Added phantom types to Vectors

linear_algebra/lib/diis.ml

@@ -1,7 +1,7 @@
-type t =
+type 'a t =
 {
-  p : Vector.t list;
+  p : 'a Vector.t list;
-  e : Vector.t list;
+  e : 'a Vector.t list;
   m : int;
   mmax : int;
 }

linear_algebra/lib/diis.mli

@@ -48,15 +48,15 @@ $$ %}
 
 *)
 
-type t
+type 'a t
 
-val make : ?mmax:int -> unit -> t
+val make : ?mmax:int -> unit -> 'a t
 (** Initialize DIIS with a maximum size.*)
 
-val append : p:Vector.t -> e:Vector.t -> t -> t
+val append : p:'a Vector.t -> e:'a Vector.t -> 'a t -> 'a t
 (** Append a parameter vector [p] and the corresponding error vector [e]. *)
 
-val next : t -> Vector.t
+val next : 'a t -> 'a Vector.t
 (** Returns a new parameter vector. *)
 
 

linear_algebra/lib/four_idx_storage.mli

@@ -47,10 +47,10 @@ val increment_chem : t -> int -> int -> int -> int -> float -> unit
 val increment_phys : t -> int -> int -> int -> int -> float -> unit
 (** Increments an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
 
-val get_chem_all_i : t -> j:int -> k:int -> l:int -> Vector.t
+val get_chem_all_i : t -> j:int -> k:int -> l:int -> 'a Vector.t
 (** Get all integrals in an array [a.{i} =] {% $(\cdot j|kl)$ %} . *)
 
-val get_phys_all_i : t -> j:int -> k:int -> l:int -> Vector.t
+val get_phys_all_i : t -> j:int -> k:int -> l:int -> 'a Vector.t
 (** Get all integrals in an array [a.{i} =] {% $\langle \cdot j|kl \rangle$ %} . *)
 
 val get_chem_all_ij : t -> k:int -> l:int -> Matrix.t

linear_algebra/lib/matrix.mli

@@ -73,16 +73,16 @@ val to_bigarray_inplace :
   t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t
 (** Converts the matrix into a Bigarray in Fortran layout in place*)
 
-val to_col_vecs : t -> Vector.t array
+val to_col_vecs : t -> 'a Vector.t array
 (** Converts the matrix into an array of vectors *)
 
-val to_col_vecs_list : t -> Vector.t list
+val to_col_vecs_list : t -> 'a Vector.t list
 (** Converts the matrix into a list of vectors *)
 
-val of_col_vecs : Vector.t array -> t
+val of_col_vecs : 'a Vector.t array -> t
 (** Converts an array of vectors into a matrix *)
 
-val of_col_vecs_list : Vector.t list -> t
+val of_col_vecs_list : 'a Vector.t list -> t
 (** Converts a list of vectors  into a matrix *)
 
 val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> t 
@@ -98,7 +98,7 @@ val copy: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> ?ar:int -> ?ac:int -> t -> t
 val copy_inplace: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> b:t -> ?ar:int -> ?ac:int -> t -> unit
 (** Copies all or part of a two-dimensional matrix A to an existing matrix B *)
 
-val col: t -> int -> Vector.t
+val col: t -> int -> 'a Vector.t
 (** Returns a column of the matrix as a vector *)
 
 val detri: t -> t 
@@ -109,10 +109,10 @@ val detri_inplace: t -> unit
 (** Takes an upper-triangular matrix, and makes it a symmetric matrix
 by mirroring the defined triangle along the diagonal. *)
 
-val as_vec_inplace: t -> Vector.t
+val as_vec_inplace: t -> 'a Vector.t
 (** Interpret the matrix as a vector (reshape). *)
   
-val as_vec: t -> Vector.t
+val as_vec: t -> 'a Vector.t
 (** Return a copy of the reshaped matrix into a vector *)
   
 val random:  ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> int -> t
@@ -131,19 +131,19 @@ val scale: float -> t -> t
 val scale_inplace: float -> t -> unit
 (** Multiplies the matrix by a constant *)
   
