mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-06-01 19:05:18 +02:00
605 lines
18 KiB
OCaml
605 lines
18 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 rec to_vector_array ?(threshold=epsilon) = function
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| Sparse {m ; n ; v} -> v
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| Dense m -> to_vector_array (sparse_of_dense ~threshold (Dense m))
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let identity n =
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Sparse { n ; m=n ;
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v = Array.init n (fun i -> Vector.sparse_of_assoc_list n [(i+1,1.0)])
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}
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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.make0 (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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(* Dense x sparse *)
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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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(* Sparse x dense *)
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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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(* Sparse x Sparse *)
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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 mv ?(sparse=false) ?(trans=`N) ?(threshold=epsilon) a b =
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let f =
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match trans with
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| `N -> dim2
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| `T -> dim1
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in
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if f a <> Vector.dim b then
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invalid_arg "Inconsistent dimensions";
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let spmv a b =
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let {m ; n ; v} =
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if trans = `N then
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match transpose (Sparse a) with
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| Sparse x -> x
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| _ -> assert false
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else
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a
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in
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Array.map (fun row_a -> Vector.dot row_a b) v
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|> Vec.of_array
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in
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let mv a b =
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let f_a =
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match trans with
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| `N -> (fun i -> Mat.copy_row a i)
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| `T -> (fun i -> Mat.col a i)
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in
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Vec.init (Mat.dim1 a) (fun i ->
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Vector.dense_of_vec (f_a i)
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|> Vector.dot b )
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in
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let dense_result =
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match a, Vector.is_dense b with
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| Dense a, true -> gemv ~trans a (Vector.to_vec b)
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| Dense a, false -> mv a b
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| Sparse a, true -> spmv a b
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| Sparse a, false -> spmv a b
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in
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if sparse then
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Vector.sparse_of_vec dense_result
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else
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Vector.dense_of_vec dense_result
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let rec op2 dense_op sparse_op a b =
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if dim1 a <> dim1 b || dim2 a <> dim2 b then
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failwith "Inconsistent dimensions";
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match a, b with
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| (Dense a), (Dense b) -> Dense (dense_op a b)
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| (Dense _), (Sparse _) -> op2 dense_op sparse_op (sparse_of_dense a) b
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| (Sparse _), (Dense _) -> op2 dense_op sparse_op a (sparse_of_dense b)
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| (Sparse a), (Sparse b) -> Sparse
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{ m=a.m ; n=a.n ;
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v = Array.map2 sparse_op a.v b.v
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}
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let add = op2 (fun a b -> Mat.add a b) (fun a b -> Vector.add a b)
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let sub = op2 (fun a b -> Mat.sub a b) (fun a b -> Vector.sub a b)
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let scale f = function
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| Dense a -> let b = lacpy a in (Mat.scal f b ; Dense b)
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| Sparse a -> Sparse
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{ a with
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v = if f = 1.0 then a.v
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else Array.map (fun v -> Vector.scale f v) a.v }
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let frobenius_norm = function
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| Dense a -> lange ~norm:`F a
