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https://gitlab.com/scemama/QCaml.git
synced 2024-06-02 03:15:19 +02:00
355 lines
9.2 KiB
OCaml
355 lines
9.2 KiB
OCaml
open Lacaml.D
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type sparse_matrix =
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{
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m: int;
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n: int;
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v: Vector.t array;
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}
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type t =
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| Dense of Mat.t
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| Sparse of sparse_matrix
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let epsilon = Constants.epsilon
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let is_sparse = function
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| Sparse _ -> true
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| Dense _ -> false
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let is_dense = function
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| Sparse _ -> false
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| Dense _ -> true
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let dim1 = function
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| Dense m -> Mat.dim1 m
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| Sparse {m ; n ; v} -> m
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let dim2 = function
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| Dense m -> Mat.dim2 m
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| Sparse {m ; n ; v} -> n
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let get = function
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| Dense m -> (fun i j -> m.{i,j})
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| Sparse {m ; n ; v } -> (fun i j -> Vector.get v.(i-1) j)
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let sparse_of_dense ?(threshold=epsilon) = function
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| Sparse _ -> invalid_arg "Expected a dense matrix"
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| Dense m' ->
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let m = Mat.dim1 m'
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and n = Mat.dim2 m'
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and v =
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Mat.to_col_vecs m'
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|> Array.map (fun v -> Vector.sparse_of_vec ~threshold v)
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in Sparse {m ; n ; v}
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let dense_of_sparse = function
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| Dense _ -> invalid_arg "Expected a sparse matrix"
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| Sparse {m ; n ; v} ->
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let m' =
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Array.map (fun v -> Vector.to_vec v) v
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|> Mat.of_col_vecs
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in Dense m'
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let dense_of_mat m = Dense m
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let sparse_of_mat ?(threshold=epsilon) m =
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dense_of_mat m
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|> sparse_of_dense ~threshold
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let sparse_of_vector_array v =
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let m =
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Array.fold_left (fun accu v' ->
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if Vector.dim v' <> accu then
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invalid_arg "Inconsistent dimension"
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else accu) (Vector.dim v.(0)) v
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and n = Array.length v
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in
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Sparse {m ; n ; v}
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let rec to_mat = function
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| Dense m -> m
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| Sparse m ->
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dense_of_sparse (Sparse m)
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|> to_mat
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let transpose = function
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| Dense m -> Dense (Mat.transpose_copy m)
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| Sparse {m ; n ; v} ->
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begin
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let v' = Array.init m (fun i -> ref []) in
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Array.iteri (fun j v_j ->
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Vector.to_assoc_list v_j
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|> List.iter (fun (i, v_ij) ->
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v'.(i-1) := (j+1, v_ij) :: !(v'.(i-1))
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)
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) v;
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let v' =
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Array.map (fun x -> Vector.sparse_of_assoc_list n (List.rev !x) ) v'
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in
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Sparse {m=n ; n=m ; v=v'}
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end
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let outer_product ?(threshold=epsilon) v1 v2 =
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match Vector.(is_dense v1, is_dense v2) with
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| (true, true) ->
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let v1 = Vector.to_vec v1
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and v2 = Vector.to_vec v2
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in
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let a = Mat.create (Vec.dim v1) (Vec.dim v2) in
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ger v1 v2 a;
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Dense a
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| (true, false) ->
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let v = Vector.to_vec v1
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and v' = Vector.to_vec v2
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in
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let v =
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Array.init (Vector.dim v2) (fun j ->
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Vec.map (fun x -> x *. v'.{j+1}) v
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|> Vector.sparse_of_vec)
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in
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Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v}
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| (false, true)
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| (false, false) ->
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let v = Vector.to_assoc_list v1
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and v' = Vector.to_vec v2
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in
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let v =
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Array.init (Vector.dim v2) (fun j ->
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List.map (fun (i, x) ->
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let z = x *. v'.{j+1} in
