Introduced infix operators for Vector and Matrices

gaussian_integrals/lib/electron_nucleus.ml

@@ -51,7 +51,6 @@ let of_basis_nuclei ~basis nuclei =
   in
 
   let eni_array = Matrix.create n n in
-  let eni_array_x = Matrix.to_bigarray_inplace eni_array in
 
   (* Pre-compute all shell pairs *)
   let shell_pairs =
@@ -83,8 +82,8 @@ let of_basis_nuclei ~basis nuclei =
                 let value = 
                   Zmap.find cls key 
                 in
-                eni_array_x.{j_c,i_c} <- value;
+                Matrix.set eni_array j_c i_c value;
-                eni_array_x.{i_c,j_c} <- value;
+                Matrix.set eni_array i_c j_c value;
               ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j))))
           ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i))))
     done;
@@ -96,11 +95,10 @@ let of_basis_nuclei ~basis nuclei =
 let to_file ~filename eni_array =
   let n = Matrix.dim1 eni_array in
   let oc = open_out filename in
-  let eni_array_x = Matrix.to_bigarray_inplace eni_array in
 
   for j=1 to n do
     for i=1 to j do
-      let value = eni_array_x.{i,j} in
+      let value = eni_array%:(i,j) in
       if (value <> 0.) then
         Printf.fprintf oc " %5d %5d %20.15f\n" i j value;
     done;

gaussian_integrals/lib/kinetic.ml

@@ -134,7 +134,6 @@ let of_basis basis =
   in
 
   let result = Matrix.create n n in
-  let result_x = Matrix.to_bigarray_inplace result in
   for j=0 to (Array.length shell) - 1 do
     for i=0 to j do
       (* Compute all the integrals of the class *)
@@ -155,8 +154,8 @@ let of_basis basis =
                 try Zmap.find cls key
                 with Not_found -> 0.
               in
-              result_x.{i_c,j_c} <- value;
+              Matrix.set result i_c j_c value;
-              result_x.{j_c,i_c} <- value;
+              Matrix.set result j_c i_c value;
             ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i))))
         ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j))))
     done;
@@ -175,11 +174,10 @@ let to_file ~filename kinetic =
     Matrix.dim1 kinetic
   in
 
-  let kinetic_x = Matrix.to_bigarray_inplace kinetic in
   for j=1 to n  do
     for i=1 to j do
-      if (abs_float kinetic_x.{i,j} > cutoff) then
+      if (abs_float (kinetic%:(i,j)) > cutoff) then
-        Printf.fprintf oc "%4d %4d %20.12e\n" i j kinetic_x.{i,j}
+        Printf.fprintf oc "%4d %4d %20.12e\n" i j (kinetic%:(i,j))
     done;
   done;
   close_out oc

gaussian_integrals/lib/orthonormalization.ml

@@ -50,7 +50,6 @@ let make_lowdin ~thresh ~overlap =
   let u_vec, u_val =
     Matrix.diagonalize_symm overlap
   in
-  let u_vec_x = Matrix.to_bigarray_inplace u_vec in
 
   Vector.iter (fun x -> if x < thresh then
     invalid_arg (__FILE__^": make_lowdin") ) u_val;
@@ -59,7 +58,7 @@ let make_lowdin ~thresh ~overlap =
 
   let u_vec' =
     Matrix.init_cols (Matrix.dim1 u_vec) (Matrix.dim2 u_vec)
-      (fun i j -> u_vec_x.{i,j} *. (Vector.at u_val j))
+      (fun i j -> u_vec%:(i,j) *. (u_val%.(j)) )
   in
   Matrix.gemm_nt u_vec' u_vec
 

gaussian_integrals/lib/overlap.ml

@@ -99,7 +99,6 @@ let of_basis basis =
   in
 
   let result = Matrix.create n n in
-  let result_x = Matrix.to_bigarray_inplace result in
   for j=0 to (Array.length shell) - 1 do
     for i=0 to j do
       (* Compute all the integrals of the class *)
@@ -120,8 +119,8 @@ let of_basis basis =
                 try Zmap.find cls key
                 with Not_found -> 0.
               in
-              result_x.{i_c,j_c} <- value;
+              Matrix.set result i_c j_c value;
-              result_x.{j_c,i_c} <- value;
+              Matrix.set result j_c i_c value;
             ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i))))
         ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j))))
     done;
@@ -146,7 +145,6 @@ let of_basis_pair first_basis second_basis =
   in
 
