如何在MATLAB中向量化分段周期函数?

问题描述

我注意到，matlab内置函数可以处理标量或矢量参数.示例:

I've noticed that matlab builtin functions can handle either scalar or vector parameters. Example:

sin(pi/2)
ans =
     1

sin([0:pi/5:pi])
ans =
         0    0.5878    0.9511    0.9511    0.5878    0.0000

例如，如果我编写自己的函数，则为分段周期性函数:

If I write my own function, for example, a piecewise periodic function:

function v = foo(t)
t = mod( t, 2 ) ;

if ( t < 0.1 )
   v = 0 ;
elseif ( t < 0.2 )
   v = 10 * t - 1 ;
else
   v = 1 ;
end

我可以用单个值来调用它:

I can call this on individual values:

[foo(0.1) foo(0.15) foo(0.2)]
ans =
         0    0.5000    1.0000

但是，如果函数的输入是向量，则不会像内置函数那样自动向量化:

however, if the input for the function is a vector, it is not auto-vectorized like the builtin function:

foo([0.1:0.05:0.2])
ans =
     1

在函数的定义中是否存在可用于指示向量的语法，如果提供了向量，则应产生向量?还是像sin，cos这样的内建函数会检查其输入的类型，以及输入是否为向量会产生相同的结果?

Is there a syntax that can be used in the definition of the function that indicates that if a vector is provided, a vector should be produced? Or do builtin functions like sin, cos, ... check for the types of their input, and if the input is a vector produce the same result?

推荐答案

您需要稍微更改语法，以便能够处理任何大小的数据.我通常会使用逻辑过滤器对if语句进行矢量化处理，

You need to change your syntax slightly to be able to handle data of any size. I typically use logical filters to vectorise if-statements, as you're trying to do:

function v = foo(t)

v = zeros(size(t));
t = mod( t, 2 ) ;

filt1 = t<0.1;
filt2 = ~filt1 & t<0.2;
filt3 = ~filt1 & ~filt2;

v(filt1) = 0;
v(filt2) = 10*t(filt2)-1;
v(filt3) = 1;

在此代码中，我们有三个逻辑过滤器.第一个选择所有元素，例如t<0.1.第二个选择所有元素，例如第一个过滤器中没有的t<0.2.最终的过滤器可以获取其他所有内容.

In this code, we've got three logical filters. The first picks out all elements such that t<0.1. The second picks out all of the elements such that t<0.2 that weren't in the first filter. The final filter gets everything else.

然后我们使用它来设置向量v.我们将与第一个过滤器匹配的v的每个元素都设置为0.我们在v中设置所有与第二个过滤器匹配的10*t-1.我们将与第三个过滤器匹配的v的每个元素都设置为1.

We then use this to set the vector v. We set every element of v that matches the first filter to 0. We set everything in v which matches the second filter to 10*t-1. We set every element of v which matches the third filter to 1.

要更全面地了解矢量化，请查看 MATLAB帮助页面.

For a more comprehensive coverage of vectorisation, check the MATLAB help page on it.

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