Applying logic to Curve Fitter Output

I am trying to use Curve Fitter and generating the code to help teach myself how to process my data without Curve Fitter.

Is there a way to apply a logic that a certain data point should be lower/higher than another certain data point, and have the coefficients adjust accordingly?

%CREATEFIT(TWOSOUSANDTQSPK,TWOSOUSANDTQAPC,TWOSOUSANDTQNM)
%  Create a fit.
%
%  Data for '2000 copy 1' fit:
%      X Input: twosousandTQSPK
%      Y Input: twosousandTQAPC
%      Z Output: twosousandTQnm
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 18-Jul-2024 20:43:50


%% Fit: '2000 copy 1'.
[xData, yData, zData] = prepareSurfaceData( twosousandTQSPK, twosousandTQAPC, twosousandTQnm );

% Set up fittype and options.
ft = fittype( 'A+(x*B)+(C*x*x)+(y*x*D)+(y*x*x*E)+(y*F)', 'independent', {'x', 'y'}, 'dependent', 'z' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.MaxFunEvals = 60000;
opts.MaxIter = 40000;
opts.StartPoint = [0.0526769976807926 0.737858095516997 0.269119426398556 0.422835615008808 0.547870901214845 0.942736984276934];
opts.TolFun = 0.1;
opts.TolX = 0.1;

% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft, opts );

% Plot fit with data.
figure( 'Name', '2000 copy 1' );
h = plot( fitresult, [xData, yData], zData );
legend( h, '2000 copy 1', 'twosousandTQnm vs. twosousandTQSPK, twosousandTQAPC', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'twosousandTQSPK', 'Interpreter', 'none' );
ylabel( 'twosousandTQAPC', 'Interpreter', 'none' );
zlabel( 'twosousandTQnm', 'Interpreter', 'none' );
grid off
view( -2.9, 15.3 );

I am looking to apply that the output data should follow the 'twosousandTQSPK' axis relative. I reserached the weighting function, but I I don't know how I could accurately match the data inputs I have to weight it.

This is an example of what I am expecting with a different set of variables, but the results above in question should resemble this outcome to some degree.

%CREATEFIT(SIXTEENTQSPK,SIXTEENTQAPC,SIXTEENTQNM)
%  Create a fit.
%
%  Data for '1600 copy 2' fit:
%      X Input: sixteenTQSPK
%      Y Input: sixteenTQAPC
%      Z Output: sixteenTQnm
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 18-Jul-2024 20:55:15


%% Fit: '1600 copy 2'.
[xData, yData, zData] = prepareSurfaceData( sixteenTQSPK, sixteenTQAPC, sixteenTQnm );

% Set up fittype and options.
ft = fittype( '(y*A)+B+(x*C)+(D*x*x)+(y*x*E)+(y*x*x*F)', 'independent', {'x', 'y'}, 'dependent', 'z' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.MaxFunEvals = 60000;
opts.MaxIter = 40000;
opts.StartPoint = [0.0430238016578078 0.168990029462704 0.649115474956452 0.73172238565867 0.647745963136307 0.450923706430945];
opts.TolFun = 0.1;
opts.TolX = 0.1;

% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft, opts );

% Plot fit with data.
figure( 'Name', '1600 copy 2' );
h = plot( fitresult, [xData, yData], zData );
legend( h, '1600 copy 2', 'sixteenTQnm vs. sixteenTQSPK, sixteenTQAPC', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'sixteenTQSPK', 'Interpreter', 'none' );
ylabel( 'sixteenTQAPC', 'Interpreter', 'none' );
zlabel( 'sixteenTQnm', 'Interpreter', 'none' );
grid off
view( -0.5, -13.0 );

[Steven Lord]

I am looking to apply that the output data should follow the 'twosousandTQSPK' axis relative.

I'm not quite sure I understand what you mean. Do you mean that if the value in twosousandTQSPK corresponding to one point P1 is greater than the value in twosousandTQSPK corresponding to another point P2 that the value of the fitted surface at point P1 must also be greater than the value of the fitted surface at point P2? Or do you have something else in mind for "follow the axis relative"?

Can you upload (or post code to create) a small sample data set (let's say points on a 20-by-20 or smaller grid) and show us exactly what you're hoping to achieve using that smaller data set?

[Eric]

Thanks again for the quick response. I shouldnt of asked a question quite yet. I just stumbled accross how the starting point in curve fitter can affect the output data quite a bit. I will dabble into this new venture for awhile.

Thank You again!

[Eric]

Im trying to produce a general trend that point z should be increasing as x and/or y is increasing, with exceptions.

This screenshot is pretty much what I am trying to mimic with my dataset. I can't physically produce the same variety of data points as that example, so I feel that is why I am having difficulty estimating a fit. I have been looking into some sort of a Monte Carlo simulation to help generalize my data, being the TWOSOUSANDTQNM in the raw form is extrememly noisy, and the TWOSOUSANDTQAPC in raw form has known varying +/-5 percent error.

