Accessing function output for different values of variable

This question could be very basic (in which case please refer me to relevent guide/tutorial to study), however I am stuck. My code is something like this:

P=@(rho) P0 + P1*sin(rho) + P2*cos(rho);
Q=@(rho) Q0 + Q1*sin(rho) + Q2*cos(rho);

Later, P and Q are solved and co-efficients are stored. Then I use them in

rho_grid= -1:0.1:1
for i=1:length(rho_grid)
    rho=rho_grid(i);
    Rq=  @(rho) chol(value(Q(rho)),'upper');
    Rp=  @(rho) chol(value(P(rho)),'lower');
    pro=@(rho) Rq(rho)*Rp(rho);
    [U,S,V] = svd(pro(rho));
end

Please notice that only final values are being stored in U,S and V. I want to access U(rho), V(rho) and S(rho). How can I achieve that?

I tried using something like

[U,S,V] = @(rho) svd(pro(rho));

to which Matlab shows error "Only functions can return multiple values."

Answer 1

[Walter Roberson]

rho_grid= -1:0.1:1;
Nrho = length(rho_grid);

for i = Nrho : -1 : 1                        %backwards! For pre-allocation reasons
    rho = rho_grid(i);
    Rq = @(rho) chol(value(Q(rho)),'upper');
    Rp = @(rho) chol(value(P(rho)),'lower');
    pro = @(rho) Rq(rho)*Rp(rho);
    [Uvals(:,:,i), Svals(:,:,i), Vvals(:,:,i)] = svd(pro(rho));
end

U = @(rho) Uvals(:,:,interp1(rho_grid, 1:Nrho, rho, 'nearest'));
S = @(rho) Svals(:,:,interp1(rho_grid, 1:Nrho, rho, 'nearest'));
V = @(rho) Vvals(:,:,interp1(rho_grid, 1:Nrho, rho, 'nearest'));

Instead of using 'nearest' in computing the index, you could go for something more sophisticated such as determining the mixing between the two closest values, and doing a weighted calculation to interpolate at the rho.

[Sandeep Parameshwara]

Thanks a lot, this is excatly what I needed. Now onwards, I will use the interpolation functions like you demonstreted.