Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aepk_v1_0.tar.gz(152 Kbytes)|
|Manuscript Title: Penalized Splines for Smooth Representation of High-dimensional Monte Carlo Datasets|
|Authors: Nathan Whitehorn, Jakob van Santen, Sven Lafebre|
|Program title: Photospline|
|Catalogue identifier: AEPK_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 184(2013)2214|
|Programming language: C, Python.|
|Computer: 32- and 64-bit x86, 32- and 64-bit PowerPC.|
|Operating system: Linux, Mac OS X, FreeBSD.|
|Has the code been vectorised or parallelized?: Both|
|RAM: Approximately proportional to number of knots used in fitting, depends on problem condition|
|Keywords: Splines, Monte Carlo, Histograms, Maximum Likelihood.|
External routines: SuiteSparse (http://www.cise.ufl.edu/research/sparse/SuiteSparse/), Python (http://www.python.org/), BLAS (http://www.netlib.org/blas/), Numpy (http://www.numpy.org/)
Nature of problem:
An algorithm to smoothly represent histogram, including mathematical operations and convolutions. Using histograms of Monte Carlo simulation for likelihood fitting can be unstable due to binning artifacts from statistical fluctuations and hard bin-to-bin transitions. This package provides a toolkit for using penalized spline fits on extremely large multi-dimensional datasets to reduce or eliminate such issues.
Uses sparse matrix operations, non-negative least-squares fitting, and generalized linear array models in conjunction with a number of other algorithms to allow fits to be made, manipulated, and saved with very low computational requirements. This enables even very large problems to be solved on commercially available machines.
Required computation time and memory increases very rapidly with the number of dimensions. Fits without stacking involving more than 5 dimensions and 20 knots on each are usually not practical on 2012-era hardware.
Roughly proportional to the cube of the number of knots used, depends strongly on conditioning of the problem.
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