Fast Matlab compatible sparse assembly on multicore computers

Abstract

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of interest to design a highly efficient implementation. We show how to do this, and moreover, we show how our implementation can be parallelized to utilize the power of modern multicore computers. Our freely available code, fully Matlab compatible, achieves about a factor of 5 times in speedup on a typical 6-core machine and 10 times on a dual-socket 16 core machine compared to the built-in serial implementation

Mixed Finite Element Formulations for Polyconvex Anisotropic Material Formulations

“…To solve the linear systems of equations we use the Pardiso solver from Reference [9]. For the assembly procedure we use the fast sparse routine shown in Reference [10].…”

On the parameter estimation problem of magnetic resonance advection imaging

“…is an m × m matrix and b( v, ρ 0 ) is a vector of length m. This is possible, since ρ i,j,k,l appears only linearly in (9). In order to assemble the system matrix A( v), note first that (9) naturally divides into four parts, each part corresponding to the differential quotient with respect to one of the variables t, x, y or z.…”

“…The implementation of the method was done in MATLAB R2015b. Since some built-in MATLAB functions were too slow for our purposes, we had to rely on fsparse.m, a function for creating sparse matrices, see [9].…”

“…• Create an all-zero m × m matrix A. For the matrices A t , A y ( v) and A z ( v), the assembly procedure looks similar, with obvious modifications due to the respective definitions of D yj , D z k and the backwards time difference quotient in (9).…”

A Tutorial on Machine Learning and Data Science Tools with Python

“…For example, typing 1 >>> abs ? 2 Docstring : 3 abs ( number ) -> number 4 5 Return the absolute value of the argument . For larger projects, or for projects that you may want to share, IPython may not be ideal.…”