the minimiser of a linear program in standard form, min c.x under A x = b, x >= 0

Syntax

x = linearProgram(c, A, b)

The solution, None when there is none.

res = linearProgram(c, A, b, diagnostics=True)

With its status, pivot count and residual.

Description

A scaled two phase simplex with Bland’s rule, the kind of program the Taylor model solves for every strain: phase one finds a feasible vertex on artificial variables, every row scaled to unit size, phase two walks to the optimum. Without diagnostics the result is None when the program is infeasible, unbounded, out of iterations or numerically failed; with diagnostics a LinearProgramResult (solution, status, iterations, residual), the residual the largest entry of |A x - b| relative to max(1, |b|).

Input

c the cost vector, n numbers
A the m x n matrix of the constraints
b the right hand side, m numbers

Keywords

keyword default description
tol 1e-09 the tolerance below which a reduced cost or a pivot counts as zero
maxIter 10000 the largest number of pivots
diagnostics False return a LinearProgramResult instead of the bare solution

Output

x the minimiser, n numbers, or None
res LinearProgramResult

See also

calcTaylor

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/linearProgram_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.