2. The Basics of Numpy Arrays

Numpy Array Attributes

• We'll use Numpy's random number generator, which we will seed with a set value in order to ensure that the same random arrays are generated each time this code is run:

# In[1]
import numpy as np
rng=np.random.default_rng(seed=1701) # seed for reproducibility

x1 = rng.integers(10,size=6)
x2 = rng.integers(10,size=(3,4))
x3 = rng.integers(10,size=(3,4,5))

print("x3 ndim: ",x3.ndim)
print("x3 shape: ",x3.shape)
print("x3 size: ",x3.size)
print("x3 dtype: ",x3.dtype)

# Out[1]
x3 ndim:  3
x3 shape:  (3, 4, 5)
x3 size:  60
x3 dtype:  int64

Array Indexing : Accessing Single Elements

# In[2]
print(x2)
print(x2[2,-1])

# Out[2]
[[3 1 3 7]
 [4 0 2 3]
 [0 0 6 9]]
9

---

# In[3]
x2[0,0]=12
print(x2)

# Out[3]
[[12  1  3  7]
 [ 4  0  2  3]
 [ 0  0  6  9]]

• Unlike Python lists, Numpy array have a fixed type. For example, that if you attempt to insert a floating-point value to an integer array, the value will be truncated.

  # In[4]
  x1[0]=3.14
  print(x1)

  # Out[4]
  [3 0 3 3 7 9]

Array Slicing : Accessing Subarrays

• Numpy slicing syntax follows that of the standard Python lists; to access a slice of an array 'x', use this:
  x[start:stop:step]

One dimensional subarray

# In[5]
x=np.arange(10)
x

# Out[5]
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

---

# In[6]
print("first five elements:",x[:5])
print("elements after index 5:",x[5:])
print("middle subarray:",x[4:7])
print("every other element that step is 2:",x[::2])
print("every other element, starting at index 1 and step 2:",x[1::2])
print("all reversed elements:",x[::-1])
print("reversed every other element from index 5:",x[5::-2])

# Out[6]
first five elements: [0 1 2 3 4]
elements after index 5: [5 6 7 8 9]
middle subarray: [4 5 6]
every other element that step is 2: [0 2 4 6 8]
every other element, starting at index 1 and step 2: [1 3 5 7 9]
all reversed elements: [9 8 7 6 5 4 3 2 1 0]
reversed every other element from index 5: [5 3 1]

Multidimensional subarray

# In[7]
x2

# Out[7]
array([[12,  1,  3,  7],
       [ 4,  0,  2,  3],
       [ 0,  0,  6,  9]])

---

# In[8]
print("two rows, three columns:",x2[:2,:3])
print("all rows, every other column:",x2[:3,::2])
print("reversed array:",x2[::-1,::-1])

# Out[8]
two rows, three columns: [[12  1  3]
 [ 4  0  2]]
all rows, every other column: [[12  3]
 [ 4  2]
 [ 0  6]]
reversed array: [[ 9  6  0  0]
 [ 3  2  0  4]
 [ 7  3  1 12]]

Accessing array rows and columns

• You can access single rows or columns of an array by combining indexing and slicing, using an empty slice marked by a single colon(:)
• However, In the case of row access, you can omit colon(:) for a more compact syntax

  # In[9]
  print("first column of x2:",x2[:,0])
  print("first row of x2:",x2[0,:])
  print("equivalent to x2[0,:]:",x2[0])

  # Out[9]
  first column of x2: [12  4  0]
  first row of x2: [12  1  3  7]
  equivalent to x2[0,:]: [12  1  3  7]

Subarrays as no-copy views

• Unlike Python list slices, Numpy array slices are returned as views rather than copies of the array data.

# In[10]
x2_sub=x2[:2,:2]
print(x2_sub)

x2_sub[0,0]=99
print(x2_sub)

print(x2)

# Out[10]
[[12  1]
 [ 4  0]]
[[99  1]
 [ 4  0]]
[[99  1  3  7]
 [ 4  0  2  3]
 [ 0  0  6  9]]

• If we modify this subarray, orginal array will be changed.

Creating copies of Arrays

• Using copy() method

  # In[11]
  x2_sub_copy=x2[:2,:2].copy()
  print(x2_sub_copy)

  # Out[11]
  [[99  1]
  [ 4  0]]

---

# In[12]
x2_sub_copy[0,0]=42
print(x2_sub_copy)

print(x2)

# Out[12]
[[42  1]
 [ 4  0]]
[[99  1  3  7]
 [ 4  0  2  3]
 [ 0  0  6  9]]

• If we modify this subarray, the original array is not touched.

Reshaping of Arrays

• Using reshape() method

  # In[13]
  grid=np.arange(1,10).reshape((3,3))
  print(grid)

  # Out[13]
  [[1 2 3]
  [4 5 6]
  [7 8 9]]

---

# In[14]
x=np.array([1,2,3])
print(x.reshape((1,3))) # row vector via reshape
print(x.reshape((3,1))) # column vector via reshape

