F# - Sort a matrix containing tuples - sorting

Question

I do not find a way to sort the values included in the columns of the following matrix of tuples :
Matrix<float * float> =
matrix [[(1.0, 145.0); (1.0, 45.0); (1.0, 130.0); (1.0, 30.0); (1.0, 130.0)]
[(2.0, 45.0); (2.0, 45.0); (2.0, 30.0); (2.0, 30.0); (2.0, 30.0)]
[(3.0, 130.0); (3.0, 30.0); (3.0, 145.0); (3.0, 45.0); (3.0, 130.0)]
[(4.0, 30.0); (4.0, 30.0); (4.0, 45.0); (4.0, 45.0); (4.0, 30.0)]
[(5.0, 130.0); (5.0, 30.0); (5.0, 130.0); (5.0, 30.0); (5.0, 145.0)]]
I would like to sort each column depending on the second element of the tuple. For example here the answer would be :
matrix [[(1.0, 145.0); (1.0, 45.0); (3.0, 145.0); (3.0, 45.0); (5.0, 145.0)]
[(3.0, 130.0); (2.0, 45.0); (1.0, 130.0); (4.0, 45.0); (1.0, 130.0)]
[(5.0, 130.0); (3.0, 30.0); (5.0, 130.0); (1.0, 30.0); (3.0, 130.0)]
[(2.0, 45.0); (4.0, 30.0); (4.0, 45.0); (2.0, 30.0); (2.0, 30.0)]
[(4.0, 30.0); (5.0, 30.0); (2.0, 30.0); (5.0, 30.0); (4.0, 30.0)]]
Thank you in advance !

Answer 1

In my experience, when working with arrays (2D and/or matrix) I found that working with arrays internally is often the fastest way to go.
For example, combining Daniel's and Ankur's approaches in a mutable way:
let mutableSortByCol f (m:Matrix<'T>) =
let columns = [| for c in 0 .. m.NumCols - 1 ->
m.Column c |> Vector.Generic.toArray |]
for c in 0 .. m.NumCols - 1 do
columns.[c] |> Array.sortInPlaceBy f
Matrix.Generic.init (m.NumRows) (m.NumCols) (fun r c -> columns.[c].[r])
I converted the matrix to an array of columns ('a[][], not 'a[,]), and performed an in-place sort on each column. After that, I filled a new matrix with the sorted result. Note that the original matrix remains unmodified: the columns array is populated with copies of the column vectors (Vector.toArray creates a new array).
This approach is faster because it needs no transposes, sorts columns in place, and needs no conversion to and from intermediate list structures by keeping everything array-oriented. I suspect it could be made even faster if the Matrix module supported conversion to/from 'a[][] as well, although it's perhaps not really suited for matrices.
Also, in case you didn't know: you can make use of F#'s structural comparison of tuples to sort by second element descending, first element ascending:
Example:
> mutableSortByCol (fun (a,b) -> (-b,a)) M;;
val it : Matrix<float * float> =
matrix [[(1.0, 145.0); (1.0, 45.0); (3.0, 145.0); (3.0, 45.0); (5.0, 145.0)]
[(3.0, 130.0); (2.0, 45.0); (1.0, 130.0); (4.0, 45.0); (1.0, 130.0)]
[(5.0, 130.0); (3.0, 30.0); (5.0, 130.0); (1.0, 30.0); (3.0, 130.0)]
[(2.0, 45.0); (4.0, 30.0); (4.0, 45.0); (2.0, 30.0); (2.0, 30.0)]
[(4.0, 30.0); (5.0, 30.0); (2.0, 30.0); (5.0, 30.0); (4.0, 30.0)]]

Answer 2

Below is such a function:
let sortByCol f (m:Matrix<'T>) =
let n = m.Transpose
[for i = 0 to n.NumRows-1 do
yield [for j in n.Row(i) -> j]
|> List.sortBy f ]
|> Matrix.Generic.ofList
|> Matrix.Generic.transpose
Usage as particular to this question:
matrix |> sortByCol (fun (_,b) -> -b)
UPDATED: To make the sort by col function generic.

Answer 3

I've never used Matrix before so there might be a better way, but this seems to work:
let sortMatrix (m:Matrix<_>) =
seq {
for c in 0 .. (m.NumCols - 1) do
let arr = [| for r in 0 .. (m.NumRows - 1) -> m.[r, c] |]
arr |> Array.sortInPlaceBy (fun (_, b) -> -b : float) //(snd >> (~-))
yield arr
}
|> Matrix.Generic.ofSeq
|> Matrix.Generic.transpose