August 2015
Intermediate to advanced
384 pages
7h 42m
Chinese
Content preview from 高效能PYTHON程式設計
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第六章
問題介紹
這一節主要是為了讓我們更深入理解本章即將解決的方程式，然而，就探索本
章其餘部分而言，瞭解這一節嚴格來說並非必要。如果你希望略過這一節，請
務必檢視過範例 6-1 和 6-2 的演算法，確實瞭解我們即將最佳化的程式碼。
另一方面，如果你讀過這一節，並且想要瞭解更多資訊，請參閱《
Numerical
Recipes
》（ 第 3 版，William Press 等著，劍橋大學出版社）的第 17 章。
為了探索本章的矩陣與向量計算，我們將反覆地使用流體擴散的範例。擴散
（diffusion）是移動流體，並試圖讓它們均勻混合的機制之一。
在這一節裡，我們將探索擴散方程式（diffusion equation）背後的數學問題，看起來可
能有些複雜，但是別擔心！我們會迅速簡化這個問題，讓它更容易被理解。此外，務必
注意，雖然對我們正在解決的方程式具有基本的認識有助於本章的閱讀，但並非必要；
後續章節主要聚焦於程式碼的各種規劃，而不是方程式本身。不過，理解方程式將有助
於你洞悉如何最佳化你的程式碼。這基本上是真實的—瞭解程式碼背後的動機以及演算
法的錯綜複雜，將讓你深入洞察可能的最佳化方法。
一個簡單的擴散範例就是水裡頭的染料︰如果你在室溫下把幾滴染料放進水中，它將慢
慢擴散，直到完全與水融合。因為我們沒有攪動，水的溫度不會提高到足以產生對流，
擴散將是混合二種液體的主要過程。在以數值方法解決這些方程式時，我們挑選想要
的初始條件，並且能夠隨著時間持續演進，看看一段時間過後會是什麼模樣（參閱圖
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.