   let result = Matrix.create n m in
-  let result_x = Matrix.to_bigarray_inplace result in
   for j=0 to (Array.length second) - 1 do
     for i=0 to  (Array.length first) - 1 do
       (* Compute all the integrals of the class *)
@@ -167,7 +165,7 @@ let of_basis_pair first_basis second_basis =
                 try Zmap.find cls key
                 with Not_found -> 0.
               in
-              result_x.{i_c,j_c} <- value;
+              Matrix.set result i_c j_c value;
             ) (Am.zkey_array (Singlet (Cs.ang_mom first.(i))))
         ) (Am.zkey_array (Singlet (Cs.ang_mom second.(j))))
     done;
@@ -184,11 +182,10 @@ let to_file ~filename overlap =
     Matrix.dim1 overlap
   in
 
-  let overlap_x = Matrix.to_bigarray_inplace overlap in
   for j=1 to n  do
     for i=1 to j do
-      if (abs_float overlap_x.{i,j} > cutoff) then
+      if (abs_float (overlap%:(i,j)) > cutoff) then
-        Printf.fprintf oc "%4d %4d %20.12e\n" i j overlap_x.{i,j}
+        Printf.fprintf oc "%4d %4d %20.12e\n" i j (overlap%:(i,j))
     done;
   done;
   close_out oc

gaussian_integrals/lib/two_electron_rr_vectorized.ml

@@ -638,8 +638,8 @@ let contracted_class_shell_pairs ?operator ~zero_m ?schwartz_p ?schwartz_q shell
                         raise NullQuartet;
 
                       let expo_p_inv, expo_q_inv =
-                        (Vector.at expo_p_inv i),
+                        (expo_p_inv%.(i)),
-                        (Vector.at expo_q_inv j)
+                        (expo_q_inv%.(j))
                       in
 
                       let center_pq =

linear_algebra/lib/conventions.ml

@@ -5,18 +5,20 @@
 
 *)
 
+open Vector
+    
 let in_phase vec =
   let s = Vector.sum vec in
   if s = 0. then 
     let rec first_non_zero k =
       if k > Vector.dim vec then
         k-1
-      else if Vector.at vec k = 0. then
+      else if vec%.(k) = 0. then
         first_non_zero (k+1)
       else k
     in
     let k = first_non_zero 1 in
-    Vector.at vec k >= 0.
+    vec%.(k) >= 0.
   else
     s > 0.
 

linear_algebra/lib/matrix.ml

@@ -41,8 +41,6 @@ let add_const_inplace x a =
 let add_const x a =
   Mat.add_const x a
 
-let at t i j = t.{i,j}
-
 external to_bigarray_inplace : ('a,'b) t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t = "%identity"
 
 external of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> ('a,'b) t = "%identity"
@@ -108,6 +106,43 @@ let scale_inplace x t =
 let scale x t = 
   out_of_place (fun t -> scale_inplace x t) t
 
+let of_diag v =
+  Vector.to_bigarray_inplace v
+  |> Mat.of_diag 
+
+let diag t =
+  Mat.copy_diag t
+  |> Vector.of_bigarray_inplace
+       
+let gemv_n_inplace ?m ?n ?(beta=0.) y ?(alpha=1.) ?(ar=1) ?(ac=1) t v =
+  let y = Vector.to_bigarray_inplace y in
+  let v = Vector.to_bigarray_inplace v in
+  ignore @@ gemv ?m ?n ~beta ~trans:`N ~y ~alpha ~ar ~ac t v
+
+let gemv_t_inplace ?m ?n ?(beta=0.) y ?(alpha=1.) ?(ar=1) ?(ac=1) t v =
+  let y = Vector.to_bigarray_inplace y in
+  let v = Vector.to_bigarray_inplace v in
+  ignore @@ gemv ?m ?n ~beta ~trans:`T ~y ~alpha ~ar ~ac t v
+
+let gemv_n ?m ?n ?(beta=0.) ?y ?(alpha=1.) ?(ar=1) ?(ac=1) t v =
+  let v = Vector.to_bigarray_inplace v in
+  let y =
+    match y with
+    | None -> None
+    | Some y -> Some (Vector.to_bigarray_inplace y)
+  in
+  gemv ?m ?n ~beta ?y ~trans:`N ~alpha ~ar ~ac t v
+  |> Vector.of_bigarray_inplace
+
+let gemv_t ?m ?n ?(beta=0.) ?y ?(alpha=1.) ?(ar=1) ?(ac=1) t v =
+  let v = Vector.to_bigarray_inplace v in
+  let y =
+    match y with
+    | None -> None
+    | Some y -> Some (Vector.to_bigarray_inplace y)
+  in
+  gemv ?m ?n ~beta ?y ~trans:`T ~alpha ~ar ~ac t v
+  |> Vector.of_bigarray_inplace
 
 let gemm_inplace ?m ?n ?k ?(beta=0.) ~c ?(transa=`N) ?(alpha=1.0) a ?(transb=`N) b =
   ignore @@ gemm ?m ?n ?k ~beta ~c ~transa ~alpha a ~transb b
@@ -312,3 +347,9 @@ let qr a =
   orgqr ~tau result;
   let q = result in
   q, r
+
+let (%:) t (i,j) = t.{i,j}
+
+let set  t i j v = t.{i,j} <- v
+
+

linear_algebra/lib/matrix.mli

@@ -26,6 +26,12 @@ val init_cols : int -> int -> (int -> int -> float) -> ('a,'b) t
 val identity: int -> ('a,'b) t
 (** Creates an identity matrix. *)
 
+val of_diag: 'a Vector.t -> ('a,'a) t
+(** Creates a diagonal matrix. *)
+
+val diag: ('a,'a) t -> 'a Vector.t 
+(** Returns the diagonal of a matrix. *)
+
 val fill_inplace: ('a,'b) t -> float -> unit
 (** Fills the matrix with the give value. *)
 
@@ -65,9 +71,6 @@ val mul_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
 val div_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
 (** [div_inplace c a b] : performs [c = a/b] element-wise in-place. *)
   
-val at : ('a,'b) t -> int -> int -> float
-(** [at i j] returns the element at i,j. *)
-
 (*
 val to_bigarray : ('a,'b) t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t
 (** Converts the matrix into a Bigarray in Fortran layout *)
@@ -156,6 +159,39 @@ val outer_product_inplace : ('a,'b) t -> ?alpha:float -> 'a Vector.t -> 'b Vecto
 (** Computes M = %{ $\alpha u.v^t$ %} *)
 
 
+val gemv_n_inplace : ?m:int -> ?n:int -> ?beta:float -> 'a Vector.t ->
+  ?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'b Vector.t -> 
+  unit
+(** Performs the Lapack GEMV operation. Default values:
+[beta=0.] [alpha=1.0].
+[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M V$
+The vector Y is updated in-place.
+*)
+
+val gemv_t_inplace : ?m:int -> ?n:int -> ?beta:float -> 'b Vector.t ->
+  ?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'a Vector.t ->
+  unit
+(** Performs the Lapack GEMV operation. Default values:
+[beta=0.] [alpha=1.0].
+[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$
+The vector Y is updated in-place.
+*)
+
+val gemv_n : ?m:int -> ?n:int -> ?beta:float -> ?y:'a Vector.t ->
+  ?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'b Vector.t ->
+  'a Vector.t
+(** Performs the Lapack GEMV operation. Default values:
+[beta=0.] [alpha=1.0].
+[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$ *)
+
+val gemv_t : ?m:int -> ?n:int -> ?beta:float -> ?y:'b Vector.t ->
+  ?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'a Vector.t ->
+  'b Vector.t
+(** Performs the Lapack GEMV operation. Default values:
+[beta=0.] [alpha=1.0].
+[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$
+*)
+
 val gemm_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
   c:('a,'b) t -> ?transa:[`N | `T] -> ?alpha:float ->
     ('c,'d) t -> ?transb:[`N | `T] -> ('e,'f) t -> unit
@@ -265,5 +301,11 @@ val sysv_inplace : b:('a,'b) t -> ('a,'a) t -> unit
 val sysv : b:('a,'b) t -> ('a,'a) t -> ('a,'b) t
 (** Solves %{ $AX=B$ %} when A is symmetric *)
   
