LCP¶

Usage¶

In python the LinearComplementarityProblem from C API is renamed LCP.

The solution of the problem exposed in Dense matrices and vectors:

import siconos.numerics as Numerics
lcp = Numerics.LCP([[2., 1.], [1., 2.]], [-5., -6.])

can be reached with the Numerics module by first providing a guess. This guess is made of the two vectors z and w. As it will be an input as well as an output parameter for the solver, we must use a numpy array that can be modified in place. Standard python sequences cannot be modified in this interface and are not suitable for this kind of parameter:

from numpy import array
z = array([0., 0.])
w = array([0., 0.])

We must also provide a solver options object:

SO = Numerics.SolverOptions(lcp, Numerics.SICONOS_LCP_LEMKE)

That object brings the decision to use a Lemke method. It also allows the manipulation of the different solver parameters such as the wanted precision. The integer option parameters are in an iparam array and the double option parameters are in a dparam array.

For the Lemke method the default precision is the first element of SO.dparam array:

>>> SO.dparam
array([  1.00000000e-06,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00])

The solution may be now computed with a Lemke solver:

info = Numerics.lcp_lexicolemke(lcp, z, w, SO)

The info output is an integer. For all Numerics solvers, 0 means a successfull resolution. z and w now contain a correct solution for the asked precision:

>>> z
array([ 1.33333333,  2.33333333])
>>> w
array([ 0.,  0.])

We may then compute the error:

d = Numerics.lcp_compute_error(lcp, z, w, 1e-6)
[ ... ]

LCP¶

Usage¶

LCP API¶