README.md

Example code for Projected Rayleigh Quotient Iteration

This is the code that was used to produce the results and figures of Friess, Gilbert, Scheichl: A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues, 2023 (Preprint).

Instructions for Example 1

This example requires a C++ 11 compiler and Python 3. The C++ program generates the results, the Python script then visualises them.

To compile the C++ executable the Blaze library is required which itself relies on LAPACK. See the Blaze documentation for details on how to install both. To compile the program (e.g., using the Clang compiler) inside the example1 directory run

$ clang++ -O3 -ogen_results -llapack main.cc

and then execute

$ ./gen_results 2000

to generate the results using 2000 runs (the more runs, the more accurate the final figures). To generate the figures, run (this assumes that both numpy and matplotlib are available)

$ mkdir figures
$ python main.py

This generates the figures in a subdirectory figures. Note that the generated figures differ slightly from those in the paper. The published figures were post-processed to increase readability when printed in greyscale.

Instructions for Example 2

This example only requires MATLAB. It was tested in MATLAB R2023b. To generate the results just run the script generate_results.m in MATLAB.

To generate the figure directly from the command line, run

$ matlab -nodisplay -nosplash -nodesktop -r "run('generate_results.m');exit;"

Instructions for Example 3

This example only requires MATLAB. It was tested in MATLAB R2023b. To generate the results just run the script generate_results.m in MATLAB. Note that this only creates Figure 5 of the paper and the results that were used to create Table 1. The other figures are simple plots of MATLAB vectors and are therefore not included here.

To generate the figure directly from the command line, run

$ matlab -nodisplay -nosplash -nodesktop -r "run('generate_results.m');exit;"