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mirror of https://gitlab.com/scemama/QCaml.git synced 2024-10-31 19:23:40 +01:00
QCaml/Utils/Matrix.ml

857 lines
26 KiB
OCaml

open Lacaml.D
type sparse_matrix =
{
m: int;
n: int;
v: Vector.t array;
}
type computed =
{
m: int;
n: int;
f: int -> int -> float;
}
type t =
| Dense of Mat.t
| Sparse of sparse_matrix
| Computed of computed
let epsilon = Constants.epsilon
let is_computed = function
| Computed _ -> true
| _ -> false
let is_sparse = function
| Sparse _ -> true
| _ -> false
let is_dense = function
| Dense _ -> true
| _ -> false
let dim1 = function
| Dense m -> Mat.dim1 m
| Sparse {m ; _} -> m
| Computed {m ; _} -> m
let dim2 = function
| Dense m -> Mat.dim2 m
| Sparse {n ; _} -> n
| Computed {n ; _} -> n
let check_bounds m n i j =
if (i <= 0 || i > m || j <= 0 || j > n) then
raise (Invalid_argument "Index out of bounds")
let get = function
| Dense m -> (fun i j -> m.{i,j})
| Sparse { m ; n ; v } -> (fun i j -> Vector.get v.(j-1) i)
| Computed { m ; n ; f } -> (fun i j -> check_bounds m n i j ; f i j)
let sparse_of_dense ?(threshold=epsilon) = function
| Dense m' ->
let m = Mat.dim1 m'
and n = Mat.dim2 m'
and v =
Mat.to_col_vecs m'
|> Array.map (fun v -> Vector.sparse_of_vec ~threshold v)
in Sparse {m ; n ; v}
| _ -> invalid_arg "Expected a dense matrix"
let dense_of_sparse = function
| Sparse {m ; n ; v} ->
let m' =
Array.map (fun v -> Vector.to_vec v) v
|> Mat.of_col_vecs
in Dense m'
| _ -> invalid_arg "Expected a sparse matrix"
let sparse_of_computed ?(threshold=epsilon) = function
| Computed {m ; n ; f} ->
Sparse { m ; n ; v=Array.init n (fun j ->
Util.list_range 1 m
|> List.map (fun i ->
let x = f i (j+1) in
if abs_float x > threshold then Some (i, x)
else None)
|> Util.list_some
|> Vector.sparse_of_assoc_list m
) }
| _ -> invalid_arg "Expected a computed matrix"
let dense_of_computed x = dense_of_sparse @@ sparse_of_computed x
let dense_of_mat m = Dense m
let of_fun m n f = Computed {m ; n ; f}
let rec to_vector_array ?(threshold=epsilon) = function
| Sparse {m ; n ; v} -> v
| Dense m -> to_vector_array (sparse_of_dense ~threshold (Dense m))
| Computed m -> to_vector_array (sparse_of_computed ~threshold (Computed m))
let identity n =
Sparse { n ; m=n ;
v = Array.init n (fun i -> Vector.sparse_of_assoc_list n [(i+1,1.0)])
}
let sparse_of_mat ?(threshold=epsilon) m =
dense_of_mat m
|> sparse_of_dense ~threshold
let sparse_of_vector_array v =
let m =
Array.fold_left (fun accu v' ->
if Vector.dim v' <> accu then
invalid_arg "Inconsistent dimension"
else accu) (Vector.dim v.(0)) v
and n = Array.length v
in
Sparse {m ; n ; v}
let rec to_mat = function
| Dense m -> m
| Sparse m ->
dense_of_sparse (Sparse m)
|> to_mat
| Computed m -> sparse_of_computed (Computed m) |> dense_of_sparse |> to_mat
let transpose = function
| Dense m -> Dense (Mat.transpose_copy m)
| Sparse {m ; n ; v} ->
begin
let v' = Array.init m (fun i -> ref []) in
Array.iteri (fun j v_j ->
Vector.to_assoc_list v_j
|> List.iter (fun (i, v_ij) ->
v'.(i-1) := (j+1, v_ij) :: !(v'.(i-1))
)
) v;
let v' =
Array.map (fun x -> Vector.sparse_of_assoc_list n (List.rev !x) ) v'
in
Sparse {m=n ; n=m ; v=v'}
end
| Computed {m ; n ; f} ->
let f' i j = f j i in
Computed { m=n ; n=m ; f=f' }
let outer_product ?(threshold=epsilon) v1 v2 =
match Vector.(is_dense v1, is_dense v2) with