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| Sparse a ->
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Array.fold_left (fun accu v -> accu +. Vector.dot v v) 0. a.v
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|> sqrt
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let ax_eq_b_conj_grad ?x a b =
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(* /!\ : A needs to be positive definite and symmetric *)
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let x =
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match x with
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| Some x0 -> x0
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| None -> b
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in
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let r = Vector.sub b (mv a x) in
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let p = r in
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let rsold = Vector.dot r r in
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let rec aux rsold r p x = function
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| 0 -> x
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| i ->
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let ap = mv a p in
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let alpha = rsold /. (Vector.dot p ap) in
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let x = Vector.add x (Vector.scale alpha p) in
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let r = Vector.sub r (Vector.scale alpha ap) in
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let rsnew = Vector.dot r r in
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if rsnew < Constants.epsilon then
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x
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else
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let p =
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Vector.add r (Vector.scale (rsnew /. (rsold +. 1.e-12) ) p)
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in
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aux rsnew r p x (i-1)
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in
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aux rsold r p x (Vector.dim b *2)
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let rec ax_eq_b ?(trans=`N) a b =
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match a, b with
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| (Dense a), (Dense b) ->
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let a = lacpy a in
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let x = lacpy b in
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(getrs ~trans a x; Dense x)
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| (Dense _), (Sparse _) ->
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let b = dense_of_sparse b in
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ax_eq_b ~trans a b
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| _ ->
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let ata, atb =
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if trans = `N then
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mm ~transa:`T a a, mm ~transa:`T a b
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else
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mm ~transa:`N a a, mm ~transa:`N a b
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in
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Sparse { m=dim1 b ; n=dim2 b ;
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v=Array.map (fun v -> ax_eq_b_conj_grad ata v) (to_vector_array atb)
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}
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(* ------------ Printers ------------ *)
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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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(* ---------- Unit tests ------------ *)
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let test_case () =
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let d1 = 30
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and d2 = 40
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and d3 = 50
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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 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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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 d1 (fun i -> float_of_int i)
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and x2 = Vec.init d2 (fun i -> float_of_int i -. 0.3)
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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 d1 d2 (fun i j -> (float_of_int i) *. (float_of_int j -. 0.3)))
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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 (float 1.e-10)) "dense dense " 0. (norm_diff m1 (outer_product v1 v2));
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Alcotest.(check (float 1.e-10)) "sparse dense " 0. (norm_diff m1_s (outer_product v1_s v2));
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Alcotest.(check (float 1.e-10)) "dense sparse" 0. (norm_diff m1_s (outer_product v1 v2_s));
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Alcotest.(check (float 1.e-10)) "sparse sparse" 0. (norm_diff m1_s (outer_product v1_s v2_s));
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in
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let test_add_sub () =
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let x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d1 d2) in
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let m2 = dense_of_mat x2 in
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let m3 = Mat.add x1 x2 |> dense_of_mat in
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let m4 = Mat.sub x1 x2 |> dense_of_mat in
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let m2_s = sparse_of_mat x2 in
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let m3_s = Mat.add x1 x2 |> sparse_of_mat in
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let m4_s = Mat.sub x1 x2 |> sparse_of_mat in
