def pytorch_orgqr_with_roundtrip(v, tau, checks=True):
if checks:
assert torch.is_tensor(v) and torch.is_tensor(tau)
assert v.dim() == 2 and tau.dim() == 1
assert v.shape[0] >= v.shape[1]
assert v.shape[1] == tau.numel()
assert v.device == tau.device
if v.device == 'cpu':
return torch.orgqr(v, tau)
device = v.device
v, tau = v.cpu(), tau.cpu()
out = torch.orgqr(v, tau).to(device)
return out
def basis(A):
"""Return orthogonal basis of A columns."""
if A.is_cuda:
# torch.orgqr is not available in CUDA
Q = torch.linalg.qr(A).Q
else:
Q = torch.orgqr(*torch.geqrf(A))
return Q
def basis(A):
"""Return orthogonal basis of A columns.
"""
if A.is_cuda:
# torch.orgqr is not available in CUDA
Q, _ = torch.qr(A, some=True)
else:
Q = torch.orgqr(*torch.geqrf(A))
return Q
print('Error:', torch.linalg.norm(M - Q @ R).item())
print('Orthogonality:', torch.linalg.norm(torch.eye(n,n, device = device) - Q @ Q.t()).item())
print('--- torch.qr ---')
begin = time.time()
Q, R = torch.qr(M)
end = time.time()
print('Time:', end - begin)
print('Error:', torch.linalg.norm(M - Q @ R).item())
print('Orthogonality:', torch.linalg.norm(torch.eye(n,n, device = device) - Q @ Q.t()).item())
if device == 'cpu':
print('--- LAPACK geqrf + orgqr ---')
begin = time.time()
a, tau = torch.geqrf(M)
Q = torch.orgqr(a, tau)
end = time.time()
print('Time:', end - begin)
#print('--- NUMPY linalg.qr ---')
#M = M.numpy()
#begin = time.time()
#Q, R = np.linalg.qr(M)
#end = time.time()
#print('Time:', end - begin)