Algorithme d’Élimination de Gauss en Matlab

Algorithme d’Élimination de Gauss en Matlab :

function x = gauss(A,B) %The sizes of matrices A,B are supposed to be NA x NA and NA x NB. %This function solves Ax = B by Gauss elimination algorithm. NA = size(A,2); [NB1,NB] = size(B); if NB1 ~= NA, error(’A and B must have compatible dimensions’); end N = NA + NB; AB = [A(1:NA,1:NA) B(1:NA,1:NB)]; % Augmented matrix epss = eps*ones(NA,1); for k = 1:NA %Scaled Partial Pivoting at AB(k,k) by Eq.(2.2.20) [akx,kx] = max(abs(AB(k:NA,k))./ ... max(abs([AB(k:NA,k + 1:NA) epss(1:NA - k + 1)]’))’); if akx < eps, error(’Singular matrix and No unique solution’); end mx = k + kx - 1; if kx > 1 % Row change if necessary tmp_row = AB(k,k:N); AB(k,k:N) = AB(mx,k:N); AB(mx,k:N) = tmp_row; end % Gauss forward elimination AB(k,k + 1:N) = AB(k,k+1:N)/AB(k,k); AB(k,k) = 1; %make each diagonal element one for m = k + 1: NA AB(m,k+1:N) = AB(m,k+1:N) - AB(m,k)*AB(k,k+1:N); %Eq.(2.2.5) AB(m,k) = 0; end end %backward substitution for a upper-triangular matrix eqation % having all the diagonal elements equal to one x(NA,:) = AB(NA,NA+1:N); for m = NA-1: -1:1 x(m,:) = AB(m,NA + 1:N)-AB(m,m + 1:NA)*x(m + 1:NA,:); %Eq.(2.2.7) end