Aggregate Operations, Array Indexing, Array Slicing

Aggregate (Reduction) Operations

Aggregate functions reduce an array to a single summary value.

import numpy as np

a = np.array([12, 45, 7, 23, 56, 9])

print(a.sum())        # 152
print(a.min())          # 7
print(a.max())            # 56
print(a.mean())              # 25.333...
print(a.std())                  # standard deviation
print(a.var())                    # variance
print(np.median(a))                 # 17.5
print(a.argmax())                     # 4  -- index of the max value
print(a.argmin())                       # 2  -- index of the min value

Aggregates on 2D arrays (row-wise / column-wise using axis)

m = np.array([[1, 2, 3], [4, 5, 6]])

print(m.sum())              # 21  -- total of all elements
print(m.sum(axis=0))          # [5 7 9]   -- column-wise sum (down each column)
print(m.sum(axis=1))            # [6 15]    -- row-wise sum (across each row)
print(m.max(axis=0))              # [4 5 6]

axis=0  -> operate DOWN the columns (result has 1 value per column)
axis=1  -> operate ACROSS the rows  (result has 1 value per row)

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Array Indexing

a = np.array([10, 20, 30, 40, 50])
print(a[0])       # 10 (first)
print(a[-1])       # 50 (last)

m = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(m[0, 0])       # 1  (row 0, col 0)
print(m[1, 2])         # 6  (row 1, col 2)
print(m[-1, -1])         # 9  (last row, last col)

Boolean (fancy) indexing

a = np.array([5, 12, 8, 20, 3])
print(a[a > 10])   # [12 20] -- only elements greater than 10

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Array Slicing

a = np.array([10, 20, 30, 40, 50, 60])
print(a[1:4])       # [20 30 40]
print(a[:3])          # [10 20 30]
print(a[::2])           # [10 30 50]
print(a[::-1])             # [60 50 40 30 20 10]

Slicing a 2D array

m = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

print(m[0:2, 1:3])
# [[2 3]
#  [5 6]]

print(m[:, 1])         # [2 5 8]  -- entire column 1
print(m[1, :])           # [4 5 6]  -- entire row 1

Important: array slices are views, not copies — modifying a slice modifies the original array too. Use .copy() to get an independent copy.

a = np.array([1, 2, 3, 4, 5])
b = a[1:3]
b[0] = 999
print(a)   # [1 999 3 4 5] -- original changed!