object --+    
                               |    
BoxConstraintsTransformationBase --+
                                   |
                                  BoxConstraintsLinQuadTransformation

Details

Partly due to numerical considerations depend the values al and au on abs(lb) and abs(ub) which makes the transformation non-translation invariant. In contrast to sin(.), the transformation is robust to "arbitrary" values for boundaries, e.g. a lower bound of -1e99 or np.Inf or None.

Examples

Example to use with cma:

>>> import cma
>>> # only the first variable has an upper bound
>>> tf = cma.BoxConstraintsLinQuadTransformation([[1,2], [1,None]]) # second==last pair is re-cycled
>>> cma.fmin(cma.felli, 9 * [2], 1, {'transformation': [tf.transform, tf.inverse], 'verb_disp': 0})
>>> # ...or...
>>> es = cma.CMAEvolutionStrategy(9 * [2], 1)
>>> while not es.stop():
...     X = es.ask()
...     f = [cma.felli(tf(x)) for x in X]  # tf(x) == tf.transform(x)
...     es.tell(X, f)

Example of the internal workings:

>>> import cma
>>> tf = cma.BoxConstraintsLinQuadTransformation([[1,2], [1,11], [1,11]])
>>> tf.bounds
[[1, 2], [1, 11], [1, 11]]
>>> tf([1.5, 1.5, 1.5])
[1.5, 1.5, 1.5]
>>> tf([1.52, -2.2, -0.2, 2, 4, 10.4])
[1.52, 4.0, 2.0, 2.0, 4.0, 10.4]
>>> res = np.round(tf._au, 2)
>>> assert list(res[:4]) == [ 0.15, 0.6, 0.6, 0.6]
>>> res = [round(x, 2) for x in tf.shift_or_mirror_into_invertible_domain([1.52, -12.2, -0.2, 2, 4, 10.4])]
>>> assert res == [1.52, 9.2, 2.0, 2.0, 4.0, 10.4]
>>> tmp = tf([1])  # call with lower dimension