cma.sampler.GaussFullSampler

sm *= factor is a shortcut for sm = sm.__imul__(factor).

Multiplies the covariance matrix with factor.

declarative init, doesn't need to be executed

return correlation between variables i and j.

return scalar correction alpha such that X and f fit to f(x) = (x-mean) (alpha * C)**-1 (x-mean)

bound condition number to limit by adding eps to the trace.

This method only changes the sampling distribution, but not the underlying covariance matrix.

We add eps = (a - limit * b) / (limit - 1) to the diagonal variances, derived from limit = (a + eps) / (b + eps) with a, b = lambda_max, lambda_min.

>>> import cma
>>> es = cma.CMAEvolutionStrategy(3 * [1], 1, {'CMA_diagonal_decoding':False, 'verbose':-9})
>>> _ = es.optimize(cma.ff.elli)
>>> assert es.sm.condition_number > 1e4
>>> es.sm.limit_condition(1e4 - 1)
>>> assert es.sm.condition_number < 1e4

multiply self.C with factor updating internal states.

factor can be a scalar, a vector or a matrix. The vector is used as outer product and multiplied element-wise, i.e., multiply_C(diag(C)**-0.5) generates a correlation matrix.

Details:

compute the Mahalanobis norm that is induced by the statistical model / sample distribution, specifically by covariance matrix C. The expected Mahalanobis norm is about sqrt(dimension).

>>> import cma, numpy as np
>>> sm = cma.sampler.GaussFullSampler(np.ones(10))
>>> x = np.random.randn(10)
>>> d = sm.norm(x)

reset distribution while keeping all other parameters.

If standard_deviations is not given, np.ones is used, which might not be the original initial setting.

return list of i.i.d. samples.

"re-scale" C to a correlation matrix and return the scaling factors as standard deviations.

See also: to_linear_transformation.

return associated linear transformation.

If B = sm.to_linear_transformation() and z ~ N(0, I), then np.dot(B, z) ~ Normal(0, sm.C) and sm.C and B have the same eigenvectors. With reset=True, np.dot(B, sm.sample(1)[0]) obeys the same distribution after the call.

See also: to_unit_matrix

return inverse of associated linear transformation.

If B = sm.to_linear_transformation_inverse() and z ~ Normal(0, sm.C), then np.dot(B, z) ~ Normal(0, I) and sm.C and B have the same eigenvectors. With reset=True, also sm.sample(1)[0] ~ Normal(0, I) after the call.

See also: to_unit_matrix

apply linear transformation C**0.5 to x.

apply inverse linear transformation C**-0.5 to x.

update/learn by natural gradient ascent.

The natural gradient used for the update is:

np.dot(weights * vectors.T, vectors)

and equivalently:

sum([outer(weights[i] * vec, vec)
     for i, vec in enumerate(vectors)], axis=0)

Details:

• The weights include the learning rate and -1 <= sum( weights[idx]) <= 1 must be True for idx = weights > 0 and for idx = weights < 0.
• The content (length) of vectors with negative weights is changed!

update internal variables for sampling the distribution with the current covariance matrix C.

This method is O(dim^3) by calling _decompose_C.

If lazy_update_gap is None the lazy_update_gap from init is taken. If lazy_update_gap < 0 the (possibly expensive) update is done even when the model seems to be up to date.