Parallelizing the element wise multiplication of two matrices in F# - f#

Question

I'm trying to parallelize the element by element multiplication of two matrices in F#. I can't quite figure it out thought. I keep trying to create tasks but it never wants to compile. My non-working messy code is the following:
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

You have made several small mistakes, e.g., you haven't figured how to do matrix multiplication.
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
One thing to notice is that this code would perform very badly because m.[i,j] is an inefficient way to access elements in a matrix. You'd better use a 2D array:
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
testing:
let r = new Random()
let A = Matrix.init 280 10340 (fun i j -> r.NextDouble() )
let B = A.Transpose
some timing:
> 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 = ()
>
Check here by using ParallelFor, which should have a better performance than async.

Answer 2

Here's at least some code that compiles, perhaps this will get you headed in the right direction?
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

There's no point. Out-of-place element-wise multiplication of a pair of matrices is little more that copying at which point a single core will happily max out the entire memory bandwidth of your machine and adding more cores will not improve performance. So it is almost certainly a waste of time.