How to use polyfit to get the difference out of two functions?

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Stelios Fanourakis 2019-4-20

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评论： Stelios Fanourakis 2019-4-24

I have two datasets (X,Y). For every value of Y that corresponds to a value of X.

I am thinking of applying a polyfit command to get the best curve fitting for the data, and as a result I will come up with a function (slope+intercept).

How do I find the difference between those two functions? What command do I apply to subtract Function A from Function B?

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Walter Roberson 2019-4-21

One of the functions is the one implied by polyfit(x,y,1) . But what is the other function?

A collection of points is not considered a function except in mathematical theory (in which case, the collection of ordered values is considered to define the function, and formulae are just shorthand for the collection of values.)

Stelios Fanourakis 2019-4-21

@Walter. The datasets are curves. If I plot them in excel and apply a polynomial curve fitting of high degree (e.g. 6) then I get the best line fit and a function. I need to get the same function in Matlab. And then subtract one function from another since the datasets are very close each other, to find their difference. How do I do that?

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采纳的回答

Walter Roberson 2019-4-21

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P1 = polyfit((1:length(X)).', X(:), 6);

Likewise for Y producing P2

Pd = polyval(P1, 1:length(X)) - polyval(P2, 1:length(X))

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Walter Roberson 2019-4-21

在 MATLAB Online 中打开

Supposing that X and Y have two columns, with X(K,1) corresponding to Y(K,1) and X(K,2) corresponding to Y(K,2) then

P1 = polyfit(X(:,1), Y(:,1), 6);
P2 = polyfit(X(:,2), Y(:,2), 6);
allX = union(X(:,1), X(:,2));
Pd = polyval(P1, allX) - polyval(P2, allX);
plot(allX, Pd);

In MATLAB, ' is complex conjugate transpose, formal name ctranspose() . But I did not use it. I used .' which is regular transpose without complex conjugate, formal name transpose() .

polyfit() can accept X and Y that are both rows, or X and Y that are both columns, but it does not like a mix such as a row X = 1:20 and a column Y = rand(20,1) . I do not know the orientation of your dataset so I cannot assume that your Y is a row, so it is not safe for me to program polyfit(1:length(Y), Y, 6) because Y might be a column. Therefore I need to force both X and Y to be rows, or force both to be columns. Using (:) forces a column so Y(:) to force a column for Y is easy, but the two ways to force Y to be a row are Y(:).' or else reshape(Y,1,[]) which are a bit ugly. So it is easiest to force X to be a column by using the .' operator on what is known to be a row, 1:length(X), and use Y(:) . I could also have written

P1 = polyfit(1:length(X), Y(:).', 6)

Now, if someone happened to be writing this as part of a sequence of statements and had reason to know that Y was a row already, then they could just use

P1 = polyfit(1:length(X), Y, 6)

but since I do not know because the person asking the problem did not specify the shape, then I have to put in the protections to make the code work either way.

Stelios Fanourakis 2019-4-23

在 MATLAB Online 中打开

I get the below error

P1 =
     0     0     0     0     0     0     0
Warning: Polynomial is not unique; degree >= number of data points. 
> In polyfit (line 74)
  In curvefitdif (line 19) 
P2 =
     0     0     0     0     0     0     0
Pd =
  0×1 empty double column vector
P11 =
  0×1 empty double column vector
P22 =
  0×1 empty double column vector

Stelios Fanourakis 2019-4-24

在 MATLAB Online 中打开

I also get the error

Error using isnan
Too many input arguments.
Error in see (line 38)
mask = isnan(x1{:,:}) | isnan(y1{:,:});

Why?

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更多回答（2 个）

John D'Errico 2019-4-21

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Polynomials are linear in the coefficients. So the difference of two polynomials is obtained by just subtracting the coefficients. If they are different order polynomials, just pad the low order polynomial with zeros as necessary to correspond to the higher order coefficients that are effectively zero.