Is it possible to vectorize a function script in matlab? - matlab

Question

If I have explicit function, I can vectorise it. How about if I have a function script? For example, if I have a script Fun.m such that Fun(x,y,z) gives a value and I want to compute x=[1,2,3] and y=[4,5] (i.e. (1,4), (1,5), (2,4), (2,5),(3,4), (3,5)) when z=10, are there any possible way to do it apart from using for-loop? Indeed, I may need to compute x,y for a long vector. I want to use bsxfun(#(x,y)Fun(x,y,10),[1,2,3],[4,5]') but it does not work. It says matrix dimension does not match.
Let me post the function Fun.m I have:
function density=HittingDensityOUlevel0(beta,r0,sigma,lambda,t0,i,p,MinOrMax)
g=zeros(1,i);
g(:,1)=-1.*MinOrMax.*2.*Integrand(r0,sigma,lambda,t0+p,t0,beta,r0);
for k=2:size(g,2)
Sum=0;
weight=zeros(1,k-1);
for m=1:k-1
R1=mod(k,2); Q1=floor(k./2);
R2=mod(m,2); Q2=floor(m./2);
if R1==0 && R2==1 && Q2<=Q1-1
weight(:,m)=4./3;
elseif R1==0 && R2==0 && Q2<=Q1-2
weight(:,m)=2./3;
elseif R1==1 && R2==1 && Q2<=Q1-2
weight(:,m)=4./3;
elseif R1==1 && R2==0 && Q2<=Q1-3 && Q1>=3
weight(:,m)=2./3;
elseif R1==1 && R2==0 && m==2*(Q1-1)
weight(:,m)=17./24;
elseif R1==1 && m==2*Q1-1 && Q1>=1
weight(:,m)=9./8;
elseif R1==1 && m==2*Q1 && Q1>=1
weight(:,m)=9./8;
end
end
TimeTicker=(t0+p):p:(t0+(k-1)*p);
Sum=Sum+2.*p.*sum(weight.*g(:,1:(k-1)).*arrayfun(#(t)Integrand(r0,sigma,lambda,t0+k.*p,t,beta,beta),TimeTicker));
g(:,k)=-1.*MinOrMax.*2.*...
Integrand(r0,sigma,lambda,t0+k.*p,t0,beta,r0)+MinOrMax.*Sum;
end
density=g(:,end);
function ret=Integrand(r0,sigma,lambda,t,tau,x,y)
ret=(lambda.*r0.*exp(-lambda.*t)./2+...
(x-r0.*exp(-lambda.*t))./2.*lambda.*cosh(lambda.*(tau-t))./sinh(lambda.*(tau-t))-...
(y-r0.*exp(-lambda.*tau))./2.*lambda./sinh(lambda.*(tau-t))).*...
...
(1./sqrt(pi.*sigma.^2./lambda.*(1-exp(-2.*lambda.*(t-tau))))).*...
...
(exp(-((x-r0.*exp(-lambda.*t)-exp(-lambda.*(t-tau)).*(y-r0.*exp(-lambda.*tau))).^2)./...
(sigma.^2./lambda.*(1-exp(-2.*lambda.*(t-tau))))));
I want to vectorize this Fun with (for example) t0=[1,2,3] and r0=[4,5]. But it does not work.

Answer 1

Use meshgrid to generate all possible pairs of inputs to your function.
[tt0,rr0] = meshgrid([1,2,3],[4,5])
so that tt0 = [1,2,3,1,2,3] and rr0 = [4,4,4,5,5,5]
Then pass that to bsxfun.