1 files changed, 87 insertions, 0 deletions
diff --git a/Functions/luFactor/luFactor.m b/Functions/luFactor/luFactor.m
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+++ b/Functions/luFactor/luFactor.m
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+function [L, U, P] = luFactor(A)
+% luFactor(A)
+%	LU decomposition with pivoting
+% inputs:
+%	A = coefficient matrix
+% outputs:
+%	L = lower triangular matrix
+%	U = upper triangular matrix
+%       P = the permutation matrix
+
+
+[m,n] = size(A);
+if m~=n, error('Enter a square matrix.'); end
+nb = n + 1;
+L=zeros(m,m);
+U=zeros(m,m);
+P=eye(m);
+
+%Partial pivoting
+for j = 1:n - 1
+	for p = j+1:m
+		if (abs(A(j,j)) < abs(A(p,j)))
+			A([j p],:) = A([p j],:);
+			P([j p],:) = P([p j],:);
+		end
+	end
+end
+%	[big,i] = max(abs(A(j:n,j)));
+%	ipr = i + j - 1;
+%	if ipr ~= j
+%		A([j,ipr],:) = A([ipr,j],:);
+%	end
+%end
+
+for i=1:m
+	% Computing L
+	for k=1:i-1
+		L(i,k)=A(i,k);
+		for j=1:k-1
+			L(i,k)= L(i,k)-L(i,j)*U(j,k);
+		end
+		L(i,k) = L(i,k)/U(k,k);
+	end
+
+	% Computing U
+	for k=i:m
+		U(i,k) = A(i,k);
+		for j=1:i-1
+			U(i,k)= U(i,k)-L(i,j)*U(j,k);
+		end
+	end
+end
+
+for i=1:m
+	L(i,i)=1;
+end
+
+%% Checks
+if P*A ~= L*U, error('LU factorization failed to be computed correctly.'); end
+
+% Checks output size
+if size(L) ~= size(A) | size(U) ~= size(A) | size(P) ~= size(A)
+	error('Incorrect output size')
+end
+
+% Checks if matrices are triangular
+%for i=1:m
+%	for j=1:n		
+%	error('Incorrect output: LU decomposition are not triangular')
+%end
+
+% Checks the permutation matrix P is valid
+%P_str = string(P)
+%for k = m
+%	num1=count(P(:,1:n),1)
+%	if num1 ~=1
+%		error('Incorrect P matrix output. Too many 1's on the same line')
+%	end
+%	num0=count(P(:,1:n),0)
+%	if num0 ~= n-1
+%		error('Incorrect P matric output. Wrong number of 0's')
+%	end
+%end
+
+%}
+
+end
+\ No newline at end of file