# Out[14]
array([[1, 2, 3]])
array([[1],
       [2],
       [3]])

• A convenient shorthad for this is to use np.newaxis in the slicing syntax

  # In[15]
  print(x[np.newaxis,:]) # row vector via reshape
  print(x[:,np.newaxis]) # column vector via reshape

  # Out[15]
  array([[1, 2, 3]])
  array([[1],
       [2],
       [3]])

Array Concatenation and Splitting

Concatenation of Arrays

• Using np.concatenate, np.vstack(vertical stack), np.hstack(horizontal stack)

np.concatenate

# In[16]
x=np.array([1,2,3])
y=np.array([3,2,1])
np.concatenate([x,y])

# Out[16]
array([1, 2, 3, 3, 2, 1])

---

# In[17]
grid=np.array([[1,2,3],[4,5,6]])
np.concatenate([grid,grid])

# Out[17]
array([[1, 2, 3],
       [4, 5, 6],
       [1, 2, 3],
       [4, 5, 6]])

---

# In[18]
np.concatenate([grid,grid],axis=1)

# Out[18]
array([[1, 2, 3, 1, 2, 3],
       [4, 5, 6, 4, 5, 6]])

• For More Information about the axis, reference this blog: About the axis

np.vstack

# In[19]
x=np.array([1,2,3])
grid=np.array([[9,8,7],[6,5,4]])
np.vstack([x,grid])

# Out[19]
array([[1, 2, 3],
       [9, 8, 7],
       [6, 5, 4]])

np.hstack

# In[20]
y=np.array([[99],[99]])
np.hstack([grid,y])

# Out[20]
array([[ 9,  8,  7, 99],
       [ 6,  5,  4, 99]])

Splitting of Arrays

• Using np.split, np.hsplit(horizontal split), np.vsplit(vertical split)

np.split

• np.split(array,indices_or_sections,axis=0)
• indices or sections are int or 1-dimensional array
• For example, indices or sections = [2,3]
  • array[:2]
  • array[2:3]
  • array[3:]

# In[21]
x=[1,2,3,99,99,3,2,1]
x1,x2,x3=np.split(x,[3,5])
print(x1,x2,x3)

# Out[21]
[1 2 3] [99 99] [3 2 1]

np.hsplit

• Split an array into multiple sub-arrays horizontally(column-wise)
• hsplit is equivalent to split with axis=1
• The array is always split along the second axis except for 1-dimensional arrays, where it is split at axis=0

  # In[22]
  grid=np.arange(16).reshape((4,4))
  grid

  # Out[22]
  array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])

---

# In[23]
left,right=np.hsplit(grid,2)
a=np.hsplit(grid,(2,3))
print(left)
print(right)
print(a)

# Out[23]
[[ 0  1]
 [ 4  5]
 [ 8  9]
 [12 13]]
[[ 2  3]
 [ 6  7]
 [10 11]
 [14 15]]
[array([[ 0,  1],
       [ 4,  5],
       [ 8,  9],
       [12, 13]]), 
array([[ 2],
       [ 6],
       [10],
       [14]]), 
array([[ 3],
       [ 7],
       [11],
       [15]])]

• With a higher dimensional array, the split is still along the second axis

  # In[24]
  x=np.arange(8).reshape(2,2,2)
  a=np.hsplit(x,2)
  print(x)
  print(a)

  # Out[24]
  [[[0 1]
  [2 3]]
  
  [[4 5]
  [6 7]]]
  [array([[[0, 1]],
  
       [[4, 5]]]), 
  array([[[2, 3]],
  
       [[6, 7]]])]

• With a 1-D array, the split is along the axis=0

  # In[25]
  x=np.array([0,1,2,3,4,5])
  np.hsplit(x,3)

  # Out[25]
  [array([0, 1]), array([2, 3]), array([4, 5])]

np.vsplit

• Split an array into multiple sub-arrays vertically(row-wise)

• vsplit is equivalent to split with axis=0 (default)

• The array is always split along the first axis regardless of the array dimension.

  # In[26]
  upper,lower=np.vsplit(grid,2)
  a=np.vsplit(grid,(2,3))
  print(upper)
  print(lower)
  print(a)

  # Out[26]
  [[0 1 2 3]
  [4 5 6 7]]
  [[ 8  9 10 11]
  [12 13 14 15]]
  [array([[0, 1, 2, 3],
         [4, 5, 6, 7]]),
  array([[ 8,  9, 10, 11]]),
  array([[12, 13, 14, 15]])]

• With a higher dimensional array, the split is still along the first axis

  # In[27]
  x=np.arange(8).reshape(2,2,2)
  a=np.vsplit(x,2)
  print(x)
  print(a)

  # Out[27]
  [[[0, 1],
  [2, 3]],
  
  [[4, 5],
  [6, 7]]]
  [array([[[0, 1],
         [2, 3]]]),
  array([[[4, 5],
         [6, 7]]])]

np.dsplit

• Split array into multiple sub-arrays along the third axis(depth) in higher-dimensional arrays.
• dsplit is equivalent to split with axis=2
• The array is always split along the third axis provided the array dimension is greater than or equal to 3

# In[28]
x=np.arange(16).reshape(2,2,4)
a=np.dsplit(x,2)
b=np.dsplit(x,(2,3))
print(x)
print(a)
print(b)

# Out[28]
[[[ 0,  1,  2,  3],
 [ 4,  5,  6,  7]],

[[ 8,  9, 10, 11],
 [12, 13, 14, 15]]]
[array([[[ 0,  1],
         [ 4,  5]],

        [[ 8,  9],
         [12, 13]]]),
 array([[[ 2,  3],
         [ 6,  7]],

        [[10, 11],
         [14, 15]]])
[array([[[ 0,  1],
        [ 4,  5]],

       [[ 8,  9],
        [12, 13]]]), 
array([[[ 2],
        [ 6]],

       [[10],
        [14]]]), 
array([[[ 3],
        [ 7]],

       [[11],
        [15]]])]