-val scale_cols: t -> Vector.t -> t
+val scale_cols: t -> 'a Vector.t -> t
 (** Multiplies the matrix by a constant *)
   
-val scale_cols_inplace: t -> Vector.t -> unit
+val scale_cols_inplace: t -> 'a Vector.t -> unit
 (** Multiplies the matrix by a constant *)
   
 val sycon: t -> float
 (** Returns the condition number of a matrix *)
   
-val outer_product : ?alpha:float -> Vector.t -> Vector.t -> t
+val outer_product : ?alpha:float -> 'a Vector.t -> 'b Vector.t -> t
 (** Computes M = %{ $\alpha u.v^t$ %} *)
 
-val outer_product_inplace : t -> ?alpha:float -> Vector.t -> Vector.t -> unit
+val outer_product_inplace : t -> ?alpha:float -> 'a Vector.t -> 'b Vector.t -> unit
 (** Computes M = %{ $\alpha u.v^t$ %} *)
 
 val gemm_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float -> c:t -> ?transa:[`N | `T] -> ?alpha:float ->
@@ -163,7 +163,7 @@ val gemm_trace: ?transa:[`N | `T] -> t -> ?transb:[`N | `T] -> t -> float
 [transa=`N] [transb=`N] 
 [gemm_trace a b]: %{ $C =  Tr(A B)$ *)
 
-val svd: t -> t * Vector.t * t
+val svd: t -> t * 'b Vector.t * t
 (** Singular value decomposition. *)
 
 val qr: t -> t * t
@@ -175,7 +175,7 @@ val normalize_mat : t -> t
 val normalize_mat_inplace : t -> unit
 (** Returns the matrix with all the column vectors normalized *)
 
-val diagonalize_symm : t -> t * Vector.t
+val diagonalize_symm : t -> t * 'a Vector.t
 (** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *)
 
 val xt_o_x : o:t -> x:t -> t

linear_algebra/lib/vector.ml

@@ -1,6 +1,6 @@
 open Lacaml.D
    
-type t = Vec.t
+type 'a t = Vec.t
 
 let copy ?n ?ofsy ?incy ?y ?ofsx ?incx t = copy ?n ?ofsy ?incy ?y ?ofsx ?incx t 
 let norm t = nrm2 t

linear_algebra/lib/vector.mli

@@ -8,121 +8,122 @@ The indexing of vectors is 1-based.
 
 open Lacaml.D
 
-type t = Vec.t
+type 'a t = Vec.t
+(* Parameter ['a] defines the basis on which the vector is expanded. *)
 
-val dim : t -> int
+val dim : 'a t -> int
 (** Returns the dimension of the vector *)
 
-val add : t -> t -> t
+val add : 'a t -> 'a t -> 'a t
 (** [c = add a b] : %{ $c = a + b$ %} *)
 
-val sub : t -> t -> t
+val sub : 'a t -> 'a t -> 'a t
 (** [c = sub a b] : %{ $c = a - b$ %} *)
 
-val mul : t -> t -> t
+val mul : 'a t -> 'a t -> 'a t
 (** [c = mul a b] : %{ $c_i = a_i \times b_i$ %} *)
 
-val div : t -> t -> t
+val div : 'a t -> 'a t -> 'a t
 (** [c = div a b] : %{ $c_i = a_i / b_i$ %} *)
 
-val dot : t -> t -> float
+val dot : 'a t -> 'a t -> float
 (** [dot v1 v2] : Dot product between v1 and v2 *)
 
-val norm : t -> float
+val norm : 'a t -> float
 (** Norm of the vector : %{ ||v|| = $\sqrt{v.v}$ %} *)
   
-val sqr  : t -> t
+val sqr  : 'a t -> 'a t
 (** [sqr t = map (fun x -> x *. x) t] *)
   
-val sqrt : t -> t
+val sqrt : 'a t -> 'a t
 (** [sqrt t = map sqrt t] *)
 
-val neg  : t -> t
+val neg  : 'a t -> 'a t
 (** [neg  t = map (f x -> -. x) t *)
   
-val reci : t -> t
+val reci : 'a t -> 'a t
 (** [reci t = map (f x -> 1./x) t *)
   
