如何产生x的前20个幂? [英] How to generate the first twenty powers of x?

问题描述

所以，我有X，一个300×1的向量，我想要[1，X，X * X，X * X * X，...，X * X * ... * X]，一个300 x 20的矩阵.

So, I've got X, a 300-by-1 vector and I'd like [1, X, X*X, X*X*X, ... , X*X*...*X], a 300-by-twenty matrix.

我应该怎么做?

X=[2;1]
[X,X.*X,X.*X.*X]

ans =

   2   4   8
   1   1   1

那行得通，但是我不能面对整个事情.当然我不必编写for循环了吗?

That works, but I can't face typing out the whole thing. Surely I don't have to write a for loop?

推荐答案

如果您要最小化操作次数:

cumprod(repmat(X(:),1,20),2) %// replace "20" by the maximum exponent you want

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基准化:对于大小为300x1的X，最大指数为20.我用tic，toc来测量时间，平均为1000次.结果(平均值):

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Benchmarking: for X of size 300x1, maximum exponent 20. I measure time with tic, toc, averaging 1000 times. Results (averages):

• 使用cumprod(此答案):8.0762e-005秒
• 使用bsxfun(@ thewaywewalk的回答):8.6170e-004秒

• Using cumprod (this answer): 8.0762e-005 seconds
• Using bsxfun (answer by @thewaywewalk): 8.6170e-004 seconds

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