UT3Tangent.apply_derivatives

t3toolbox.uniform_manifold.UT3Tangent.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:                           # scalar jets, shape=(order+1,)+W+K+C

Symmetric all-modes apply derivatives (derivative twin of apply(); the bare 𝒥, a scalar jet per stack element). Structural precondition as in probe_derivatives(). Uniform mirror of apply_derivatives().

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.uniform_tucker_tensor_train as ut3
>>> import t3toolbox.uniform_manifold as ut3m
>>> np.random.seed(0)
>>> x = ut3.UniformTuckerTensorTrain.from_t3(t3.TuckerTensorTrain.randn((10, 11, 12), (5, 6, 4), (1, 2, 3, 1)))
>>> v = ut3m.UNIFORM_COREWISE.randn(ut3m.UNIFORM_MANIFOLD.frame(x))
>>> 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, bool(np.allclose(yj[0], v.apply(ww))))          # (order+1,); order 0 == apply
(4,) True

Parameters:

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

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

• order (int)

Return type:

NDArray