the values of the kernels at the centres at the nodes, rows the nodes, columns the centres; MATLAB’s createSummationMatrix

Syntax

M = summationMatrix(psi, S3G, nodes)

Sparse, the pairs within 3.5 halfwidths.

M = summationMatrix(psi, S3G, nodes, epsilon=20*degree)

The pairs within 20 degree.

M = summationMatrix(psi, S3G, nodes, exact=True)

Every pair, dense.

Description

An entry is the mean of the kernel over the symmetric equivalents of the centre, as SO3FunRBF evaluates; a fit M c = y of values y at the nodes gives the weights c of the kernels. For centres that are orientations and a radius below pi the matrix is a sparse csr_matrix from the radius search, which keeps the nearest equivalent within the radius only; otherwise it is a dense array over every pair and every equivalent.

Input

psi SO3Kernel
centres orientation, the centres of the kernels, an SO3Grid
nodes orientation, where the values are given

Keywords

keyword default description
exact False every pair and every equivalent, a dense matrix
epsilon None the radius beyond which the kernel counts as zero, by default 3.5 halfwidths

Output

M scipy.sparse.csr_matrix or ndarray, nodes x centres

See also

SO3FunRBF.interpolate, mlsq

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/summationMatrix_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.