Tensor Operators

Batched linear-algebra and angular operators implemented as CUDA/C++ kernels and exposed via pyc::operators.

pyc::operators Functions

Function	Description
Dot(v1, v2)	Batch inner (dot) product of two vector tensors
CosTheta(v1, v2)	Cosine of the opening angle between v1 and v2
SinTheta(v1, v2)	Sine of the opening angle
Rx(angle)	Rotation matrix around x-axis for each element in angle
Ry(angle)	Rotation matrix around y-axis
Rz(angle)	Rotation matrix around z-axis
RT(pmc_b, pmc_mu)	Combined rotation aligning b-quark to z-axis in the lepton rest frame
CoFactors(matrix)	Cofactor matrix of each \(3\times3\) element in the batch
Determinant(matrix)	Determinant of each matrix in the batch
Inverse(matrix)	Returns (inv, valid) — Moore–Penrose pseudo-inverse and validity mask
Eigenvalue(matrix)	Returns (eigenvalues, eigenvectors) for symmetric matrices
Cross(mat1, mat2)	Batch 3-vector cross product

namespace operators

Tensor-based matrix/vector operations.

Functions

torch::Tensor Dot(torch::Tensor v1, torch::Tensor v2)

Element-wise inner product.

torch::Tensor CosTheta(torch::Tensor v1, torch::Tensor v2)

Compute cos θ between two vectors.

torch::Tensor SinTheta(torch::Tensor v1, torch::Tensor v2)

Compute sin θ between two vectors.

torch::Tensor Rx(torch::Tensor angle)

Batched rotation matrix about x.

torch::Tensor Ry(torch::Tensor angle)

Batched rotation matrix about y.

torch::Tensor Rz(torch::Tensor angle)

Batched rotation matrix about z.

torch::Tensor RT(torch::Tensor pmc_b, torch::Tensor pmc_mu)

Compute the rotation from the b–lepton decay frame to the lab frame.

torch::Tensor CoFactors(torch::Tensor matrix)

Compute the cofactor matrix.

torch::Tensor Determinant(torch::Tensor matrix)

Compute the determinant.

std::tuple<torch::Tensor, torch::Tensor> Inverse(torch::Tensor matrix)

Compute the inverse and a validity mask.

Returns:

(inverse, valid_mask).

std::tuple<torch::Tensor, torch::Tensor> Eigenvalue(torch::Tensor matrix)

Compute eigenvalues and a validity mask.

Returns:

(eigenvalues, valid_mask).

torch::Tensor Cross(torch::Tensor mat1, torch::Tensor mat2)

Batched cross product.

Internal Kernel Namespace

namespace operators_

Internal namespace for batched matrix/vector operators.

Functions

torch::Tensor Dot(torch::Tensor *v1, torch::Tensor *v2)

Batched element-wise dot product.

Parameters:

• v1 – [N, D] first vectors.

• v2 – [N, D] second vectors.

Returns:

[N] dot products.

torch::Tensor Cross(torch::Tensor *v1, torch::Tensor *v2)

Batched cross product of 3-vectors.

Parameters:

• v1 – [N, 3].

• v2 – [N, 3].

Returns:

[N, 3] cross products.

torch::Tensor Determinant(torch::Tensor *matrix)

Batched 3×3 determinant.

Parameters:

matrix – [N, 3, 3].

Returns:

[N] determinants.

torch::Tensor CosTheta(torch::Tensor *v1, torch::Tensor *v2)

Batched cosine of angle between v1 and v2.

Returns:

[N] cosines.

torch::Tensor SinTheta(torch::Tensor *v1, torch::Tensor *v2)

Batched sine of angle between v1 and v2.

Returns:

[N] sines.

torch::Tensor Pi_2(torch::Tensor *trn)

Compute π/2 - θ for each element.

Parameters:

trn – [N] angle tensor.

Returns:

[N] result.

torch::Tensor Rx(torch::Tensor *angle)

Batched rotation matrix about x.

Parameters:

angle – [N].

Returns:

[N, 3, 3].

torch::Tensor Ry(torch::Tensor *angle)

Batched rotation matrix about y.

Returns:

[N, 3, 3].

torch::Tensor Rz(torch::Tensor *angle)

Batched rotation matrix about z.

Returns:

[N, 3, 3].

torch::Tensor RT(torch::Tensor *pmc_b, torch::Tensor *pmc_mu, torch::Tensor *base)

Compute the rotation from the decay frame to the lab frame for each (b, lepton) pair.

Parameters:

• pmc_b – [N, 4] b-quark Cartesian momenta.

• pmc_mu – [N, 4] lepton Cartesian momenta.

• base – Pre-computed base matrix.

Returns:

[N, 3, 3] rotation matrices.

torch::Tensor CoFactors(torch::Tensor *matrix)

Batched cofactor matrix.

Parameters:

matrix – [N, 3, 3].

Returns:

[N, 3, 3] cofactor matrices.

std::tuple<torch::Tensor, torch::Tensor> Inverse(torch::Tensor *matrix)

Batched 3×3 matrix inverse.

Returns:

(inverse [N, 3, 3], valid_mask [N]).

std::tuple<torch::Tensor, torch::Tensor> Eigenvalue(torch::Tensor *matrix)

Batched 3×3 eigenvalue computation.

Returns:

(eigenvalues [N, 3], valid_mask [N]).