least square curve fit

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sanket neharkar
sanket neharkar on 16 Jun 2022
Commented: Walter Roberson on 17 Jun 2022
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');
  4 Comments
Walter Roberson
Walter Roberson on 17 Jun 2022
title(points_curve_fit + " point curve fit")
Note that double quotes instead of apostrophe is important here.

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