denis-bz

timeit scipy.sparse linear solvers: spsolve qmr lgmres splu spilu

Here is a simple test of 5 scipy.sparse solvers of Ax = b, with A = diag*I + sparse random-uniform 4000 x 4000, density 1e-3.

Keywords: sparse linear solver, test case, random matrix, scipy, GMRES, Krylov

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denis-bz

3-point and 5-point finite-difference derivative approximations

Central differences like

diff1 = (f_{t+1} - f{t-1}) / 2,  [0 -1 0 1 0] / 2
diff2 = (f_{t+2} - f{t-2}) / 4,  [-1 0 0 0 1] / 4

approximate the derivative f'(t) much better then the one-sided difference f_{t+1} - f_t; see e.g. Wikipedia

denis-bz

ABXC nonsmooth optimization problems

ABXC is a range of nonsmooth optimization problems from Curtis et al.; see the problem description and links in abxc.py below. They're hard to optimize, very noisy near minima, and some are infeasible. Here's a plot of scipy.optimize.trust-constr creeping up an infeasible slope:

denis-bz

Mopta08-py

MOPTA08 is a test case for optimization from D.R. Jones, "Large-scale multi-disciplinary mass optimization in the auto industry" , 2008. It has 124 variables in 0 .. 1, a linear objective function, and 68 nonlinear constraints.

The purpose of mopta08-py is to try out various optimizers -> python -> MOPTA08,

denis-bz

#!/usr/bin/env python2
""" coord_sketch: k * dim func() values, varying one coordinate at a time,
    give a cheap starting point for further optimization
    especially if func() is monotone, up or down, in each coordinate.
"""

from __future__ import division
import sys
import numpy as np
    # from https://github.com/SMTorg/smt  Surrogate Modeling Toolbox

denis-bz

# Py-BOBYQA example: minimize the Rosenbrock function
# from https://github.com/numericalalgorithmsgroup/pybobyqa
# run this.py [dim= lo= hi= ...] in sh or ipython

# sensitive to rhobeg rhoend:
# $nlopt/bobyqa/bobyqa.c --
# Typically, RHOBEG should be about one tenth of the greatest expected change to a variable,
# while RHOEND should indicate the accuracy that is required in the final values of the variables.

from __future__ import print_function

denis-bz

bump2: an optimization problem from A.J.Keane, https://www.southampton.ac.uk/~ajk/bump.html .

Keywords: optimization, test case, random search, python

Problems in mathematical optimization have several different aspects:

• contest: whose program reaches minimum __ in cpu time __ and time-to-understand __
• learning how to explore particular function terrains
• learning how to constrain.

denis-bz

Gish: sharing files on gist.github by name

Keywords: file sharing, gist, github, CLI, python, remote file server

gish is a command-line program to copy files between local computers and gist.github.com, using file names or gist ids. An example:

Alice:  gish put @Alice AA.md aa.py bb.py  # upload a gist with 3 files

denis-bz

#!/usr/bin/env python2
""" A = noisyUSV( n, d, r, noise ): U S V + noise, n x d, rank r  """

from __future__ import division
import numpy as np
from numpy.linalg import norm

from etc import znumpyutil as nu

__version__ = "2018-05-15 May  denis-bz-py t-online de"  # scale noise * S.max

denis-bz

NO2 in Munich 2016: high traffic => high NO2

This plot shows NO2 levels over the day in Munich in June and December 2016. München-Landshuter-Allee on the left has about the highest NO2 levels in all Germany, and a lot of traffic — 120,000 to 150,000 cars and light trucks per day.
Surprise: high traffic => high NO2.