%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Plot misfit function ||Ls-t|| for a nlinex2 system 
% of equations against variables s(1) and s(2).
%
%  N        - input  - Number of equations in matrix-vector Ls=t
%  slope    - input  - Slope of line
%  L        -variable- Nx2 matrix
%  s        -variable- 2x1 vector of unknowns
%  t        -variable- Nx1 RHS vector
%  eps      -output  - misfit function ||Lx-t||
%    | -m  1 | |s(1)|     |t(1)|
%    | -m  1 | |s(2)|  =  |t(2)|
%    | -m  1 |            |t(3)|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t=0;L=0;s=0;
for iter=1:7;
N=5;slope=.1*iter
xstart=-30;xend=30;
x=xstart:1:xend;y=x;
x0=0;y0=1;subplot(111)
% Compute Nx2 L matrix and Nx1 t vector
for m=1:N
   mm=(m-3)*slope;
   if m==1;L=[-mm 1];t=L*[x0 y0]';else;
   L=[L;-mm 1];t0=[-mm 1]*[x0 y0]';t=[t;t0];end
end;
s = inv(L'*L)*L'*t;e = (L*s-t)'*(L*s-t)
%
% Compute Misfit Function for different values s(1) & s(2)
%
for i=xstart:xend
ii=i-xstart+1;
for j=xstart:xend
jj=j-xstart+1;xx=[i j];eps(ii,jj)=(L*xx'-t)'*(L*xx'-t);
end;end
imagesc([xstart:xend],[xstart:xend],eps');colorbar;hold on
title('Misfit Function: ||Ls-t||');xlabel('s(1)');ylabel('s(2)');hold on;
axis([xstart xend xstart xend])
%
% Plot Lines
%
for m=1:N;plot(x,-L(m,1)*x+t(m),'-w');end;hold off;c1=cond(L);
text(xstart+2,xstart+2,['condition # =',num2str(c1)]);
pause(1);end