T3Tangent.apply_derivatives#

t3toolbox.manifold.T3Tangent.apply_derivatives(ww, pp, order)#
def apply_derivatives(
        self,
        ww:     typ.Sequence[NDArray],  # apply vectors X,        len=d, elm_shape=W+(Ni,)
        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 applying this tangent vector in all modes.

The all-modes analogue of probe_derivatives() (and the 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 + K + C. X and P must share the sample stack W.

See also

apply, probe_derivatives, apply_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)
>>> ww = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> pp = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> yj = v.apply_derivatives(ww, pp, 3)
>>> print(yj.shape)                        # (order+1,) -- one scalar per order
(4,)
>>> print(bool(np.allclose(yj[0], v.apply(ww))))     # order 0 == apply
True
Parameters:

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

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

  • order (int)

Return type:

NDArray