MATLAB Examples

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Difference in Solve Time Between Solvers

This example shows the difference between the '\' and the 'normal' solver. The gist is use the '\' for accuracy or ill conditioned problems otherwise use 'normal' for speed. 'normal' is 2-3 times faster than '\' on this data set.

% setup some input points, output points, and noise
x = 0.5:0.1:4.5;
y = 0.5:0.1:5.5;
[xx,yy] = ndgrid(x,y);
z = tanh(xx-3).*sin(2*pi/6*yy);
noise = (rand(size(xx))-0.5).*xx.*yy/30;
zNoise = z + noise;

% setup the grid for lookup table
xGrid = linspace(0,6,600);
yGrid = linspace(0,6.6,1950);
gridPoints = {xGrid, yGrid};

% setup some difference in scale between the different dimensions/axes to
% just show the effectiveness of regularizeNd's capability of handling
% different scales in different dimensions.
xScale = 100;
x = xScale*x;
xx=xScale*xx;
xGrid = xScale*xGrid;
gridPoints{1} = xGrid;

% smoothness parameter. i.e. fit is weighted 1000 times greater than
% smoothness.
smoothness = 0.001;

'normal' Solver

tic;
zGrid1 = regularizeNd([xx(:), yy(:)], zNoise(:), gridPoints, smoothness);
toc;
% Note this s the same as
% zGrid = regularizeNd([xx(:), yy(:)], zNoise(:), gridPoints, smoothness, 'linear', 'normal');
Elapsed time is 7.142000 seconds.

'\' Solver

tic;
zGrid2 = regularizeNd([xx(:), yy(:)], zNoise(:), gridPoints, smoothness,[], '\');
toc;
Elapsed time is 19.546341 seconds.