This data was visually cherrypicked moving means to rule out error and noise.

TWOSOUSANDTQAPC

207.500000000000
296.500000000000
367.200000000000
419.300000000000
461.800000000000
506.800000000000
540.600000000000

TWOSOUSANDTQSPK

35.9000000000000
28.5000000000000
22.1000000000000
19.3000000000000
17
14.8000000000000
13.3000000000000

TWOSOUSANDTQNM

95.2000000000000
174.300000000000
227.800000000000
270
301.800000000000
334.600000000000
355.500000000000

Answer 1

[Ayush]

Hi Eric,

I am assming that you are trying to fit a surface to your data using MATLAB and want the fitted model to respect specific logical constraints, such as ensuring one data point is always greater or less than another based on one of the input axes. You're exploring how to achieve this, possibly through weighting or other methods.

Here is an example of how you might achieve that:

constrainedFit();

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0       7    1.764000e+03    0.000e+00    4.600e+02
    1      18    5.667642e+02    0.000e+00    2.600e+02    2.449e+00
    2      25    3.859390e+00    0.000e+00    1.990e+00    4.094e+00
    3      32    1.578186e+00    0.000e+00    1.880e+00    1.661e+00
    4      39    6.026830e-05    0.000e+00    1.493e-01    3.046e+00
    5      46    2.549846e-03    0.000e+00    6.153e-01    1.147e+00
    6      53    2.523078e-05    0.000e+00    7.506e-02    2.652e-01
    7      60    6.041650e-04    0.000e+00    2.666e-01    4.997e-01
    8      67    2.460235e-03    0.000e+00    5.374e-01    1.012e+00
    9      74    4.110286e-03    0.000e+00    6.943e-01    1.781e+00
   10      81    3.269262e-03    0.000e+00    6.188e-01    3.716e+00
   11      88    8.390159e-04    0.000e+00    3.135e-01    7.957e+00
   12      95    3.204689e-04    0.000e+00    1.941e-01    2.197e+01
   13     102    3.624003e-03    0.000e+00    6.519e-01    4.046e+01
   14     109    3.266266e-03    0.000e+00    6.189e-01    2.274e+01
   15     116    5.677525e-04    0.000e+00    2.581e-01    4.691e+01
   16     123    6.708764e-07    0.000e+00    8.586e-03    5.115e+01
   17     134    6.355372e-09    0.000e+00    7.720e-04    2.869e-04
   18     164    3.976033e-09    0.000e+00    9.726e-05    2.977e-04
   19     175    2.915154e-09    0.000e+00    8.691e-05    2.977e-04
   20     187    9.286582e-10    0.000e+00    2.365e-04    1.489e-04
   21     198    5.229195e-10    0.000e+00    7.814e-05    1.489e-04
   22     210    4.052741e-10    0.000e+00    2.828e-04    7.443e-05
   23     221    2.586847e-12    0.000e+00    8.366e-05    7.443e-05
   24     238    1.608539e-12    0.000e+00    7.508e-05    1.163e-06
   25     249    4.972323e-13    0.000e+00    7.093e-05    1.163e-06
   26     262    4.084079e-13    0.000e+00    6.867e-05    2.908e-07

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

Fitted Parameters:
    0.0000 -141.2530  151.2530    1.0000    1.0000    1.0000

Objective Function Value:
   4.0841e-13

function constrainedFit()
    % Example data
    xData = [1, 2, 3, 4];
    yData = [1, 2, 3, 4];
    zData = [10, 20, 30, 40]; % Example outputs

    % Initial guess for parameters
    initialParams = [1, 1, 1, 1, 1, 1];

    % Define the objective function
    objective = @(params) fitError(params, xData, yData, zData);

    % Perform constrained optimization
    options = optimoptions('fmincon', 'Display', 'iter');
    [fittedParams, fval] = fmincon(objective, initialParams, [], [], [], [], [], [], @nonlinearConstraints, options);

    % Display results
    disp('Fitted Parameters:');
    disp(fittedParams);
    disp('Objective Function Value:');
    disp(fval);
end

function error = fitError(params, xData, yData, zData)
    % Define the Model: custom model function that describes the relationship you want to fit
    % Example model: z = A + B*x + C*y
    A = params(1);
    B = params(2);
    C = params(3);
    predictedZ = A + B*xData + C*yData;

    % Calculate error
    error = sum((predictedZ - zData).^2);
end

function [c, ceq] = nonlinearConstraints(params)
    % Define nonlinear inequality constraints
    % Example: ensure z1 > z2 (Add a term like penalty = max(0, z2 - z1)
    % to your objective function)
    z1 = params(1); % Example output for first data point
    z2 = params(2); % Example output for second data point
    c = z2 - z1; % Constraint: z1 > z2 implies c < 0
    ceq = []; % No equality constraints
end

Hope this was helpful!