.16,  0.17,  0.18,  0.19,  0.2 ],
       [ 0.21,  0.22,  0.23,  0.24,  0.25,  0.26,  0.27,  0.28,  0.29,  0.3 ],
       [ 0.31,  0.32,  0.33,  0.34,  0.35,  0.36,  0.37,  0.38,  0.39,  0.4 ],
       [ 0.41,  0.42,  0.43,  0.44,  0.45,  0.46,  0.47,  0.48,  0.49,  0.5 ],
       [ 0.51,  0.52,  0.53,  0.54,  0.55,  0.56,  0.57,  0.58,  0.59,  0.6 ],
       [ 0.61,  0.62,  0.63,  0.64,  0.65,  0.66,  0.67,  0.68,  0.69,  0.7 ],
       [ 0.71,  0.72,  0.73,  0.74,  0.75,  0.76,  0.77,  0.78,  0.79,  0.8 ],
       [ 0.81,  0.82,  0.83,  0.84,  0.85,  0.86,  0.87,  0.88,  0.89,  0.9 ],
       [ 0.91,  0.92,  0.93,  0.94,  0.95,  0.96,  0.97,  0.98,  0.99,  1.  ]])
In [22]:
np.arange(0.01, 1.01, .01).reshape(10, 10)
Out[22]:
array([[0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ],
       [0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 ],
       [0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 ],
       [0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 ],
       [0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 ],
       [0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6 ],
       [0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7 ],
       [0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8 ],
       [0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9 ],
       [0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 1.  ]])

Create an array of 20 linearly spaced points between 0 and 1:

In [27]:
np.linspace(0, 1, 20)
Out[27]:
array([0.        , 0.05263158, 0.10526316, 0.15789474, 0.21052632,
       0.26315789, 0.31578947, 0.36842105, 0.42105263, 0.47368421,
       0.52631579, 0.57894737, 0.63157895, 0.68421053, 0.73684211,
       0.78947368, 0.84210526, 0.89473684, 0.94736842, 1.        ])
In [26]:
np.linspace(0, 1, 20, endpoint=True)
# linspace returns an array of evenly spaced numbers.  (start, spop, numbers, default include endpoint=True)
Out[26]:
array([0.        , 0.05263158, 0.10526316, 0.15789474, 0.21052632,
       0.26315789, 0.31578947, 0.36842105, 0.42105263, 0.47368421,
       0.52631579, 0.57894737, 0.63157895, 0.68421053, 0.73684211,
       0.78947368, 0.84210526, 0.89473684, 0.94736842, 1.        ])

Numpy Indexing and Selection

Now you will be given a few matrices, and be asked to replicate the resulting matrix outputs:

In [28]:
mat = np.arange(1,26).reshape(5,5)
mat
Out[28]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15],
       [16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25]])
In [31]:
# WRITE CODE HERE THAT REPRODUCES THE OUTPUT OF THE CELL BELOW
# BE CAREFUL NOT TO RUN THE CELL BELOW, OTHERWISE YOU WON'T
# BE ABLE TO SEE THE OUTPUT ANY MORE
Out[31]:
array([[12, 13, 14, 15],
       [17, 18, 19, 20],
       [22, 23, 24, 25]])
In [32]:
mat[2:6, 1:6]
# Indexing is same as list indexing.
Out[32]:
array([[12, 13, 14, 15],
       [17, 18, 19, 20],
       [22, 23, 24, 25]])
In [34]:
# Try negative indexing.
mat[-3:, -4:]
Out[34]:
array([[12, 13, 14, 15],
       [17, 18, 19, 20],
       [22, 23, 24, 25]])
In [38]:
# Negative indexing.  Always counts from top-left.  [Row start:end, Col start:end]
mat[:-3, :-4]
Out[38]:
array([[1],
       [6]])
In [29]:
# WRITE CODE HERE THAT REPRODUCES THE OUTPUT OF THE CELL BELOW
# BE CAREFUL NOT TO RUN THE CELL BELOW, OTHERWISE YOU WON'T
# BE ABLE TO SEE THE OUTPUT ANY MORE
In [39]:
mat[3, -1]
Out[39]:
20
In [41]:
Out[41]:
20
In [40]:
# WRITE CODE HERE THAT REPRODUCES THE OUTPUT OF THE CELL BELOW
# BE CAREFUL NOT TO RUN THE CELL BELOW, OTHERWISE YOU WON'T
# BE ABLE TO SEE THE OUTPUT ANY MORE
mat
Out[40]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15],
       [16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25]])
In [43]:
# mat 2nd column, 0 to 2 rows.
mat[:3, 1].reshape(3, 1)
Out[43]:
array([[ 2],
       [ 7],
       [12]])
In [42]:
Out[42]:
array([[ 2],
       [ 7],
       [12]])
In [31]:
# WRITE CODE HERE THAT REPRODUCES THE OUTPUT OF THE CELL BELOW
# BE CAREFUL NOT TO RUN THE CELL BELOW, OTHERWISE YOU WON'T
# BE ABLE TO SEE THE OUTPUT ANY MORE
In [46]:
mat[-1, :]
Out[46]:
array([21, 22, 23, 24, 25])
In [46]:
Out[46]:
array([21, 22, 23, 24, 25])
In [32]:
# WRITE CODE HERE THAT REPRODUCES THE OUTPUT OF THE CELL BELOW
# BE CAREFUL NOT TO RUN THE CELL BELOW, OTHERWISE YOU WON'T
# BE ABLE TO SEE THE OUTPUT ANY MORE
In [47]:
mat[-2:, :]  # Last two rows, all columns.
Out[47]:
array([[16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25]])
In [49]:
Out[49]:
array([[16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25]])

Now do the following

Get the sum of all the values in mat

In [51]:
mat.sum()  # Method applied to mat object?
# mat is an ndarray object, a built-in numpy class.
# This class object has a method .sum() and .std().
Out[51]:
325
In [50]:
Out[50]:
325

Get the standard deviation of the values in mat

In [57]:
mat.std()
Out[57]:
7.211102550927978
In [51]:
Out[51]:
7.2111025509279782

Get the sum of all the columns in mat

In [58]:
sum(mat)
# sum() function applied to mat ndarray object produce column sums by default.
Out[58]:
array([55, 60, 65, 70, 75])
In [70]:
sum(mat[:3, -2:])
# [row 0 to 2, col 4 to 5]
Out[70]:
array([27, 30])
In [71]:
## mat.sum(axis=0)
# Columns axis=0, not 1.
x = mat.sum(axis=0)
y = mat.sum(axis=1)
print(x, y)

[55 60 65 70 75] [ 15  40  65  90 115]
In [53]:
Out[53]:
array([55, 60, 65, 70, 75])

End