| (true, true) ->
let v1 = Vector.to_vec v1
and v2 = Vector.to_vec v2
in
let a = Mat.make0 (Vec.dim v1) (Vec.dim v2) in
ger v1 v2 a;
Dense a
| (true, false) ->
let v = Vector.to_vec v1
and v' = Vector.to_vec v2
in
let v =
Array.init (Vector.dim v2) (fun j ->
Vec.map (fun x -> x *. v'.{j+1}) v
|> Vector.sparse_of_vec)
in
Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v}
| (false, true)
| (false, false) ->
let v = Vector.to_assoc_list v1
and v' = Vector.to_vec v2
in
let v =
Array.init (Vector.dim v2) (fun j ->
List.map (fun (i, x) ->
let z = x *. v'.{j+1} in
if abs_float z < threshold then
None
else
Some (i, z)
) v
|> Util.list_some
|> Vector.sparse_of_assoc_list (Vector.dim v1)
)
in
Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v}
let rec mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b =
let f, f' =
match transa, transb with
| `N, `N -> dim2, dim1
| `T, `N -> dim1, dim1
| `T, `T -> dim1, dim2
| `N, `T -> dim2, dim2
in
if f a <> f' b then
Printf.sprintf "%d %d : Inconsistent dimensions" (f a) (f' b)
|> invalid_arg;
(* Dense x sparse *)
let mmsp transa transb a b =
let a =
match transa with
| `N -> Mat.transpose_copy a
| `T -> a
in
let m' = Mat.dim2 a in
let a =
Mat.to_col_vecs a
|> Array.map (fun v -> Vector.dense_of_vec v)
in
let {m ; n ; v} =
if transb = `T then
match transpose (Sparse b) with
| Sparse x -> x
| _ -> assert false
else
b
in
let v' =
Array.map (fun b_j ->
Array.map (fun a_i ->
Vector.dot a_i b_j) a
|> Vec.of_array
|> Vector.sparse_of_vec
) v
in
Sparse {m=m' ; n ; v=v'}
in
(* Sparse x dense *)
let spmm transa transb a b =
let b =
match transb with
| `N -> b
| `T -> Mat.transpose_copy b
in
let n' = Mat.dim2 b in
let b =
Mat.to_col_vecs b
|> Array.map (fun v -> Vector.dense_of_vec v)
in
let m, n, v =
if transa = `N then
match transpose (Sparse a) with
| Sparse {m ; n ; v} -> n, m, v
| _ -> assert false
else
match Sparse a with
| Sparse {m ; n ; v} -> n, m, v
| _ -> assert false
in
let v' =
Array.map (fun b_j ->
Array.map (fun a_i ->
Vector.dot a_i b_j) v
|> Vec.of_array
|> Vector.sparse_of_vec
) b
in
Sparse {m ; n=n' ; v=v'}
in
(* Sparse x Sparse *)
let mmspmm transa transb a b =
let {m ; n ; v} =
if transb = `T then
match transpose (Sparse b) with
| Sparse x -> x
| _ -> assert false
else
b
in
let m', n', v' =
if transa = `N then
match transpose (Sparse a) with
| Sparse {m ; n ; v} -> n, m, v
| _ -> assert false
else
match Sparse a with
| Sparse {m ; n ; v} -> n, m, v
| _ -> assert false
in
let v'' =
Array.map (fun b_j ->
Array.map (fun a_i ->
Vector.dot a_i b_j) v'
|> Vec.of_array
|> Vector.sparse_of_vec
) v
in
Sparse {m=m' ; n=n ; v=v''}
in
let mmcc transa transb a b =
let {m ; n ; f} =
if transb = `T then
match transpose (Computed b) with
| Computed x -> x
| _ -> assert false
else
b
in
let m', n', f' =
if transa = `T then
match transpose (Computed a) with
| Computed {m ; n ; f} -> m, n, f
| _ -> assert false
else
let {m ; n ; f} = a in
m, n, f
in
if n' <> m then
invalid_arg "Inconsistent dimensions";
let g i j =
let result = ref 0. in
for k=1 to m do
let a = f k j in
if a <> 0. then
result := !result +. (f' i k) *. a ;
done;
!result
in
Computed {m=m' ; n=n ; f=g}
in
let mmccde transa transb a b =
let m', n', f' =
if transa = `T then
match transpose (Computed a) with
| Computed {m ; n ; f} -> m, n, f
| _ -> assert false
else
