hello
I played with your data (and had to use some available alternatives to spline smoothing as I don't have the required toolbox) but e final goal and what you want to do is still unclear to me
maybe you should tell us a bit more about what is the end goal and then we can come up with a solution.
clearvars, close all;
load('data.mat')
x = xs;
y = yb2;
clear xs yb2
id = x<700;
x=x(id);
y=y(id);
% smoothdata realisation
ys = smoothdata(y,"loess",20);
% B spline smoothing
m = 8;% B-Spline Degree
s = f_Bspline([x';y'], m, 0.5);% B-Spline
xspl = s(1,:);
yspl = s(2,:);
% curve fit using fminsearch
f = @(a,b,c,x) a.*exp(-(x-b).^2 / c.^2);
obj_fun = @(params) norm(f(params(1), params(2), params(3),x)-y);
sol = fminsearch(obj_fun, [max(y),max(x)/2,max(x)/6]);
a_sol = sol(1);
b_sol = sol(2);
c_sol = sol(3);
xx = linspace(min(x),max(x),300);
y_fit = f(a_sol, b_sol,c_sol, xx);
yy = interp1(x,y, xx);
Rsquared = my_Rsquared_coeff(yy,y_fit); % correlation coefficient
plot(x,y, 'r',x,ys, 'k',xspl,yspl, 'g',xx, y_fit, '-' , 'Linewidth', 2.5)
title(['Gaussian Fit / R² = ' num2str(Rsquared) ], 'FontSize', 5)
ylabel('Intensity (arb. unit)', 'FontSize', 14)
xlabel('x(nm)', 'FontSize', 14)
legend('raw data','smoothdata','B spline smooth','gaussian fit')
%%%%%%%%%%%%%%%%%%%%%%%%%
function s = f_Bspline(C, m, step)
% Calculates a B-Spline of degree m using the control points C.
%
% C: 2-dimensional control points (x_0, ... , x_n; y_0, ... , y_n)
% m: B-Spline degree
% step: Step size of t.
%
% s: B-Spline. s(1,:) -> x component, s(2,:) -> y component
%% Parameters
% Control point's x and y components
x = C(1,:);
y = C(2,:);
% Number of control point - 1
n = size(x,2) - 1;
% Knot vector
T = f_BSpline_KnotVector(m,n);
% B-Spline intervall
t = 0:step:(n-m+1);
%% Calculate B-Spline
for z=1:1:size(t,2)
ti = t(z);
s(1,z) = 0;
s(2,z) = 0;
for i=0:1:n
% Base B-Spline
B = f_BSpline_BaseSpline(i, m, ti, T);
% x component
s(1,z) = s(1,z) + x(i+1) * B;
% y component
s(2,z) = s(2,z) + y(i+1) * B;
end
end
end
function T = f_BSpline_KnotVector(m,n)
% Calculate knot sequence.
% m: Degree of B-Spline
% n: Number of control points - 1
%
% T = [t0, ... , t_n+m+1] : Knot sequence / vector
T = zeros(1, (n+m+2));
for j=0:1:(n+m+1)
if j <= m
Ti = 0;
elseif j >= (m+1) && j <= n
Ti = j - m;
elseif j > n
Ti = n - m + 1;
end
T(j+1) = Ti;
end
end
function B = f_BSpline_BaseSpline(i, k, t, T)
% Calculate Base B-Spline B_i,k
% k: B-Spline degree
% T: Knot sequence
% t: Current t parameter
%
% B: Base B-Spline at t.
% Index shift
j = i + 1;
if k == 0
% Corrected end of recursion
if (t >= T(j) && t < T(j+1))
B = 1;
% Exception: the last basis function is equal to 1 also at the last knot.
% There might be a more elegant way of writing it; I am no Matlab expert.
elseif ( T(j+1) == T(end) && t == T(end))
B = 1;
else
B = 0;
end
else
% Check dividing by zero
if T(j+k) ~= T(j)
A = (t -T(j))/(T(j+k) - T(j));
else
A = 0;
end
if T(j+k+1) ~= T(j+1)
B = (T(j+k+1) - t) / (T(j+k+1) - T(j+1));
else
B = 0;
end
% Calculate base B-Spline
B1 = f_BSpline_BaseSpline(i, k-1, t, T);
B2 = f_BSpline_BaseSpline(i+1, k-1, t, T);
B = A * B1 + B * B2;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Rsquared = my_Rsquared_coeff(data,data_fit)
% R2 correlation coefficient computation
% The total sum of squares
sum_of_squares = sum((data-mean(data)).^2);
% The sum of squares of residuals, also called the residual sum of squares:
sum_of_squares_of_residuals = sum((data-data_fit).^2);
% definition of the coefficient of correlation is
Rsquared = 1 - sum_of_squares_of_residuals/sum_of_squares;
end
