cma.transformations.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. When ub-lb is small compared to min(|lb|, |ub|), the linear proportion becomes zero.

In contrast to sin(.), the transformation is robust to "arbitrary" large values for boundaries, e.g. a lower bound of -1e99 or upper bound of np.inf or bound None.

Examples

Example to use with cma:

>>> import warnings
>>> import cma
>>> from cma.transformations import BoxConstraintsLinQuadTransformation
>>> # only the first variable has an upper bound
>>> tf = BoxConstraintsLinQuadTransformation([[1,2], [1,None]]) # second==last pair is re-cycled
>>> with warnings.catch_warnings(record=True) as warns:
...     x, es = cma.fmin2(cma.ff.elli, 9 * [2], 1,
...                 {'transformation': [tf.transform, tf.inverse],
...                  'verb_disp':0, 'tolflatfitness': 1e9, 'verbose': -2})
>>> not warns or str(warns[0].message).startswith(('in class GenoPheno: user defi',
...                                   'flat fitness'))
True

or:

>>> es = cma.CMAEvolutionStrategy(4 * [2], 1, {'verbose':0, 'verb_log':0})  # doctest: +ELLIPSIS
(4_w,8)-aCMA-ES (mu_w=...
>>> with warnings.catch_warnings(record=True) as warns:  # flat fitness warning, not necessary anymore
...     while not es.stop():
...         X = es.ask()
...         f = [cma.ff.elli(tf(x)) for x in X]  # tf(x)==tf.transform(x)
...         es.tell(X, f)
>>> assert 'tolflatfitness' in es.stop(), str(es.stop())

Example of the internal workings:

>>> import cma.transformations as ts
>>> ts.linquad_margin_width = ts.margin_width1
>>> tf = ts.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]
>>> np.round(tf([1.52, -2.2, -0.2, 2, 4, 10.4]), 9).tolist()
[1.52, 4.0, 2.0, 2.0, 4.0, 10.4]
>>> res = np.round(tf._au, 2)
>>> assert res[:4].tolist() == [ 0.15, 0.6, 0.6, 0.6], res[:4].tolist()
>>> 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], res
>>> tmp = tf([1])  # call with lower dimension

>>> ts.linquad_margin_width = ts.margin_width2
>>> tf = ts.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]
>>> np.round(tf([1.52, -2.2, -0.2, 2, 4, 10.4]), 9).tolist()
[1.52, 4.1, 2.1, 2.0, 4.0, 10.4]
>>> res = np.round(tf._au, 2)
>>> assert list(res[:4]) == [ 0.1, 0.55, 0.55, 0.55], list(res[:4])
>>> 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, 9.0, 2.1, 2.0, 4.0, 10.4], res
>>> tmp = tf([1])  # call with lower dimension
>>> for i in range(5):
...     lb = np.random.randn(4) - 1000 * i * np.random.rand()
...     ub = lb + (1e-7 + np.random.rand(4)) / (1e-9 + np.random.rand(4)) + 1001 * i * np.random.rand()
...     lb[-1], ub[-1] = lb[-2], ub[-2]
...     b = ts.BoxConstraintsLinQuadTransformation([[l, u] for (l, u) in zip(lb[:3], ub[:3])])
...     for x in [(ub - lb) * np.random.randn(4) / np.sqrt(np.random.rand(4)) for _ in range(11)]:
...         assert all(lb <= b.transform(x)), (lb, ub, b.transform(x), b.__dict__)
...         assert all(b.transform(x) <= ub), (lb, ub, b.transform(x), b.__dict__)
...         assert all(b.transform(lb - b._al) == lb), (lb, ub, b.transform(x), b.__dict__)
...         assert all(b.transform(ub + b._au) == ub), (lb, ub, b.transform(x), b.__dict__)