Optimized ERIs

Basis/Basis.ml

@@ -1,4 +1,4 @@
-type t
+type t = Contracted_shell.t array
 
 (** Returns an array of the basis set per atom *)
 let of_nuclei_and_general_basis n b =
@@ -12,6 +12,8 @@ let of_nuclei_and_general_basis n b =
       in
       Contracted_shell.create ~expo ~coef ~totAngMom ~center)
   ) n
+  |> Array.to_list
+  |> Array.concat
 
 
 let to_string b =
@@ -27,14 +29,12 @@ Angular     Coordinates (Bohr)           Exponents       Coefficients
 Momentum  X         Y          Z
 -----------------------------------------------------------------------
 "
-  ^( Array.mapi (fun atom_id basis ->
+  ^
-      Array.map (fun i -> 
+    ( Array.map (fun i -> 
-          Contracted_shell.to_string i) basis
+          Contracted_shell.to_string i) b
       |> Array.to_list
       |> String.concat line
-    ) b
+    )
-    |> Array.to_list
-    |> String.concat line)
     ^ line
 
 

Basis/Basis.mli

@@ -0,0 +1,3 @@
+type t = Contracted_shell.t array
+val of_nuclei_and_general_basis : Nuclei.t -> General_basis.t list -> t
+val to_string : t -> string

Basis/ERI.ml

@@ -1,11 +1,15 @@
+(** Electron-electron repulsion integrals *)
+
 open Util
 
 (** (00|00)^m : Fundamental electron repulsion integral
-  $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
+    $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
 
-  maxm        : Maximum total angular momentum
+    maxm        : Maximum total angular momentum
-  expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of $\phi_p$ and $\phi_q$
+    expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of
-  norm_pq_sq  : square of the distance between the centers of $\phi_p$ and $\phi_q$
+                $\phi_p$ and $\phi_q$
+    norm_pq_sq  : square of the distance between the centers of $\phi_p$
+                and $\phi_q$
 *)
 let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
   let exp_pq =
@@ -21,7 +25,179 @@ let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
     )
 
 
-(** Electron-electron repulsion integral *)
+(** Compute all the integrals of a contracted class *)
-let contracted_class shell_a shell_b shell_c shell_d : float Zmap.t =
+let contracted_class  shell_a shell_b shell_c shell_d : float Zmap.t =
   TwoElectronRR.contracted_class ~zero_m shell_a shell_b shell_c shell_d 
 
