t3toolbox.backend.probing.probe_dense
=====================================

.. py:function:: t3toolbox.backend.probing.probe_dense(vectors: t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], T: t3toolbox.backend.common.NDArray, use_jax: bool = False) -> t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray]

   Probe a dense tensor.

   :param T: Tensor to be probed. shape=Z+(N1,...,Nd)
   :type T: NDArray
   :param vectors: Probing input vectors.
                   len=d.
                   elm_shape=K+(Ni,)
   :type vectors: typ.Sequence[NDArray]
   :param xnp: Linear algebra backend. Default: np (numpy)

   :returns: Probes.
             len=d.
             elm_shape=(Ni,) or elm_shape=Z+K+(Ni,)
   :rtype: typ.Tuple[NDArray]

   .. rubric:: Examples

   Probe with one set of vectors:

   >>> import numpy as np
   >>> import t3toolbox.backend.probing as t3p
   >>> T = np.random.randn(10,11,12)
   >>> u0 = np.random.randn(10)
   >>> u1 = np.random.randn(11)
   >>> u2 = np.random.randn(12)
   >>> yy = t3p.probe_dense((u0,u1,u2),T)
   >>> y0 = np.einsum('ijk,j,k', T, u1, u2)
   >>> y1 = np.einsum('ijk,i,k', T, u0, u2)
   >>> y2 = np.einsum('ijk,i,j', T, u0, u1)
   >>> print(np.linalg.norm(yy[0] - y0))
   2.0928808318295785e-14
   >>> print(np.linalg.norm(yy[1] - y1))
   1.0841599276764049e-14
   >>> print(np.linalg.norm(yy[2] - y2))
   1.2970142174948615e-14

   Vectorize over probing vectors

   >>> import numpy as np
   >>> import t3toolbox.backend.probing as t3p
   >>> T = np.random.randn(10,11,12)
   >>> u0 = np.random.randn(2,3, 10)
   >>> u1 = np.random.randn(2,3, 11)
   >>> u2 = np.random.randn(2,3, 12)
   >>> yy = t3p.probe_dense((u0,u1,u2),T)
   >>> y0 = np.einsum('ijk,uvj,uvk->uvi', T, u1, u2)
   >>> y1 = np.einsum('ijk,uvi,uvk->uvj', T, u0, u2)
   >>> y2 = np.einsum('ijk,uvi,uvj->uvk', T, u0, u1)
   >>> print(np.linalg.norm(yy[0] - y0))
   2.0928808318295785e-14
   >>> print(np.linalg.norm(yy[1] - y1))
   1.0841599276764049e-14
   >>> print(np.linalg.norm(yy[2] - y2))
   1.2970142174948615e-14

   Vectorize over probing vectors and big tensor

   >>> import numpy as np
   >>> import t3toolbox.backend.probing as t3p
   >>> T = np.random.randn(4,5,6, 10,11,12)
   >>> u0 = np.random.randn(2,3, 10)
   >>> u1 = np.random.randn(2,3, 11)
   >>> u2 = np.random.randn(2,3, 12)
   >>> yy = t3p.probe_dense((u0,u1,u2),T)
   >>> y0 = np.einsum('xyzijk,uvj,uvk->xyzuvi', T, u1, u2)
   >>> y1 = np.einsum('xyzijk,uvi,uvk->xyzuvj', T, u0, u2)
   >>> y2 = np.einsum('xyzijk,uvi,uvj->xyzuvk', T, u0, u1)
   >>> print(np.linalg.norm(yy[0] - y0))
   2.0928808318295785e-14
   >>> print(np.linalg.norm(yy[1] - y1))
   1.0841599276764049e-14
   >>> print(np.linalg.norm(yy[2] - y2))
   1.2970142174948615e-14