6.1. Matrix proxy#

With the fully discrete weak formulation wf, we can bring it into its algebraic proxy by calling its method mp, standing for matrix proxy,

>>> mp = wf.mp()

which is an instance of MatrixProxy,

class MatrixProxy(wf)[source]#

ls()[source]#

Convert self to an abstract linear system.

Returns:

lsMatrixProxyLinearSystem

The linear system instance.

nls()[source]#

Convert self to an abstract nonlinear system.

Returns:

nlsMatrixProxyNoneLinearSystem

The nonlinear system instance.

pr(figsize=(12, 8))[source]#

Print the representation, a figure, of this weak formulation.

Parameters:

figsizetuple, optional

The figure size. It has no effect when the figure is over-sized. A tight configuration will be applied when it is the case. The default value is (12, 8).

Similarly, its pr method can illustrate it properly,

>>> mp.pr()
<Figure size ...

6.2. Algebraic representation#

Depend on mp is linear or nonlinear, an algebraic system can be produced through either method ls or nls of mp, see MatrixProxy.ls() and MatrixProxy.nls().

Method ls gives an instance of MatrixProxyLinearSystem, i.e.,

class MatrixProxyLinearSystem(mp, ls, mp_bc)[source]#

And method nls leads to an instance of MatrixProxyNoneLinearSystem, namely,

class MatrixProxyNoneLinearSystem(mp, mp_ls, nls)[source]#

In this case, mp is a linear system. Thus, we should call ls method of it,

>>> ls = mp.ls()
>>> ls.pr()
<Figure size ...

Eventually, a fully discrete abstract linear system is obtained. We can send it a particular implementation which will objectivize it, for example by making matrices 2-dimensional arrays and making the vectors 1-dimensional arrays. These implementations will be introduced in the following section.