T3Tangent.entries_derivatives

t3toolbox.manifold.T3Tangent.entries_derivatives(index, pp, order)

def entries_derivatives(
        self,
        index:  NDArray,                # int, shape=(d,)+W -- grid points
        pp:     typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
        order:  int,                    # highest derivative order
) -> NDArray:                           # shape=(order+1,)+W+K+C

Symmetric directional derivatives of this tangent’s entries at index, in direction P.

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

See also

entries, apply_derivatives, entries_derivatives_transpose

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.frame_variations_format as bvf
>>> import t3toolbox.manifold as t3m
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((10, 11, 12), (5, 6, 4), (1, 2, 3, 1))
>>> frame, variations = bvf.t3_orthogonal_representations(x)
>>> v = t3m.T3Tangent(frame, variations)
>>> index = np.array([3, 5, 7])
>>> pp = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> yj = v.entries_derivatives(index, pp, 3)
>>> print(yj.shape)
(4,)
>>> print(bool(np.allclose(yj[0], v.entries(index))))   # order 0 == entries
True

Parameters:

• index (NDArray)

• pp (t3toolbox.backend.common.typ.Sequence[NDArray])

• order (int)

Return type:

NDArray