denis-bz

A few Mittelmann LP benchmarks run with HiGHS-ipm

Keywords, tags: linear programming, benchmark, Mittelmann, HiGHS, python, scipy, sparse-matrix

Here are logfiles for a few of the Mittelmann linear programming benchmark problems, run with the HiGHS interior-point solver via python-scipy. lpbar

Stripy: percentile stripes for scatterplots

Keywords: scatterplot, percentiles, quantiles, visualize, regression, nonparametric

What does this show ? Consider a fat vertical line at a given x in one of these plots. The colored bands are, from low to high,

Invop() inverse operator for scipy.sparse eigenvalues with ARPACK

Problem: find a few eigenvalues λ and eigenvectors v of
A v = λ v, \ A a scipy.sparse matrix, largest or smallest |λ|
or K v = λ M v with stiffness matrix K and mass matrix M.

Purpose: experiment with different linear solvers, with verbose to track solver calls.
Keywords: scipy.sparse, linear-solvers, eigenvalue, generalized-eigenvalue, Arpack, logging

In the following examples, eigs( A [M] [Minv] [OPinv] [sigma] ... ) \

Covid-19 cases hospitalized in Germany, March up to 6 September 2020

Keywords: Covid-19, hospitalized, Germany, plot, python

This plot shows the number of Covid-19 cases per week, the number hospitalized, and number of deaths, in Germany for weeks 10 to 36 2020:

The data is taken from this report: \

How to make a Python package for other people to use

Keywords, tags: python packaging setup.py setuptools

Purpose: describe how to make a "package" of a Python program for other people to use. This introduction builds on the excellent oa-packaging-guide-preview.readthedocs.io — read that first.

Do numpy and scipy use different LAPACK drivers for eigvalsh on macos ?

eigvals-numpy-scipy.py below runs numpy vs scipy eigvalsh on a dense random matrix:

np.linalg.eigvalsh: 201 sec
scipy.linalg.eigvalsh: 83 sec  driver ev
scipy.linalg.eigvalsh: 84 sec  driver evd

Maybe this is only on macos ?

How shift-invert finds eigenvalues, in pictures

Keywords: eigenvalues, eigenvectors, shift-invert, ARPACK, scipy, python

Pictures first:

Background

Plots of some eigenvalues and eigenvectors

Keywords: eigenvalues, eigenvectors, test-matrix, scipy, python

Eigenvectors of Suitesparse Norris/fv1

See SuiteSparse Matrix Collection / Norris, "Finite element modelling of human body parts, Laplace equation on a 2D mesh".

	#!/usr/bin/env python
	""" lpgen34.py LP testcase generator
	d=3: 3n^2 x n^3, 3 1s in each column
	n=55: A 9075 x 166375, 499125 nnz, glpsol simplex 100 minutes
	d=4: 4n^3 x n^4, 4 1s in each column, n in each row
	n=16: A 2^14 x 2^16, 2^18 nnz, glpsol simplex 10 hours
	"""
	# keywords: linear programming, test case, generator, Latin-square
	# https://stackoverflow.com/questions/57936789/many-vertex-test-problems-for-the-simplex-method
	# https://math.stackexchange.com/questions/3370934/3d-permutation-matrices -- 4d too

	#!/usr/bin/env python3
	""" triangles in a sparse graph """
	# Keywords: sparse-graph, sparse-matrix, scipy, mesh, triangles
	# w Polygon_mesh Mesh_generation ...

	import numpy as np
	from scipy import sparse
	# https://docs.scipy.org/doc/scipy/reference/sparse.csgraph.html

	# some type names --