MATLAB: How to do least square error estimation to find the coeffcient values for a quadratic type equation with set of constraints on coefficients least square estimationMATLAB and Simulink Student Suitematlab coderoptimizationOptimization Toolboxregression I have measured and actual values need to find the values of a,b,c. for y=ax^2+bx+c constraints are: a+b+c=1 0<a<1, 0<b<1,0<c<1 Best Answer I love this answer from Star Strider: https://ch.mathworks.com/matlabcentral/answers/126146-curve-fitting-without-the-toolboxThis allows you to fit any curve with vanilla matlab.You just need to write a function that constrains your parameters and your own cost function.Try this:% i don't know your data, so i'll demonstrate fitting a second% order over an inverse cosinex = -1:0.01:1;y = 1 - cos(x .* 1.5);% define 2nd order polynomial functionfun = @(b, x) b(1) .* x.^2 + b(2) .* x + b(3);% i use square to constrain parameters to be positive% and divide by the sum to have the parameters to sum up to 1constrainParams = @(b) b.^2 ./ sum(b.^2);% cost function to optimize is just a least square functioncost = @(b) sum((fun(constrainParams(b),x) - y).^2);% find parameters using fminsearch (in the domain of all real% numbers) with an initial guess (probably you have one that% fits your data).b = fminsearch(cost, [1 0 0]);% then you just have to apply the constrain function to those% parametersparams = constrainParams(b);% there you have a, b and ca = params(1);b = params(2);c = params(3);% quickly verify it with a plotplot(x,y, x,fun(params, x));CheersManuel Related SolutionsMATLAB: How to fit inverse proportional function Your function could be difficult to fit. You can use the fminsearch function to estimate the parameters:% Define ‘x’ and ‘y’ here% Parameter Vector: b(1) = a, b(2) = b, b(3) = cyfit = @(b,x) b(1)./(x + b(2)) + b(3); % Objective FunctionCF = @(b) sum((y-yfit(b,x)).^2); % Cost Functionb0 = rand(1,3)*10; % Initial Parameter Estimates[B, fv] = fminsearch(CF, b0); % Estimate ParametersNote that ‘x’ and ‘y’ have to be defined in your workspace MATLAB: Fitting a normal distribution function to a set of data If you have the Statistics Toolbox, use the histfit function.Otherwise, this works:d = 2*randn(250,1)+20; % Created Databinrs = min(d):(max(d)-min(d))/25:max(d); % Bin Definitionsknt = histc(d, binrs); % Histogram Countss = std(d); % Intial Parameter Estimatem = mean(d); % Intial Parameter Estimate% b(1) = mean, b(2) = std, b(3) = amplitudepdfnrm = @(x,b) b(3) * 1./(b(2)*sqrt(2*pi)) .* exp(-((x-b(1)).^2./(2*b(2).^2)));SSECF = @(b) sum((knt-pdfnrm(binrs,b)').^2); % Sum-Squared-Error Cost Function[B,SSE] = fminsearch(SSECF, [m; s; 10]);figure(1)bar(binrs,knt,'g') % Plot Histogramhold onplot(binrs,pdfnrm(binrs,B),'r') % Plot Normal Distributionhold offgrid Related QuestionDetermining coefficients of an equation using your experimental dataWhat is the best non-linear least square fitting method that will parameter error in addition to parameters
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