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Working on pivoted Cholesky

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This commit is contained in:
Anthony Scemama 2019-04-12 18:48:23 +02:00
parent 41fde2d11a
commit c517a6d6a5
2 changed files with 105 additions and 35 deletions
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114
Utils/Cholesky.ml
View File

@ -5,12 +5,14 @@ let full_ldl m_A =
let n = Mat.dim1 m_A in
assert (Mat.dim2 m_A = n);
let v_D = Vec.make0 n in
let m_L = Mat.identity n in
let v_D = Vec.make0 n in
let m_Lt = Mat.identity n in
let v_D_inv = Vec.make0 n in
let compute_d j =
let l_jk =
Mat.copy_row m_L j
Mat.col m_Lt j
in
let l_jk__d_k =
Vec.mul ~n:(j-1) l_jk v_D
@ -18,29 +20,99 @@ let full_ldl m_A =
m_A.{j,j} -. dot ~n:(j-1) l_jk l_jk__d_k
in
let compute_l i j =
assert (i > j);
let l_jk__d_k =
Mat.copy_row m_L j
|> Vec.mul ~n:(j-1) v_D
and l_ik =
Mat.copy_row m_L i
let compute_l i =
let l_ik__d_k =
Mat.col m_Lt i
|> Vec.mul ~n:(i-1) v_D
in
1. /. v_D.{j} *. ( m_A.{i,j} -. dot l_jk__d_k l_ik )
fun j ->
assert (i > j);
let l_jk =
Mat.col m_Lt j
in
v_D_inv.{j} *. ( m_A.{j,i} -. dot ~n:(j-1) l_ik__d_k l_jk )
in
v_D.{1} <- m_A.{1,1};
for i=2 to n do
for i=1 to n do
for j=1 to (i-1) do
m_L.{i,j} <- compute_l i j
m_Lt.{j,i} <- compute_l i j;
done;
v_D.{i} <- compute_d i
let d_i = compute_d i in
v_D.{i} <- d_i;
v_D_inv.{i} <- 1. /. d_i;
done;
m_L, v_D
m_Lt, v_D
let make_ldl ?target_rank m_A =
full_ldl m_A
let pivoted_ldl threshold m_A =
let n = Mat.dim1 m_A in
assert (Mat.dim2 m_A = n);
let pi = Array.init (n+1) (fun i -> i) in
let v_D = Vec.init n (fun i -> abs_float m_A.{i,i}) in
let m_Lt = Mat.identity n in
let v_D_inv = Vec.make0 n in
let compute_d j =
let l_jk =
Mat.col m_Lt j
in
let l_jk__d_k =
Vec.mul ~n:(j-1) l_jk v_D
in
m_A.{pi.(j),pi.(j)} -. dot ~n:(j-1) l_jk l_jk__d_k
in
let compute_l i =
let l_ik__d_k =
Mat.col m_Lt i
|> Vec.mul ~n:(i-1) v_D
in
fun j ->
assert (i > j);
let l_jk =
Mat.col m_Lt j
in
v_D_inv.{j} *. ( m_A.{pi.(j),pi.(i)} -. dot ~n:(j-1) l_ik__d_k l_jk )
in
let pivot i =
let rec aux (pos,value) i =
if i > n then
pos
else if m_D.{i} > value then
aux i m_D.{i} (i+1)
else
aux pos value (i+1)
in
let j = aux i m_D.{i} (i+1) in
let p_i, p_j = pi.(i), pi.(j) in
pi.(i) <- pj;
pi.(j) <- pi;
in
for i=1 to n do
pivot i;
for j=1 to (i-1) do
m_Lt.{j,i} <- compute_l i j;
done;
let d_i = compute_d i in
v_D.{i} <- d_i;
v_D_inv.{i} <- 1. /. d_i;
done;
m_Lt, v_D
let make_ldl ?(threshold=Constants.epsilon) m_A =
pivoted_ldl m_A
@ -68,19 +140,17 @@ let test_case () =
[| -4. ; 5. ; 1. |] |]
in
(*
let m_Lt_ref =
Mat.transpose_copy m_L_ref
in
*)
let v_D_ref =
Vec.of_array [| 4. ; 1. ; 9. |]
in
let m_L, v_D = full_ldl m_A in
let m_Lt, v_D = full_ldl m_A in
Alcotest.(check (float 1.e-15)) "full L" 0. (matrix_diff m_L m_L_ref);
Alcotest.(check (float 1.e-15)) "full L" 0. (matrix_diff m_Lt m_Lt_ref);
Alcotest.(check (float 1.e-15)) "full D" 0. (vector_diff v_D v_D_ref)
in
[

26
run_tests.ml
View File

@ -1,5 +1,17 @@
let test_water_dz () =
let () =
Alcotest.run "Unit tests" [
"Util", Util.test_case ();
"Bitstring", Bitstring.test_case ();
"Spindeterminant", Spindeterminant.test_case ();
"Determinant", Determinant.test_case ();
"Excitation", Excitation.test_case ();
"Sparse vectors", Vector.test_case ();
"Sparse matrices", Matrix.test_case ();
"Cholesky", Cholesky.test_case ();
];
let basis_file = "test_files/cc-pvdz"
and nuclei_file = "test_files/h2o.xyz"
@ -12,21 +24,9 @@ let test_water_dz () =
let ao_basis =
Simulation.ao_basis simulation_closed_shell
in
Alcotest.run "Unit tests" [
"Util", Util.test_case ();
"Bitstring", Bitstring.test_case ();
"Spindeterminant", Spindeterminant.test_case ();
"Determinant", Determinant.test_case ();
"Excitation", Excitation.test_case ();
"Sparse vectors", Vector.test_case ();
"Sparse matrices", Matrix.test_case ();
];
Alcotest.run "Water, cc-pVDZ" [
"AO_Basis", AOBasis.test_case ao_basis;
"Guess", Guess.test_case ao_basis;
]
let () =
test_water_dz ()