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if abs_float z < threshold then
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None
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else
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Some (i, z)
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) v
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|> Util.list_some
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|> Vector.sparse_of_assoc_list (Vector.dim v1)
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)
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in
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Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v}
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let mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b =
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let f, f' =
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match transa, transb with
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| `N, `N -> dim2, dim1
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| `T, `N -> dim1, dim1
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| `T, `T -> dim1, dim2
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| `N, `T -> dim2, dim2
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in
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if f a <> f' b then
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invalid_arg "Inconsistent dimensions";
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let mmsp transa transb a b =
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let a =
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match transa with
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| `N -> Mat.transpose_copy a
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| `T -> a
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in
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let m' = Mat.dim2 a in
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let a =
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Mat.to_col_vecs a
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|> Array.map (fun v -> Vector.dense_of_vec v)
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in
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let {m ; n ; v} =
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if transb = `T then
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match transpose (Sparse b) with
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| Sparse x -> x
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| _ -> assert false
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else
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b
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in
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let v' =
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Array.map (fun b_j ->
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Array.map (fun a_i ->
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Vector.dot a_i b_j) a
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|> Vec.of_array
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|> Vector.sparse_of_vec
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) v
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in
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Sparse {m=m' ; n ; v=v'}
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in
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let spmm transa transb a b =
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let b =
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match transb with
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| `N -> b
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| `T -> Mat.transpose_copy b
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in
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let n' = Mat.dim2 b in
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let b =
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Mat.to_col_vecs b
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|> Array.map (fun v -> Vector.dense_of_vec v)
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in
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let m, n, v =
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if transa = `N then
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match transpose (Sparse a) with
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| Sparse {m ; n ; v} -> n, m, v
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| _ -> assert false
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else
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match Sparse a with
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| Sparse {m ; n ; v} -> n, m, v
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| _ -> assert false
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in
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let v' =
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Array.map (fun b_j ->
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Array.map (fun a_i ->
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Vector.dot a_i b_j) v
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|> Vec.of_array
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|> Vector.sparse_of_vec
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) b
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in
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Sparse {m ; n=n' ; v=v'}
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in
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let mmspmm transa transb a b =
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let {m ; n ; v} =
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if transb = `T then
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match transpose (Sparse b) with
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| Sparse x -> x
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| _ -> assert false
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else
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b
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in
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let m', n', v' =
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if transa = `N then
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match transpose (Sparse a) with
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| Sparse {m ; n ; v} -> n, m, v
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| _ -> assert false
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else
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match Sparse a with
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| Sparse {m ; n ; v} -> n, m, v
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| _ -> assert false
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in
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let v'' =
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Array.map (fun b_j ->
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Array.map (fun a_i ->
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Vector.dot a_i b_j) v'
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|> Vec.of_array
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|> Vector.sparse_of_vec
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) v
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in
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Sparse {m=m' ; n=n ; v=v''}
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in
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match a, b with
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| (Dense a), (Dense b) -> Dense (gemm ~transa ~transb a b)
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| (Sparse a), (Dense b) -> spmm transa transb a b
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| (Dense a), (Sparse b) -> mmsp transa transb a b