-val abs  : t -> t
+val abs  : 'a t -> 'a t
 (** [abs  t = map (f x -> abs_float x) t *)
   
-val cos  : t -> t
+val cos  : 'a t -> 'a t
 (** [cos  t = map (f x -> cos x) t *)
   
-val sin  : t -> t
+val sin  : 'a t -> 'a t
 (** [sin  t = map (f x -> sin x) t *)
   
-val tan  : t -> t
+val tan  : 'a t -> 'a t
 (** [tan  t = map (f x -> tan x) t *)
   
-val acos  : t -> t
+val acos  : 'a t -> 'a t
 (** [acos  t = map (f x -> acos x) t *)
 
-val asin  : t -> t
+val asin  : 'a t -> 'a t
 (** [asin  t = map (f x -> asin x) t *)
   
-val atan  : t -> t
+val atan  : 'a t -> 'a t
 (** [atan  t = map (f x -> atan x) t *)
   
-val normalize : t -> t
+val normalize : 'a t -> 'a t
 (** Returns the vector normalized *)
 
-val init : int ->  (int -> float) -> t 
+val init : int ->  (int -> float) -> 'a t 
-(** Initialized the vector with a function taking the index as parameter.*)
+(** Initialize the vector with a function taking the index as parameter.*)
 
-val sum  : t -> float
+val sum  : 'a t -> float
 (** Returns the sum of the elements of the vector *)
   
-val copy : ?n:int -> ?ofsy:int -> ?incy:int -> ?y:vec -> ?ofsx:int -> ?incx:int ->  t -> t
+val copy : ?n:int -> ?ofsy:int -> ?incy:int -> ?y:vec -> ?ofsx:int -> ?incx:int ->  'a t -> 'a t
 (** Returns a copy of the vector X into Y. [ofs] controls the offset and [inc]
     the increment.  *)
   
-val map  : (float -> float) -> t -> t
+val map  : (float -> float) -> 'a t -> 'a t
 (** Equivalent to [Array.map] *)
 
-val iter : (float -> unit) -> t -> unit
+val iter : (float -> unit) -> 'a t -> unit
 (** Equivalent to [Array.iter] *)
 
-val iteri : (int -> float -> unit) -> t -> unit
+val iteri : (int -> float -> unit) -> 'a t -> unit
 (** Equivalent to [Array.iteri] *)
 
-val of_array : float array -> t
+val of_array : float array -> 'a t
 (** Converts an array of floats into a vector *)
 
-val of_list : float list -> t
+val of_list : float list -> 'a t
 (** Converts a list of floats into a vector *)
 
-val to_array : t -> float array
+val to_array : 'a t -> float array
 (** Converts to an array of floats *)
 
-val to_list : t -> float list
+val to_list : 'a t -> float list
 (** Converts to a list of floats *)
 
-val create : int -> t
+val create : int -> 'a t
 (** Creates an uninitialized vector *)
                       
-val make : int -> float -> t
+val make : int -> float -> 'a t
 (** Creates a vector initialized with the given [float].*)
                       
-val make0 : int -> t
+val make0 : int -> 'a t
 (** Creates a zero-initialized vector.*)
                       
-val fold : ('a -> float -> 'a) -> 'a -> t -> 'a
+val fold : ('a -> float -> 'a) -> 'a -> 'a t -> 'a
 (** Equivalent to [Array.fold] *)
 
-val random : ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> t
+val random : ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> 'a t
 (** Returns a vector of uniform random numbers %{ $ f \le u \le f+r $
  %} where [f] is [from] and [r] is [range].
  Default values: [from:-1.0] [range:2.0] *)
 
-val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> t
+val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> 'a t
 (** Builds by converting from a Fortran bigarray *)
 
-val to_bigarray : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t
+val to_bigarray : 'a t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t
 (** Converts the vector into a Fortran bigarray *)
 
-val of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> t
+val of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> 'a t
 (** Builds by converting from a Fortran bigarray *)
 
-val to_bigarray_inplace : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t
+val to_bigarray_inplace : 'a t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t
 (** Converts the vector into a Fortran bigarray *)