import torch
import numpy as np
# General torch settings and devices.
torch.set_num_threads(8)
gpu = torch.device('cuda:0')
cpu = torch.device('cpu')
from timeit import default_timer as timer
[docs]def compute_cov_pushforward(lambda0, F, cells_coords, device, n_chunks=200,
n_flush=50):
""" Compute the covariance pushforward.
The covariance pushforward is just KF^T, where K is the model
covariance matrix.
Note that the sigam0^2 is not included, and one has to manually add it when
using the covariance pushforward computed here.
Parameters
----------
lambda0: float
Lenght-scale parameter
F: tensor
Forward operator matrix
cells_coords: tensor
n_cells * n_dims: cells coordinates
device: toch.Device
Device to perform the computation on, CPU or GPU.
n_chunks: int
Number of chunks to split the matrix into.
Default is 200. Increase if get OOM errors.
n_flush: int
Synchronize threads and flush GPU cache every *n_flush* iterations.
This is necessary to avoid OOM errors.
Default is 50.
Returns
-------
Tensor
n_model * n_data covariance pushforward K F^t.
"""
start = timer()
# Transfer everything to device.
lambda0 = torch.tensor(lambda0, requires_grad=False).to(device)
F = F.to(device)
cells_coords = cells_coords.to(device)
inv_lambda2 = - np.sqrt(3) / lambda0
n_dims = 3
n_model = F.shape[1]
# Array to hold the results. We will compute line by line and concatenate.
tot = torch.Tensor().to(device)
# Compute K * F^T chunk by chunk.
# That is, of all the cell couples, we compute the distance between some
# cells (here x) and ALL other cells. Then repeat for other chunk and
# concatenate.
for i, x in enumerate(torch.chunk(cells_coords, chunks=n_chunks, dim=0)):
# Empty cache every so often. Otherwise we get out of memory errors.
if i % n_flush == 0 and torch.cuda.is_available():
torch.cuda.synchronize()
torch.cuda.empty_cache()
# Euclidean distance.
d = torch.sqrt(torch.pow(
x.unsqueeze(1).expand(x.shape[0], n_model, n_dims)
- cells_coords.unsqueeze(0).expand(x.shape[0], n_model, n_dims)
, 2).sum(2))
tot = torch.cat((
tot,
torch.matmul(
torch.mul(
torch.ones(d.shape, device=device) - inv_lambda2 * d,
torch.exp(inv_lambda2 * d))
, F.t())))
# Wait for all threads to complete.
if torch.cuda.is_available():
torch.cuda.synchronize()
torch.cuda.empty_cache()
end = timer()
print((end - start)/60.0)
return tot.cpu()
[docs]def compute_cov(lambda0, cells_coords, i, j):
""" Compute the covariance between two points.
Note that, as always, sigma0 has been stripped.
Parameters
----------
lambda0: float
Lenght-scale parameter
cells_coords: tensor
n_cells * n_dims: cells coordinates
i: int
Index of first cell (index in the cells_coords array).
j: int
Index of second cell.
Returns
-------
Tensor
(Stripped) covariance between cell nr i and cell nr j.
"""
# Convert to torch.
lambda0 = torch.tensor(lambda0, requires_grad=False)
inv_lambda2 = - np.sqrt(3) / lambda0
# Euclidean distance.
d = torch.sqrt(torch.pow(
cells_coords[i, :] - cells_coords[j, :]
, 2).sum())
return (1 - inv_lambda2 * d) * torch.exp(inv_lambda2 * d)
[docs]def compute_full_cov(lambda0, cells_coords, device, n_chunks=200,
n_flush=50):
""" Compute the full covariance matrix.
Note that the sigam0^2 is not included, and one has to manually add it when
using the covariance pushforward computed here.
Parameters
----------
lambda0: float
Lenght-scale parameter
cells_coords: tensor
n_cells * n_dims: cells coordinates
device: toch.Device
Device to perform the computation on, CPU or GPU.
n_chunks: int
Number of chunks to split the matrix into.
Default is 200. Increase if get OOM errors.
n_flush: int
Synchronize threads and flush GPU cache every *n_flush* iterations.
This is necessary to avoid OOM errors.
Default is 50.
Returns
-------
Tensor
n_cells * n_cells covariance matrix.
"""
# Transfer everything to device.
lambda0 = torch.tensor(lambda0, requires_grad=False).to(device)
cells_coords = cells_coords.to(device)
inv_lambda2 = - np.sqrt(3) / lambda0
n_dims = 3
n_cells = cells_coords.shape[0]
# Array to hold the results. We will compute line by line and concatenate.
tot = torch.Tensor().to(device)
# Compute K * F^T chunk by chunk.
# That is, of all the cell couples, we compute the distance between some
# cells (here x) and ALL other cells. Then repeat for other chunk and
# concatenate.
for i, x in enumerate(torch.chunk(cells_coords, chunks=n_chunks, dim=0)):
# Empty cache every so often. Otherwise we get out of memory errors.
if i % n_flush == 0 and torch.cuda.is_available():
torch.cuda.synchronize()
torch.cuda.empty_cache()
# Euclidean distance.
d = torch.sqrt(torch.pow(
x.unsqueeze(1).expand(x.shape[0], n_cells, n_dims)
- cells_coords.unsqueeze(0).expand(x.shape[0], n_cells, n_dims)
, 2).sum(2))
tot = torch.cat((
tot,
torch.mul(
torch.ones(d.shape, device=device) - inv_lambda2 * d,
torch.exp(inv_lambda2 * d))))
# Wait for all threads to complete.
if torch.cuda.is_available():
torch.cuda.synchronize()
torch.cuda.empty_cache()
return tot.cpu()