README.md

GraphMatFunData

This repository contains data files for the julia package GraphMatFun.jl in particular the data files for the experiments in the manuscript Computation graph for matrix fucntions.

Examples:

Julia

You can use the generated files to efficiently compute the matrix exponential.

julia> using GraphMatFun, BenchmarkTools, LinearAlgebra;
julia> # Download from https://github.com/matrixfunctions/GraphMatFunData/tree/main/data/generated/exp
julia> include("exp_sid_m5_opt_rho1_9.jl");
julia> A=randn(1000,1000); A=1.8*A/norm(A);
julia> E1=@btime exp($A);
  1.111 s (23 allocations: 76.31 MiB)
julia> E2=@btime exp_sid_m5_opt_rho1_9($A);
  332.667 ms (19 allocations: 68.67 MiB)
julia> norm(E1-E2)/norm(E2)
3.1592474046054336e-16

Matlab

The following illustrates that the fixed topology optimization improves the error.

>> % Download exp_sid_m5.m and exp_sid_m5_opt_rho1_9.m from https://github.com/matrixfunctions/GraphMatFunData/tree/main/data/generated/exp
>> xv=0:0.01:3;
>> err1=zeros(size(xv)); for j=1:length(xv); err1(j)=exp_sid_m5(xv(j))-exp(xv(j)); end
>> err2=zeros(size(xv)); for j=1:length(xv); err2(j)=exp_sid_m5_opt_rho1_9(xv(j))-exp(xv(j)); end
>> semilogy(xv,abs(err1)./exp(xv))
>> clf
>> semilogy(xv,abs(err1)./exp(xv))
>> hold on
>> semilogy(xv,abs(err2)./exp(xv))
>> pwd

Produces:

Directory structure:

• data/exp: The graphs (in CGR-format) for the exponential
• data/sqrt_plus_one: The graphs (in CGR-format) for the square root
• data/generated: The code generated (in matlab, julia and C-format) for all the filies in data/exp and data/sqrt_plus_one
• src/opt: The design by optimization of the exponential and square root. Can generate files in data/
• src/cputimg: The cpu-timing for the expontial. Reads the data files from data/
• src/matlab: Loading and evaluation of degree optimal polynomials in matlab