StepModel._create_basis_center¶

StepModel._create_basis_center()¶

This function creates the basis part in every bin of the Step model for the free energy and the radial diffusion profile. The following explanation is for the free energy profile. For the radial diffusion profile the number of free energy coefficients \(n_{\mathrm{df}}\) has to exchange with \(n_{\mathrm{diff\_radial}}\). The Dimension of the basis matrix is \(n_{\mathrm{bin}} \times n_{\mathrm{df}}\). For a bin the basis is calculated with

\[\begin{split}\mathrm{basis} = \begin{cases} 1 & (\mathrm{bin}+0.5)\geq \Delta x\ \& \ (\mathrm{bin}+0.5)\leq n_{\mathrm{bin}}-\Delta x \\ 0 & \mathrm{else} \ \end{cases}\end{split}\]

hereby is \(\mathrm{bin} = [0,...,n_{bin}]\) with \(n_{\mathrm{bin}}\) as the number of the bins. The variable \(\Delta x\) is define by

\[\Delta x = \left [ 0,i \cdot \frac{n_{\mathrm{bin}}}{n_{\mathrm{df}} \cdot 2},\frac{n_{\mathrm{bin}}}{2} \right ]\]

with \(i = [1,...,n_{\mathrm{df}}-1]\).