+val (%:) : ('a,'b) t -> (int*int) -> float
+(** [t%.(i,j)] returns the element at i,j. *)
+
+val set : ('a,'b) t -> int -> int -> float -> unit
+(** [set t i j v] sets the (i,j)-th element to v *)
+
 val pp : Format.formatter -> ('a,'b) t -> unit
 

linear_algebra/lib/vector.ml

@@ -65,5 +65,6 @@ let normalize v =
   result
 
 
-let at t i = t.{i}
+let (%.) t i = t.{i}
                
+let set t i v = t.{i} <- v

linear_algebra/lib/vector.mli

@@ -76,9 +76,6 @@ val init : int ->  (int -> float) -> 'a t
 val sum  : 'a t -> float
 (** Returns the sum of the elements of the vector *)
   
-val at : 'a t -> int -> float
-(** Returns t.{i} *)
-  
 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.  *)
@@ -134,3 +131,11 @@ val of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.f
 
 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 *)
+
+
+val (%.) : 'a t -> int -> float
+(** [t%.(i)] Returns the i-th element of the vector *)
+
+val set : 'a t -> int -> float -> unit
+(** Modifies the value in-place at the i-th position *)
+  

mo/lib/basis.ml

@@ -0,0 +1,201 @@
+open Linear_algebra
+open Common.Util
+open Common.Constants
+
+(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *)
+
+module HF = HartreeFock
+module Si = Simulation
+
+type mo_type =
+  | RHF | ROHF | UHF | CASSCF | Projected
+  | Natural of string
+  | Localized of string
+
+type t =
+  {
+    simulation      : Simulation.t;      (* Simulation which produced the MOs *)
+    mo_type         : mo_type;           (* Kind of MOs (RHF, CASSCF, Localized...) *)
+    mo_occupation   : t Vector.t;        (* Occupation numbers *)
+    mo_coef         : (Ao.Basis.t,t) Matrix.t;       (* Matrix of the MO coefficients in the AO basis *)
+    eN_ints         : (t,t) Matrix.t lazy_t;         (* Electron-nucleus potential integrals *)
+    ee_ints         : t Four_idx_storage.t lazy_t; (* Electron-electron potential integrals *)
+    kin_ints        : (t,t) Matrix.t lazy_t;      (* Kinetic energy integrals *)
+    one_e_ints      : (t,t) Matrix.t lazy_t;      (* One-electron integrals *)
+    (* TODO 
+    f12_ints        : F12.t lazy_t;      (* F12 integrals *)
+    *)
+  }
+
+
+let size t =
+  Matrix.dim2 t.mo_coef
+
+let simulation    t = t.simulation
+let mo_type       t = t.mo_type
+let ao_basis      t = Si.ao_basis t.simulation
+let mo_occupation t = t.mo_occupation
+let mo_coef       t = t.mo_coef
+let eN_ints       t = Lazy.force t.eN_ints
+let ee_ints       t = Lazy.force t.ee_ints
+let kin_ints      t = Lazy.force t.kin_ints
+let two_e_ints    t = Lazy.force t.ee_ints
+(* TODO
+let f12_ints      t = Lazy.force t.f12_ints
+*)
+let one_e_ints    t = Lazy.force t.one_e_ints
+
+
+let mo_energies t =
+  let m_C = mo_coef t in
+  let f =
+    let m_N = Matrix.of_diag @@ mo_occupation t in
+    let m_P = Matrix.x_o_xt m_N m_C in
+    match t.mo_type with
+    | RHF  -> Fock.make_rhf  ~density:m_P (ao_basis t)
+    | Projected
+    | ROHF -> (Matrix.scal 0.5 m_P;
+               Fock.make_uhf  ~density_same:m_P ~density_other:m_P (ao_basis t))
+    | _ -> failwith "Not implemented"
+  in
+  let m_F0 = Fock.fock f in
+  Matrix.xt_o_x m_F0 m_C
+  |> Matrix.diag
+
+
+let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
+  Matrix.xt_o_x ~x:mo_coef ~o:ao_matrix
+
+
+let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix =
+  let sc = Matrix.gemm ao_overlap mo_coef  in
+  Matrix.x_o_xt ~x:sc ~o:mo_matrix
+
+
+let make ~simulation ~mo_type ~mo_occupation ~mo_coef ()  =
