UniformTuckerTensorTrain.randn#

static t3toolbox.uniform_tucker_tensor_train.UniformTuckerTensorTrain.randn(shape, tucker_ranks, tt_ranks, stack_shape=(), use_jax=False)#

def randn(
        shape:        Sequence[int],                          # (N0,...,N(d-1))
        tucker_ranks: typ.Union[int, Sequence[int], NDArray], # int|len-d|(d,)+stack
        tt_ranks:     typ.Union[int, Sequence[int], NDArray], # int|len-(d+1)|(d+1,)+stack
        stack_shape:  Sequence[int] = (),
        use_jax:      bool = False,
) -> 'UniformTuckerTensorTrain':

Uniform Tucker tensor train with random N(0,1) supercores (padded regions masked to zero).

tucker_ranks/tt_ranks accept a scalar, a per-mode sequence, or a full (d,)+stack / (d+1,)+stack array – the latter setting per-stack-element ranks (the variety) while keeping one padded supercore shape, which a ragged round-trip cannot express.

Examples

>>> import numpy as np
>>> import t3toolbox.uniform_tucker_tensor_train as ut3
>>> np.random.seed(0)
>>> x = ut3.UniformTuckerTensorTrain.randn((5, 6, 7), (3, 4, 2), (1, 3, 2, 1), stack_shape=(2,))
>>> print(x.shape, x.stack_shape)
(5, 6, 7) (2,)
>>> print(np.reshape(x.tucker_ranks, (3, 2))[:, 0].tolist())   # uniform across the stack here
[3, 4, 2]
>>> print(bool(np.any(x.tucker_supercore != 0.0)))            # random, not zeros
True

Per-stack-element ranks (the variety): a full (d,)+stack array gives each stack element its own ranks under one padded shape.

>>> tucker_ranks = np.array([[2, 4], [3, 5], [2, 3]])         # (d=3, stack=2)
>>> tt_ranks = np.array([[1, 1], [2, 4], [2, 3], [1, 1]])     # (d+1=4, stack=2)
>>> xv = ut3.UniformTuckerTensorTrain.randn((6, 7, 8), tucker_ranks, tt_ranks, stack_shape=(2,))
>>> print(np.asarray(xv.tucker_ranks).tolist())              # ranks genuinely differ per element
[[2, 4], [3, 5], [2, 3]]
>>> print(xv.n, xv.r)                                        # one padded shape: n=max, r=max
5 4

Parameters:

shape (Sequence[int])
tucker_ranks (Union[int, Sequence[int], NDArray])
tt_ranks (Union[int, Sequence[int], NDArray])
stack_shape (Sequence[int])
use_jax (bool)

Return type:

UniformTuckerTensorTrain