April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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2.6 對移動子串列進行函數映射
|
45
討論說明
前文闡述的是基本概念，但不易推廣，因為窗口大小與目標函數都固定在程式碼內。以
下提供可使用任意窗口大小與目標函數的指令。
事實上 Mathematica 內建有
MovingAverage
與
MovingMedian
指令可計算移動平均數與移
動中位數，其中
MovingAverage
也可指定權重。當你需要運算移動平均數與移動中位數
時，建議使用內建函數，它們能提供較佳的執行效率。
Mathematica 提供兩個特別指令：
ListConvolve
與
ListCorrelate
，用來進行更廣義的子
串列運算，它們的功能很多，花些時間深入了解是很值得的。以下只針對
ListConvolve
指令做介紹，因為這兩個指令在使用上相似，只是針對不同問題處理的方式不同。我們
就從移動平均數的計算介紹起。
ListConvolve
指令的第一個引數稱為
核心
（
kernel
），它是一個數字串列，用來定義子
串列的長度及權重，子串列將與核心相乘後再加總起來。以下使用符號使你更容易了解
運作。
此處使用簡單的核心
{1,1}
，其代表子串列的長度為 2，且每個元素會直接相加（因為
乘以 1 的結果仍不變），因此運算結果為連續子串列的和。只要將核心除以
n
便可得到
移動平均數。[Page-045]
這可輕易推廣至加權移動平均數，在此就不多做介紹了，畢竟 Mathematica 已提供了內
建指令。以下繼續討論
ListConvolve
指令。
ch02.indd 45 2014/4/2 上午 03:32:12 ...
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