How to speed up code with ppval and integral

Hi I want to speed up my code as much as possible. Everything that could help me reduce the time to run the code is appreciated. A simplification of my code is given below and it takes on my computer 120 seconds to run which is a little too long.

data=[0 1 2 3 4 5];%  X data for first datapoints
X=repmat(Xdata,44000,1); %  make all data points from first example 
Ydata=[10 8.3 5.2 4.2 2.9 1.1];%  X data for first datapoints  
Y=repmat(Ydata,44000,1); %  make all data points from first example 
Xqdata=[2 2.1 2.3 2.6 3.0 3.6 3.9 4.0 4.2 4.4 4.8];% X data for second datapoints  
xq=repmat(Xqdata,44000,1);%  make all data points from second example 

for i=1:44000 % loop over all datapoints
 yi=pchip(X(i,:),Y(i,:), xq(i,:)); % make pchip over first data points and generate yi points
pp=pchip(xq(i,:),yi); % creates a piecewise polynomial structure for use with ppval
Result = integral(@(varible)ppval(pp,varible),xq(i,1),xq(i,end)); % integrates over xq  (this is the time consuming part)
end

Is there any way to speed up the integration step?

Answer 1

[David Goodmanson]

Hi Martin,

Here's some code to integrate a piecewise polynomial on the basis of its polynomial coefficients, no actual numerical integration. On my pc with the 44000 repetitions, replacing integral(...) with intpp(pp) cut down the execution time by about a factor of three.

function defint = intpp(pp)

% definite integral of a piecwise polynomial
% c has highest power coefficient in first col, const coefficient in last col

brk = pp.breaks;
c = pp.coefs;
%   [brk c] = unmkpp(pp);   % still works, one less line of code
dbrk = diff(brk);
dbrk = dbrk(:);  
[nrow ncol] = size(c);
intseg = zeros(nrow,1);
for k = 1:ncol
  c(:,k) = c(:,k)/(ncol+1-k);
  intseg = (intseg + c(:,k)).*dbrk;
end
defint = sum(intseg);  % sum of integrations over the segments