NumPy: Vectorized Scientific Computing

1. Overview#

NumPy (Numerical Python) is the foundational library for scientific computing and matrix operations in Python. It provides high-performance multidimensional array objects (ndarray) and vectorized mathematical operations implemented in contiguous C memory buffers.

NumPy arrays are homogeneous (all elements share the same dtype) and contiguous in memory, eliminating Python bytecode interpretation overhead during large array computations.

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2. Array Creation & Vectorization#

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import numpy as np

# 1. Array Creation
vectors = np.array([[1.0, 2.5, 3.8], [4.1, 5.0, 6.2]], dtype=np.float32)
print("Shape:", vectors.shape) # (2, 3)
print("Memory footprint:", vectors.nbytes, "bytes")

# 2. Vectorized Math (No Python loops needed)
angles_rad = np.linspace(0, np.pi, num=5)
sin_vals = np.sin(angles_rad)
print("Sine values:", sin_vals)

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3. Broadcasting Rules#

Broadcasting allows NumPy to perform arithmetic operations on arrays with different shapes without copying data:

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# Matrix (3, 3) + Row Vector (1, 3)
matrix = np.ones((3, 3))
row_bias = np.array([10, 20, 30])

# row_bias is broadcast along axis 0 automatically
result = matrix + row_bias
print(result)
# [[11., 21., 31.],
# [11., 21., 31.],
# [11., 21., 31.]]

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4. Summary & Best Practices Checklist#

• Use np.dot or @ for matrix multiplication instead of element-wise *.
• Avoid resizing or appending to NumPy arrays inside loops; preallocate with np.zeros() or np.empty().
• Leverage boolean masking (arr[arr > 0]) for ultra-fast filtering.