[Scilab-users] Scicolpack toolbox

[Stéphane Mottelet]

Hi all,

A new toolbox has been uploaded at 
https://atoms.scilab.org/toolboxes/scicolpack:

Scicolpack is is the Scilab interface to CSCsw/ColPack 
(https://github.com/CSCsw/ColPack), a Graph Coloring Algorithm Package 
applied to efficient computation of sparse Jacobian and Hessian.

When you have to compute the Jacobian of a function f or the Hessian of 
f knowing its gradient g, once you know its sparsity pattern, even if 
you have derived it symbolically, it may still be faster to estimate it 
by using the techniques which are used by Colpack. Roughly speaking, 
this works by building a graph where each vertex is associated to a 
column of the Jacobian or Hessian, and an edge connects to 
vertices/columns if they are not structurally orthogonal, i.e. have at 
least one non-zero term in a common row. Then a proper coloring is done 
on this graph: at least, two adjacent vertices cannot have the same 
color, but more properties of the coloring may be expected. The coloring 
defines a partition of the columns under the form of p subsets and the 
Jacobian (resp. Hessian) can be recovered from only p evaluation of 
directional derivatives of f (resp. g). For example, for a tridiagonal 
matrix the value of p is 3. In the Scilab interface these directional 
derivatives are approximated by using finite differences (the toolbox 
allows to compute them by using the complex step technique up to machine 
precision).

This toolbox can be an nice addon to SciIpopt toolbox 
(https://atoms.scilab.org/toolboxes/sci_ipopt) where the Interior Point 
algorithm can be greatly accelerated when the Hessian of the Lagrangian 
is sparse. When I have time I will update the demo section of the module 
to add such an example.

Don't hesitate to report successful uses, bugs or whishes. For the 
moment the toolbox is available under OSX and Linux. Any help for a 
Windows build is welcome !

Best,

-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet