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matrix vector product OK
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parent
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117
Utils/Matrix.ml
117
Utils/Matrix.ml
@ -107,7 +107,7 @@ let outer_product ?(threshold=epsilon) v1 v2 =
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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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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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@ -256,16 +256,71 @@ let mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) 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 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 = 3
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and d2 = 4
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and d3 = 5
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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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@ -280,6 +335,11 @@ let test_case () =
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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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@ -309,8 +369,8 @@ let test_case () =
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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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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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@ -319,15 +379,43 @@ let test_case () =
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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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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 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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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_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
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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);
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Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (mv m1 v_s) v3);
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Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (mv ~trans:`T m1 v2_s) v4);
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Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (mv m1_s v) v3);
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Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (mv ~trans:`T m1_s v2) v4);
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Alcotest.(check (float 1.e-10)) "sparse sparse 7" 0. (norm_diff (mv m1_s v_s) v3);
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Alcotest.(check (float 1.e-10)) "sparse sparse 8" 0. (norm_diff (mv ~trans:`T m1_s v2_s) v4);
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in
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let test_mm () =
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@ -339,10 +427,6 @@ let test_case () =
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and m5 = dense_of_mat x2 |> transpose
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and m5_s = sparse_of_mat x2 |> transpose
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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 dense 2" 0. (norm_diff (mm ~transa:`T m4 m2) m3);
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Alcotest.(check (float 1.e-10)) "dense dense 3" 0. (norm_diff (mm ~transb:`T m1 m5) m3);
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@ -367,7 +451,8 @@ let test_case () =
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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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"Outer product", `Quick, test_outer;
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"Matrix Vector", `Quick, test_mv;
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"Matrix Matrix", `Quick, test_mm;
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]
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71
Utils/Matrix.mli
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71
Utils/Matrix.mli
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@ -0,0 +1,71 @@
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(* Sparse or dense matrices *)
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open Lacaml.D
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type t
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(** {1 Accessors} *)
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val is_sparse : t -> bool
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(** True is the matrix is sparse. *)
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val is_dense : t -> bool
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(** True is the matrix is dense. *)
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val dim1 : t -> int
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(** First dimension of the matrix *)
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val dim2 : t -> int
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(** Secons dimension of the matrix *)
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val get : t -> int -> int -> float
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(** [get m i j] returns {% $\mathbf{m}_{ij}$ %}. *)
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(** {1 Converters } *)
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val to_mat : t -> Mat.t
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(** Convert into a Lacaml Mat. *)
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val to_vector_array : t -> Vector.t array
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(** Convert the matrix into an array of column vectors. *)
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val sparse_of_dense : ?threshold:float -> t -> t
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(** Creates a sparse matrix from a dense matrix. Default threshold is {!Constants.epsilon}. *)
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val dense_of_sparse : t -> t
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(** Creates a dense matrix from a sparse matrix. *)
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val dense_of_mat : Mat.t -> t
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(** Create a dense matrix from a Lacaml Mat *)
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val sparse_of_mat : ?threshold:float -> Lacaml.D.Mat.t -> t
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(** Create a sparse matrix from a Lacaml Mat. Default threshold is {!Constants.epsilon}. *)
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val sparse_of_vector_array : Vector.t array -> t
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(** Create a sparse matrix from an array of column vectors. *)
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val transpose : t -> t
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(** Returns the transposed matrix. *)
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(** {1 Operations} *)
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val outer_product : ?threshold:float -> Vector.t -> Vector.t -> t
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(** Creates the matrix formed by the outer product of two vectors. *)
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val mm : ?transa:trans3 -> ?transb:trans3 -> ?threshold:float -> t -> t -> t
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(** Matrix multiplication *)
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val mv : ?sparse:bool -> ?trans:trans3 -> ?threshold:float -> t -> Vector.t -> Vector.t
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(** Matrix Vector product *)
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(** {1 Printers } *)
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val pp_matrix : Format.formatter -> t -> unit
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(** {1 Unit testing} *)
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val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list
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@ -1,7 +1,7 @@
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open Lacaml.D
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(* Sparse or dense vectors *)
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open Lacaml.D
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type t
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(** {1 Accessors} *)
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