cherab.phix.tools.derivative.compute_dmat#

cherab.phix.tools.derivative.compute_dmat(voxel_map, kernel_type='laplacian4', kernel=None)#

Generate derivative sparse matrix.

Parameters:

  • voxel_map (numpy.ndarray) – (N, M) voxel map matrix (negative value must be input into masked voxels) If the additional dimension size of the matrix is 1, then it is squeezed to a 2-D matrix.

  • kernel_type ({"x", "y", "r", "z", "laplacian4", "laplacian8", "custom"}, optional) – Derivative kernel type. Default is “laplacian8”. "custom" is available only when kernel is specified. “r” and “z” are the same as “y” and “x”, respectively.

  • kernel (numpy.ndarray, optional) – (3, 3) custom kernel matrix. Default is None.

Returns:

(N, N) derivative Compressed Sparse Column matrix (if N > M)

Return type:

scipy.sparse.csc_matrix

Notes

The derivative matrix is generated by the kernel convolution method. The kernel is a 3x3 matrix, and the convolution is performed as follows:

\[I_{x, y}' = \sum_{i=-1}^{1}\sum_{j=-1}^{1} K_{i,j} \times I_{x + i, y + j},\]

where \(I_{x, y}\) is the 2-D image at the point \((x, y)\) and \(K_{i,j}\) is the kernel matrix. Using derivative kernel like a laplacian filter, the derivative matrix defined as follows is generated:

\[\mathbf{I}' = \mathbf{K} \cdot \mathbf{I},\]

where \(\mathbf{I}\) is the vecotrized image and \(\mathbf{K}\) is the derivative matrix.

The implemented derivative kernels are as follows:

  • First derivative in x-direction (kernel_type="x" or "z"): \(\mathbf{K} = \begin{bmatrix} 0 & 0 & 0 \\ -1 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)

  • First derivative in y-direction (kernel_type="y" or "r"): \(\mathbf{K} = \begin{bmatrix} 0 & -1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)

  • Laplacian-4 (kernel_type="laplacian4"): \(\mathbf{K} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{bmatrix}\)

  • Laplacian-8 (kernel_type="laplacian8"): \(\mathbf{K} = \begin{bmatrix} 1 & 1 & 1 \\ 1 & -8 & 1 \\ 1 & 1 & 1 \end{bmatrix}\)

Examples

from raysect.optical import World
from cherab.phix.tools.raytransfer import import_phix_rtc
from cherab.phix.tools import compute_dmat

world = World()
rtc = import_phix_rtc(world)

laplacian = compute_dmat(rtc.voxel_map)
laplacian.toarray()
array([[-8.,  1.,  0., ...,  0.,  0.,  0.],
       [ 1., -8.,  1., ...,  0.,  0.,  0.],
       [ 0.,  1., -8., ...,  0.,  0.,  0.],
       ...,
       [ 0.,  0.,  0., ..., -8.,  1.,  0.],
       [ 0.,  0.,  0., ...,  1., -8.,  1.],
       [ 0.,  0.,  0., ...,  0.,  1., -8.]])