NumPy

In [5]:

    

# Getting set up to use the NumPy Library
import numpy as np


    

In [8]:

    

# Arrays have shape (dimensions) and data types
rows = 1
cols = 3
np.zeros(shape=(rows, cols), dtype=float)


    

    
Out[8]:





array([[ 0.,  0.,  0.]])

In [9]:

    

# Arrays have shape (dimensions) and data types
rows = 3
cols = 3
np.zeros(shape=(rows, cols), dtype=float)


    

    
Out[9]:





array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.],
       [ 0.,  0.,  0.]])

In [11]:

    

# Three dimensional array
rows = 3
cols = 3
depth = 3
np.zeros(shape=(rows, cols, depth), dtype=float)


    

    
Out[11]:





array([[[ 0.,  0.,  0.],
        [ 0.,  0.,  0.],
        [ 0.,  0.,  0.]],

       [[ 0.,  0.,  0.],
        [ 0.,  0.,  0.],
        [ 0.,  0.,  0.]],

       [[ 0.,  0.,  0.],
        [ 0.,  0.,  0.],
        [ 0.,  0.,  0.]]])

In [14]:

    

my_ones = np.ones(shape=(rows, cols), dtype=int)
my_ones


    

    
Out[14]:





array([[1, 1, 1],
       [1, 1, 1],
       [1, 1, 1]])

In [13]:

    

print(my_ones)


    

    




[[1 1 1]
 [1 1 1]
 [1 1 1]]

In [31]:

    

a = np.arange(16)


    

In [32]:

    

a


    

    
Out[32]:





array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

In [33]:

    

a[0:4]


    

    
Out[33]:





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

In [34]:

    

a[4:6]


    

    
Out[34]:





array([4, 5])

In [35]:

    

a[0:]


    

    
Out[35]:





array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

In [36]:

    

a[:]


    

    
Out[36]:





array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

In [40]:

    

a[:-1]


    

    
Out[40]:





array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])

In [39]:

    

a[::-1]


    

    
Out[39]:





array([15, 14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1,  0])

In [38]:

    

a + 20


    

    
Out[38]:





array([20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35])

In [41]:

    

a


    

    
Out[41]:





array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

In [42]:

    

a.reshape(4, 4)


    

    
Out[42]:





array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])

In [46]:

    

a.cumsum()


    

    
Out[46]:





array([  0,   1,   3,   6,  10,  15,  21,  28,  36,  45,  55,  66,  78,
        91, 105, 120])

In [51]:

    

M = np.matrix('1.0 2.0 3.0 4.0; 5.0 6.0 10.0 11.0; 12.0 20.0 50.0 9.0')


    

In [52]:

    

M


    

    
Out[52]:





matrix([[  1.,   2.,   3.,   4.],
        [  5.,   6.,  10.,  11.],
        [ 12.,  20.,  50.,   9.]])

In [53]:

    

# Transpose
M.T


    

    
Out[53]:





matrix([[  1.,   5.,  12.],
        [  2.,   6.,  20.],
        [  3.,  10.,  50.],
        [  4.,  11.,   9.]])

In [62]:

    

X = np.matrix('100 0 0 0; 0 100 0 0; 0 0 100 0')
X


    

    
Out[62]:





matrix([[100,   0,   0,   0],
        [  0, 100,   0,   0],
        [  0,   0, 100,   0]])

In [63]:

    

M + X


    

    
Out[63]:





matrix([[ 101.,    2.,    3.,    4.],
        [   5.,  106.,   10.,   11.],
        [  12.,   20.,  150.,    9.]])

In [64]:

    

# Inverse
X.I


    

    
Out[64]:





matrix([[ 0.01,  0.  ,  0.  ],
        [ 0.  ,  0.01,  0.  ],
        [ 0.  ,  0.  ,  0.01],
        [ 0.  ,  0.  ,  0.  ]])

In [1]:

    

print("Hello Linear Algebra")


    

    




Hello Linear Algebra

In [2]:

    

print("Numbers, numbers, and more numbers")


    

    




Numbers, numbers, and more numbers

In [19]:

    

# FFT Fast Fourier Transform
import numpy as np
PI = np.pi
t = np.linspace(0,120,4000)
signal = 12*np.sin(3 * 2*PI*t) # 3 Hz
signal += 6*np.sin(8 * 2*PI*t) # 8 Hz 
signal += 1.5*np.random.random(len(t)) # noise 
FFT = abs(np.fft.fft(signal))
freqs = np.fft.fftfreq(signal.size, t[1]-t[0])


    

In [16]:

    




    

    
Out[16]:





<matplotlib.colorbar.Colorbar at 0x10704a0f0>

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