+  let ao_basis =
+    Si.ao_basis simulation
+  in
+  let eN_ints = lazy (
+    Ao.Basis.eN_ints ao_basis
+    |> mo_matrix_of_ao_matrix ~mo_coef
+  )
+  and kin_ints = lazy (
+    Ao.Basis.kin_ints ao_basis
+    |> mo_matrix_of_ao_matrix ~mo_coef
+  )
+  and ee_ints = lazy (
+    Ao.Basis.ee_ints ao_basis
+    |> Eri.four_index_transform mo_coef
+  )
+(*
+  and f12_ints = lazy (
+    Ao.Basis.f12_ints ao_basis
+    |> F12.four_index_transform mo_coef
+  )
+*)
+  in
+  let one_e_ints = lazy (
+    Matrix.add (Lazy.force eN_ints) (Lazy.force kin_ints) )
+  in
+  { simulation ; mo_type ; mo_occupation ; mo_coef ;
+    eN_ints ; ee_ints ; kin_ints ; one_e_ints ;
+  }
+
+
+let values t point =
+  let c = mo_coef t in
+  let a = Ao.Basis.values (Simulation.ao_basis t.simulation) point in
+  Matrix.gemv ~trans:`T c a
+
+let of_hartree_fock hf =
+  let mo_coef       = HF.eigenvectors hf in
+  let simulation    = HF.simulation   hf in
+  let mo_occupation = HF.occupation   hf in
+  let mo_type =
+    match HF.kind hf with
+    | HartreeFock.RHF  -> RHF
+    | HartreeFock.ROHF -> ROHF
+    | HartreeFock.UHF  -> UHF
+  in
+  make ~simulation ~mo_type ~mo_occupation ~mo_coef ()
+
+
+let of_mo_basis simulation other =
+
+  let mo_coef =
+    let basis = Simulation.ao_basis simulation in
+    let basis_other = ao_basis other in
+    let m_S =
+      Overlap.(matrix @@ of_basis_pair
+        (AOBasis.basis basis)
+        (AOBasis.basis basis_other) )
+    in
+    let m_X = AOBasis.ortho basis in
+    (* Project other vectors in the current basis *)
+    let m_C =
+      gemm m_S @@ mo_coef other
+    in
+    (* Append dummy vectors to the input vectors *)
+    let result =
+      let vecs = Mat.to_col_vecs m_X in
+      Array.iteri (fun i v -> if (i < Array.length vecs) then vecs.(i) <- v)
+	(Mat.to_col_vecs m_C) ;
+      Mat.of_col_vecs vecs
+    in
+    (* Gram-Schmidt Orthonormalization *)
+    gemm m_X @@ (Util.qr_ortho @@ gemm ~transa:`T m_X result)
+    |> Util.remove_epsilons
+    |> Conventions.rephase
+  in
+
+  let mo_occupation =
+    let occ = mo_occupation other in
+    Vec.init (Mat.dim2 mo_coef) (fun i ->
+      if (i <= Vec.dim occ) then occ.{i}
+      else 0.)
+  in
+  make ~simulation ~mo_type:Projected ~mo_occupation ~mo_coef ()
+
+
+
+
+
+let pp ?(start=1) ?(finish=0) ppf t =
+    let open Lacaml.Io in
+    let rows = Mat.dim1 t.mo_coef
+    and cols = Mat.dim2 t.mo_coef
+    in
+    let finish =
+      match finish with
+      | 0 -> cols
+      | x -> x
+    in
+
+    let rec aux first =
+
+      if (first > finish) then ()
+      else
+        begin
+          Format.fprintf ppf "@[<v>@[<v4>@[<h>%s@;" "Eigenvalues:";
+
+          Array.iteri (fun i x ->
+              if (i+1 >= first) && (i+1 <= first+4 ) then
+                Format.fprintf ppf "%12f@ " x)
+            (Vec.to_array @@ mo_energies t);
+
+          Format.fprintf ppf "@]@;";
+          Format.fprintf ppf "@[%a@]"
+            (Lacaml.Io.pp_lfmat
+              ~row_labels:
+                (Array.init rows (fun i -> Printf.sprintf "%d  " (i + 1)))
+              ~col_labels:
+                (Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) ))
+              ~print_right:false
+              ~print_foot:false
+              () ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) (t.mo_coef)) ;
+          Format.fprintf ppf "@]@;@;@]";
+          (aux [@tailcall]) (first+5)
+        end
+    in
+    aux start

