MATLAB: With a given set of X and Y values, how to determine (m+jn) for the equation—Y = (a+jb)X^3+(c+jd)X^2+(p+jq)X+(m+jn). X and Y values are in complex form

curve fittingcurve fitting with complex valuesregressionregression with complex numbers

With a given set of X and Y values, how to determine (m+jn) for the equation: Y = (a+jb)X^3+(c+jd)X^2+(p+jq)X+(m+jn). X and Y values are also in complex form

Best Answer

You can get the values like this

output = [X.^3 X.^2 X.^1 ones(size(X))]\Y

It will return 4 complex numbers. Depending on the number of elements in X and Y, the solution is either unique (if the number of elements in X is equal to 4), one of infinitely many (if the number of elements in X is less than 4) or solution in least square sense (if the number of elements in X is greater than 4).

Related Solutions

MATLAB: Lsqcurvefit

Since the distance between two complex numbers a+i*b and c+i*d is (a-c)^2 + (b-d)^2, you could treat each complex number as a pair of independent real numbers. Wrap fun in a function rfun that returns the real and complex parts of the output. For example, assuming rfun returns a column vector,

function y = rfun(x)
  y = rfun(x);
  y = [real(y); imag(y)];
end

Similarly, you could replace ydata by

rdata = [real(ydata); imag(ydata)].

Then you have the first two inputs for lsqcurvefit.

MATLAB: How to threshold only real part of a complex matrix

>> A = complex(randi([-3,3],4,4),randi([-3,3],4,4)) % fake data
A =
  -2 + 3i  -2 + 1i   2 - 3i  -2 + 1i
  -2 + 0i   3 + 0i  -3 + 3i   0 + 0i
   2 + 0i   2 - 2i   3 + 3i   0 - 3i
   1 - 2i  -3 - 2i   3 + 2i   0 - 2i
>> B = complex(real(A).*(real(A)<=0.5),imag(A)) % set real(A)>0.5 to 0.
B =
  -2 + 3i  -2 + 1i   0 - 3i  -2 + 1i
  -2 + 0i   0 + 0i  -3 + 3i   0 + 0i
   0 + 0i   0 - 2i   0 + 3i   0 - 3i
   0 - 2i  -3 - 2i   0 + 2i   0 - 2i

Best Answer

Related Solutions

MATLAB: Lsqcurvefit

MATLAB: How to threshold only real part of a complex matrix

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