Blockdiagonal variation grid - matlab

Question

I have the feeling I am missing something intuitive in my solution for generating a partially varied block-diagonal grid. In any case, I would like to get rid of the loop in my function (for the sake of challenge...)
Given tuples of parameters, number of intervals and percentage variation:
params = [100 0.5 1
24 1 0.9];
nint = 1;
perc = 0.1;
The desired output should be:
pspacegrid(params,perc,nint)
ans =
90.0000 0.5000 1.0000
100.0000 0.5000 1.0000
110.0000 0.5000 1.0000
100.0000 0.4500 1.0000
100.0000 0.5000 1.0000
100.0000 0.5500 1.0000
100.0000 0.5000 0.9000
100.0000 0.5000 1.0000
100.0000 0.5000 1.1000
21.6000 1.0000 0.9000
24.0000 1.0000 0.9000
26.4000 1.0000 0.9000
24.0000 0.9000 0.9000
24.0000 1.0000 0.9000
24.0000 1.1000 0.9000
24.0000 1.0000 0.8100
24.0000 1.0000 0.9000
24.0000 1.0000 0.9900
where you can see that the variation occurs at the values expressed by this mask:
mask =
1 0 0
1 0 0
1 0 0
0 1 0
0 1 0
0 1 0
0 0 1
0 0 1
0 0 1
1 0 0
1 0 0
1 0 0
0 1 0
0 1 0
0 1 0
0 0 1
0 0 1
0 0 1
The function pspacegrid() is:
function out = pspacegrid(params, perc, nint)
% PSPACEGRID Generates a parameter space grid for sensitivity analysis
% Size and number of variation steps
sz = size(params);
nsteps = nint*2+1;
% Preallocate output
out = reshape(permute(repmat(params,[1,1,nsteps*sz(2)]),[3,1,2]),[],sz(2));
% Mask to index positions where to place interpolated
[tmp{1:sz(2)}] = deal(true(nsteps,1));
mask = repmat(logical(blkdiag(tmp{:})),sz(1),1);
zi = cell(sz(1),1);
% LOOP per each parameter tuple
for r = 1:sz(1)
% Columns, rows, rows to interpolate and lower/upper parameter values
x = 1:sz(2);
y = [1; nint*2+1];
yi = (1:nint*2+1)';
z = [params(r,:)*(1-perc); params(r,:)*(1+perc)];
% Interpolated parameters
zi{r} = interp2(x,y,z, x, yi);
end
out(mask) = cat(1,zi{:});

Answer 1

I think I got it, building off your pre-loop code:
params = [100 0.5 1
24 1 0.9];
nint = 1;
perc = 0.1;
sz = size(params);
nsteps = nint*2+1;
% Preallocate output
out = reshape(permute(repmat(params,[1,1,nsteps*sz(2)]),[3,1,2]),[],sz(2));
%Map of the percentage moves
[tmp{1:sz(2)}] = deal(linspace(-perc,perc,nint*2+1)');
mask = repmat(blkdiag(tmp{:}),sz(1),1) + 1; %Add one so we can just multiply at the end
mask.*out
So instead of making your mask replicate the ones I made it replicate the percentage moves each element makes which is a repeating pattern, the basic element is made like this:
linspace(-perc,perc,nint*2+1)'
Then it's as simple as adding 1 to the whole thing and multiplying by your out matrix
I tested it as follows:
me = mask.*out;
you = pspacegrid(params, perc, nint);
check = me - you < 0.0001;
mean(check(:))
Seemed to work when I fiddled with the inputs. However I did get an error with your function, I had to change true(...) to ones(...). This might be because I'm running it online which probably uses Octave rather than Matlab.