mo/lib/basis.mli

@@ -0,0 +1,97 @@
+(** Data structure to represent the molecular orbitals.
+
+    The MO indices start from 1.
+    
+*)
+
+open Linear_algebra
+open Common
+       
+type mo_type =
+  | RHF | ROHF | UHF | CASSCF | Projected
+  | Natural of string
+  | Localized of string
+      
+type t
+
+(** {1 Accessors} *)
+
+val simulation : t -> Simulation.t
+(** Simulation which produced the MOs *)
+
+val mo_type : t -> mo_type
+(** Kind of MOs (RHF, CASSCF, Localized...) *)
+
+val ao_basis : t -> Ao.Basis.t
+(** Matrix of the MO coefficients in the AO basis *)
+
+val mo_occupation : t -> t Vector.t
+(** Occupation numbers *)
+
+val mo_coef : t -> (Ao.Basis.t, t) Matrix.t
+(** Molecular orbitcal coefficients *)
+
+val eN_ints : t -> (t,t) Matrix.t
+(** Electron-nucleus potential integrals *)
+
+val ee_ints : t -> t Four_idx_storage.t
+(** Electron-electron repulsion integrals *)
+
+val kin_ints : t -> (t,t) Matrix.t
+(** Kinetic energy integrals *)
+
+val one_e_ints : t -> (t,t) Matrix.t
+(** One-electron integrals {% $\hat{T} + V$ %} *)
+
+val two_e_ints : t -> t Four_idx_storage.t
+(** Electron-electron repulsion integrals *)
+
+(* TODO
+val f12_ints : t -> F12.t
+(** F12 integrals *)
+*)
+
+val size : t -> int
+(** Number of molecular orbitals in the basis *)
+
+val mo_energies : t -> t Vector.t
+(** Fock MO energies *)
+
+val values : t -> Coordinate.t -> t Vector.t
+(** Values of the MOs evaluated at a given coordinate. *)
+
+(** {1 Creators} *)
+
+val make : simulation:Simulation.t ->
+  mo_type:mo_type ->
+  mo_occupation:t Vector.t ->
+  mo_coef:(Ao.Basis.t,t) Matrix.t ->
+  unit -> t
+(** Function to build a data structure representing the molecular orbitals. *)
+
+val of_hartree_fock : HartreeFock.t -> t
+(** Build MOs from a Restricted Hartree-Fock calculation. *)
+
+val of_mo_basis : Simulation.t -> t -> t
+(** Project the MOs of the other basis on the current one. *)
+
+
+val mo_matrix_of_ao_matrix :
+  mo_coef:(Ao.Basis.t,t) Matrix.t ->
+  (Ao.Basis.t,Ao.Basis.t) Matrix.t ->
+  (t,t) Matrix.t
+(** Build a matrix in MO basis from a matrix in AO basis. *)
+
+val ao_matrix_of_mo_matrix :
+  mo_coef:(Ao.Basis.t,t) Matrix.t ->
+  ao_overlap:(Ao.Basis.t,Ao.Basis.t) Matrix.t ->
+  (t,t) Matrix.t ->
+  (Ao.Basis.t,Ao.Basis.t) Matrix.t
+(** Build a matrix in AO basis from a matrix in MO basis. *)
+
+(** {1 Printers} *)
+
+val pp : ?start:int -> ?finish:int -> Format.formatter -> t -> unit
+        
+ 
+

