Using custom fit equation for surface

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Xymbu 2022-4-29

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https://ww2.mathworks.cn/matlabcentral/answers/1708375-using-custom-fit-equation-for-surface

评论： Xymbu 2022-4-29

If I do a fittype for a cruve like this

ft = fittype('a + b*x + c *x^2')

it works fine, but if i want to do a surface fit with a custom equation like with y as a variable like this (just an example not the equation im using)

ft = fittype('a + b*x + c x^2 + d*y^2')

it gives me this error

"The name y cannot be used for both a coefficient and the dependent variable"

How do I work around this.

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Answer 1

Torsten 2022-4-29

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https://ww2.mathworks.cn/matlabcentral/answers/1708375-using-custom-fit-equation-for-surface#answer_954000

在 MATLAB Online 中打开

ft = fittype('a + b*x + c x^2 + d*y^2','dependent',{'z'},'independent',{'x','y'},'coefficients'{'a','b','c','d'})

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Riccardo Scorretti 2022-4-29

在 MATLAB Online 中打开

Torsten is right. The documents of ftitype reads: "fittype assumes x is the independent variable, y is the dependent variable, and all other variables are coefficients of the model. x is used if no variable exists.", Basically, it is mandatory to set a different name for the dependent variable, which is y by default.

Hereis a full example:

% Generate some noisy data

a0 = 1 ; b0 = 3 ; c0 = -2 ; d0 = 2;

[x, y] = meshgrid(-3:3, -3:3);

data = a0 + b0*x + c0*x.^2 + d0*y.^2;

data = data + 2*randn(size(data));

% fittype assumes x is the independent variable, y is the dependent variable,

% and all other variables are coefficients of the model. x is used if no variable exists.

opt = fitoptions('Method','NonlinearLeastSquares', 'StartPoint', [0 0 0 0]);

fun = fittype('a + b*x + c*x^2 + d*y^2', ...

'independent', {'x', 'y'}, ...

'dependent', 'f', ...

'options', opt);

myfit = fit([x(:) y(:)], data(:), fun)

General model: myfit(x,y) = a + b*x + c*x^2 + d*y^2 Coefficients (with 95% confidence bounds): a = 0.5926 (-0.5208, 1.706) b = 3.125 (2.835, 3.416) c = -1.996 (-2.164, -1.828) d = 2.103 (1.935, 2.271)

% Let's check

hndl = plot(myfit, [x(:) y(:)], data(:));

hndl(1).FaceAlpha = 0.5;