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| (Sparse a), (Sparse b) -> mmspmm transa transb a b
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let rec pp_matrix ppf = function
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| Dense m -> Util.pp_matrix ppf m
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| Sparse m -> pp_matrix ppf @@ dense_of_sparse (Sparse m)
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let test_case () =
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let d1 = 3
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and d2 = 4
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and d3 = 5
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in
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let x1 = Mat.map (fun x -> if abs_float x < 0.6 then 0. else x) (Mat.random d1 d2)
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and x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d2 d3)
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in
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let m1 = dense_of_mat x1
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and m2 = dense_of_mat x2
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in
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let m1_s = sparse_of_mat x1
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and m2_s = sparse_of_mat x2
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in
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let test_dimensions () =
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Alcotest.(check int) "dim1 1" d1 (dim1 m1 );
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Alcotest.(check int) "dim1 2" d1 (dim1 m1_s);
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Alcotest.(check int) "dim2 3" d2 (dim2 m1 );
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Alcotest.(check int) "dim2 4" d2 (dim2 m1_s);
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Alcotest.(check int) "dim1 5" d2 (dim1 m2 );
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Alcotest.(check int) "dim1 6" d2 (dim1 m2_s);
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Alcotest.(check int) "dim2 7" d3 (dim2 m2 );
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Alcotest.(check int) "dim2 8" d3 (dim2 m2_s);
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in
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let test_conversion () =
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Alcotest.(check bool) "sparse -> dense 1" true (dense_of_sparse m1_s = m1 );
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Alcotest.(check bool) "sparse -> dense 2" true (dense_of_sparse m2_s = m2 );
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Alcotest.(check bool) "dense -> sparse 1" true (sparse_of_dense m1 = m1_s);
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Alcotest.(check bool) "dense -> sparse 3" true (sparse_of_dense m2 = m2_s);
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in
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let test_transpose () =
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let m1t = Mat.transpose_copy x1 |> dense_of_mat
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and m2t = Mat.transpose_copy x2 |> dense_of_mat
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in
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Alcotest.(check bool) "dense 1" true (transpose m1 = m1t);
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Alcotest.(check bool) "dense 2" true (transpose m2 = m2t);
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Alcotest.(check bool) "sparse 1" true (transpose m1_s = sparse_of_dense m1t);
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Alcotest.(check bool) "sparse 2" true (transpose m2_s = sparse_of_dense m2t);
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in
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let test_outer () =
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let x1 = Vec.init 3 (fun i -> float_of_int i)
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and x2 = Vec.init 4 (fun i -> float_of_int i -. 3.)
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in
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let v1 = Vector.dense_of_vec x1
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and v2 = Vector.dense_of_vec x2
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in
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let v1_s = Vector.sparse_of_vec x1
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and v2_s = Vector.sparse_of_vec x2
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in
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let m1 =
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Dense (Mat.init_cols 3 4 (fun i j -> (float_of_int i) *. (float_of_int j -. 3.)))
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in
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let m1_s =
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sparse_of_dense m1
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in
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Alcotest.(check bool) "dense dense " true (m1 = outer_product v1 v2);
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Alcotest.(check bool) "sparse dense " true (m1_s = outer_product v1_s v2);
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Alcotest.(check bool) "dense sparse" true (m1_s = outer_product v1 v2_s);
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Alcotest.(check bool) "sparse sparse" true (m1_s = outer_product v1_s v2_s);
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in
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let test_mm () =
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let x3 = gemm x1 x2 in
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let m3 = dense_of_mat x3
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and m3_s = sparse_of_mat x3
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in
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let norm_diff m1 m2 =
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(Mat.sub (to_mat m1) (to_mat m2)
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|> Mat.syrk_trace)
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in
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Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mm m1 m2) m3);
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Alcotest.(check (float 1.e-10)) "dense sparse 2" 0. (norm_diff (mm m1 m2_s) m3_s);
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Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (transpose (mm m2 m1_s ~transa:`T ~transb:`T)) m3_s);
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Alcotest.(check (float 1.e-10)) "sparse dense 4" 0. (norm_diff (mm m1_s m2) m3_s);
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Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (transpose (mm m2_s m1 ~transa:`T ~transb:`T)) m3_s);
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Alcotest.(check (float 1.e-10)) "sparse sparse 6" 0. (norm_diff (mm m1_s m2_s) m3_s);
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Alcotest.(check (float 1.e-10)) "sparse sparse 7" 0. (norm_diff (transpose (mm m2_s m1_s ~transa:`T ~transb:`T)) m3_s);
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in
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[
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"Conversion", `Quick, test_conversion;
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"Dimensions", `Quick, test_dimensions;
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"Transposition", `Quick, test_transpose;
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"Oueter product", `Quick, test_outer;
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"Matrix Matrix", `Quick, test_mm;
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]
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