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---
name: python-scientific-computing-1-use-vectorization
description: 'Sub-skill of python-scientific-computing: 1. Use Vectorization (+4).'
version: 1.0.0
category: data
type: reference
scripts_exempt: true
---
# 1. Use Vectorization (+4)
## 1. Use Vectorization
```python
# ❌ 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
```python
# 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
```python
# ❌ Slower and less stable
x = np.linalg.inv(A) @ b
# ✅ Faster and more stable
x = np.linalg.solve(A, b)
```
## 4. Use Broadcasting
```python
# 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
```python
# 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
```