mo/lib/class.ml

@@ -0,0 +1,141 @@
+open Particles
+    
+type mo_class =                                                                              
+  | Core       of int  (* Always doubly occupied *)
+  | Inactive   of int  (* With 0,1 or 2 holes *)
+  | Active     of int  (* With 0,1 or 2 holes or particles *)
+  | Virtual    of int  (* With 0,1 or 2 particles *)
+  | Deleted    of int  (* Always unoccupied *)
+  | Auxiliary  of int  (* Auxiliary basis function *)
+
+type t = mo_class list
+
+
+let pp_mo_class ppf = function
+  | Core      i -> Format.fprintf ppf "@[Core %d@]" i
+  | Inactive  i -> Format.fprintf ppf "@[Inactive %d@]" i
+  | Active    i -> Format.fprintf ppf "@[Active %d@]" i
+  | Virtual   i -> Format.fprintf ppf "@[Virtual %d@]" i
+  | Deleted   i -> Format.fprintf ppf "@[Deleted %d@]" i
+  | Auxiliary i -> Format.fprintf ppf "@[Auxiliary %d@]" i
+
+let pp ppf t =
+  Format.fprintf ppf "@[[@,";
+  let rec aux = function
+  | [] -> Format.fprintf ppf "]@]"
+  | x :: [] -> Format.fprintf ppf "%a@,]@]" pp_mo_class x
+  | x :: rest -> ( Format.fprintf ppf "%a@,;@," pp_mo_class x; aux rest )
+  in
+  aux t
+
+
+let of_list t = t
+
+let to_list t = t
+
+
+let core_mos t =
+  List.filter_map (fun x ->
+      match x with 
+      | Core i -> Some i
+      | _ -> None) t
+
+
+let inactive_mos t =
+  List.filter_map (fun x ->
+      match x with 
+      | Inactive i -> Some i
+      | _ -> None ) t
+
+
+let active_mos t =
+  List.filter_map (fun x ->
+      match x with 
+      | Active i -> Some i
+      | _ -> None ) t
+
+
+let virtual_mos t =
+  List.filter_map (fun x ->
+      match x with 
+      | Virtual i -> Some i
+      | _ -> None ) t
+
+
+let deleted_mos t =
+  List.filter_map (fun x ->
+      match x with                                                                           
+      | Deleted i -> Some i
+      | _ -> None ) t
+
+
+
+let auxiliary_mos t =
+  List.filter_map (fun x ->
+      match x with                                                                           
+      | Auxiliary i -> Some i
+      | _ -> None ) t
+
+
+let mo_class_array t =
+  let sze = List.length t + 1 in
+  let result = Array.make sze (Deleted 0) in
+  List.iter (fun c ->
+      match c with
+      |  Core      i  ->  result.(i)  <-  Core      i
+      |  Inactive  i  ->  result.(i)  <-  Inactive  i
+      |  Active    i  ->  result.(i)  <-  Active    i
+      |  Virtual   i  ->  result.(i)  <-  Virtual   i
+      |  Deleted   i  ->  result.(i)  <-  Deleted   i
+      |  Auxiliary i  ->  result.(i)  <-  Auxiliary i
+    ) t;
+  result
+
+
+let fci ~frozen_core mo_basis =
+  let mo_num = Basis.size mo_basis in
+  let ncore  = (Nuclei.small_core @@ Simulation.nuclei @@ Basis.simulation mo_basis) / 2 in
+  of_list (
+    if frozen_core then
+      List.concat [
+        Util.list_range 1 ncore
+        |> List.map (fun i -> Core i) ;
+        Util.list_range (ncore+1) mo_num
+        |> List.map (fun i -> Active i) 
+      ]
+    else
+      Util.list_range 1 mo_num
+      |> List.map (fun i -> Active i)
+  )
+
+let cas_sd mo_basis ~frozen_core n m =
+  let mo_num = Basis.size mo_basis in
+  let n_alfa = Basis.simulation mo_basis |> Simulation.electrons |> Electrons.n_alfa in
+  let n_beta = Basis.simulation mo_basis |> Simulation.electrons |> Electrons.n_beta in
+  let n_unpaired = n_alfa - n_beta in
+  let n_alfa_in_cas = (n - n_unpaired)/2 + n_unpaired in
+  let last_inactive = n_alfa - n_alfa_in_cas in
+  let last_active  = last_inactive + m in
+  let ncore  =
+    if frozen_core then
+      (Nuclei.small_core @@ Simulation.nuclei @@ Basis.simulation mo_basis) / 2
+      |> min last_inactive
+    else 0
+  in
+  of_list (
+    List.concat [
+        if ncore > 0 then
+          Util.list_range 1 ncore
+          |> List.map (fun i -> Core i) 
+        else
+          [] ;
+        Util.list_range (ncore+1) last_inactive
+        |> List.map (fun i -> Inactive i) ;
+        Util.list_range (last_inactive+1) last_active
+        |> List.map (fun i -> Active i) ;
+        Util.list_range (last_active+1) mo_num
+        |> List.map (fun i -> Virtual i) 
+      ]
+  )
+
+