+
+type n_cls = { n : int ; cls : Z.t array }
+(** Write all integrals to a file *)
+let to_file ~filename basis =
+  let oc = open_out filename in
+  let key_array =  Array.make 12 0 in
+  let zkey = Array.map (fun b -> 
+      let result =
+        Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
+      in
+      { n=Array.length result ;  cls=result }
+    ) basis
+  in 
+  let i_shift = ref 1 in
+  let j_shift = ref 1 in
+  let k_shift = ref 1 in
+  let l_shift = ref 1 in
+  for i=0 to (Array.length basis) - 1 do
+    print_int !i_shift ; print_newline ();
+    j_shift := 1;
+    for j=0 to i do
+      k_shift := 1;
+      for k=0 to i do
+        l_shift := 1;
+        for l=0 to k do
+          let cls =
+            contracted_class basis.(i) basis.(j) basis.(k) basis.(l)
+          in
+
+          for i_c = 0 to zkey.(i).n - 1 do
+            let x = Zkey.(to_int_array Kind_3 zkey.(i).cls.(i_c)) in
+            key_array.(0) <- x.(0);
+            key_array.(1) <- x.(1);
+            key_array.(2) <- x.(2);
+            for j_c = 0 to zkey.(j).n - 1 do
+              let x = Zkey.(to_int_array Kind_3 zkey.(j).cls.(j_c)) in
+              key_array.(3) <- x.(0);
+              key_array.(4) <- x.(1);
+              key_array.(5) <- x.(2);
+              for k_c = 0 to zkey.(k).n - 1 do
+                let x = Zkey.(to_int_array Kind_3 zkey.(k).cls.(k_c)) in
+                key_array.(6) <- x.(0);
+                key_array.(7) <- x.(1);
+                key_array.(8) <- x.(2);
+                for l_c = 0 to zkey.(l).n - 1 do
+                  let x = Zkey.(to_int_array Kind_3 zkey.(l).cls.(l_c)) in
+                  key_array.( 9) <- x.(0);
+                  key_array.(10) <- x.(1);
+                  key_array.(11) <- x.(2);
+                  let key = 
+                    Zkey.(of_int_array Kind_12  key_array)
+                  in
+                  let value = 
+                    Zmap.find cls key 
+                  in
+                  if (abs_float value > cutoff) then
+                    Printf.fprintf oc "%4d %4d %4d %4d %20.12e\n"
+                      (!i_shift+i_c) (!j_shift+j_c) (!k_shift+k_c) (!l_shift+l_c) 
+                      value
+                done
+              done
+            done
+          done;
+          l_shift := !l_shift + zkey.(l).n
+        done;
+        k_shift := !k_shift + zkey.(k).n
+      done;
+      j_shift := !j_shift + zkey.(j).n
+    done;
+    i_shift := !i_shift + zkey.(i).n
+  done
+  ;
+  close_out oc
+
+
+(*
+let to_file ~filename basis =
+  let oc = open_out filename in
+  let zkey = Array.map (fun b -> 
+      let result =
+        Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
+      in
+      { n=Array.length result ;  cls=result }
+    ) basis
+  in 
+
+  let key_array =  Array.make 12 0 in
+  let result = ref [] in
+
+  let i_shift = ref 1 in
+  for i=0 to (Array.length basis) - 1 do
+    print_int !i_shift ; print_newline ();
+    let j_shift = ref 1 in
+    for j=0 to i do
+      let k_shift = ref 1 in
+      for k=0 to i do
+        let l_shift = ref 1 in
+        for l=0 to k do
+          let cls =
+            contracted_class basis.(i) basis.(j) basis.(k) basis.(l)
+          in
+
+          for i_c = 0 to zkey.(i).n - 1 do
+            let x = Zkey.(to_int_array Kind_3 zkey.(i).cls.(i_c)) in
+            key_array.(0) <- x.(0);
+            key_array.(1) <- x.(1);
+            key_array.(2) <- x.(2);
+            for j_c = 0 to zkey.(j).n - 1 do
+              let x = Zkey.(to_int_array Kind_3 zkey.(j).cls.(j_c)) in
+              key_array.(3) <- x.(0);
+              key_array.(4) <- x.(1);
+              key_array.(5) <- x.(2);
+              for k_c = 0 to zkey.(k).n - 1 do
+                let x = Zkey.(to_int_array Kind_3 zkey.(k).cls.(k_c)) in
+                key_array.(6) <- x.(0);
+                key_array.(7) <- x.(1);
+                key_array.(8) <- x.(2);
+                for l_c = 0 to zkey.(l).n - 1 do
+                  let x = Zkey.(to_int_array Kind_3 zkey.(l).cls.(l_c)) in
+                  key_array.( 9) <- x.(0);
+                  key_array.(10) <- x.(1);
+                  key_array.(11) <- x.(2);
+                  let key = 
+                    Zkey.(of_int_array Kind_12  key_array)
+                  in
+                  let value = 
+                    Zmap.find cls key 
+                  in
+                  if (abs_float value > cutoff) then
+                    let key =
+                      Zkey.of_int_array Zkey.Kind_4 [|
+                          (!i_shift+i_c);(!j_shift+j_c);(!k_shift+k_c);(!l_shift+l_c) 
+                        |] 
+                    in
+                    result := (key, value) :: !result
+                done
+              done
+            done
+          done;
+          l_shift := !l_shift + zkey.(l).n
+        done;
+        k_shift := !k_shift + zkey.(k).n
+      done;
+      j_shift := !j_shift + zkey.(j).n
+    done;
+    i_shift := !i_shift + zkey.(i).n
+  done
+  ;
+
+  let result = Array.of_list !result in
+  let result = Zmap.create (Array.length result) in
+
+  for i=0 to !i_shift - 2 do
+    for j=0 to !i_shift - 2 do
+      for k=0 to !i_shift - 2 do
+        for l=0 to !i_shift - 2 do
+          let key =
+            Zkey.of_int_array Zkey.Kind_4 [| i;j;k;l |]
+          in
+          try
+            let value = 
+              Zmap.find result key 
+            in
+            Printf.fprintf oc "%4d %4d %4d %4d %20.12e\n"
+                      i j k l value
+          with Not_found -> ()
+        done
+      done
+    done
+  done;
+  close_out oc
+*)

