The key to improving Python numerical computing performance is its vectorized operations and efficient memory management. 1. Use NumPy arrays instead of Python lists to reduce memory usage and improve computing speed; 2. Make rational use of broadcast mechanisms so that arrays of different shapes can be directly computed to avoid explicit loops; 3. Avoid Python native loops, try to use vectorized operations to significantly improve execution efficiency; 4. Choose the appropriate data type (such as float32 instead of float64), save memory and speed up computing, and pay attention to accuracy issues. Following these principles can give full play to the advantages of NumPy in high-performance numerical calculations.
Python itself is not designed for high performance computing, but with NumPy, it does a great job of numerical calculations. NumPy provides efficient array operations and mathematical functions, allowing Python to maintain good performance when processing large-scale data. If you need to use Python for scientific computing, data analysis or machine learning, NumPy is almost an inescapable basic tool.

The following parts will start from the perspective of actual use and talk about how to use NumPy well for high-performance numerical calculations.
Use NumPy array instead of Python lists
Although Python's own list (list) is flexible, it is not efficient when processing large amounts of numerical data. In contrast, NumPy's ndarray
is a data structure optimized for numerical operations.

- Lower memory footprint: NumPy arrays store the same type of data, unlike Python lists that carry type information.
- Faster calculation: NumPy's vectorized operation is implemented in C, which is much faster than Python loops.
For example: You want to add 1 to each number in a list. It is possible to use Python native writing like this:
a = [x 1 for x in range(1000000)]
And using NumPy can do this:

import numpy as np a = np.arange(1000000) 1
The latter not only has the code more concise, but also has significantly improved execution speed.
Rational use of broadcasting mechanisms (Broadcasting)
Broadcasting is a very powerful feature in NumPy, which allows arrays of different shapes to perform operations without having to manually expand the dimensions.
For example, you have a two-dimensional array A (shape is (3,4)) and a one-dimensional array B (shape is (4,)) that you can write directly:
C = AB
NumPy will automatically extend B into (3,4) shapes for calculation. This mechanism avoids a lot of unnecessary loops and makes the code look more intuitive.
But be aware of:
- Broadcasting is not omnipotent, the dimensions of the two arrays must be "compatible" (i.e. one of the dimensions is 1 or equal)
- If you accidentally use the broadcast, the results may be inconsistent with expectations.
Avoid using Python loops and try to vectorize operations
This is one of the core principles of NumPy performance optimization. Because the underlying layer of NumPy is implemented with C, its vectorization operations can almost reach a speed close to C. Python's native loops are much slower.
For example, calculate the sum of the squared differences of the corresponding elements of two arrays:
# Not recommended result = 0 for i in range(len(a)): result = (a[i] - b[i]) ** 2 # Recommended result = np.sum((a - b) ** 2)
The latter not only has short code, but also runs dozens or even hundreds of times faster.
If you find yourself writing a for loop to process arrays, then you have to think about whether there is a way to replace it with NumPy's built-in functions.
Save memory and speed up using the right data type
NumPy supports a variety of data types, such as int32
, float64
, complex128
, etc. Choosing the right data type not only saves memory, but also speeds up computing speed.
For example, if you don't need too high precision, you can replace the default float64
float32
:
arr = np.array([1.0, 2.0, 3.0], dtype=np.float32)
This way, the memory usage is halved, and some operations will be faster. Of course, you should also pay attention to the issue of accuracy loss, especially when doing a lot of accumulated calculations.
Basically that's it. NumPy's performance advantages mainly come from its vectorized design and efficient memory management. As long as you avoid Python native loops and use broadcast and data types reasonably, you can write fast and clear numerical calculation code.
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