NumPy
NumPy is the fundamental package for scientific computing in Python. It provides a high-performance multidimensional array object and tools for working with these arrays. Understanding NumPy's array operations, broadcasting rules, and linear algebra routines is essential for any data science or numerical computing workflow.
Array Creation
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For more examples and detailed explanations, see the Real Python guide on array creation.
Create arrays from Python lists or use specialized constructors for common patterns.
>>> import numpy as np
# From lists
>>> a = np.array([1, 2, 3, 4, 5])
>>> b = np.array([[1, 2], [3, 4]])
# Filled arrays
>>> np.zeros((2, 3))
array([[0., 0., 0.],
[0., 0., 0.]])
>>> np.ones((2, 3))
array([[1., 1., 1.],
[1., 1., 1.]])
>>> np.eye(3) # Identity matrix
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
# Sequence arrays
>>> np.arange(0, 10, 2) # Start, stop, step
array([0, 2, 4, 6, 8])
>>> np.linspace(0, 1, 5) # 5 evenly spaced points
array([0. , 0.25, 0.5 , 0.75, 1. ])
# Random arrays
>>> np.random.rand(2, 3) # Uniform [0, 1)
>>> np.random.randn(2, 3) # Standard normal
>>> np.random.randint(0, 10, size=(2, 3))
>>> np.random.seed(42) # ReproducibilityShape Manipulation
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For more examples and detailed explanations, see the Real Python guide on shape manipulation.
Reshape, flatten, and rearrange array dimensions without copying data when possible.
>>> a = np.arange(12)
>>> a.reshape(3, 4) # Returns a view when possible
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> a.ravel() # Flatten to 1D (returns view if contiguous)
>>> a.flatten() # Always returns a copy
>>> np.expand_dims(a, axis=0).shape # Add dimension
(1, 12)
>>> a = np.array([[1, 2, 3], [4, 5, 6]])
>>> np.squeeze(a).shape # Remove length-1 dimensions
(2, 3)
>>> a.T # Transpose
array([[1, 4],
[2, 5],
[3, 6]])
>>> a.transpose(1, 0) # Explicit axis permutation
array([[1, 4],
[2, 5],
[3, 6]])
>>> a = a.reshape(3, 4)
>>> a.reshape(-1) # Auto-infer dimensionWARNING
reshape on non-contiguous arrays may return a copy; use np.ascontiguousarray(a) first if you need a view.
Indexing and Slicing
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For more examples and detailed explanations, see the Real Python guide on indexing and slicing.
NumPy supports powerful indexing including slicing, fancy indexing, and boolean masking.
>>> a = np.arange(12).reshape(3, 4)
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
# Basic slicing
>>> a[1, 2] # Single element: 6
>>> a[0] # First row
>>> a[:, 1] # Second column
>>> a[0:2, 1:3] # Submatrix
# Fancy indexing with integer arrays
>>> a[[0, 2], [1, 3]] # (0,1) and (2,3): array([1, 11])
>>> a[[0, 2]] # Rows 0 and 2
>>> a[:, [1, 3]] # Columns 1 and 3
# Boolean masking
>>> mask = a > 5
>>> a[mask]
array([ 6, 7, 8, 9, 10, 11])
>>> a[a % 2 == 0] = -1 # Set even elements to -1Broadcasting
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For more examples and detailed explanations, see the Real Python guide on numpy broadcasting.
Broadcasting allows arithmetic between arrays of different shapes by automatically expanding dimensions.
>>> a = np.array([[1, 2, 3], [4, 5, 6]]) # (2, 3)
>>> b = np.array([10, 20, 30]) # (3,) → broadcasts to (1, 3) → (2, 3)
>>> a + b
array([[11, 22, 33],
[14, 25, 36]])
>>> a * np.array([[10], [20]]) # (2, 3) * (2, 1) → (2, 3)
array([[10, 40, 90],
[80, 100, 120]])
# Broadcasting rules: trailing dimensions must match or be 1/missing
>>> x = np.ones((3, 1, 5))
>>> y = np.ones((1, 4, 1))
>>> (x + y).shape # (3, 4, 5)WARNING
Broadcasting can create large intermediate arrays in memory. Be mindful when working with very high-dimensional data.
Universal Functions (ufunc)
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For more examples and detailed explanations, see the Real Python guide on numpy ufunc.
Element-wise operations optimized in C. Most math operations are ufuncs.
