Added Cholesky

Utils/Cholesky.ml

@@ -0,0 +1,89 @@
+open Lacaml.D
+
+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 compute_d j =
+    let l_jk = 
+      Mat.copy_row m_L j
+    in
+    let l_jk__d_k = 
+      Vec.mul ~n:(j-1) l_jk v_D
+    in
+    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
+    in
+    1. /. v_D.{j} *. ( m_A.{i,j} -. dot l_jk__d_k l_ik )
+  in
+
+  v_D.{1} <- m_A.{1,1};
+  for i=2 to n do
+    for j=1 to (i-1) do
+      m_L.{i,j} <- compute_l i j
+    done;
+    v_D.{i} <- compute_d i
+  done;
+  m_L, v_D
+
+
+let make_ldl ?target_rank m_A =
+  full_ldl m_A
+
+
+
+let test_case () =
+
+  let matrix_diff m_A m_B = 
+    Mat.syrk_trace (Mat.sub m_A m_B) 
+  in
+
+  let vector_diff v_A v_B = 
+    let v = Vec.sub v_A v_B in
+    dot v v
+  in
+
+  let test_full () =
+    let m_A =
+      Mat.of_array [| [|   4. ;  12. ; -16. |] ;
+                      [|  12. ;  37. ; -43. |] ;
+                      [| -16. ; -43. ;  98. |] |]
+    in
+
+    let m_L_ref = 
+      Mat.of_array [| [|   1. ;   0. ;   0. |] ;
+                      [|   3. ;   1. ;   0. |] ;
+                      [|  -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
+
+    Alcotest.(check (float 1.e-15)) "full L" 0. (matrix_diff m_L m_L_ref);
+    Alcotest.(check (float 1.e-15)) "full D" 0. (vector_diff v_D v_D_ref)
+  in
+  [
+    "Full", `Quick, test_full;
+  ]
+