function [k,mu,M,match,aBirth,rBirth] = radialBirth(match,aBirth,rBirth,k,mu,M,delta,x,y,hyper,t,bFunction,walkInt,walk);if nargin < 14, error('Not enough input arguments.'); end[N,d] = size(x);      % N = number of data, d = dimension of x.[N,c] = size(y);      % c = dimension of y, i.e. number of outputs.insideBirth=1;uB=rand(1);% INITIALISE H AND P MATRICES:% ===========================invH=zeros(k(t)+1+d,k(t)+1+d,c);P=zeros(N,N,c);invHproposal=zeros(k(t)+2+d,k(t)+2+d,c);Pproposal=zeros(N,N,c);for i=1:c,  invH(:,:,i) = (M'*M + (1/delta(t,i))*eye(k(t)+1+d));  P(:,:,i) = eye(N) - M*inv(invH(:,:,i))*M';end;% PROPOSE A NEW BASIS FUNCTION:% ============================proposal=zeros(1,d);for i=1:d,  proposal(1,i)= (min(x(:,i))-walk(i)) + ((max(x(:,i))+walk(i))-(min(x(:,i))-walk(i)))*rand(1,1);end;% CHECK IF THE PROPOSED CENTRE ALREADY EXISTS:% =========================================== match1=0;notEnded=1;i=1;if k(t)>0  while ((match1==0)&(notEnded==1)),    if k(t)>0      if (mu{t}(i,:)==proposal),        match1=1;      elseif (i<k(t)),        i=i+1;      else        notEnded=0;      end;    else      notEnded=0;    end;  end;end;if (match1>0),  match=match+1;  mu{t+1} = mu{t};  k(t+1) = k(t);  M=M;else  % IF IT DOESN'T EXIST, PERFORM A BIRTH MOVE:  % =========================================  Mproposal = [M feval(bFunction,proposal,x)];  for i=1:c,    invHproposal(:,:,i) = (Mproposal'*Mproposal + inv(delta(t,i))*eye(k(t)+2+d));    Pproposal(:,:,i) = eye(N) - Mproposal*inv(invHproposal(:,:,i))*Mproposal';   end;  ratio= inv(k(t)+1) * inv(sqrt(delta(t,1))) * sqrt((det(invH(:,:,1)))/(det(invHproposal(:,:,1)))) * ((hyper.gamma+y(:,1)'*P(:,:,1)*y(:,1))/(hyper.gamma+y(:,1)'*Pproposal(:,:,1)*y(:,1)))^((hyper.v+N)/2);        for i=2:c,    ratio= ratio * inv(sqrt(delta(t,i))) * sqrt((det(invH(:,:,i)))/(det(invHproposal(:,:,i)))) * ((hyper.gamma+y(:,i)'*P(:,:,i)*y(:,i))/(hyper.gamma+y(:,i)'*Pproposal(:,:,i)*y(:,i)))^((hyper.v+N)/2);   end;  acceptance = min(1,ratio);     if (uB<acceptance),    mu{t+1} = [mu{t}; proposal];    k(t+1) = k(t)+1;    M=Mproposal;    aBirth=aBirth+1;  else    mu{t+1} = mu{t};    k(t+1) = k(t);    rBirth=rBirth+1;    M=M;  end;end;