>>> a = np.array([1, 2, 3, 4])
# Arithmetic ufuncs
>>> np.add(a, 10)
>>> np.subtract(a, 2)
>>> np.multiply(a, 2)
>>> np.divide(a, 3)
>>> np.power(a, 2)
# Trigonometric
>>> np.sin(a), np.cos(a), np.tan(a)
# Exponential and logarithmic
>>> np.exp(a), np.log(a), np.log10(a), np.log2(a)
# Rounding
>>> np.round(np.array([1.234, 5.678]), 1)
array([1.2, 5.7])
# Comparison
>>> np.greater(a, 2)
>>> np.where(a > 2, a, 0) # Condition, x, y
# Clip
>>> np.clip(a, 1, 3)
array([1, 2, 3, 3])Aggregation
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For more examples and detailed explanations, see the Real Python guide on aggregation.
Compute summary statistics across entire arrays or along specific axes.
>>> a = np.array([[1, 2, 3], [4, 5, 6]])
>>> a.sum() # 21
>>> a.sum(axis=0) # Column sums: array([5, 7, 9])
>>> a.sum(axis=1) # Row sums: array([6, 15])
>>> a.mean() # 3.5
>>> a.mean(axis=0) # array([2.5, 3.5, 4.5])
>>> a.std() # Standard deviation
>>> a.min() # 1
>>> a.max() # 6
>>> a.argmin() # Index of min: 0
>>> a.argmax() # Index of max: 5
>>> np.median(a)
>>> np.percentile(a, [25, 50, 75])
>>> np.cumsum(a) # Cumulative sum
# Axis-specific argmin/argmax
>>> a.argmax(axis=0) # array([1, 1, 1])Linear Algebra
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For more examples and detailed explanations, see the Real Python guide on linear algebra.
NumPy's linalg submodule provides common linear algebra operations.
>>> A = np.array([[1, 2], [3, 4]])
>>> b = np.array([5, 6])
# Dot product (preferred over a.dot(b))
>>> np.dot(A, b)
array([17, 39])
# Matrix multiplication (Python 3.5+)
>>> A @ b
array([17, 39])
>>> np.matmul(A, np.array([[2], [3]]))
array([[ 8],
[18]])
# Matrix inverse
>>> np.linalg.inv(A)
array([[-2. , 1. ],
[ 1.5, -0.5]])
# Solve linear system Ax = b
>>> np.linalg.solve(A, b)
array([-4., 4.5])
# Eigenvalues and eigenvectors
>>> vals, vecs = np.linalg.eig(A)
>>> vals
array([-0.37228132, 5.37228132])
# Singular value decomposition
>>> U, S, Vt = np.linalg.svd(A)
# Norms
>>> np.linalg.norm(A) # Frobenius norm
>>> np.linalg.norm(A, ord=2) # Spectral norm
# Determinant and trace
>>> np.linalg.det(A)
>>> np.trace(A)
# Outer and inner products
>>> np.outer(np.array([1, 2]), np.array([3, 4]))
array([[3, 4],
[6, 8]])Saving and Loading
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For more examples and detailed explanations, see the Real Python guide on saving and loading.
Persist numpy arrays to disk in binary or text formats.
>>> a = np.array([1, 2, 3, 4, 5])
# Single array — binary .npy format
>>> np.save('array.npy', a)
>>> loaded = np.load('array.npy')
# Multiple arrays — compressed .npz archive
>>> b = np.array([10, 20])
>>> np.savez('arrays.npz', x=a, y=b)
>>> data = np.load('arrays.npz')
>>> data['x'], data['y']
# Compressed archive (smaller file size)
>>> np.savez_compressed('arrays.npz', x=a, y=b)
# Text format — human readable
>>> np.savetxt('array.csv', a, delimiter=',')
>>> loaded = np.loadtxt('array.csv', delimiter=',')
# Structured text with header
>>> np.savetxt('array.csv', a, delimiter=',', header='values', comments='')Set Operations
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For more examples and detailed explanations, see the Real Python guide on set operations.
Treat 1D arrays as sets for common set operations.
>>> a = np.array([1, 2, 3, 4])
>>> b = np.array([3, 4, 5, 6])
>>> np.intersect1d(a, b)
array([3, 4])
>>> np.union1d(a, b)
array([1, 2, 3, 4, 5, 6])
>>> np.setdiff1d(a, b)
array([1, 2])
>>> np.setxor1d(a, b)
array([1, 2, 5, 6])
>>> np.in1d(a, b)
array([False, False, True, True])