Class GeneralExpansionNode

Expands the input samples by applying to them one or more functions provided.

The functions to be applied are specified by a list [f_0, ..., f_k], where 
f_i, for 0 <= i <= k, denotes a particular function. 
The input data given to these functions is a two-dimensional array and
the output is another two-dimensional array. The dimensionality of the output 
should depend only on the dimensionality of the input.
Given a two-dimensional input array x, the output of the node 
is then [f_0(x), ..., f_k(x)], that is, the concatenation of each one of 
the computed arrays f_i(x).

This node has been designed to facilitate nonlinear, fixed but arbitrary  
transformations of the data samples within MDP flows.
    
**Example**::

    >>> import mdp
    >>> from mdp import numx
    
    >>> def identity(x): return x
    
    >>> def u3(x): return numx.absolute(x)**3 #A simple nonlinear transformation
    
    >>> def norm2(x): #Computes the norm of each sample returning an Nx1 array
    >>>     return ((x**2).sum(axis=1)**0.5).reshape((-1,1)) 
      
    >>> x = numx.array([[-2., 2.], [0.2, 0.3], [0.6, 1.2]])
    >>> gen = mdp.nodes.GeneralExpansionNode(funcs=[identity, u3, norm2])
    >>> print(gen.execute(x))
    >>> [[-2.          2.          8.          8.          2.82842712]
    >>>  [ 0.2         0.3         0.008       0.027       0.36055513]
    >>>  [ 0.6         1.2         0.216       1.728       1.34164079]]

Original code contributed by Alberto Escalante.

Short argument description:

  ``funcs``
       list of functions f_i that realize the expansion.

Process the data contained in `x`.

If the object is still in the training phase, the function
`stop_training` will be called.
`x` is a matrix having different variables on different columns
and observations on the rows.

By default, subclasses should overwrite `_execute` to implement
their execution phase. The docstring of the `_execute` method
overwrites this docstring.

The expanded dim is computed by directly applying the expansion
functions f_i to a zero input of dimension n.

Return True if the node can be inverted, False otherwise.

Return True if the node can be trained, False otherwise.

Return the individual output sizes of each expansion function
when the input has lenght n.

Calculate a pseudo inverse of the expansion using
scipy.optimize.

``use_hint``
       when calculating a pseudo inverse of the expansion,
       the hint determines the starting point for the approximation.
       For details on this parameter see the function 
       ``invert_exp_funcs2`` in ``mdp.utils.routines.py``.

This method requires scipy.