%
% Matlab file for the solution of the final, Spring 2006
%

%
% test of the subroutine -- second test
%

n=5;
k=3;

a=[ 2.4154    0.9708    0.2140    0.4120    0.6833;
    0.3050    2.9901    0.6435    0.7446    0.2126;
    0.8744    0.7889    2.3200    0.2679    0.8392;
    0.0150    0.4387    0.9601    2.4399    0.6288;
    0.7680    0.4983    0.7266    0.9334    2.1338 ]
%
% compute the LU decomposition of the (incorrect) matrix a
%

[l u] = lu(a);

%
% suppose that the k-th column should be
%

akt = [ 0.6756    0.6992    0.7275    0.4784    0.5548 ]';

%
% definition of the right-hand side
%

b=   [0.1210    0.4508    0.7159    0.8928    0.2731 ]';


z=smartsolve(l,u,b,akt,k,n);

a(:,k)=akt;

sqrt(sum((a*z-b).^2))

z



%
% test of the subroutine -- second test
%

n=10;
k=4;

a=[ 2.9501    0.6154    0.0579    0.0153    0.8381    0.1934    0.4966    0.7271    0.7948    0.1365;
    0.2311    2.7919    0.3529    0.7468    0.0196    0.6822    0.8998    0.3093    0.9568    0.0118;
    0.6068    0.9218    2.8132    0.4451    0.6813    0.3028    0.8216    0.8385    0.5226    0.8939;
    0.4860    0.7382    0.0099    2.9318    0.3795    0.5417    0.6449    0.5681    0.8801    0.1991;
    0.8913    0.1763    0.1389    0.4660    2.8318    0.1509    0.8180    0.3704    0.1730    0.2987;
    0.7621    0.4057    0.2028    0.4186    0.5028    2.6979    0.6602    0.7027    0.9797    0.6614;
    0.4565    0.9355    0.1987    0.8462    0.7095    0.3784    2.3420    0.5466    0.2714    0.2844;
    0.0185    0.9169    0.6038    0.5252    0.4289    0.8600    0.2897    2.4449    0.2523    0.4692;
    0.8214    0.4103    0.2722    0.2026    0.3046    0.8537    0.3412    0.6946    2.8757    0.0648;
    0.4447    0.8936    0.1988    0.6721    0.1897    0.5936    0.5341    0.6213    0.7373    2.9883 ];
%
% compute the LU decomposition of the (incorrect) matrix a
%

[l u] = lu(a);

%
% suppose that the k-th column should be
%

akt = [ 0.5828    0.4235    0.5155    0.3340    0.4329    0.2259    0.5798    0.7604    0.5298    0.6405]';

%
% definition of the right-hand side
%

b=   [ 0.2091    0.3798    0.7833    0.6808    0.4611    0.5678    0.7942    0.0592    0.6029    0.0503]';


z=smartsolve(l,u,b,akt,k,n);

a(:,k)=akt;

sqrt(sum((a*z-b).^2))

z