denis-bz

A small example of Holt-Winters double exponential smoothing

in Python2 with NumPy and scipy.signal . This is a good bad example, in that yhat[n] == x[n], i.e. predict next == current (a = 1, b = 0) is ~ optimal.

The files:

denis-bz

#!/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

denis-bz

Runtimes of GLPK, the gnu Linear Programming kit, on some Netlib test cases

Keywords: linear programming, LP, GLPK, runtime, test case, Netlib

# 16 Aug 2019 08:34z  ~bz/py/opt/lp/netlib  Denis-iMac 10.10.5
Intel(R) Core(TM) i5-3330S CPU @ 2.70GHz
Apple LLVM version 7.0.2 (clang-700.1.81)
GLPSOL: GLPK LP/MIP Solver, v4.65  (uses only 1 core)

denis-bz

How to make SuiteSparse CHOLMOD for scikit-sparse

scikit-sparse - Sparse matrix extensions for SciPy provides the function cholmod for scipy.sparse arrays. (It's used for solving linear systems Ax = b with A symmetric and positive-deefinite, see cholmod ).

denis-bz

A 6 x 6 linprog testcase from glpk: 3 methods x sparse / dense give different results

transp-linprog.py below is a 6 x 6 testcase of scipy.optimize.linprog from a GLPK example, transp. In outline:

for method in ["interior-point", "revised simplex", "simplex"]:
    for sparse in [True, False]
        try:
            linprog( ... )

denis-bz

Easy lower-risk stochastic programming: the Dakota problem

Keywords: stochastic programming, risk, linear programming, python

Users of stochastic programming sometimes look only at "expected" payoff and ignore risk. For example, a well-known tutorial problem, Dakota furniture from Higle 2005, gives a max-expected profit $ 1730, but with 30 % chance of $ 650 loss, 70 % $2750 profit. That looks risky to me (an engineer, not a businessman).

denis-bz

Intergrid: interpolate data given on an N-d rectangular grid
============================================================

Purpose: interpolate data given on an N-dimensional rectangular grid,
uniform or non-uniform,
with the fast `scipy.ndimage.map_coordinates` .
Non-uniform grids are first uniformized with `numpy.interp` .

Background:
the reader should know some Python and NumPy

denis-bz

# A summary of the problems in glpk-4.65/examples/*.mod
#            lp/mip  min/max  rows  cols  nnz
assign     p lp min 17 64 192
bpp        p mip min 11 28 56
cal        p lp min 0 0 0
cf12a      p lp min 20 40 113
cf12b      p lp min 58 41 152
cflsq      p lp min 40 40 114
color      p mip min 92 48 288
cpp        p lp min 30 14 59

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

---

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