lgatr.primitives.linear

Linear operations on multivectors, in particular linear basis maps.

Functions

`equi_linear`(x, coeffs)	Pin-equivariant linear map `f(x) = sum_{a,j} coeffs_a W^a_ij x_j`.
`grade_involute`(x)	Computes the grade involution of a multivector.
`grade_project`(x)	Projects an input tensor to the individual grades.
`reverse`(x)	Computes the reversal of a multivector.

lgatr.primitives.linear.equi_linear(x, coeffs)[source]

Pin-equivariant linear map f(x) = sum_{a,j} coeffs_a W^a_ij x_j.

The W^a are seven pre-defined basis elements.

Parameters:

x (torch.Tensor) – Input multivector with shape (…, in_channels, 16). Batch dimensions must be broadcastable between x and coeffs.
coeffs (torch.Tensor) – Coefficients for the basis elements with shape (out_channels, in_channels, 10). Batch dimensions must be broadcastable between x and coeffs.

Returns:

outputs – Result with shape (…, 16). Batch dimensions are result of broadcasting between x and coeffs.

Return type:

torch.Tensor

lgatr.primitives.linear.grade_involute(x)[source]

Computes the grade involution of a multivector.

The reversal has the same scalar, bivector, and pseudoscalar components, but flips sign in the vector and trivector components.

lgatr.primitives.linear.grade_project(x)[source]

Projects an input tensor to the individual grades.

The return value is a single tensor with a new grade dimension.

Parameters:: x (torch.Tensor) – Input multivector with shape (…, 16).
Returns:: outputs – Output multivector with shape (…, 5, 16). The second-to-last dimension indexes the grades.
Return type:: torch.Tensor

lgatr.primitives.linear.reverse(x)[source]

Computes the reversal of a multivector.

The reversal has the same scalar, vector, and pseudoscalar components, but flips sign in the bivector and trivector components.