Fitting a plot with interpolation

I need to interpolate some data involving a logarithm using the fit function but I'm not sure how to interpolate in matlab. Generally speaking, how does one interpolate data in MATLAB?

Answer 1

[Walter Roberson]

interp1() for 1D cases, interp2() for 2D cases

However, it does not sound to be as if you want to use either. It looks to me as if you want to use the Curve Fitting Toolbox fittype() and fit() functions. Then you want to evaluate the fitted model at a particular location, which you can do by using the returned fit object as if it were a function.

F = fittype('poly2')

F = 
     Linear model Poly2:
     F(p1,p2,p3,x) = p1*x^2 + p2*x + p3

p = fit((1:5).', rand(5,1), F)

p = 
     Linear model Poly2:
     p(x) = p1*x^2 + p2*x + p3
     Coefficients (with 95% confidence bounds):
       p1 =    -0.01913  (-0.5426, 0.5044)
       p2 =     0.05751  (-3.144, 3.259)
       p3 =      0.4766  (-3.725, 4.678)

p(7)

ans = -0.0583

Except that you would be constructing a different fittype() object, and using real data instead of the fake data I used here.

[SALAH ALRABEEI]

I am not quite sure if polynomial interpolation can fit his logarithmic data

[Walter Roberson]

I do believe that I wrote,

"Except that you would be constructing a different fittype() object, and using real data instead of the fake data I used here."

The list of already-built library models for fittype() is at https://www.mathworks.com/help/curvefit/list-of-library-models-for-curve-and-surface-fitting.html . You can also create custom equations, either using a quoted string that is an expression https://www.mathworks.com/help/curvefit/fittype.html#btpaend-1-expression or using the handle to a function https://www.mathworks.com/help/curvefit/fittype.html#btpaend-1-anonymousFunction

[SALAH ALRABEEI]

Thank you, this resource is really useful.

[laurent jalabert]

how can I write the syntax of a nonlinear regression fitting model involving an interp1 that contains a fitting parameter ?

table_theory is a table of X and Y vector (length ~ 300)

table_exper is a table of x and y experimental data (length ~50)

RP = interp1(table_theory,500)

modelR = @(x )beta * RP(alpha * x)

alpha and beta the fitting parameters

h_mdl = fitnlm(table_exper,modelR,beta,'CoefficientNames',{'apha';'beta'});

I would like to take table_exper, then find the best coefficient alpha (on x-axis) and beta (on y-axis) so that the resulting y=beta * RP(alpha * x) will be the closest to the table_theory.