Return (inv) root of KroneckerProductAddedDiagLinearOperator as lazy #14
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Previously, `_root_decomposition` and `_inv_root_decomposition` were returning the (inv) root from the eigendecomposition as a dense tensor, which can be inefficient. This now returns the root as `MatmulLazyTensor` instead. E.g. a matrix vector product of the root with some vector `v` is now implicitly computed as `q_matrix @ (evals \dot v)` rather than `(q_matrix @ diag(evals)) @ v`, which can make a big difference since `q_matrix` is a Kronecker product. This can help runtime, but more importantly it significantly reduces memory footprint, since we don't need to instantiate the (inv) root, but only the constitutent components. This is a clone of cornellius-gp/gpytorch#1430
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I am not sure why in the case of using a |
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This is a clone of cornellius-gp/gpytorch#1430
Previously,
_root_decompositionand_inv_root_decompositionwere returning the (inv) root from the eigendecomposition as a dense tensor, which can be inefficient. This now returns the root asMatmulLazyTensorinstead. E.g. a matrix vector product of the root with some vectorvis now implicitly computed asq_matrix @ (evals \dot v)rather than(q_matrix @ diag(evals)) @ v, which can make a big difference sinceq_matrixis a Kronecker product.This can help runtime, but more importantly it significantly reduces memory footprint, since we don't need to instantiate the (inv) root, but only the constituent components.
This also fixes an issue with
KroneckerProductAddedDiagLinearOperatorimplicitly assuming the diagonal to be constant, and returning incorrect results if that was not the case. The changes here make the tensor fall back to the superclass implementation in case of non-constant diagonals.