let {m ; n ; f} = a in
m, n, f
in
let m, n =
match transb with
| `N -> Mat.dim1 b , Mat.dim2 b
| `T -> Mat.dim2 b , Mat.dim1 b
in
if n' <> m then
invalid_arg "Inconsistent dimensions";
let matrix =
Array.init n (fun j ->
let bj =
if transb = `T then
(Mat.copy_row b (j+1))
else
(Mat.to_col_vecs b).(j)
in
let accu = Vec.make0 m' in
let v = Vec.make0 m' in
let bj = Vec.to_array bj in
Array.iteri (fun k a ->
if a <> 0. then
begin
for i = 1 to m' do
Bigarray.Array1.unsafe_set v i (f' i (k+1));
done;
axpy ~alpha:a v accu
end
) bj;
accu
)
|> Mat.of_col_vecs
in
Dense matrix
in
match a, b with
| (Dense a), (Dense b) -> Dense (gemm ~transa ~transb a b)
| (Sparse a), (Dense b) -> spmm transa transb a b
| (Dense a), (Sparse b) -> mmsp transa transb a b
| (Sparse a), (Sparse b) -> mmspmm transa transb a b
| (Computed a), (Computed b) -> mmcc transa transb a b
| (Computed a), (Dense b) -> mmccde transa transb a b
| (Computed a), (Sparse _) ->
let b = { m = dim1 b ; n = dim2 b ; f = get b } in
mmcc transa transb a b
|> sparse_of_computed ~threshold
| _, (Computed _) ->
begin
match transa, transb with
| `N, `N -> mm ~transa:`T ~transb:`T ~threshold b a
| `N, `T -> mm ~transa:`N ~transb:`T ~threshold b a
| `T, `N -> mm ~transa:`T ~transb:`N ~threshold b a
| `T, `T -> mm ~transa:`N ~transb:`N ~threshold b a
end |> transpose
let mv ?(sparse=false) ?(trans=`N) ?(threshold=epsilon) a b =
let f =
match trans with
| `N -> dim2
| `T -> dim1
in
if f a <> Vector.dim b then
invalid_arg "Inconsistent dimensions";
let spmv a b =
let {m ; n ; v} =
if trans = `N then
match transpose (Sparse a) with
| Sparse x -> x
| _ -> assert false
else
a
in
Array.map (fun row_a -> Vector.dot row_a b) v
|> Vec.of_array
in
let mv a b =
let f_a =
match trans with
| `N -> (fun i -> Mat.copy_row a i)
| `T -> (fun i -> Mat.col a i)
in
Vec.init (Mat.dim1 a) (fun i ->
Vector.dense_of_vec (f_a i)
|> Vector.dot b )
in
let cmv a b =
match trans with
| `N -> Vec.init a.m (fun i ->
let accu = ref 0. in
for j=1 to a.n do
accu := !accu +. a.f i j *. Vector.get b j
done;
!accu)
| `T -> Vec.init a.m (fun i ->
let accu = ref 0. in
for j=1 to a.n do
accu := !accu +. a.f j i *. Vector.get b j
done;
!accu)
in
let dense_result =
match a, Vector.is_dense b with
| Dense a, true -> gemv ~trans a (Vector.to_vec b)
| Dense a, false -> mv a b
| Sparse a, _ -> spmv a b
| Computed a, _ -> cmv a b
in
if sparse then
Vector.sparse_of_vec dense_result
else
Vector.dense_of_vec dense_result
let rec op2 dense_op sparse_op a b =
if dim1 a <> dim1 b || dim2 a <> dim2 b then
failwith "Inconsistent dimensions";
match a, b with
| (Dense a), (Dense b) -> Dense (dense_op a b)
| (Dense _), (Sparse _) -> op2 dense_op sparse_op (sparse_of_dense a) b
| (Sparse _), (Dense _) -> op2 dense_op sparse_op a (sparse_of_dense b)
| (Sparse a), (Sparse b) -> Sparse
{ m=a.m ; n=a.n ;
v = Array.map2 sparse_op a.v b.v
}
| _ -> failwith "Not implemented"
let add = op2 (fun a b -> Mat.add a b) (fun a b -> Vector.add a b)
let sub = op2 (fun a b -> Mat.sub a b) (fun a b -> Vector.sub a b)
let scale f = function
| Dense a -> let b = lacpy a in (Mat.scal f b ; Dense b)
| Sparse a -> Sparse
{ a with
v = if f = 1.0 then a.v
else Array.map (fun v -> Vector.scale f v) a.v }
| _ -> failwith "Not implemented"
let frobenius_norm = function
| Dense a -> lange ~norm:`F a
| Sparse a ->
