Curve Fitting Toolbox for Surface Extrapolation

Hi everyone,

I am working with a fairly simple X,Y, Z dataset to extrapolate some datapoints outside of the data region. I have used the Curve Fitting toolbox to fit a surface to the datapoints which seems pretty good. I have used the toolbox to generate the code which can be found below. It shows me a nice figure which I am happy with. Unfortunately, I don't know how to use this surface.

My aim is to feed in xq, and xy values and it would tell me zq. How can I achieve this?

Many thanks.

% Data for 'Lowess' fit:

% X Input : BH_X

% Y Input : BH_Y

% Z Output: BH_Z

%% Fit: 'Lowess'.

[xData, yData, zData] = prepareSurfaceData( BH_X, BH_Y, BH_Z );

% Set up fittype and options.

ft = fittype( 'loess' );

opts = fitoptions( 'Method', 'LowessFit' );

opts.Normalize = 'on';

opts.Robust = 'Bisquare';

opts.Span = 0.2;

% Fit model to data.

[fitresult{2}, gof(2)] = fit( [xData, yData], zData, ft, opts );

% Create a figure for the plots.

figure( 'Name', 'Lowess' );

% Plot fit with data.

subplot( 2, 1, 1 );

h = plot( fitresult{2}, [xData, yData], zData );

legend( h, 'Lowess', 'BH_Z vs. BH_X, BH_Y', 'Location', 'NorthEast', 'Interpreter', 'none' );

% Label axes

xlabel( 'BH_X', 'Interpreter', 'none' );

ylabel( 'BH_Y', 'Interpreter', 'none' );

zlabel( 'BH_Z', 'Interpreter', 'none' );

grid on

view( -1.3, 14.3 );

% Plot residuals.

subplot( 2, 1, 2 );

h = plot( fitresult{2}, [xData, yData], zData, 'Style', 'Residual' );

legend( h, 'Lowess - residuals', 'Location', 'NorthEast', 'Interpreter', 'none' );

% Label axes

xlabel( 'BH_X', 'Interpreter', 'none' );

ylabel( 'BH_Y', 'Interpreter', 'none' );

zlabel( 'BH_Z', 'Interpreter', 'none' );

grid on

view( -1.3, 14.3 );

Answer 1

[Torsten]

[fitresult, gof] = fit( [xData, yData], zData, ft, opts );
xq = (xData(1)+xData(2))/2;
yq = (yData(1)+yData(2))/2;
zq = feval(fitresult,[xq yq])

[MATLAB_Soldier]

Thank you. This is what I needed.

However, what are these two lines for?

xq = (xData(1)+xData(2))/2;

yq = (yData(1)+yData(2))/2;

[Torsten]

Just test values for interpolation in [xq yq].

Answer 2

[William Rose]

@Tamas,

I think interp2() is good.

Vq = interp2(X,Y,V,Xq,Yq)

Try it.