如何将函数应用于浮点数组? [英] How To Apply a Function to an Array of float Arrays?

问题描述

假设我有n个数组，其中n是一个变量(一些数字大于2，通常小于10).

Let's suppose I have n arrays, where n is a variable (some number greater than 2, usually less than 10).

每个数组都有k个元素.

Each array has k elements.

我还有一个长度为n的数组，其中包含一组权重，这些权重决定了我希望如何线性组合所有数组.

I also have an array of length n that contains a set of weights that dictate how I would like to linearly combine all the arrays.

我正在尝试创建一个高性能的高阶函数，以在F#中组合这些数组.

I am trying to create a high performance higher order function to combine these arrays in F#.

如何执行此操作，以便获得一个函数，该函数需要一个数组数组(arrs是一个样本)，一个weights数组(weights)，然后根据这些权重计算加权总和?

How can I do this, so that I get a function that takes an array of arrays (arrs is a sample), a weights array (weights), and then computed a weighted sum based on the weights?

let weights = [|.6;;.3;.1|]

let arrs = [| [|.0453;.065345;.07566;1.562;356.6|] ; 
              [|.0873;.075565;.07666;1.562222;3.66|] ; 
              [|.06753;.075675;.04566;1.452;3.4556|] |]

感谢任何想法.

推荐答案

这里是一种解决方案:

let combine weights arrs =
  Array.map2 (fun w -> Array.map ((*) w)) weights arrs 
  |> Array.reduce (Array.map2 (+))

编辑

这里有一些(非常需要的)解释它是如何工作的.从逻辑上讲，我们要执行以下操作:

Here's some (much needed) explanation of how this works. Logically, we want to do the following:

1. 将每个权重应用于其对应的行.
2. 将权重调整后的行加在一起.

上面的两行就是这样做的.

The two lines above do just that.

1. 我们使用Array.map2函数组合相应的权重和行；我们将它们组合的方式是将行中的每个元素乘以权重，这是通过内部的Array.map来实现的.
2. 现在我们有一个加权行数组，需要将它们加在一起.我们可以通过保持一个连续的总和，依次添加每个数组，一次完成一个步骤.我们逐点求和两个数组的方法是再次使用Array.map2，并使用(+)作为合并每个数组中元素的函数.我们将其包装在Array.reduce中，以便从第一行开始依次将此附加功能应用于每行.

1. We use the Array.map2 function to combine corresponding weights and rows; the way that we combine them is to multiply each element in the row by the weight, which is accomplished via the inner Array.map.
2. Now we have an array of weighted rows and need to add them together. We can do this one step at a time by keeping a running sum, adding each array in turn. The way we sum two arrays pointwise is to use Array.map2 again, using (+) as the function for combining the elements from each. We wrap this in an Array.reduce to apply this addition function to each row in turn, starting with the first row.

希望这是解决问题的一种相当优雅的方法，尽管公认的无点风格使其遵循起来有些棘手.但是，请注意，它并不是特别出色；进行就地更新，而不是使用map，map2和reduce的每个应用程序创建新的数组会更有效.不幸的是，标准库没有包含这些可以就地工作的操作的相似物.但是，创建这样的类似物相对容易，并且它们的使用方式几乎与我在此处使用的方式完全相同.

Hopefully this is a reasonably elegant approach to the problem, though the point-free style admittedly makes it a bit tricky to follow. However, note that it's not especially performant; doing in-place updates rather than creating new arrays with each application of map, map2, and reduce would be more efficient. Unfortunately, the standard library doesn't contain nice analogues of these operations which work in-place. It would be relatively easy to create such analogues, though, and they could be used in almost exactly the same way as I've done here.

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