如何使用 cftool 去拟合复数数据？

如何使用 cftool 去拟合复数数据？

Answer 1

[MathWorks Support Team]

可以使用 lsqcurvefit 函数，请参考：

https://www.mathworks.com/help/curvefit/fit.html#bto2vuv-1-x

这里也给出一个例子：

%%Create target data 

tmpData = 100*rand(10, 4); 

targetData = tmpData(:, 1) + 3i*tmpData(:, 2) + 0.5*tmpData(:, 3) - 2*tmpData(:, 4); 

% goal is to approximate x + yi + w + zi 

%%Split target data into real and imaginary parts 

uData = [real(targetData) imag(targetData)]; 

%%Input data 

inputData = ones(10, 4); 

% these are all ones because the function to approximate can be written as: 

% x * 1 + y * 1 * 1i + z * 1 + w * 1 * 1i 

% we want to find x, y, z, w 

% so the input data are all ones 

%%Starting assumption for x, y, z, w values 

coeff0 = zeros(size(inputData)); 

%%Create options for the function call 

opts = optimoptions(@lsqcurvefit, 'Algorithm', 'levenberg-marquardt'); 

%%Call the optimization function 

coeffVals = lsqcurvefit(@curveFunc, coeff0, inputData, uData, [], [], opts); 

%%Get the predicted data based on output of the optimization routine 

predictedData = curveFunc(coeffVals, inputData); 

%%Plot the original data and predicted data 

figure; hold on; 

plot(uData(:, 1), uData(:, 2), 'g*'); 

plot(predictedData(:, 1), predictedData(:, 2), 'bo'); 

function uout = curveFunc(v, xdata) 

      % this part is broken down to show how the "curveFunc" relates to the function that we are trying to approximate 

      tmpUout = v(:, 1) .* xdata(:, 1); % a values 

      tmpUout = tmpUout + 1i * v(:, 2) .* xdata(:, 2); % b values 

      tmpUout = tmpUout + v(:, 3) .* xdata(:, 3); % c values 

      tmpUout = tmpUout + 1i * v(:, 4) .* xdata(:, 4); % d values 

      uout = [real(tmpUout) imag(tmpUout)]; 

end