SmoothTensor (version 0.1.1)

simulation: Generate a symmetric tensor observation from the smooth signal tensor, Gaussian noise tensor, and permutation.

Description

Generate a symmetric tensor observation from the smooth signal tensor, Gaussian noise tensor, and permutation. Users can select one of 5 different smooth signal tensors generated from functions specified in Table 4 of the reference given below.

Usage

simulation(d, mode = 1, sigma = 0.5, signal_level=5)

Arguments

d

Dimension of a tensor to be generated.

mode

An integer from 1 to 5 corresponding to models specified. Default model is 1.

sigma

Standard deviation of the Gaussian noise tensor. Default value is 0.5.

signal_level

A scale of the magnitude of the signal tensor to be generated.

Value

The returned object is a list of components.

signal - A true signal tensor generated from a function specified.

observe - A noisy observation generated from the smooth signal tensor, Gaussian noise tensor, and permutation.

permutation - A true permutation.

References

C. Lee and M. Wang. Smooth tensor estimation with unknown permutations. arXiv:2111.04681, 2021.

Examples

# NOT RUN {
d = 20
# Generate 20 by 20 by 20 observed tesnor generated from model 1
sim1 = simulation(d,mode = 1)
observed_tensor = sim1$observe
signal_tensor = sim1$signal
permutation = sim1$permutation
# }