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Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (add m1 m2) m3);
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Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (sub m1 m2) m4);
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Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (add m1 m2_s) m3_s);
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Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (sub m1 m2_s) m4_s);
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Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (add m1_s m2) m3);
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Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (sub m1_s m2) m4);
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Alcotest.(check (float 1.e-10)) "dense sparse 7" 0. (norm_diff (add m1_s m2_s) m3_s);
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Alcotest.(check (float 1.e-10)) "dense sparse 8" 0. (norm_diff (sub m1_s m2_s) m4_s);
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Alcotest.(check (float 1.e-10)) "dense sparse 9" (frobenius_norm m1_s) (frobenius_norm m1);
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in
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let test_mv () =
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let y = Vec.random d2 in
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let z = Vec.random d1 in
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let x3 = gemv x1 y in
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let x4 = gemv ~trans:`T x1 z in
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let v = Vector.dense_of_vec y in
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let v2 = Vector.dense_of_vec z in
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let v3 = Vector.dense_of_vec x3 in
|
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let v4 = Vector.dense_of_vec x4 in
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let v_s = Vector.sparse_of_vec y in
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let v2_s = Vector.sparse_of_vec z in
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let norm_diff v1 v2 =
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Vec.sub (Vector.to_vec v1) (Vector.to_vec v2)
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|> nrm2
|
|
in
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|
Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mv m1 v) v3);
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|
Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (mv ~trans:`T m1 v2) v4);
|
|
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (mv m1 v_s) v3);
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (mv ~trans:`T m1 v2_s) v4);
|
|
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (mv m1_s v) v3);
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (mv ~trans:`T m1_s v2) v4);
|
|
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 7" 0. (norm_diff (mv m1_s v_s) v3);
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 8" 0. (norm_diff (mv ~trans:`T m1_s v2_s) v4);
|
|
in
|
|
|
|
let test_mm () =
|
|
let x3 = gemm x1 x2 in
|
|
let m3 = dense_of_mat x3
|
|
and m3_s = sparse_of_mat x3
|
|
and m4 = dense_of_mat x1 |> transpose
|
|
and m4_s = sparse_of_mat x1 |> transpose
|
|
and m5 = dense_of_mat x2 |> transpose
|
|
and m5_s = sparse_of_mat x2 |> transpose
|
|
in
|
|
Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mm m1 m2) m3);
|
|
Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (mm ~transa:`T m4 m2) m3);
|
|
Alcotest.(check (float 1.e-10)) "dense dense 3" 0. (norm_diff (mm ~transb:`T m1 m5) m3);
|
|
Alcotest.(check (float 1.e-10)) "dense dense 4" 0. (norm_diff (mm ~transa:`T ~transb:`T m2 m1) (transpose m3));
|
|
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 5" 0. (norm_diff (mm m1 m2_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 6" 0. (norm_diff (mm ~transa:`T m4 m2_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 7" 0. (norm_diff (mm ~transb:`T m1 m5_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 8" 0. (norm_diff (transpose (mm m2 m1_s ~transa:`T ~transb:`T)) m3_s);
|
|
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 9" 0. (norm_diff (mm m1_s m2) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 10" 0. (norm_diff (mm ~transa:`T m4_s m2) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 11" 0. (norm_diff (mm ~transb:`T m1_s m5) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 12" 0. (norm_diff (transpose (mm m2_s m1 ~transa:`T ~transb:`T)) m3_s);
|
|
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 13" 0. (norm_diff (mm m1_s m2_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 14" 0. (norm_diff (mm ~transa:`T m4_s m2_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 15" 0. (norm_diff (mm ~transb:`T m1_s m5_s) m3_s);
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 16" 0. (norm_diff (transpose (mm m2_s m1_s ~transa:`T ~transb:`T)) m3_s);
|
|
in
|
|
|
|
let test_solve () =
|
|
let x1 = Mat.map (fun x -> if abs_float x < 0.6 then 0. else x) (Mat.random 30 30)
|
|
and x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random 30 5)
|
|
in
|
|
|
|
let m1 = dense_of_mat x1
|
|
and m2 = dense_of_mat x2
|
|
in
|
|
|
|
let m1_s = sparse_of_mat x1
|
|
and m2_s = sparse_of_mat x2
|
|
in
|
|
|
|
let a = m1 and b = m2 in
|
|
let x = ax_eq_b a b in
|
|
Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mm a x) b);
|
|
|
|
let a = m1 and b = m2_s in
|
|
let x = ax_eq_b a b in
|
|
Alcotest.(check (float 1.e-10)) "dense sparse 2" 0. (norm_diff (mm a x) b);
|
|
|
|
let a = m1_s and b = m2 in
|
|
let x = ax_eq_b a b in
|
|
Alcotest.(check (float 1.e-10)) "sparse dense 3" 0. (norm_diff (mm a x) b);
|
|
|
|
let a = m1_s and b = m2_s in
|
|
let x = ax_eq_b a b in
|
|
Alcotest.(check (float 1.e-10)) "sparse sparse 4" 0. (norm_diff (mm a x) b);
|
|
in
|
|
|
|
[
|
|
"Conversion", `Quick, test_conversion;
|
|
"Dimensions", `Quick, test_dimensions;
|
|
"Transposition", `Quick, test_transpose;
|
|
"Outer product", `Quick, test_outer;
|
|
"Add sub", `Quick, test_add_sub;
|
|
"Matrix Vector", `Quick, test_mv;
|
|
"Matrix Matrix", `Quick, test_mm;
|
|
"Linear solve", `Quick, test_solve;
|
|
]
|
|
|