TuckerTensorTrain.entries_derivatives#

t3toolbox.tucker_tensor_train.TuckerTensorTrain.entries_derivatives(index, pp, order)#
def entries_derivatives(
        self,
        index:  NDArray,            # int, shape=(d,)+W -- grid points
        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 this T3’s entries at index, in direction P.

The Taylor data of the represented tensor’s multilinear extension at grid corner index, in direction P: y^(t) = d^t/ds^t apply(e_{index} + s P)|_0. Index 0 is the ordinary entries(). Stacks order + W + C. index and P share W.

See also

entries, apply_derivatives, entries_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))
>>> index = np.array([3, 5, 7])
>>> pp = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
>>> yj = x.entries_derivatives(index, pp, 3)
>>> print(yj.shape)
(4,)
>>> print(bool(np.allclose(yj[0], x.entries(index))))   # order 0 == entries
True
Parameters:
Return type:

NDArray