AAE-NA-Labs/01_Direct-Methods-for-Solving-Linear-Systems/Code/Alg3.m
Sergiusz Warga a3fa9eb91d refac
2023-03-11 20:08:05 +01:00

30 lines
556 B
Matlab

function b = Al3(L, b)
% Algorithm 3: Forward Substitution
% b = Alg3_forward_substitution(L, b) overwrites b with the solution to
% Lx = b.
[m, n] = size(L);
if m ~= n
error('Matrix is not square!')
end
if length(b) ~= m
error('Vector b has wrong length!')
end
if det(L) < eps
error("Matrix is not nonsingular!")
end
% The following algorithm is based on the Algrotihm 3.1.1 from [2].
% b(m, :) so that matrices are also accepted
b(1, :) = b(1, :)/L(1,1);
for i = 2:m
b(i, :) = (b(i, :) - L(i, 1:i-1)*b(1:i-1, :))/L(i, i);
end
end