1. Use Vectorization (+4)
1. Use Vectorization
# ❌ Slow: Loop
result = []
for x in x_array:
result.append(np.sin(x) * np.exp(-x))
# ✅ Fast: Vectorized
result = np.sin(x_array) * np.exp(-x_array)
2. Choose Right Data Type
# Use appropriate precision
float32_array = np.array([1, 2, 3], dtype=np.float32) # Less memory
float64_array = np.array([1, 2, 3], dtype=np.float64) # More precision
# Use integer when possible
int_array = np.array([1, 2, 3], dtype=np.int32)
3. Avoid Matrix Inverse When Possible
# ❌ Slower and less stable
x = np.linalg.inv(A) @ b
# ✅ Faster and more stable
x = np.linalg.solve(A, b)
4. Use Broadcasting
# Broadcasting allows operations on arrays of different shapes
A = np.array([[1, 2, 3],
[4, 5, 6]]) # Shape (2, 3)
b = np.array([10, 20, 30]) # Shape (3,)
# Broadcast adds b to each row of A
C = A + b # Shape (2, 3)
5. Check Numerical Stability
# Check condition number
cond = np.linalg.cond(A)
if cond > 1e10:
print("Warning: Matrix is ill-conditioned")
# Use appropriate solver for symmetric positive definite
if np.allclose(A, A.T) and np.all(np.linalg.eigvals(A) > 0):
x = np.linalg.solve(A, b) # Can use Cholesky internally
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