Accessing function output for different values of variable

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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)
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));
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."

Accepted Answer

Walter Roberson
Walter Roberson on 22 Dec 2019
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));
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.
  1 Comment
Sandeep Parameshwara
Sandeep Parameshwara on 22 Dec 2019
Thanks a lot, this is excatly what I needed. Now onwards, I will use the interpolation functions like you demonstreted.

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