qmctorch.utils.algebra_utils module

qmctorch.utils.algebra_utils.btrace(M)

Computes the trace of batched matrices

Parameters:

M (torch.tensor) – matrices of size (Na, Nb, … Nx, N, N)

Returns:

trace of matrices (Na, Nb, … Nx)

Return type:

torch.tensor

Example

>>> m = torch.rand(100,5,5)
>>> tr = btrace(m)

qmctorch.utils.algebra_utils.bproj(M, P)

Project batched marices using P^T M P

Parameters:

• M (torch.tensor) – batched matrices size (…, N, M)

• P (torch.tensor) – Porjectors size (…, N, M)

Returns:

Projected matrices

Return type:

torch.tensor

qmctorch.utils.algebra_utils.bdet2(M)

Computes the determinant of batched 2x2 matrices

Parameters:

M (torch.tensor) – input matrices

Returns:

determinants of the matrices

Return type:

torch.tensor

class qmctorch.utils.algebra_utils.BatchDeterminant(*args: Any, **kwargs: Any)

Bases: Function

static forward(ctx, input)

static backward(ctx, grad_output)

using jaobi’s formula

d det(A) / d A_{ij} = adj^T(A)_{ij}

using the adjunct formula

d det(A) / d A_{ij} = ( (det(A) A^{-1})^T )_{ij}