Array.fold_left (fun accu v -> accu +. Vector.dot v v) 0. a.v
|> sqrt
| _ -> failwith "Not implemented"
let split_cols nrows = function
| Dense a ->
begin
Mat.to_col_vecs a
|> Array.to_list
|> Util.list_pack nrows
|> List.map (fun l ->
Dense (Mat.of_col_vecs @@ Array.of_list l) )
end
| Sparse a ->
begin
Array.to_list a.v
|> Util.list_pack nrows
|> List.map Array.of_list
|> List.map (fun v -> Sparse { m=a.m ; n= Array.length v ; v })
end
| Computed a ->
begin
Util.list_range 0 (a.n-1)
|> Util.list_pack nrows
|> List.map Array.of_list
|> List.map (fun v -> Computed { m=a.m ; n= Array.length v ; f = (fun i j -> a.f i (j+v.(0)) ) })
end
let join_cols l =
let rec aux_dense accu = function
| [] -> Dense (Mat.of_col_vecs_list (List.concat accu))
| (Dense a) :: rest -> aux_dense ((Mat.to_col_vecs_list a) :: accu) rest
| _ -> assert false
and aux_sparse m n accu = function
| [] -> Sparse { m ; n ; v=Array.of_list (List.concat accu) }
| (Sparse a) :: rest -> aux_sparse a.m (n+a.n) ((Array.to_list a.v)::accu) rest
| _ -> assert false
and aux = function
| [] -> Sparse { m=0 ; n=0 ; v=[| |] }
| (Dense a) :: rest -> aux_dense [] ((Dense a) :: rest)
| (Sparse a) :: rest -> aux_sparse 0 0 [] ((Sparse a) :: rest)
| (Computed a) :: rest -> aux_sparse 0 0 [] (List.map sparse_of_computed ( (Computed a) :: rest ))
in aux (List.rev l)
let ax_eq_b_conj_grad ?x a b =
(* /!\ : A needs to be positive definite and symmetric *)
let x =
match x with
| Some x0 -> x0
| None -> b
in
let r = Vector.sub b (mv a x) in
let p = r in
let rsold = Vector.dot r r in
let rec aux rsold r p x = function
| 0 -> x
| i ->
let ap = mv a p in
let alpha = rsold /. (Vector.dot p ap) in
let x = Vector.add x (Vector.scale alpha p) in
let r = Vector.sub r (Vector.scale alpha ap) in
let rsnew = Vector.dot r r in
if rsnew < Constants.epsilon then
x
else
let p =
Vector.add r (Vector.scale (rsnew /. (rsold +. 1.e-12) ) p)
in
(aux [@tailcall]) rsnew r p x (i-1)
in
aux rsold r p x (Vector.dim b *2)
let rec ax_eq_b ?(trans=`N) a b =
match a, b with
| (Dense a), (Dense b) ->
let a = lacpy a in
let x = lacpy b in
(getrs ~trans a x; Dense x)
| (Dense _), (Sparse _) ->
let b = dense_of_sparse b in
ax_eq_b ~trans a b
| _ ->
let ata, atb =
if trans = `N then
mm ~transa:`T a a, mm ~transa:`T a b
else
mm ~transa:`N a a, mm ~transa:`N a b
in
Sparse { m=dim1 b ; n=dim2 b ;
v=Array.map (fun v -> ax_eq_b_conj_grad ata v) (to_vector_array atb)
}
(* ------- Parallel routines ---------- *)
let parallel_mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b =
let n =
match transa with
| `N -> dim2 a
| `T -> dim1 a
in
let n = n / (Parallel.size * 7) in
let b =
match transb with
| `T -> transpose b
| `N -> b
in
split_cols n b
|> Stream.of_list
|> Farm.run ~ordered:true ~f:(fun b ->
match a, b with
| Computed _, Computed _ ->
mm ~transa ~threshold a b
|> sparse_of_computed ~threshold
| _ ->
mm ~transa ~threshold a b
)
|> Util.stream_to_list
|> join_cols
(* ------------ Printers ------------ *)
let rec pp ppf = function
| Dense m -> Util.pp_matrix ppf m
| Sparse m -> pp ppf @@ dense_of_sparse (Sparse m)
| Computed m -> pp ppf @@ dense_of_computed (Computed m)
(* ---------- Unit tests ------------ *)
let test_case () =
let d1 = 30
and d2 = 40
and d3 = 50
in
let x1 = Mat.map (fun x -> if abs_float x < 0.6 then 0. else x) (Mat.random d1 d2)