Basis/Gamess_parser.mly

@@ -26,7 +26,7 @@ basis:
   | element shell_array EOF { ($1, $2) }
 
 element:
-  | ELEMENT { $1 }
+  | ELEMENT { Element.of_string $1 }
 
 shell_array:
   | shell_list { Array.of_list @@ List.rev $1 }

Basis/Gamess_reader.ml

@@ -7,12 +7,9 @@ let read ~filename =
   in
   let rec aux accu = 
     try
-      let element, basis =
+      let key, basis =
         Gamess_parser.input Basis_lexer.read_all lexbuf
       in
-      let key =
-        Element.of_string element
-      in
       aux ((key, basis)::accu)
     with
     | Parsing.Parse_error -> List.rev accu

Basis/General_basis.ml

@@ -4,11 +4,9 @@ type primitive = {
     coefficient: float
     }
 
-type element_name = string
-
 type general_contracted_shell = Angular_momentum.t * (primitive array)
 
-type t = element_name * (general_contracted_shell array)
+type t = Element.t * (general_contracted_shell array)
 
 
 let string_of_primitive ?id prim =

Basis/TwoElectronRR.ml

@@ -257,4 +257,3 @@ let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
 
 
 
-

Makefile

@@ -4,6 +4,7 @@ INCLUDE_DIRS=Nuclei,Utils,Basis
 LIBS=
 PKGS=
 OCAMLCFLAGS="-g"
+OCAMLCFLAGS="-unsafe -noassert -safe-string"
 OCAMLBUILD=ocamlbuild -j 0 -cflags $(OCAMLCFLAGS) -lflags $(OCAMLCFLAGS) -Is $(INCLUDE_DIRS)
 MLLFILES=$(wildcard */*.mll) $(wildcard *.mll) 
 MLYFILES=$(wildcard */*.mly) $(wildcard *.mly) 

Nuclei/Nuclei.ml

@@ -1,4 +1,4 @@
-type coordinates = ( (Element.t * Coordinate.t) array)
+type t = (Element.t * Coordinate.t) array
 
 let of_xyz_file ~filename =
   let lexbuf =

Utils/Angular_momentum.ml

@@ -53,10 +53,18 @@ let of_int = function
 
 
 type kind =
+| Kind_1 of  t
 | Kind_2 of (t*t)
 | Kind_4 of (t*t*t*t)
 
 
+let n_functions a =
+  let a = 
+    to_int a
+  in
+  (a*a + 3*a + 2)/2
+
+
 (** Returns an array of Zkeys corresponding to all possible angular momenta *)
 let zkey_array a = 
   let keys_1d l =
@@ -84,6 +92,14 @@ let zkey_array a =
 
   begin
     match a with
+    | Kind_1 l1 -> 
+
+      let a = Array.init 3 (fun _ -> 0) in
+      List.map (fun (cx,cy,cz) ->
+          a.(0) <- cx ; a.(1) <- cy ; a.(2) <- cz ;
+          Zkey.(of_int_array Kind_3 a)
+        ) (keys_1d @@ to_int l1)
+
     | Kind_2 (l1, l2) -> 
 
