Fit Data to N-D Lookup Table Using fitlookupn

Fit an N-D lookup table from scattered data using the fitlookupn function.

Load Data and Create a 3-D Plot

Load the example data file dgasData.mat. Use the plot3 function to create a 3-D plot.

load data.mat GasolineData
plot3(GasolineData.LOAD,GasolineData.Speed,GasolineData.BSFC,'x')
grid on
xlabel('LOAD')
ylabel('Speed [rpm]')
zlabel('BSFC [g/Kwh]')

Define Breakpoints

Specify load and speed breakpoints in a cell array.

loadBreakpoints = 0.2:0.1:1.4;
speedBreakpoints = 500:500:5000;
breakPoints = { loadBreakpoints , speedBreakpoints };

Define Smoothness Penalty

Specify the smoothness penalty, smoothnessPenalty, using the slider.

Note that the slider is on a log scale, as the smoothness penalty usually requires adjusting by several orders of magnitude.

smoothnessPenalty = 10.^-2

smoothnessPenalty = 
0.0100

Define Input Data

Set the load and speed as inputData.

inputData = [GasolineData.LOAD,GasolineData.Speed];

Fit Lookup Table

Fit the lookup table using the fitlookupn function and plot result.

[tableValues,rmse] = fitlookupn(breakPoints, inputData, ...
    GasolineData.BSFC, smoothnessPenalty, ShowPlot=true);
grid on
xlabel('LOAD')
ylabel('Speed [rpm]')
zlabel('BSFC [g/Kwh]')

Calculate Lookup Table Output

Use the griddedInterpolant function to calculate the output from the lookup table. Calculate the lookup table value for LOAD=0.45 and Speed=2250rpm and show on the plot.

Note: You can use the interpn function as an alternative to griddedInterpolant.

rmse

rmse = 
5.9891

%yinterpn = interpn(loadBreakpoints,speedBreakpoints,tableValues,x(1),x(2))
g = griddedInterpolant(breakPoints,tableValues);
x = [0.45, 2250];
y= g(x)

y = 
269.5463

Specify Bounds

Specify bounds on the table values.

Note: An Optimization Toolbox™ license is required to fit lookup tables with bounds.

tableValues = fitlookupn(breakPoints, inputData, ...
    GasolineData.BSFC, 0.1, Bounds = [0 350], ...
    ShowPlot=true);
grid on
xlabel('LOAD')
ylabel('Speed [rpm]')
zlabel('BSFC [g/Kwh]')

Set Row-Major Order

You can use the IsRowMajor option to change the order of the inputs (first input=columns, second input=rows). The resulting lookup table is the transpose of the default value IsRowMajor=false.

tableValuesRM = fitlookupn(breakPoints, inputData, ...
    GasolineData.BSFC, 0.1, ...
    IsRowMajor=true, ...
    ShowPlot=true);
grid on
ylabel('LOAD')
xlabel('Speed [rpm]')
zlabel('BSFC [g/Kwh]')

Use the griddedInterpolant function to calculate the output from the lookup table. Calculate the lookup table value for LOAD=0.45 and Speed=2250rpm and show the results on the plot. You must swap the breakpoints and input order when IsRowMajor=true.

breakPointsRM = {speedBreakpoints, loadBreakpoints};
g = griddedInterpolant(breakPointsRM,tableValuesRM);
xrm = [2250 0.45];
y= g(xrm)

y = 
273.6243

hold on
plot3(xrm(1),xrm(2),y,'.r','MarkerSize',20)
hold off
view([-20 37])

When you use the interp2 function, the inputs are already in row-major (meshgrid) order.

yinterpn = interpn(speedBreakpoints,loadBreakpoints, ...
    tableValuesRM,xrm(1),xrm(2))

yinterpn = 
273.6243

yinterp2 = interp2(loadBreakpoints,speedBreakpoints, ...
    tableValuesRM,x(1),x(2))

yinterp2 = 
273.6243