How do I get a symbolic differentiation of cfit/sfit functions?

Question

Tim Baur 2019-12-12

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https://ww2.mathworks.cn/matlabcentral/answers/496351-how-do-i-get-a-symbolic-differentiation-of-cfit-sfit-functions

评论： Tim Baur 2020-1-2

Hi everyone,

I am trying to get the symbolic partial derivative of a sfit function. Best case would be having the differentition as an sfit function, too.

Thanks in advance!

EDIT:

Here's an example:

%data
x = [0.5850;0.0734;0.8223;0.7229;0.9259;0.4926];
y = [0.6549;0.8901;0.5385;0.2822;0.9760;0.0364];
z = [0.3262;0.9730;0.3650;0.3091;0.1209;0.9158];
%surface fit
sf = fit([x, y],z,'poly22')
plot(sf)
%      Linear model Poly22:
%      sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
%      Coefficients:
%        p00 =       5.048
%        p10 =      -11.04
%        p01 =      -1.326
%        p20 =       5.179
%        p11 =       5.682
%        p02 =      -3.135

Now I could use the differentiate method to get the derivative at specific points but I would like to have the derived function, like this (witthout having to derive it manually):

% sf_x(x,y) = p10 + 2*p20*x + p11*y

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Tim Baur 2019-12-13

Yes, I did. diff does not take sfit as input argument, unfortunately.

darova 2019-12-13

Can you provide an example please?

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Answer 1

Walter Roberson 2019-12-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/496351-how-do-i-get-a-symbolic-differentiation-of-cfit-sfit-functions#answer_406552

在 MATLAB Online 中打开

When sf is the fit object,

f = subs(str2sym(formula(sf)),coeffnames(sf),num2cell(coeffvalues(sf).'));
vars = sym(indepnames(sf));
diff(f, vars(1))

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Walter Roberson 2019-12-16

在 MATLAB Online 中打开

It appears to me that to do that you would use a different approach:

vars = sym(indepnames(sf));
df = diff( str2sym(formula(sf)), vars(1))    %or appropriate variable number
dfun = matlabFunction(df, 'vars', sym(argnames(sf)));
ft = fittype(dfun, 'independent', indepnames(sf), 'dependent', dependnames(sf), 'options', fitoptions(sf));

However, this does not construct an sfit object, as it is not the result of fitting. You could use it to fit something.

More subtly, the fittype() call will fail, because it tries to use all of the coefficient names from sf to provide a direct correspondance, but the differential formula omits some of the coefficients because they vanish in the derivative. The fix using the used coefficient names is

vars = sym(indepnames(sf));
df = diff( str2sym(formula(sf)), vars(1))    %or appropriate variable number
used_coeffs = sym(intersect(symvar(df), sym(coeffnames(sf))));
var_order = [used_coeffs; sym(indepnames(sf))];
dfun = matlabFunction(df, 'vars', var_order);
ft = fittype(dfun, 'independent', indepnames(sf), 'dependent', dependnames(sf), 'options', fitoptions(sf));