plotting 3 figures in a single figure when they are in loop

i had plotted a least square fit plot and i have calculate the error , i have fitted a curve withe the 5,7,9 points approximations, now i have to draw the graphs of the error for all the approximations in a single figure for comparison,

function phi = curvefit3(x,y)
clear all;
close all;
clc;
[data, ~] = xlsread('filename.xlsx'); 
x_imp           = data(:,1); %%reading rows  and first column
y_imp           = data(:,2); %%reading rows  and second column
[rows, ~] = size(data);
for i = 5:2:9
    window    = i;
    fig(i) = figure('name', sprintf('%d points curve fit', i),'NumberTitle','off');
    for i           =  1: 1 : rows -window     %%loop to read i+1 to i+5 rows    
        x           =  x_imp(i:i+window-1,1);
        y           =  y_imp(i:i+window-1,1);
        x0          = x(1);
        var1        = x - x0;
        var2        = var1.*var1;
        %% construction of the least-squares quadratic fit to the data
        %% we use the equation y =a0 + a1t + a2t^2 %%t = (x-x0)
        %% numbers a0,a1 and a2 are the unknowns
        x_mat            = [ones(window,1) var1  var2]; 
        amat             = x_mat'*x_mat;
        bmat             = x_mat'*y;
        phi              = inv(amat)*bmat;
        a0               = phi(1);
        a1               = phi(2);
        a2               = phi(3);
        error            = y-(x_mat*phi);
        marker           = floor(window/2) + 1;
        if               (i == 1)
            err(1:marker,1)    =error(1:marker,1);
        else
            err(i+marker-1)    =error(marker);
        end
        pos_n            = (a0+a1*var1+a2*var2);
        markar           = floor(window/2) + 1;
        if                (i == 1)
            pos(1:markar,1)    = pos_n(1:markar,1);
        else 
            pos(i+markar-1)     = pos_n(markar); 
            %    plot(pos,'-ob');
        end   %if                (i == 1)  
        velo             = diff(pos);
        acc_n            = diff(diff(pos));
    end    %for i           =  1: 1 : rows-window
    n= length(pos);
    tim_pos    = x_imp(1:n);
    tim_velo   = x_imp(1:n-1);
    tim_acc_n  = x_imp(1:n-2);
    y_raw      = y_imp(1:n);
    plot(tim_pos,y_raw,'or',tim_pos,pos','-g',tim_velo,velo','--k',tim_acc_n,acc_n','*b'); grid;
    legend(' raw data', 'Curve Fit',' velocity', 'acceleration');
    xlabel(' Time(sec) ');
    ylabel(' Function ');
    fig(i) = figure('name', sprintf('%d points error', i),'NumberTitle','off');
    plot(tim_pos,err,'--k');grid;
    legend('error');
end         %for i = 5:2:9

return;

what should i do in this so that whatever the error graph i have plotted will come in a single figure ,with legend as 5pointerror,and so on

Answer 1

[Mathieu NOE]

hello

see my suggestion below (based on dummy data as you don't supply any file)

notice that to compute the velocity and acceleration you can use the function gradient instead of diff , which has the advantage to keep all data length equal . Also do not forget to use the dx spacing with diff or gradient otherwise your derivatives are wrong;

% function phi = curvefit3(x,y)
clear all;
close all;
clc;
% [data, ~] = xlsread('filename.xlsx'); 
% x_imp           = data(:,1); %%reading rows  and first column
% y_imp           = data(:,2); %%reading rows  and second column


%% dummy data
x_imp           = (0:0.1:10)';
y_imp           =  0.5 +1.2*x_imp + 0.54*x_imp.^2 + 0.02*randn(size(x_imp));
data = [x_imp y_imp];

[rows, ~] = size(data);
dx = mean(diff(x_imp));

points_curve_fit =  5:2:9;   
    
ci = 0;

for nwindow = points_curve_fit
    ci = ci+1;
    for k           =  1: 1 : rows -nwindow     %%loop to read i+1 to i+5 rows    
        x           =  x_imp(k:k+nwindow-1,1);
        y           =  y_imp(k:k+nwindow-1,1);
        x0          = x(1);
        var1        = x - x0;
        var2        = var1.*var1;
        %% construction of the least-squares quadratic fit to the data
        %% we use the equation y =a0 + a1t + a2t^2 %%t = (x-x0)
        %% numbers a0,a1 and a2 are the unknowns
        x_mat            = [ones(nwindow,1) var1  var2]; 
        amat             = x_mat'*x_mat;
        bmat             = x_mat'*y;
        phi              = inv(amat)*bmat;
        a0               = phi(1);
        a1               = phi(2);
        a2               = phi(3);
        error            = y-(x_mat*phi);
        marker           = floor(nwindow/2) + 1;
        if               (k == 1)
            err(1:marker,1)    =error(1:marker,1);
        else
            err(k+marker-1)    =error(marker);
        end
        pos_n            = (a0+a1*var1+a2*var2);
        markar           = floor(nwindow/2) + 1;
        if                (k == 1)
            pos(1:markar,1)    = pos_n(1:markar,1);
        else 
            pos(k+markar-1)     = pos_n(markar); 
            %    plot(pos,'-ob');
        end   %if                (i == 1)  
        velo             = gradient(pos,dx);
        acc_n            = gradient(velo,dx);
        
    end    
    
    % store iteration results into 2D array (1 iteration = 1 column)
    err_all(:,ci) = err; % to plot all outputs
    pos_all(:,ci) = pos; % to plot all outputs
    velo_all(:,ci) = velo; % to plot all outputs
    acc_n_all(:,ci) = acc_n; % to plot all outputs
    
    str_pos{ci} = ['Pos Curve Fit' num2str(points_curve_fit(ci)) ' points'];
    str_velo{ci} = ['Velo Curve Fit' num2str(points_curve_fit(ci)) ' points'];
    str_acc{ci} = ['Accel Curve Fit' num2str(points_curve_fit(ci)) ' points'];
    str_err{ci} = ['error ' num2str(points_curve_fit(ci)) ' points'];
    

end         

   n= length(pos);
    tim_pos    = x_imp(1:n);
    y_raw      = y_imp(1:n);
    
    fig1 = figure('name', sprintf('%d points curve fit ', points_curve_fit),'NumberTitle','off');
    plot(tim_pos,y_raw,'or',tim_pos,pos_all,'-',tim_pos,velo_all,'--',tim_pos,acc_n_all,'*'); grid on;
    legend([{' raw data'}  str_pos str_velo  str_acc]);
    xlabel(' Time(sec) ');
    ylabel(' Function ');

    fig2 = figure('name', sprintf('%d points error ', points_curve_fit),'NumberTitle','off');
    plot(tim_pos,err_all,'--');grid on;
    legend(str_err);