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To be more detailed, here's a concrete example using an Nx1 input $ y $. First, the tridiagonal matrix $C$ is
$$
C = \begin{bmatrix}
A & 0 & 0 & 0 \
-2B & A + 4B & 0 & 0 \
0 & -2B & A + 4B & 0 \
0 & 0 & -2B & A
\end{bmatrix}
$$
and the 2nd substituted matrix $ D_2 $ is
$$
C = \begin{bmatrix}
A & A y_1 & 0 & 0 \
-2B & A y_2 & 0 & 0 \
0 & A y_3 & A + 4B & 0 \
0 & A y_4 & -2B & A
\end{bmatrix}
$$
But notice that $ \det(C) $ and $ \det(D_i) $ have the same power of $ A $ because every element is a multiple of $ A $. That means All instances of $ A $ cancels out everywhere and it's not actually doing anything. Either we need to change the definition of $ A $ so that it doesn't cancel everywhere, or get rid of it.
The text was updated successfully, but these errors were encountered:
Also I now know the matrix part is using Cramer's rule to fit a 'stiff' spline onto the curve and reduce curvature on the spline. The details should be tracked down and properly documented.
unused variable x is removed; issue regarding uselessness of A is ignored for current version (4.5), will fix in a more comprehensive update when we have time for it
The variable x is not called anywhere else, might be a vestigial code (should remove)
https://github.itap.purdue.edu/Nolte-Group/alpha-prime-system/blob/841dd47dbbf2029f57cba587c1b7fb3b283dfbda/onekey4-core/smoothfit.m#L27
By design, dr (and also A) doesn't actually do anything and should be removed. They are defined on:
https://github.itap.purdue.edu/Nolte-Group/alpha-prime-system/blob/841dd47dbbf2029f57cba587c1b7fb3b283dfbda/onekey4-core/smoothfit.m#L22-L24
To be more detailed, here's a concrete example using an Nx1 input $ y $. First, the tridiagonal matrix$C$ is
$$
C = \begin{bmatrix}
A & 0 & 0 & 0 \
-2B & A + 4B & 0 & 0 \
0 & -2B & A + 4B & 0 \
0 & 0 & -2B & A
\end{bmatrix}
$$
and the 2nd substituted matrix $ D_2 $ is
$$
C = \begin{bmatrix}
A & A y_1 & 0 & 0 \
-2B & A y_2 & 0 & 0 \
0 & A y_3 & A + 4B & 0 \
0 & A y_4 & -2B & A
\end{bmatrix}
$$
But notice that $ \det(C) $ and $ \det(D_i) $ have the same power of $ A $ because every element is a multiple of $ A $. That means All instances of $ A $ cancels out everywhere and it's not actually doing anything. Either we need to change the definition of $ A $ so that it doesn't cancel everywhere, or get rid of it.
The text was updated successfully, but these errors were encountered: