Azzera filtri
Azzera filtri

Total Least squares error help. I tried a couple different things here, but i'm not exactly sure how to do a total least squares error. The numbers aren't making sense to me.

3 visualizzazioni (ultimi 30 giorni)
clear all
% A represents the sample measured in days
A = [1, 0; 1, 1; 1, 2; 1, 3; 1, 4; 1, 5; 1, 6; 1, 7]
A = 8×2
1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7
% b represents the amount of radium measured
b = [100; 82.7; 68.3; 56.5; 46.7; 38.6; 31.9; 26.4]
b = 8×1
100.0000 82.7000 68.3000 56.5000 46.7000 38.6000 31.9000 26.4000
% Least Squares
c = lsqr(A,log(b))
lsqr converged at iteration 2 to a solution with relative residual 9.5e-05.
c = 2×1
4.6051 -0.1903
g = A.'*A
g = 2×2
8 28 28 140
rhs = A.'*log(b);
x = g\rhs
x = 2×1
4.6051 -0.1903
thalf = -x(2)^-1*log(2)
thalf = 3.6417
m0 = exp(x(1))
m0 = 99.9942
m = @(t) m0*exp(x(2)*t);
predictionvalues = m([0, 1, 2, 3, 4, 5, 6, 7]);
squareddifferences = (predictionvalues - b).^2;
totalerror = sum(squareddifferences)
totalerror = 1×8
1.0e+04 * 1.9858 1.0169 0.5788 0.4646 0.5396 0.7175 0.9436 1.1847
t = [0, 1, 2, 3, 4, 5, 6, 7];
plot(t, x(1) + x(2)*t, t, log(b),'o')
%%plot(t, abs(exp(y_approx(t)-b)))
xlabel("t")
ylabel("error")
  2 Commenti
Rian Sullivan
Rian Sullivan il 17 Feb 2024
Is the total least squares function okay? I was just making sure I even did the total least squares error code right. The total error seemed really small, but maybe im misunderstanding what it actually means. totalerror =
1.0e+04 *
Is what pops up along with all the other columns and their errors. It makes sense I believe.. but I'm just struggling with thinking my number of error doesn't look right.

Accedi per commentare.

Risposte (1)

David Goodmanson
David Goodmanson il 17 Feb 2024
Modificato: David Goodmanson il 17 Feb 2024
Hi Rian,
the problem is that b is a column vector, but predictionvalues is a row vector. Using
predictionvalues = m([0, 1, 2, 3, 4, 5, 6, 7])'; % column vector
squareddifferences = (predictionvalues - b).^2;
totalerror = sum(squareddifferences)
totalerror =
0.0033
although depending on circumstances, you may want to use sqrt(totalerror/8), the rms value, as the final result
  1 Commento
Rian Sullivan
Rian Sullivan il 17 Feb 2024
Oh wow! That makes complete sense. Can't believe I missed that. I think that total error makes a lot more sense to me now. Thank you so much!

Accedi per commentare.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by