Using least square fitting function lsqr

Hello,

I need an example how to apply Matlab's built in lsqr function to solve the following task.

let's say I have a sequence of square pulses which is transformed in the following way:

rng(0)
n = 20;
s = rand(1, n) > 0.5;
s = repmat(s', 1, 100)';
s = s(:)';
t = linspace(0, n, numel(s));
subplot(2, 1, 1)
plot(t, s, 'Linewidth',2)

scale_factor = 1.05;
offset = 1.5;
t2 = t * scale_factor + offset;
subplot(2, 1, 2)
plot(t2, s, 'LineWidth',2) 

Now if that previous transformation is unknown and I need to estimate scale_factor and offset i.e. my initial condition is actually only a plot data:

or my only inputs are:

t1_n = t(s==1);
T1 = [t1_n; ones(size(t1_n))];
    
t2_n = t2(s==1);
T2 = [t2_n; ones(size(t2_n))];

How to use lsqr function to calculate scale_factor and offset. I know that for this particular case, I only need to points to calculate coefficients of line equation y = a*x+b, but in general, data can be noisy, so more points are needed and thus the obvious choise would be to use least square fitting.

Thank you!

P.S. I forgot to mention, I can solve this problem using the function lsqcurvefit, but I would like to see how lsqr can be applied.

Answer 1

[Torsten]

rng(0)
n = 20;
s = rand(1, n) > 0.5;
s = repmat(s', 1, 100)';
s = s(:)';
t = linspace(0, n, numel(s));
subplot(2, 1, 1)
plot(t, s, 'Linewidth',2)
scale_factor = 1.05;
offset = 1.5;
t2 = t * scale_factor + offset;
subplot(2, 1, 2)
plot(t2, s, 'LineWidth',2) 

t1_n = t(s==1).';
t2_n = t2(s==1).';
A = [t1_n,ones(size(t1_n))];
b = t2_n;
sol1 = A\b

sol1 = 2×1

1.0500 1.5000

sol2 = lsqr(A,b)

lsqr converged at iteration 2 to a solution with relative residual 5e-14.

sol2 = 2×1

1.0500 1.5000

sol3 = lsqlin(A,b)

sol3 = 2×1

1.0500 1.5000

sol4 = lsqminnorm(A,b)

sol4 = 2×1

1.0500 1.5000

[Askic V]

Perfect, thank you very much.