# Optimizing element-wise multiplication of large 2D NumPy arrays

## NumPy: Performance Optimization Exercise-7 with Solution

Write a NumPy program that creates a function to compute the element-wise multiplication of two large 2D arrays using nested for loops. Optimize it using NumPy's vectorized operations.

**Sample Solution:**

**Python Code:**

```
import numpy as np
# Create two large 2D NumPy arrays with shape (1000, 1000)
array1 = np.random.rand(1000, 1000)
array2 = np.random.rand(1000, 1000)
# Function to compute element-wise multiplication using nested for loops
def elementwise_multiplication_using_loops(arr1, arr2):
rows, cols = arr1.shape
result = np.zeros((rows, cols))
for i in range(rows):
for j in range(cols):
result[i, j] = arr1[i, j] * arr2[i, j]
return result
# Compute the element-wise multiplication using the nested for loops
result_loop = elementwise_multiplication_using_loops(array1, array2)
print("Element-wise multiplication using for loop (first 5x5 block):\n", result_loop[:5, :5])
# Optimize the element-wise multiplication using NumPy's vectorized operations
result_vectorized = array1 * array2
print("Element-wise multiplication using vectorized operations (first 5x5 block):\n", result_vectorized[:5, :5])
```

Output:

Element-wise multiplication using for loop (first 5x5 block): [[0.42591046 0.10735024 0.296129 0.15170064 0.28291849] [0.12879494 0.34918637 0.05554299 0.05783684 0.22553233] [0.55246279 0.47389473 0.400696 0.6222842 0.53399356] [0.3779341 0.52980174 0.26423262 0.04478953 0.0223926 ] [0.14589255 0.21884822 0.52713264 0.1099746 0.75080976]] Element-wise multiplication using vectorized operations (first 5x5 block): [[0.42591046 0.10735024 0.296129 0.15170064 0.28291849] [0.12879494 0.34918637 0.05554299 0.05783684 0.22553233] [0.55246279 0.47389473 0.400696 0.6222842 0.53399356] [0.3779341 0.52980174 0.26423262 0.04478953 0.0223926 ] [0.14589255 0.21884822 0.52713264 0.1099746 0.75080976]]

**Explanation:**

- Create large arrays: Two large 2D NumPy arrays, each with shape (1000, 1000), are created using np.random.rand().
- Function with nested for loops: A function elementwise_multiplication_using_loops performs element-wise multiplication of the arrays using nested for loops.
- Compute multiplication with loops: The element-wise multiplication is calculated using the nested for loops, and the first 5x5 block of the result is printed.
- Optimize with vectorization: The element-wise multiplication is optimized using NumPy's vectorized operations, and the first 5x5 block of the result is printed.

**Python-Numpy Code Editor:**

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