mo/lib/class.mli

@@ -0,0 +1,58 @@
+(** Classes of MOs : active, inactive, etc *)
+
+type mo_class =
+  | Core      of int  (* Always doubly occupied *)
+  | Inactive  of int  (* With 0,1 or 2 holes *)
+  | Active    of int  (* With 0,1 or 2 holes or particles *)
+  | Virtual   of int  (* With 0,1 or 2 particles *)
+  | Deleted   of int  (* Always unoccupied *)
+  | Auxiliary of int  (* Function of the auxiliary basis set *)
+
+type t
+
+(** Creation *)
+val of_list : mo_class list -> t
+
+val to_list : t -> mo_class list
+
+val fci : frozen_core:bool -> Basis.t -> t
+(** Creates the MO classes for FCI calculations : all [Active]. The 
+    [n] lowest MOs are [Core] if [frozen_core = true].
+*)
+
+val cas_sd: Basis.t -> frozen_core:bool -> int -> int -> t
+(** [cas_sd mo_basis n m ] creates the MO classes for CAS(n,m) + SD
+    calculations.  lowest MOs are [Core], then all the next MOs are [Inactive],
+    then [Active], then [Virtual].
+*)
+
+
+val core_mos : t -> int list
+(** Returns a list containing the indices of the core MOs. *)
+
+val active_mos : t -> int list
+(** Returns a list containing the indices of the active MOs. *)
+
+val virtual_mos : t -> int list
+(** Returns a list containing the indices of the virtual MOs. *)
+
+val inactive_mos : t -> int list
+(** Returns a list containing the indices of the inactive MOs. *)
+
+val deleted_mos : t -> int list
+(** Returns a list containing the indices of the deleted MOs. *)
+
+val auxiliary_mos : t -> int list
+(** Returns a list containing the indices of the auxiliary MOs. *)
+
+val mo_class_array : t -> mo_class array
+(** Returns an array [a] such that [a.(i)] returns the class of MO [i].
+    As the MO indices start from [1], the array has an extra zero entry
+    that should be ignored. *)
+
+(** {2 Printers} *)
+
+val pp_mo_class : Format.formatter -> mo_class -> unit
+
+val pp : Format.formatter -> t -> unit
+

mo/lib/dune

@@ -0,0 +1,9 @@
+; name = name of the supermodule that will wrap all source files as submodules
+; public_name = name of the library for ocamlfind and opam
+(library
+ (name mo)
+ (public_name qcaml.mo)
+ (libraries
+	qcaml.simulation
+ )
+ (synopsis "Molecular orbitals."))

simulation/lib/dune

@@ -0,0 +1,14 @@
+; name = name of the supermodule that will wrap all source files as submodules
+; public_name = name of the library for ocamlfind and opam
+(library
+ (name simulation)
+ (public_name qcaml.simulation)
+ (libraries
+        qcaml.common
+        qcaml.particles
+        qcaml.gaussian_basis
+        qcaml.gaussian_integrals
+	qcaml.operators
+	qcaml.ao
+ )
+ (synopsis "Contains data describing a simulation (AOs, operators, nuclear coordinate,...)"))