Numpy Refresher

Numpy is a package used for scientific computing in python. Numpy’s core is implemented in C/C++ providing fast implementations of matrices operations. Numpy also utilizes the processors SIMD and other instructions to make implementation faster

1 What is Numpy

Numpy is a package used for scientific computing in python. Numpy’s core is implemented in C/C++ providing fast implementations of matrices operations. Numpy also utilizes the processors SIMD and other instructions to make implementation faster. Main offering of Numpy is powerful N-dimensional array object and useful linear algebra, Fourier transform, and random number capabilities. Numpy main object is homogeneous multidimensional arrays. Indexed by the positive tuple of integers. Its dimensions are called axes. No of axes is called rank.
Axes length is the no of elements in that dimension. Normally, axes 0 is rows and axes 1 is column

2 Imporrant NumPy Arrays Attributes

1. ndim No of dimensions
2. shape Size of each dimension
3. size Total array size in bytes
4. itemsize Size of an element in bytes
5. nbytes Total array size in bytes

I will cover them in detail but first lets understand few ways to create numpy arrays.

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>>> import numpy as np

3 How to create an simple numpy array

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>>> arr = np.array([1,2,3,4,5])
>>> arr

array([1, 2, 3, 4, 5])

All items in numpy array should have same data type. If not then numpy will upcast the needed ones

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>>> arr = np.array([1.1, 2,3,4,5])
>>> arr

array([ 1.1,  2. ,  3. ,  4. ,  5. ])

Otherwise one can explicitly assign the datatype using “dtype”

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>>> arr = np.array([1.1, 2,3,4,5], dtype=int)

4 Creating a multidimensional array

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>>> np.array([range(i, i + 3) for i in [2, 4, 6]])

array([[2, 3, 4],
       [4, 5, 6],
       [6, 7, 8]])

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>>> a = np.array([range(1,100)])
>>> print(a.shape)
>>> print(a.ndim)
>>> a

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, 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, 51,
        52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68,
        69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85,
        86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])

5 Arrays from Scratch

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# np.zeros(shape, dtype=float, order='C')
>>> np.zeros((2,3))
#shape is a tuple and passed with brackets

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

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# np.ones(shape, dtype=None, order='C')
>>> np.ones((2,3), dtype=int)

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

How about a matrix of all the same value

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# np.full(shape, fill_value, dtype=None, order='C')
>>> np.full((3,2), 3.1)

array([[ 3.1,  3.1],
       [ 3.1,  3.1],
       [ 3.1,  3.1]])

5.1 How about a little more flexibility in creating the numpy array

5.1.1 1. Creating the linear sequence of array with flexibility of providing step size

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# np.arange([start,] stop[, step,], dtype=None)
>>> a = np.arange(1, 10, 1)
>>> print(a)

>>> a = np.arange(1, 10, .5, dtype=float)
>>> print(a)

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>>> a = np.arange(1, 10, .5, dtype=float)
>>> for i in a:
...    print(int(i), end=' ')

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>>> a = np.arange(1, 10, .5, dtype=int)
>>> print(a)
>>> a = np.arange(1, 10, .5).astype(int) # Floating point step size
>>> print(a)

5.1.2 2. Creating the linear sequence of array with fliexibility of providing the number values required

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# np.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)
>>> sample = np.linspace(1, 10)
>>> print("Samples ---->", sample, end=' \n')
>>> sample,step = np.linspace(1, 10, num=20, retstep=True)
>>> print("Step ---->", step)

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    Samples
    [  1.           1.18367347   1.36734694   1.55102041   1.73469388
       1.91836735   2.10204082   2.28571429   2.46938776   2.65306122
       2.83673469   3.02040816   3.20408163   3.3877551    3.57142857
       3.75510204   3.93877551   4.12244898   4.30612245   4.48979592
       4.67346939   4.85714286   5.04081633   5.2244898    5.40816327
       5.59183673   5.7755102    5.95918367   6.14285714   6.32653061
       6.51020408   6.69387755   6.87755102   7.06122449   7.24489796
       7.42857143   7.6122449    7.79591837   7.97959184   8.16326531
       8.34693878   8.53061224   8.71428571   8.89795918   9.08163265
       9.26530612   9.44897959   9.63265306   9.81632653  10.        ] 
    
    Step
    0.473684210526

5.2 Array with distributed random values

5.2.1 Array of uniformly distributed random values between 0 and 1

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# np.random.random_sample(size=None)
>>> np.random.random((3, 2))

array([[ 0.86739782,  0.56355004],
       [ 0.70993532,  0.06739621],
       [ 0.53815033,  0.59688062]])

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# np.random.normal(loc=0.0, scale=1.0, size=None)
>>> np.random.normal(0, 1, (3,3))

array([[ 0.97078719,  0.32316481,  0.64860467],
       [-0.41963849,  0.1416606 , -2.00128317],
       [-1.20452905, -0.86871742,  1.10516725]])

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#randint(low, high=None, size=None, dtype='l')
>>> np.random.randint(10, 100,size=3)

array([14, 48, 77])

5.2.2 Identity Matrix

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# np.eye(N, M=None, k=0, dtype=<class 'float'>)
>>> np.eye(4)

6 NumPy Standard Data Types

• bool_ Boolean (True or False) stored as a byte
  
• int_ Default integer type (same as C long; normally either int64 or int32)
  
• intc Identical to C int (normally int32 or int64)
  
• intp Integer used for indexing (same as C ssize_t; normally either int32 or int64)
  
• int8 Byte (–128 to 127)
  
• int16 Integer (–32768 to 32767)
  
• int32 Integer (–2147483648 to 2147483647)
  
• int64 Integer (–9223372036854775808 to 9223372036854775807)
  
• uint8 Unsigned integer (0 to 255)
  
• uint16 Unsigned integer (0 to 65535)
  
• uint32 Unsigned integer (0 to 4294967295)
  
• uint64 Unsigned integer (0 to 18446744073709551615)
  
• float_ Shorthand for float64
  
• float16 Half-precision float: sign bit, 5 bits exponent, 10 bits mantissa
  
• float32 Single-precision float: sign bit, 8 bits exponent, 23 bits mantissa
  
• float64 Double-precision float: sign bit, 11 bits exponent, 52 bits mantissa
  

7 NumPy Random Generator - Seed the RandomState

numpy random generator can be seeded with a seed value to make sure that same random arrays are generated each time the code runs.

Seeding the random generator allows the generator to generate the same random values everytime. It names values in the array predictible np.random.seed(0)

np.random.seed(0); np.random.randint(10, size=6)
np.random.seed(0); np.random.randint(10, size=6)

Above code will generate same array everytime

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>>> np.random.seed(1)
>>> x1 =np.random.randint(10, size=6)
>>> x2 = np.random.randint(10, size=(3, 4))
>>> x3 = np.random.randint(10, size=(3,4,5))

print(x1)
print(x2)
print(x3)

 [[3 6 5 1 9]
  [3 4 8 1 4]
  [0 3 9 2 0]
  [4 9 2 7 7]]

 [[9 8 6 9 3]
  [7 7 4 5 9]
  [3 6 8 0 2]
  [7 7 9 7 3]]]

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>>> np.random.seed(0); np.random.randint(10, size=6)
>>> np.random.seed(0); np.random.randint(10, size=6)

array([5, 0, 3, 3, 7, 9])