From b5b60f2ae72a3aec40263ca645c75aaed2636e8d Mon Sep 17 00:00:00 2001
From: Dimitrie David <35610675+dimitriedavid@users.noreply.github.com>
Date: Sat, 7 Mar 2020 15:40:53 +0200
Subject: [PATCH] Updated Cholesky using more vectorization

---
 matlab/lu/Cholesky.m | 53 ++++++++++++++++++++++----------------------
 1 file changed, 26 insertions(+), 27 deletions(-)

diff --git a/matlab/lu/Cholesky.m b/matlab/lu/Cholesky.m
index aececf7..00eb0e1 100644
--- a/matlab/lu/Cholesky.m
+++ b/matlab/lu/Cholesky.m
@@ -2,40 +2,39 @@
 % calculates Cholesky factorization, A = L * L'
 % A must be positive-definite
 function [L U x] = Cholesky (A, b)
-    % get the size of the matrix A
-    [n n] = size(A);
-    % initialize the lower and upper matrix of size N
-    L = zeros(n);
-    U = zeros(n);
-
-    % check if A is positive definite
-    if IsPositiveDefinite(A) == 0 || A ~= A'
+    
+    % Check positive definition and symetry of A
+    if !isequal(A, A') || IsPositiveDefinite(A) == 0
         L = NaN;
         U = NaN;
         x = NaN;
         return;
     endif
-
-    % A is positive definite and A is also symmetric, yay!
-    % calculate the factorization, A = L * L'
-    L(1, 1) = sqrt(A(1, 1));
-    % calculate only the elements situated under and on the main diagonal
-    for i = 1:n
-        for j = 1:i
-            sum_of_line = 0;
-            if i == j
-                sum_of_line = sum(L(i, 1:j - 1) .^ 2);
-                % calculate an element on the main diagonal
-                L(i, i) = sqrt(A(i, i) - sum_of_line);
-            else
-                sum_of_line = sum(L(i, 1: j - 1) .* L(j, 1: j - 1));
-                % calculate the sum of the previous elements on the same line
-                L(i, j) = (A(i, j) - sum_of_line) / L(j, j);
-            endif
-        endfor
+    
+    % Inits
+    n = length(A);
+    L = zeros(n);
+    U = zeros(n);
+    
+    for p = 1:n
+        % Calculate the elements on the main diagonal
+        tmp_sum = L(p, 1:(p - 1)) * L(p, 1:(p - 1))';
+        L(p, p) = sqrt(A(p, p) - tmp_sum);
+        
+        % p == n --> last element that we calculated above; we need
+        % to exit
+        if p == n
+            return;
+        endif
+        
+        % Calculate the elements under the main diagonal
+        % sum(A, 2) - sums matrix A with respect to the lines
+        tmp_sum2 = sum((L(p, 1:(p - 1)) .* L((p + 1):n, 1:(p - 1))), 2);        
+        L((p + 1):n, p) = ( A((p + 1):n, p) - tmp_sum2 ) / L(p, p);
     endfor
-
+    
     U = L';
+    
     % A * x = b; A = L * U; A = L * L'
     % L * (L' * x) = b
     % L' * x = y;