least square curve fit

i have written a code for least square fit and it is taking lot of time to plot the data

i want someone to verify it and update it so that i could get appropriate results within less time

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

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

points_curve_fit =  5:2:9;  



i = 0;
for nwindow = points_curve_fit
    i = i+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); 
        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(:,i) = err; % to plot all outputs
    pos_all(:,i) = pos; % to plot all outputs
    velo_all(:,i) = velo; % to plot all outputs
    acc_n_all(:,i) = acc_n; % to plot all outputs
    
    
    n= length(pos);
    tim_pos    = x_imp(1:n);
    tim_velo   = x_imp(1:n);
    tim_acc_n  = 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','-g',tim_velo,velo_all','--k',tim_acc_n,acc_n_all','--y'); grid on; 
    legend([{' raw data','position','velocity','acceleration'}]);
    xlabel(' Time(sec) ');
    ylabel(' Function ');
    
end   



fig2 = figure('name','errors' ,'NumberTitle','off');
plot(tim_pos,err_all,'--');grid on;
legend('error 5 pts','error 7 pts','error 9 pts');

[Walter Roberson]

Is there a reason you are not just using polyfit() ?

[Jeffrey Clark]

As for the execution time, see the Tips section of inv which recommends against using inv when \ (mldivide) will suffice.

Also, pre-allocate pos and move lines out of the first loop:

% before 'for k' add (check my math)
    pos = zeros((floor(nwindow/2) + 1)*(rows-nwindow),1);
    
%fix   phi = inv(amat)*bmat  to be  phi = amat\bmat
    
    % move these after 'store iteration results' comment
        velo             = gradient(pos,dx);
        acc_n            = gradient(velo,dx);

[sanket neharkar]

okk i did that

i want to update my 3 figures with the names as the for loop

for first fig it should come as 5points curve fit then

7point curve fit

9 point curvefit

plzz help me in that

[Walter Roberson]

title(points_curve_fit + " point curve fit")

Note that double quotes instead of apostrophe is important here.