       let a = Array.init 6 (fun _ -> 0) in
@@ -94,6 +110,7 @@ let zkey_array a =
               Zkey.(of_int_array Kind_6 a)
             ) (keys_1d @@ to_int l1)
         ) (keys_1d @@ to_int l2)
+        |> List.concat
 
     | Kind_4 (l1, l2, l3, l4) ->
 
@@ -113,7 +130,7 @@ let zkey_array a =
             ) (keys_1d @@ to_int l2)
           |> List.concat
         ) (keys_1d @@ to_int l1)
+        |> List.concat
   end
-  |> List.concat
   |> Array.of_list
 

Utils/Angular_momentum.mli

@@ -5,5 +5,6 @@ val to_string : t -> string
 val to_char : t -> char
 val to_int : t -> int
 val of_int : int -> t
-type kind = Kind_2 of (t * t) | Kind_4 of (t * t * t * t)
+type kind = Kind_1 of t |  Kind_2 of (t * t) | Kind_4 of (t * t * t * t)
+val n_functions : t -> int
 val zkey_array : kind -> Z.t array

Utils/Util.ml

@@ -1,4 +1,4 @@
-let cutoff = 1.e-20
+let cutoff = 1.e-50
 
 (** Constants *)
 let pi = acos (-1.)

run_integrals.ml

@@ -1,44 +1,58 @@
 let basis_file : string option ref = ref None
 let coord_file : string option ref = ref None
+let out_file   : string option ref = ref None
 
 
 let speclist = [
-( "-b" , Arg.String (fun x -> basis_file := Some x) ,
+  ( "-b" , Arg.String (fun x -> basis_file := Some x) ,
-  "File containing the atomic basis set.") ;
+    "File containing the atomic basis set") ;
-( "-c" , Arg.String (fun x -> coord_file := Some x) ,
+  ( "-c" , Arg.String (fun x -> coord_file := Some x) ,
-  "File containing the nuclear coordinates.") ;
+    "File containing the nuclear coordinates") ;
+  ( "-o" , Arg.String (fun x -> out_file := Some x) ,
+    "Output file") ;
 ]
 
-let run ~coord ~basis =
+let run ~coord ~basis ~out =
   let coord_file = 
     match coord with 
-    | None -> raise (Invalid_argument "Coordinate file should be specified")
+    | None -> raise (Invalid_argument "Coordinate file should be specified with -c")
     | Some x -> x
   and basis_file = 
     match basis with 
-    | None -> raise (Invalid_argument "Basis set file should be specified")
+    | None -> raise (Invalid_argument "Basis set file should be specified with -b")
+    | Some x -> x
+  and out_file = 
+    match out with 
+    | None -> raise (Invalid_argument "Output file should be specified with -o")
     | Some x -> x
   in
+
   let nuclei = 
     Nuclei.of_xyz_file ~filename:coord_file
-  and general_basis =
-    Gamess_reader.read ~filename:basis_file
   in
   print_endline @@ Nuclei.to_string nuclei;
 
   let basis =
+    let general_basis =
+      Gamess_reader.read ~filename:basis_file
+    in
     Basis.of_nuclei_and_general_basis nuclei general_basis
   in
-  Basis.to_string basis
+  print_endline @@ Basis.to_string basis;
-  |> print_endline 
+
+  ERI.to_file ~filename:out_file basis
+
 
 
 let () =
   let usage_msg = "Available options:" in
   Arg.parse speclist (fun _ -> ()) usage_msg;
   try
-    run ~coord:!coord_file ~basis:!basis_file 
+    run ~coord:!coord_file ~basis:!basis_file ~out:!out_file
   with
   | Invalid_argument e ->
-    (print_string "Error: " ; print_endline e; print_newline () ; Arg.usage speclist usage_msg)
+    begin
-  ;
+      print_string "Error: " ; print_endline e; print_newline ();
+      Arg.usage speclist usage_msg
+    end
+