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QCaml
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matrix vector product OK

This commit is contained in:
Anthony Scemama 2019-02-28 12:08:28 +01:00
parent 3de8e31a18
commit c5a16d0765
3 changed files with 178 additions and 22 deletions
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125
Utils/Matrix.ml
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@ -107,7 +107,7 @@ let outer_product ?(threshold=epsilon) v1 v2 =
let v1 = Vector.to_vec v1
and v2 = Vector.to_vec v2
in
let a = Mat.create (Vec.dim v1) (Vec.dim v2) in
let a = Mat.make0 (Vec.dim v1) (Vec.dim v2) in
ger v1 v2 a;
Dense a
| (true, false) ->
@ -256,16 +256,71 @@ let mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b =
| (Sparse a), (Sparse b) -> mmspmm transa transb a b
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 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, true -> spmv a b
| Sparse a, false -> spmv a b
in
if sparse then
Vector.sparse_of_vec dense_result
else
Vector.dense_of_vec dense_result
let rec pp_matrix ppf = function
| Dense m -> Util.pp_matrix ppf m
| Sparse m -> pp_matrix ppf @@ dense_of_sparse (Sparse m)
(* ---------- Unit tests ------------ *)
let test_case () =
let d1 = 3
and d2 = 4
and d3 = 5
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)
@ -280,6 +335,11 @@ let test_case () =
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);
@ -309,8 +369,8 @@ let test_case () =
in
let test_outer () =
let x1 = Vec.init 3 (fun i -> float_of_int i)
and x2 = Vec.init 4 (fun i -> float_of_int i -. 3.)
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
@ -319,30 +379,54 @@ let test_case () =
and v2_s = Vector.sparse_of_vec x2
in
let m1 =
Dense (Mat.init_cols 3 4 (fun i j -> (float_of_int i) *. (float_of_int j -. 3.)))
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 bool) "dense dense " true (m1 = outer_product v1 v2);
Alcotest.(check bool) "sparse dense " true (m1_s = outer_product v1_s v2);
Alcotest.(check bool) "dense sparse" true (m1_s = outer_product v1 v2_s);
Alcotest.(check bool) "sparse sparse" true (m1_s = outer_product v1_s v2_s);
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_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
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 = dense_of_mat x1 |> transpose
and m4_s = sparse_of_mat x1 |> transpose
and m5 = dense_of_mat x2 |> transpose
and m5 = dense_of_mat x2 |> transpose
and m5_s = sparse_of_mat x2 |> transpose
in
let norm_diff m1 m2 =
(Mat.sub (to_mat m1) (to_mat m2)
|> Mat.syrk_trace)
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);
@ -367,7 +451,8 @@ let test_case () =
"Conversion", `Quick, test_conversion;
"Dimensions", `Quick, test_dimensions;
"Transposition", `Quick, test_transpose;
"Oueter product", `Quick, test_outer;
"Outer product", `Quick, test_outer;
"Matrix Vector", `Quick, test_mv;
"Matrix Matrix", `Quick, test_mm;
]

71
Utils/Matrix.mli Normal file
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@ -0,0 +1,71 @@
(* Sparse or dense matrices *)
open Lacaml.D
type t
(** {1 Accessors} *)
val is_sparse : t -> bool
(** True is the matrix is sparse. *)
val is_dense : t -> bool
(** True is the matrix is dense. *)
val dim1 : t -> int
(** First dimension of the matrix *)
val dim2 : t -> int
(** Secons dimension of the matrix *)
val get : t -> int -> int -> float
(** [get m i j] returns {% $\mathbf{m}_{ij}$ %}. *)
(** {1 Converters } *)
val to_mat : t -> Mat.t
(** Convert into a Lacaml Mat. *)
val to_vector_array : t -> Vector.t array
(** Convert the matrix into an array of column vectors. *)
val sparse_of_dense : ?threshold:float -> t -> t
(** Creates a sparse matrix from a dense matrix. Default threshold is {!Constants.epsilon}. *)
val dense_of_sparse : t -> t
(** Creates a dense matrix from a sparse matrix. *)
val dense_of_mat : Mat.t -> t
(** Create a dense matrix from a Lacaml Mat *)
val sparse_of_mat : ?threshold:float -> Lacaml.D.Mat.t -> t
(** Create a sparse matrix from a Lacaml Mat. Default threshold is {!Constants.epsilon}. *)
val sparse_of_vector_array : Vector.t array -> t
(** Create a sparse matrix from an array of column vectors. *)
val transpose : t -> t
(** Returns the transposed matrix. *)
(** {1 Operations} *)
val outer_product : ?threshold:float -> Vector.t -> Vector.t -> t
(** Creates the matrix formed by the outer product of two vectors. *)
val mm : ?transa:trans3 -> ?transb:trans3 -> ?threshold:float -> t -> t -> t
(** Matrix multiplication *)
val mv : ?sparse:bool -> ?trans:trans3 -> ?threshold:float -> t -> Vector.t -> Vector.t
(** Matrix Vector product *)
(** {1 Printers } *)
val pp_matrix : Format.formatter -> t -> unit
(** {1 Unit testing} *)
val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list

4
Utils/Vector.mli
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@ -1,7 +1,7 @@
open Lacaml.D
(* Sparse or dense vectors *)
open Lacaml.D
type t
(** {1 Accessors} *)