function [x_f, y_f, z_f, mse_f, me_f] = find_best_table_2de(...
x_0, y_0, z_0, ...
mse_target, max_error, ...
method)
%% find_best_table_2de
%
% This function finds the best way to reduce the size of a table to the
% so that the smaller table matches the original within specified error
% bounds. That is, suppose you had a table of 100-by-100 points, but wanted
% to find the smallest table that had no more than 1.5 units of mean
% squared error. This function would find how many points are necessary
% along each axis to accomplish this and where those points go. "Goodness"
% will be measured by the difference between the original table and the new
% table sampled at the original data points. See find_best_table_demo.m for
% examples.
%
% Inputs:
% x_0 Array of values for the first independent variable
% y_0 Array of values for the second indepdendent variable
% z_0 Matrix of values for the dependent variable for all x_0 and
% y_0 using meshgrid-style syntax (e.g., z_0(2, 3) corresponds
% to x_0(3) and y_0(2)).
% mse_target Target mean squared error
% method Interpolation method to use, e.g., 'linear' (help interp2)
%
% Outputs:
% x_f Best division of first independent variable found
% y_f Best division of second independent variable found
% z_f Resulting fit of z_0 on x_f and y_f
% mse_f Mean square error of final table
%
% This builds off of work by Richard Willey, Stuart Kozola, Eric Johnson,
% Sarah Zaranek, and Peter Maloney at The MathWorks, Inc.
%
% Requires the Optimization Toolbox (TM).
% Supports the Parallel Computing Toolbox (TM).
%
% Tucker McClure @ The MathWorks
% Copyright 2013 The MathWorks, Inc.
% Default to linear interpolation.
if nargin < 6, method = 'linear'; end;
if nargin == 5 && ischar(max_error)
method = max_error;
max_error = inf;
end
if nargin == 4 || isempty(max_error), max_error = inf; end;
if isempty(mse_target), mse_target = inf; end;
% Just call the n-dimensional version. This file is here for backwards
% compatibility.
[x_fs, z_f, mse_f, me_f] = find_best_table_nde({x_0, y_0}, ...
z_0', ...
mse_target, ...
max_error, ...
method);
% n-D interpolation uses ndgrid format; 2d used meshgrid format at its
% release, so we'll preserve that for compatibility.
z_f = z_f';
% Separate the x and y breakpoints.
x_f = x_fs{1};
y_f = x_fs{2};
end
