Optimizing indirect mapping: From matrix elements to vector values

I have a 2-D matrix of values, M. There are also two vectors:

• Grid - holds values which are close to the values in M. The values in Grid are essentially "the same" values in M, just might be slightly different (by 0.001 for example).
• Density - For each value of Grid, there is a corresponding density value.

For each element in the matrix: I need to find its density based on the closest value in Grid.

The following code achieves that, but is slow:

function [ density ] = get_density(x, Density, Grid)
    [~, min_diff_idx] = min( abs( x - Grid ) );
    density = Density( min_diff_idx );
end

M_new = arrayfun( @(x) get_density(x, Density, Grid), M);

Idea for improvement ?

[dpb]

1. Are values in Grid unique?
2. Are Grid and Density fixed with just lookup from M varying?
3. Is location in Grid significant or simply the nearest value?

[dor Levi]

1. Yes, values in Grid are unique.

2. (Maybe I don't understand the question, but ) Grid and Density stay with the same values throughout the execution.

3. The nearest element value of Grid is important. The index of Grid isn't significant.

Answer 1

[dpb]

OK, with the additional information, remove the 2D nature and use interp1

function density = get_density(x, Density, Grid)
  persistent D G                     % save the 1D values for reuse
  if ~isfinite(x) & ~isempty(G), clear D G, return, end  % reset persistents
  if isempty(G)                      % initialization 
    [G,ix]=sort(Grid(:));            % interp1 requires ordered independent variable
    D=Density(ix);                   % put associated dependent variable in same sequence
  end
  density=interp1(G,D,x,'nearest');  % look up nearest based on input
end

Treat the extrapolation as desired; see documentation for further details on interp1

To use, once called initially with all three arguments, only need to call with an x value or array of values.

If want to reset the persistent variables to use a different table; then call with

get_density(inf)

then use the three-argument form with the new table values.