and x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d2 d3)
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 norm_diff m1 m2 =
(Mat.sub (to_mat m1) (to_mat m2)
|> Mat.syrk_trace)
in
let test_dimensions () =
Alcotest.(check int) "dim1 1" d1 (dim1 m1 );
Alcotest.(check int) "dim1 2" d1 (dim1 m1_s);
Alcotest.(check int) "dim2 3" d2 (dim2 m1 );
Alcotest.(check int) "dim2 4" d2 (dim2 m1_s);
Alcotest.(check int) "dim1 5" d2 (dim1 m2 );
Alcotest.(check int) "dim1 6" d2 (dim1 m2_s);
Alcotest.(check int) "dim2 7" d3 (dim2 m2 );
Alcotest.(check int) "dim2 8" d3 (dim2 m2_s);
in
let test_conversion () =
Alcotest.(check bool) "sparse -> dense 1" true (dense_of_sparse m1_s = m1 );
Alcotest.(check bool) "sparse -> dense 2" true (dense_of_sparse m2_s = m2 );
Alcotest.(check bool) "dense -> sparse 1" true (sparse_of_dense m1 = m1_s);
Alcotest.(check bool) "dense -> sparse 3" true (sparse_of_dense m2 = m2_s);
in
let test_transpose () =
let m1t = Mat.transpose_copy x1 |> dense_of_mat
and m2t = Mat.transpose_copy x2 |> dense_of_mat
in
Alcotest.(check bool) "dense 1" true (transpose m1 = m1t);
Alcotest.(check bool) "dense 2" true (transpose m2 = m2t);
Alcotest.(check bool) "sparse 1" true (transpose m1_s = sparse_of_dense m1t);
Alcotest.(check bool) "sparse 2" true (transpose m2_s = sparse_of_dense m2t);
in
let test_outer () =
let x1 = Vec.init d1 (fun i -> float_of_int i)
and x2 = Vec.init d2 (fun i -> float_of_int i -. 0.3)
in
let v1 = Vector.dense_of_vec x1
and v2 = Vector.dense_of_vec x2
in
let v1_s = Vector.sparse_of_vec x1
and v2_s = Vector.sparse_of_vec x2
in
let m1 =
Dense (Mat.init_cols d1 d2 (fun i j -> (float_of_int i) *. (float_of_int j -. 0.3)))
in
let m1_s =
sparse_of_dense m1
in
Alcotest.(check (float 1.e-10)) "dense dense " 0. (norm_diff m1 (outer_product v1 v2));
Alcotest.(check (float 1.e-10)) "sparse dense " 0. (norm_diff m1_s (outer_product v1_s v2));
Alcotest.(check (float 1.e-10)) "dense sparse" 0. (norm_diff m1_s (outer_product v1 v2_s));
Alcotest.(check (float 1.e-10)) "sparse sparse" 0. (norm_diff m1_s (outer_product v1_s v2_s));
in
let test_add_sub () =
let x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d1 d2) in
let m2 = dense_of_mat x2 in
let m3 = Mat.add x1 x2 |> dense_of_mat in
let m4 = Mat.sub x1 x2 |> dense_of_mat in
let m2_s = sparse_of_mat x2 in
let m3_s = Mat.add x1 x2 |> sparse_of_mat in
let m4_s = Mat.sub x1 x2 |> sparse_of_mat in
Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (add m1 m2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (sub m1 m2) m4);
Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (add m1 m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (sub m1 m2_s) m4_s);
Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (add m1_s m2) m3);
Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (sub m1_s m2) m4);
Alcotest.(check (float 1.e-10)) "dense sparse 7" 0. (norm_diff (add m1_s m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 8" 0. (norm_diff (sub m1_s m2_s) m4_s);
Alcotest.(check (float 1.e-10)) "dense sparse 9" (frobenius_norm m1_s) (frobenius_norm m1);
in
let test_mv () =
let y = Vec.random d2 in
let z = Vec.random d1 in
let x3 = gemv x1 y in
let x4 = gemv ~trans:`T x1 z in
let v = Vector.dense_of_vec y in
let v2 = Vector.dense_of_vec z in
let v3 = Vector.dense_of_vec x3 in
let v4 = Vector.dense_of_vec x4 in
let v_s = Vector.sparse_of_vec y in
