UT3Tangent.entries_derivatives#

t3toolbox.uniform_manifold.UT3Tangent.entries_derivatives(index, pp, order)#
def entries_derivatives(
        self,
        index:  NDArray,                # int, shape=(d,)+W -- the grid points
        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 entry derivatives at index in direction P (derivative twin of entries(); the bare 𝒥). index and pp share W. Uniform mirror of entries_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))
>>> pp = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> yj = v.entries_derivatives(np.array([3, 5, 7]), pp, 3)
>>> print(yj.shape, bool(np.allclose(yj[0], v.entries((3, 5, 7)))))  # (order+1,); order 0 == entries
(4,) True
Parameters:

  • index (NDArray)

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

  • order (int)

Return type:

NDArray