How to extend the curve fitting graph beyond given experiment values?

The following below is the code I have generated using Curve fitting option in MATLAB

I NEED TO EXTEND THE FITTED CURVE BEYOND THE GIVEN X AND Y VALUES UNTIL X VALUE OF 10 LAKH.

ALSO HOW TO FIND THE Y VALUE IF I HAVE THE CORRESPONDING X VALUE? i HAVE R_f AS 151.3 FROM

THE RESULT OF CURVE FITTING BUT i NEED TO FIND THE y VALUE CORRESPONDING TO 151.3?

tHE problem is with the highlighted portions of the code. Can someone please help?

function [fitresult, gof] = FXVol(x, y)
    %CREATEFIT(X,Y)
    %  Create a fit.
    %
    %  Data for 'Fredlund-XIng(1994)-Vvspsi' fit:
    %      X Input : x
    %      Y Output: y
    %  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 29-Jul-2021 13:22:43


    %% Fit: 'Fredlund-XIng(1994)-Vvspsi'.
    [xData, yData] = prepareCurveData( x, y );

    % Set up fittype and options.
    ft = fittype( '(1-((log(1+(x/R_F)))/(log(1+(1000000/R_F)))))*(S_F/(log(2.72+(x/a_F)^n))^m)', 'independent', 'x', 'dependent', 'y' );
    opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
    opts.Display = 'Off';
    opts.Lower = [0 0 0 0 0];
    opts.StartPoint = [0.278498218867048 0.546881519204984 0.957506835434298 0.157613081677548 0.970592781760616];

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

    % Plot fit with data.
    figure( 'Name', 'Fredlund-XIng(1994)-Vvspsi' );
    

x=linspace(1,1000000);

yhat=(1-((log(1+(x/fitresult.R_F)))/(log(1+(1000000/fitresult.R_F)))))*(fitresult.S_F/(log(2.72+(x/fitresult.a_F)^fitresult.n))^fitresult.m);

plot(x,yhat); %As before

hold on;

    plot( fitresult, xData, yData );
    set(gca,'XScale','log');
    xlim([1,1000000]);
    % Label axes
    xlabel( 'Matric Suction (kPa)', 'Interpreter', 'none' );
    ylabel( 'Volumetric Water Content (%)', 'Interpreter', 'none' );
    grid on
    

index = find(X==151.3);

Y_point = Y(index);

Answer 1

[Animesh]

Hey @CHITTI SATYA SUNDARA UDAY SRIKANTH

It looks like you are trying to extend the fitted curve to an “x” value 1,000,000 and find a corresponding “y” value for a specific “x” value (R_f = 151.3).

We can use the “fitresult” to predict the “y” values of the extended range of “x” values. The “feval’ function in MATLAB can be used for this and can also be used to get the “y” value for a specific “x” value (in this case, R_f = 151.3).

Here is something we can do to achieve the same:

function [fitresult, gof] = FXVol(x, y) 

    % ... [your code] ... 
    
    % Extend the range of x values up to 1000000 
    extended_x = linspace(min(xData), 1000000, 1000);
    
    % Evaluate the fitted model at the extended range of x values 
    extended_y = feval(fitresult, extended_x); 
    
    % Plot the extended fit with data 
    figure('Name', 'Fredlund-XIng(1994)-Vvspsi'); 
    plot(extended_x, extended_y, 'r-', 'LineWidth', 2); % Extended fit 
    hold on; 
    plot(fitresult, xData, yData); % Original data and fit 
    set(gca, 'XScale', 'log'); 
    xlim([min(xData), 1000000]);
    
    % ... [plotting code] ... 
    
    % Find the y value corresponding to R_f = 151.3 
    R_f = 151.3; 
    Y_point = feval(fitresult, R_f); 
    disp(['The y value corresponding to R_f = ', num2str(R_f), ' is: ', num2str(Y_point)]); 
end 

You can refer to the following MathWorks documentations to get more details on the “fevel” function:

https://www.mathworks.com/help/matlab/ref/feval.html