let v2_s = Vector.sparse_of_vec z in
let norm_diff v1 v2 =
Vec.sub (Vector.to_vec v1) (Vector.to_vec v2)
|> nrm2
in
Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mv m1 v) v3);
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
let c1 = of_fun (Mat.dim1 x1) (Mat.dim2 x1) (fun i j -> x1.{i,j}) in
let c2 = of_fun (Mat.dim1 x2) (Mat.dim2 x2) (fun i j -> x2.{i,j}) in
let c3 = of_fun (Mat.dim1 x3) (Mat.dim2 x3) (fun i j -> x3.{i,j}) in
let c4 = of_fun (dim1 m4) (dim2 m4) (fun i j -> get m4 i j ) in
let c5 = of_fun (dim1 m5) (dim2 m5) (fun i j -> get m5 i j ) in
Alcotest.(check (float 1.e-10)) "dense dense 0" 0. (norm_diff m3 c3);
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 c1 c2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 3" 0. (norm_diff (mm c1 m2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 4" 0. (norm_diff (mm c1 m2_s) m3);
Alcotest.(check (float 1.e-10)) "dense dense 5" 0. (norm_diff (mm m1 c2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 6" 0. (norm_diff (mm m1_s c2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 7" 0. (norm_diff (mm ~transa:`T m4 m2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 8" 0. (norm_diff (mm ~transa:`T c4 m2) m3);
Alcotest.(check (float 1.e-10)) "dense dense 9" 0. (norm_diff (mm ~transb:`T m1 m5) m3);
Alcotest.(check (float 1.e-10)) "dense dense 10" 0. (norm_diff (mm ~transb:`T m1 c5) m3);
Alcotest.(check (float 1.e-10)) "dense dense 11" 0. (norm_diff (mm ~transa:`T ~transb:`T m2 m1) (transpose m3));
Alcotest.(check (float 1.e-10)) "dense sparse 12" 0. (norm_diff (mm m1 m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 13" 0. (norm_diff (mm ~transa:`T m4 m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 14" 0. (norm_diff (mm ~transa:`T c4 m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 15" 0. (norm_diff (mm ~transb:`T m1 m5_s) m3_s);
Alcotest.(check (float 1.e-10)) "dense sparse 16" 0. (norm_diff (transpose (mm m2 m1_s ~transa:`T ~transb:`T)) m3_s);
Alcotest.(check (float 1.e-10)) "sparse dense 17" 0. (norm_diff (mm m1_s m2) m3_s);
Alcotest.(check (float 1.e-10)) "sparse dense 18" 0. (norm_diff (mm ~transa:`T m4_s m2) m3_s);
Alcotest.(check (float 1.e-10)) "sparse dense 19" 0. (norm_diff (mm ~transb:`T m1_s m5) m3_s);
Alcotest.(check (float 1.e-10)) "sparse dense 20" 0. (norm_diff (mm ~transb:`T m1_s c5) m3_s);
Alcotest.(check (float 1.e-10)) "sparse dense 21" 0. (norm_diff (transpose (mm m2_s m1 ~transa:`T ~transb:`T)) m3_s);
Alcotest.(check (float 1.e-10)) "sparse sparse 22" 0. (norm_diff (mm m1_s m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "sparse sparse 23" 0. (norm_diff (mm ~transa:`T m4_s m2_s) m3_s);
Alcotest.(check (float 1.e-10)) "sparse sparse 24" 0. (norm_diff (mm ~transb:`T m1_s m5_s) m3_s);
Alcotest.(check (float 1.e-10)) "sparse sparse 25" 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
let test_split_join () =
let m1_split = split_cols 7 m1 in
let m1_s_split = split_cols 7 m1_s in
let m2 = join_cols m1_split in
let m2_s = join_cols m1_s_split in
Alcotest.(check int) "length" 6 (List.length m1_split);
Alcotest.(check int) "length" 6 (List.length m1_s_split);
Alcotest.(check bool) "join" true (m1 = m2);
Alcotest.(check bool) "join" true (m1_s = m2_s);
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;
"split_join", `Quick, test_split_join;
]