在 F# 中并行化两个矩阵的元素乘法

Question

我正在尝试并行化 F# 中两个矩阵的逐元素乘法。我实在想不通。我一直尝试创建任务，但它永远不想编译。我的非工作混乱代码如下：

let myBigElemMultiply (m:matrix) (n:matrix) = 
  let AddTwoRows (row:int) (destination:matrix) (source1:matrix) (source2:matrix) =
      for i in 0 .. destination.NumCols
          destination.[row, i] <- source1.[row,i] + source2.[row,i]
      destination
  let result = Matrix.zero(m.NumRows)
  let operations = [ for i in 0 .. m.NumRows -> AddTwoRows i result m n ]
  let parallelTasks = Async.Parallel operations
  Async.RunSynchronously parallelTasks
  result

Answer 1

你犯了几个小错误，例如，你没有弄清楚如何进行矩阵乘法。

let myBigElemMultiply (m:matrix) (n:matrix) = 
  let AddTwoRows (row:int) (destination:matrix) (source1:matrix) (source2:matrix) =
      for col=0 to destination.NumCols-1 do
        let mutable sum = 0.0
        for k=0 to m.NumCols-1 do
          sum <- sum + source1.[row,k] * source2.[k,col]
        destination.[row,col] <- sum

  let result = Matrix.zero m.NumRows n.NumCols
  let operations = [ for i=0 to m.NumRows-1 do yield async { AddTwoRows i result m n} ]
  let parallelTasks = Async.Parallel operations
  Async.RunSynchronously parallelTasks |> ignore
  result

需要注意的一件事是，此代码的性能会非常糟糕，因为 m.[i,j] 是访问矩阵中元素的低效方法。你最好使用二维数组：

let myBigElemMultiply2 (m:matrix) (n:matrix) = 
  let AddTwoRows (row:int) (destination:matrix) (source1:matrix) (source2:matrix) =
      let destination = destination.InternalDenseValues
      let source1 = source1.InternalDenseValues
      let source2 = source2.InternalDenseValues
      for col=0 to Array2D.length2 destination - 1 do
        let mutable sum = 0.0
        for k=0 to Array2D.length1 source2 - 1 do
          sum <- sum + source1.[row,k] * source2.[k,col]
        destination.[row,col] <- sum

  let result = Matrix.zero m.NumRows n.NumCols
  let operations = [ for i=0 to m.NumRows-1 do yield async { AddTwoRows i result m n} ]
  let parallelTasks = Async.Parallel operations
  Async.RunSynchronously parallelTasks |> ignore
  result

测试：

let r = new Random()
let A = Matrix.init 280 10340 (fun i j -> r.NextDouble() )
let B = A.Transpose

一些计时：

> myBigElemMultiply A B;;
Real: 00:00:22.111, CPU: 00:00:41.777, GC gen0: 0, gen1: 0, gen2: 0
val it : unit = ()
> myBigElemMultiply2 A B;;
Real: 00:00:08.736, CPU: 00:00:15.303, GC gen0: 0, gen1: 0, gen2: 0
val it : unit = ()
> A*B;;
Real: 00:00:13.635, CPU: 00:00:13.166, GC gen0: 0, gen1: 0, gen2: 0
val it : unit = ()
> 

检查 这里使用ParallelFor，它应该比异步有更好的性能。

Answer 2

这里至少有一些可以编译的代码，也许这会让您朝着正确的方向前进？

let myBigElemMultiply (m:matrix) (n:matrix) =  
    let AddTwoRows (row:int) (destination:matrix) (source1:matrix) (source2:matrix) = 
        async {    
            for i in 0 .. destination.NumCols do
                destination.[row, i] <- source1.[row,i] + source2.[row,i] 
        }
    let result = Matrix.zero m.NumRows m.NumCols 
    let operations = [ for i in 0 .. m.NumRows -> AddTwoRows i result m n ] 
    let parallelTasks = Async.Parallel operations 
    Async.RunSynchronously parallelTasks |> ignore
    result 

Answer 3

没有意义。一对矩阵的异地逐元素乘法与复制没什么区别，此时单个核心将愉快地最大化机器的整个内存带宽，并且添加更多核心不会提高性能。所以这几乎肯定是浪费时间。