Einsums/TensorUtilities/CreateRandomSemidefinite.hpp#

Defined in header Einsums/TensorUtilities/CreateRandomSemidefinite.hpp.

See Overview for a list of names and headers that are part of the public Einsums API.

namespace einsums

Todo:

Functions

template<typename T = double, bool Normalize = false>
Tensor<T, 2> create_random_semidefinite(std::string const &name, int rows, int cols, T mean = T{1.0}, int force_zeros = 1)#

Create a random positive or negative semi-definite matrix. A positive semi-definite matrix is a symmetric matrix whose eigenvalues are all non-negative. Similarly for negative semi-definite matrices.

This function first generates a set of random eigenvectors, making sure they are non-singular. Then, it uses these to form an orthonormal eigenbasis for the new matrix. Then, it generates the eigenvalues. The eigenvalues are distributed using a Maxwell-Boltzmann distribution with the given mean, defaulting to 1. If desired, a number of eigenvalues can be forced to be zero. Then, the returned matrix is formed by computing \(P^TDP\).

Parameters:

  • name – The name for the matrix.

  • rows – The number of rows.

  • cols – The number of columns. Should equal the number of rows.

  • mean – The mean for the eigenvalues. Defaults to 1. If negative, the result is a negative semi-definite matrix.

  • force_zeros – The number of elements to force to be zero. Defaults to 1.

Returns:

A new positive or negative semi-definite matrix.