how to fit non linear equation with ten parameters

Hi everyone,

I have to computed ten parameters in non linear equation, I tryied to use 'nlinfit' command but I obtain the following error:

Error using nlinfit (line 219)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (30615-by-1).  The
model function you provided returned a result that was 1-by-1.

One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the
corresponding elementwise operators (.*, ./, .^).

Error in C_Fourier_Analysis (line 58)
F_fitted = nlinfit(x,y,f,[1 1 2*pi*rand 1 2*pi*rand 1 1 2*pi*rand 1 2*pi*rand]);

I'm attacching the complete code and the data. Thanks.

format long g
folderData = 'C:\Users\Valerio\Desktop\TRAINEESHIP\data\ACCESS1.0';
filePattern = fullfile(folderData, '*.xlsx');
xlsFiles = dir(filePattern);
nFiles = length(xlsFiles);

for ii = 1:nFiles
    filename = fullfile(xlsFiles(ii).folder, xlsFiles(ii).name);
    files{ii} = xlsread(filename);
end

IPCC = files(1);
ERA5 = files(2);

IPCC_data = unique(IPCC{:,1},'rows');
ERA5_data = unique(ERA5{:,1},'rows');

dt_IPCC = datetime([IPCC_data(:,1:3) IPCC_data(:,4)/1E4 repmat([0 0],size(IPCC_data,1),1)]);
dt_ERA5 = datetime([ERA5_data(:,1:4) repmat([0 0],size(ERA5_data,1),1)]);
[~,ia,ie] = intersect(dt_IPCC,dt_ERA5);
tt_IPCC_ERA5 = timetable(dt_IPCC(ia),IPCC_data(ia,5:end),ERA5_data(ie,5:end));
tt_IPCC_ERA5.Properties.VariableNames = {'IPCC','ERA5'};
IPCC = tt_IPCC_ERA5.IPCC;
ERA5 = tt_IPCC_ERA5.ERA5;

y = ERA5(:,1); %Hs from ERA5
dir_ERA5 = ERA5(:,3);

x1 = IPCC(:,1); %Hs from IPCC
x2 = IPCC(:,3); %Dir from IPCC
Tm_IPCC = IPCC(:,2);
Tm_ERA5 = ERA5(:,2);

figure
scatter(dir_ERA5,x2,'g');
xlabel('Dir ERA5');
ylabel('Dir IPCC');
title('Linear regression between directions');
%Plot regression linear line
dir_ERA5(isnan(x2)) = [] ;
x2(isnan(x2)) = [] ;
P = polyfit(dir_ERA5,x2,1);
x0 = min(dir_ERA5) ; x3 = max(dir_ERA5) ;
xi = linspace(x0,x3) ;
yi = P(1)*xi+P(2);
hold on
plot(xi,yi,'b');
%Computing linear regression parameters 
lin_param = fitlm(dir_ERA5,x2);
Pearson = lin_param.Rsquared;
Error_R = lin_param.RMSE;

%Fourier Analysis
x = [x1', x2'];

f = @(F,x)(F(1)+F(2)*cos(2*pi*(x(:,2)./360)-F(3))+F(4)*cos(4*pi*(x(:,2)./360)-F(5))).*x(:,1).^(F(6)+F(7)*cos(2*pi*(x(:,2)./360)-F(8))+F(9)*cos(4*pi*(x(:,2)./360)-F(10)));

F_fitted = nlinfit(x,y,f,[1 1 2*pi*rand 1 2*pi*rand 1 1 2*pi*rand 1 2*pi*rand]);

Answer 1

[Ameer Hamza]

This error is caused because vector created by this line is

x = [x1', x2'];

1*x, however, it seems that you expected it to be x*2 matrix. Changing the line to

x = [x1, x2];

will solve this issue. However, after this, there is another issue related to your function f returning inf and nan. To resolve that, you will need to check the issue with your equation.

[Valerio Gianforte]

Thank you for information but I have no idea what is the problem of my equation.

[Ameer Hamza]

It has to do with the complexity of your model. MATLAB is having difficulity to find a fit to your dataset. I tried few things but couldn't able to solve this issue. Trying to simplify the model will be helpful.

[Valerio Gianforte]

Ok, Thank you so much!