## Numpy Vectorization in Python

When working with large data sets in Python, it’s critical to optimize performance to avoid slow execution times. One of the most effective ways to do this is by using Numpy vectorization.

### Why For Loops Are Not Best for Numpy Vectorization?

For loops are slow because they require a lot of time to execute. They take a long time to evaluate and calculate the results, making them inefficient when working with large data sets.

Numpy vectorization, on the other hand, operates on entire arrays at once, without the need to loop over each element of the array. This makes the process much faster and more efficient.

### numpy.vectorize() vs Python for loop – Vectorization speed comparison

Numpy vectorization is quicker than using a for loop. Lets take an example of multiplication.

To multiply two lists without numpy.vectorize(), well need to iterate through each element one by one, hence making it slower:

```
x = [1, 2, 3]
y = [4, 5, 6]
result = []
for i in range(len(x)):
result.append(x[i] * y[i])
print(result)
```

But with the numpy.vectorize() function, we can multiply the same two arrays by simply writing:

```
import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
result = np.vectorize(lambda x,y:x*y)(x,y)
print(result)
```

This increases the code execution speed since the iterations are carried out at the C level. Using numpy.vectorize() Function for Vectorization

### Using the numpy.vectorize() Function for Vectorization

Numpy vectorize() is a Python function that takes a regular Python function and returns a new function that operates on NumPy arrays.

The syntax for vectorizing a function using numpy.vectorize() is straightforward. Here is an example of a simple Python function that we will vectorize:

```
def my_function(x, y):
return x + y
```

With numpy.vectorize(), we can vectorize this function as follows:

```
vectorized_func = np.vectorize(my_function)
```

### Numpy Vectorization with the numpy.vectorize() function

In the above example, we used a function that takes two arguments x and y and returns their sum.

To use this function with numpy.vectorize, we will first convert this Python function into a NumPy function. Here’s how we can do that:

```
import numpy as np
def my_function(x, y):
return x * y
my_numpy_function = np.vectorize(my_function)
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
results = my_numpy_function(x, y)
print(results)
```

The numpy.vectorize() function converts the Python function into a function that can operate on NumPy arrays.

### Output type of the vectorized function

The output type of a vectorized function is determined by the input data. For instance, if the input data is an int type, the output data will also be of the int type.

Similarly, if the input data is a float type, the output data will also be of the float type. If there is a single float in the input, but the function has an output of an integer type, then the output will be a float rather than an integer.

### Caching in Numpy vectorization

Caching is a technique that reduces the execution time of the function by caching the previously calculated results. By default, the numpy.vectorize() caches the function’s results to save computation time in situations where the same input is used repeatedly.

However, the cache can also cause larger memory usage if the input data set is too large, which can result in slower performance.

### Conclusion

In conclusion, numpy vectorization is a powerful tool that can significantly improve the performance of your Python applications. By using numpy.vectorize(), we can avoid the overhead of for loops over large data sets, making our code much more efficient.

Additionally, using numpy.vectorize() with NumPy arrays can simplify the code and make it more readable. So next time you’re working on a project that involves large data sets, consider using numpy.vectorize() to speed up your code.

### Vectorizing a Function

One of the primary advantages of Numpy vectorization is its ability to perform operations on arrays of data instead of using for loops. To do so, we can use the numpy.vectorize() function to vectorize a regular Python function.

### Lets take an example of a simple function and show how to vectorize it:

```
def cubed(x):
return x**3
```

We can call this function to cube a single number, like so:

```
>>> cubed(4)
64
```

But now, lets say we want to cube an entire array. We could do it using a for loop, like this:

```
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
cubed_arr = np.empty_like(arr)
for i in range(len(arr)):
cubed_arr[i] = cubed(arr[i])
print(cubed_arr)
```

### This will give us an output of:

```
array([ 1, 8, 27,
64,125])
```

This works fine for small arrays, but it can quickly become inefficient when dealing with larger arrays. Instead, we can vectorize the cubed() function using numpy.vectorize() to apply it to an entire array at once:

```
cubed_vec = np.vectorize(cubed)
cubed_arr = cubed_vec(arr)
print(cubed_arr)
```

### This will give us the same output:

```
array([ 1, 8, 27,
64, 125])
```

As we can see, the numpy.vectorize() function takes a regular Python function as an argument and returns a new function that can work with NumPy arrays. We simply need to call the new function with the array we want to apply the operation to.

### Final Remarks

In conclusion, Numpy vectorization is a powerful tool that can significantly improve the performance and readability of your Python code. Instead of using for loops to iterate over each element of an array, we can use numpy.vectorize() to apply operations to entire arrays at once, with much less overhead and more efficiently.

This can make a significant difference when working with large data sets, where performance is critical. Numpy.vectorize() is not a panacea for all performance issues.

It is still important to optimize your code for best performance. For instance, using NumPy-specific operations to perform complex calculations instead of Pythons built-in math functions can be significantly faster.

Similarly, using NumPy data types can avoid conversions between different data types, which can also slow things down.

### References

- https://numpy.org/doc/stable/reference/generated/numpy.vectorize.html
- https://towardsdatascience.com/why-you-should-always-vectorize-your-python-code-7924e773b5a4
- https://realpython.com/numpy-array-programming/

Numpy vectorization is a significant tool for optimizing Python code and improving performance when working with large data sets.

Using numpy.vectorize() to transform regular Python functions into NumPy functions that can operate on arrays is a powerful technique that can save time and improve readability. However, it is essential to optimize your code further and use NumPys built-in functions and data types for maximum performance.

Numpy vectorization is a critical tool for Python developers looking to improve code performance, and it’s a valuable technique to master.