function [A,b,x] = shaw(n)%SHAW Test problem: one-dimensional image restoration model.%% [A,b,x] = shaw(n)%% Discretization of a first kind Fredholm integral equation with% [-pi/2,pi/2] as both integration intervals.  The kernel K and% the solution f, which are given by%    K(s,t) = (cos(s) + cos(t))*(sin(u)/u)^2%    u = pi*(sin(s) + sin(t))%    f(t) = a1*exp(-c1*(t - t1)^2) + a2*exp(-c2*(t - t2)^2) ,% are discretized by simple quadrature to produce A and x.% Then the discrete right-hand b side is produced as b = A*x.%% The order n must be even.% Reference: C. B. Shaw, Jr., "Improvements of the resolution of% an instrument by numerical solution of an integral equation",% J. Math. Anal. Appl. 37 (1972), 83-112.% Per Christian Hansen, IMM, 08/20/91.% Check input.if (rem(n,2)~=0), error('The order n must be even'), end% Initialization.h = pi/n; A = zeros(n,n);% Compute the matrix A.co = cos(-pi/2 + (.5:n-.5)*h);psi = pi*sin(-pi/2 + (.5:n-.5)*h);for i=1:n/2  for j=i:n-i    ss = psi(i) + psi(j);    A(i,j) = ((co(i) + co(j))*sin(ss)/ss)^2;    A(n-j+1,n-i+1) = A(i,j);  end  A(i,n-i+1) = (2*co(i))^2;endA = A + triu(A,1)'; A = A*h;% Compute the vectors x and b.a1 = 2; c1 = 6; t1 =  .8;a2 = 1; c2 = 2; t2 = -.5;if (nargout>1)  x =   a1*exp(-c1*(-pi/2 + (.5:n-.5)'*h - t1).^2) ...      + a2*exp(-c2*(-pi/2 + (.5:n-.5)'*h - t2).^2);  b = A*x;end