TuckerTensorTrain.apply_derivatives

t3toolbox.tucker_tensor_train.TuckerTensorTrain.apply_derivatives(ww, pp, order)

def apply_derivatives(
        self,
        ww:     Sequence[NDArray],  # apply vectors X,        len=d, elm_shape=W+(Ni,)
        pp:     Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
        order:  int,                # highest derivative order
) -> NDArray:                       # shape=(order+1,)+W+C

Symmetric directional derivatives of applying this T3 in all modes, in one repeated direction.

The all-modes analogue of probe_derivatives() (derivative analogue of apply()): y^(t) = d^t/ds^t apply(X + s P)|_0 for t=0..order (a scalar per stack element). Stacks order + W + C. X and P share the sample stack W.

See also

apply, probe_derivatives, apply_corewise_derivatives_transpose

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((14, 15, 16), (4, 5, 6), (1, 3, 2, 1))
>>> ww = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
>>> pp = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
>>> yj = x.apply_derivatives(ww, pp, 3)
>>> print(yj.shape)                        # (order+1,)
(4,)
>>> print(bool(np.allclose(yj[0], x.apply(ww))))     # order 0 == apply
True

Parameters:

• ww (collections.abc.Sequence[NDArray])

• pp (collections.abc.Sequence[NDArray])

• order (int)

Return type:

NDArray