# Source code for botorch.models.transforms.utils

#!/usr/bin/env python3
#
# LICENSE file in the root directory of this source tree.

from __future__ import annotations

from typing import Tuple

import torch
from torch import Tensor

[docs]def lognorm_to_norm(mu: Tensor, Cov: Tensor) -> Tuple[Tensor, Tensor]:
"""Compute mean and covariance of a MVN from those of the associated log-MVN

If Y is log-normal with mean mu_ln and covariance Cov_ln, then
X ~ N(mu_n, Cov_n) with

Cov_n_{ij} = log(1 + Cov_ln_{ij} / (mu_ln_{i} * mu_n_{j}))
mu_n_{i} = log(mu_ln_{i}) - 0.5 * log(1 + Cov_ln_{ii} / mu_ln_{i}**2)

Args:
mu: A batch_shape x n mean vector of the log-Normal distribution.
Cov: A batch_shape x n x n covariance matrix of the log-Normal
distribution.

Returns:
A two-tuple containing:

- The batch_shape x n mean vector of the Normal distribution
- The batch_shape x n x n covariance matrix of the Normal distribution
"""
Cov_n = torch.log(1 + Cov / (mu.unsqueeze(-1) * mu.unsqueeze(-2)))
mu_n = torch.log(mu) - 0.5 * torch.diagonal(Cov_n, dim1=-1, dim2=-2)
return mu_n, Cov_n

[docs]def norm_to_lognorm(mu: Tensor, Cov: Tensor) -> Tuple[Tensor, Tensor]:
"""Compute mean and covariance of a log-MVN from its MVN sufficient statistics

If X ~ N(mu, Cov) and Y = exp(X), then Y is log-normal with

mu_ln_{i} = exp(mu_{i} + 0.5 * Cov_{ii})
Cov_ln_{ij} = exp(mu_{i} + mu_{j} + 0.5 * (Cov_{ii} + Cov_{jj})) *
(exp(Cov_{ij}) - 1)

Args:
mu: A batch_shape x n mean vector of the Normal distribution.
Cov: A batch_shape x n x n covariance matrix of the Normal distribution.

Returns:
A two-tuple containing:

- The batch_shape x n mean vector of the log-Normal distribution.
- The batch_shape x n x n covariance matrix of the log-Normal
distribution.
"""
diag = torch.diagonal(Cov, dim1=-1, dim2=-2)
b = mu + 0.5 * diag
mu_ln = torch.exp(b)
Cov_ln = (torch.exp(Cov) - 1) * torch.exp(b.unsqueeze(-1) + b.unsqueeze(-2))
return mu_ln, Cov_ln

[docs]def norm_to_lognorm_mean(mu: Tensor, var: Tensor) -> Tensor:
"""Compute mean of a log-MVN from its MVN marginals

Args:
mu: A batch_shape x n mean vector of the Normal distribution.
var: A batch_shape x n variance vectorof the Normal distribution.

Returns:
The batch_shape x n mean vector of the log-Normal distribution
"""

[docs]def norm_to_lognorm_variance(mu: Tensor, var: Tensor) -> Tensor:
"""Compute variance of a log-MVN from its MVN marginals

Args:
mu: A batch_shape x n mean vector of the Normal distribution.
var: A batch_shape x n variance vectorof the Normal distribution.

Returns:
The batch_shape x n variance vector of the log-Normal distribution.
"""
b = mu + 0.5 * var
return (torch.exp(var) - 1) * torch.exp(2 * b)