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Accelerated HRR and VRR
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@ -21,12 +21,13 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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in
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(** Vertical recurrence relations *)
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let rec vrr m angMom_a angMom_c totAngMom_a totAngMom_c =
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> zero_m_array.(m)
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| (_,0) ->
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let rec vrr0 m angMom_a = function
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| 0 -> zero_m_array.(m)
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| 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
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in expo_inv_p *.( (Coordinate.coord center_pq i) *. zero_m_array.(m+1)
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-. expo_b *. (Coordinate.coord center_ab i) *. zero_m_array.(m) )
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| totAngMom_a ->
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let key = Zkey.of_int_tuple (Zkey.Three
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(angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
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in
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@ -37,7 +38,6 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and xyz =
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match angMom_a with
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| [|0;0;_|] -> 2
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| [|0;_;_|] -> 1
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| _ -> 0
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@ -46,19 +46,25 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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amm.(xyz) <- amm.(xyz) - 2;
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if am.(xyz) < 0 then 0. else
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chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
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(fun () -> vrr m am angMom_c (totAngMom_a-1) totAngMom_c )
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(fun () -> vrr0 m am (totAngMom_a-1) )
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+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
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(fun () -> vrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c )
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(fun () -> vrr0 (m+1) am (totAngMom_a-1) )
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+. (if amm.(xyz) < 0 then 0. else
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chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
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(fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c
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(fun () -> vrr0 m amm (totAngMom_a-2)
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+. chop expo_inv_p (fun () ->
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vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) )
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vrr0 (m+1) amm (totAngMom_a-2) ) ) )
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)
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in
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if not found then
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Zmap.add map.(m) key result;
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result
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and vrr m angMom_a angMom_c totAngMom_a totAngMom_c =
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> zero_m_array.(m)
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| (_,0) -> vrr0 m angMom_a totAngMom_a
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| (_,_) ->
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let key = Zkey.of_int_tuple (Zkey.Six
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@ -104,27 +110,18 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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(** Horizontal recurrence relations *)
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and hrr m angMom_a angMom_b angMom_c angMom_d
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
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and hrr0 m angMom_a angMom_b angMom_c
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totAngMom_a totAngMom_b totAngMom_c =
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match (totAngMom_b, totAngMom_d) with
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| (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,_) ->
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let key = Zkey.of_int_tuple (Zkey.Twelve
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(( angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1),
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( angMom_b.(0)+1, angMom_b.(1)+1, angMom_b.(2)+1),
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( angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1),
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( angMom_d.(0)+1, angMom_d.(1)+1, angMom_d.(2)+1)) )
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in
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let (found, result) =
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try (true, Zmap.find map.(m) key) with
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| Not_found -> (false,
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begin
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match totAngMom_d with
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| 0 ->
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match totAngMom_b with
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| 0 -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
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| 1 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
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let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
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ap.(xyz) <- ap.(xyz) + 1;
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vrr m ap angMom_c (totAngMom_a+1) totAngMom_c
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+. chop (Coordinate.coord center_ab xyz) (fun () ->
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vrr m angMom_a angMom_c totAngMom_a totAngMom_c)
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| _ ->
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let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
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and xyz =
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@ -136,12 +133,19 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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ap.(xyz) <- ap.(xyz) + 1;
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bm.(xyz) <- bm.(xyz) - 1;
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if (bm.(xyz) < 0) then 0. else
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hrr m ap bm angMom_c angMom_d
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(totAngMom_a+1) (totAngMom_b-1) totAngMom_c totAngMom_d
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hrr0 m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
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+. chop (Coordinate.coord center_ab xyz) (fun () ->
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hrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
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totAngMom_c totAngMom_d )
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| _ ->
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hrr0 m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1)
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totAngMom_c )
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and hrr m angMom_a angMom_b angMom_c angMom_d
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
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match (totAngMom_b, totAngMom_d) with
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| (0,0) ->
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vrr m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,0) -> hrr0 m angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
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and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
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and xyz =
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@ -157,12 +161,6 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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+. chop (Coordinate.coord center_cd xyz) (fun () ->
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hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
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totAngMom_c (totAngMom_d-1) )
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end)
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in
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if not found then
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Zmap.add map.(m) key result;
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result
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in
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hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
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totAngMom_c totAngMom_d
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@ -197,21 +195,21 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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(* Compute all integrals in the shell for each pair of significant shell pairs *)
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for ab=0 to (Array.length shell_p - 1)
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do
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let b = shell_p.(ab).Shell_pair.j in
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for cd=0 to (Array.length shell_q - 1)
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do
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try
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begin
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match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d) with
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| Angular_momentum.(S,S,S,S) ->
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begin
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for ab=0 to (Array.length shell_p - 1) do
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for cd=0 to (Array.length shell_q - 1) do
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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try
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if (abs_float coef_prod) < 1.e-4*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
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in
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@ -226,18 +224,45 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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in
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match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d) with
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| Angular_momentum.(S,S,S,S) -> Array.iteri (fun i key ->
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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let integral =
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zero_m_array.(0)
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in
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contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
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) class_indices
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contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
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with NullQuartet -> ()
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done
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done;
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end
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| _ ->
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begin
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for ab=0 to (Array.length shell_p - 1) do
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let b = shell_p.(ab).Shell_pair.j in
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for cd=0 to (Array.length shell_q - 1) do
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try
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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if (abs_float coef_prod) < 1.e-4*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
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in
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let norm_pq_sq =
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Coordinate.dot center_pq center_pq
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in
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let zero_m_array =
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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in
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let d = shell_q.(cd).Shell_pair.j in
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let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
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(* Compute the integral class from the primitive shell quartet *)
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@ -300,6 +325,9 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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with NullQuartet -> ()
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done
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done;
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end
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end;
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let result =
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Zmap.create (Array.length contracted_class)
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in
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@ -1,6 +1,5 @@
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(** Key for hastables that contain tuples of integers encoded in a Zarith integer *)
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type kind_array =
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| Kind_3
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| Kind_6
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