[WIP] MatrixAlgebraKit decompositions #230
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## master #230 +/- ##
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- Coverage 82.65% 77.63% -5.03%
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The test failures on empty tensors should be resolved once QuantumKitHub/MatrixAlgebraKit.jl#37 is merged. @Jutho I think this is ready for another round of review, it definitely requires a bunch more cleanup but I think I am getting somewhere now, the improvements in MatrixAlgebraKit have definitely helped a bunch. |
src/tensors/diagonal.jl
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| @@ -265,6 +275,21 @@ function LinearAlgebra.mul!(dC::DiagonalTensorMap, | |||
| return dC | |||
| end | |||
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| function LinearAlgebra.lmul!(D::DiagonalTensorMap, t::AbstractTensorMap) | |||
| domain(D) == codomain(t) || throw(SpaceMismatch()) | |||
| for (c, b) in blocks(t) | |||
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Do we immediately want to write this using foreachblock?
src/tensors/diagonal.jl
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| end | ||
| function LinearAlgebra.rmul!(t::AbstractTensorMap, D::DiagonalTensorMap) | ||
| codomain(D) == domain(t) || throw(SpaceMismatch()) | ||
| for (c, b) in blocks(t) |
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Small fixes
Correctly implement `isisometry`
| ⊖(V::ElementarySpace, W::ElementarySpace) -> X::ElementarySpace | ||
| ominus(V::ElementarySpace, W::ElementarySpace) -> X::ElementarySpace | ||
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| Return the set difference of two elementary spaces, i.e. an instance `X::ElementarySpace` |
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| Return the set difference of two elementary spaces, i.e. an instance `X::ElementarySpace` | |
| Return a space that is equivalent to the orthogonal complement of `W` in `V`, i.e. an instance `X::ElementarySpace` |
| export leftorth, rightorth, leftnull, rightnull, | ||
| leftorth!, rightorth!, leftnull!, rightnull!, | ||
| export leftorth, rightorth, leftnull, rightnull, leftpolar, rightpolar, | ||
| leftorth!, rightorth!, leftnull!, rightnull!, leftpolar!, rightpolar!, |
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Do you want to add new methods like leftpolar here, or do we want to switch over to MatrixAlgebraKit conventions and use left_ and right_ (with underscores), and keep leftorth and friends for backward compatibility (with possible deprecations in a future version)?
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| for f! in (:svd_compact!, :svd_full!, :left_null_svd!, :right_null_svd!) | ||
| @eval function select_algorithm(::typeof($f!), t::T, alg::SVD; | ||
| kwargs...) where {T} |
| end | ||
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| function check_input(::typeof(right_polar!), t::AbstractTensorMap, (P, Wᴴ)::_T_PWᴴ) | ||
| domain(t) ≿ codomain(t) || |
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Is there a specific preference for writing the checks using ≿ versus ≾ ?
I know this is nitpicking, but I would either prefer consistent use of ≾ , or alternatively, consistent use of codomain(t) as first argument and domain(t) as second, with varying operator.
This PR is part of a large set of changes that alters the backend from
TensorKit.MatrixAlgebratoMatrixAlgebraKitfor the factorizations.Concretely, this is achieved through a new submodule
TensorKit.Factorizationsthat implements most of theMatrixAlgebraKitinterface, along with some overloads and reimplementations to be somewhat backwards compatible.New features
foreachblock(f, t::AbstractTensorMap...)is a new function that is meant to provide a uniform interface to iterate through the blocks of a collection of tensors. The main purpose is to centralize this concept to easily add multithreading over the blocks. In order to break up this PR the actual multithreading implementation is left for a follow-up PR.eig,eighandeigennow have preliminary support for a truncated version of these algorithms.ominusand its unicode variant can now be used to obtain the orthogonal complement of a space, ie ifW = oplus(V1, V2),V2 = ominus(W, V1).Breaking changes
tsvdfunction no longer outputs the truncation error, and instead just givesU, S, Vh.MatrixAlgebraKit. This meanstruncdimis replaced bytruncrank,trunctolis replaced bytruncbelow, and there are deprecation warnings for the old functions.leftorthandrightorthfunctions will now always output tensors with a single space connecting them, which was not the case forPolardecompositions previously. To retrieve the old behavior withisposdefRfactors (equal domain and codomain instead of isomorphic), new functionsleftpolarandrightpolarare added.leftorthandrightorthfunctions will now always have a connecting space withisdual=false. This is different from the previous behavior where someN,1or1,Ntensors kept theisdualflag on the connecting leg.