Opt-einsum

NumPy has been removed from `opt_einsum` as a dependency allowing for more flexible installs.

**New Features**

- [\160](https://github.com/dgasmith/opt_einsum/pull/160) Migrates docs to MkDocs Material and GitHub pages hosting.
- [\161](https://github.com/dgasmith/opt_einsum/pull/161) Adds Python type annotations to the code base.
- [\204](https://github.com/dgasmith/opt_einsum/pull/204) Removes NumPy as a hard dependency.

**Enhancements**

- [\154](https://github.com/dgasmith/opt_einsum/pull/154) Prevents an infinite recursion error when the `memory_limit` was set very low for the `dp` algorithm.
- [\155](https://github.com/dgasmith/opt_einsum/pull/155) Adds flake8 spell check to the doc strings
- [\159](https://github.com/dgasmith/opt_einsum/pull/159) Migrates to GitHub actions for CI.
- [\174](https://github.com/dgasmith/opt_einsum/pull/174) Prevents double contracts of floats in dynamic paths.
- [\196](https://github.com/dgasmith/opt_einsum/pull/196) Allows `backend=None` which is equivalent to `backend='auto'`
- [\208](https://github.com/dgasmith/opt_einsum/pull/208) Switches to `ConfigParser` insetad of `SafeConfigParser` for Python 3.12 compatability.
- [\228](https://github.com/dgasmith/opt_einsum/pull/228) `backend='jaxlib'` is now an alias for the `jax` library
- [\237](https://github.com/dgasmith/opt_einsum/pull/237) Switches to `ruff` for formatting and linting.
- [\238](https://github.com/dgasmith/opt_einsum/pull/238) Removes `numpy`-specific keyword args from being explicitly defined in `contract` and uses `**kwargs` instead.

**Bug Fixes**

- [\195](https://github.com/dgasmith/opt_einsum/pull/195) Fixes a bug where `dp` would not work for scalar-only contractions.
- [\200](https://github.com/dgasmith/opt_einsum/pull/200) Fixes a bug where `parse_einsum_input` would not correctly respect shape-only contractions.
- [\222](https://github.com/dgasmith/opt_einsum/pull/222) Fixes an erorr in `parse_einsum_input` where an output subscript specified multiple times was not correctly caught.
- [\229](https://github.com/dgasmith/opt_einsum/pull/229) Fixes a bug where empty contraction lists in `PathInfo` would cause an error.

Adds a `object` backend for optimized contractions on arbitrary Python objects.

**New Features**

- [\145](https://github.com/dgasmith/opt_einsum/pull/145) Adds a `object` based backend so that `contract(backend='object')` can be used on arbitrary objects such as SymPy symbols.

**Enhancements**

- [\140](https://github.com/dgasmith/opt_einsum/pull/140) Better error messages when the requested `contract` backend cannot be found.
- [\141](https://github.com/dgasmith/opt_einsum/pull/141) Adds a check with RandomOptimizers to ensure the objects are not accidentally reused for different contractions.
- [\149](https://github.com/dgasmith/opt_einsum/pull/149) Limits the `remaining` category for the `contract_path` output to only show up to 20 tensors to prevent issues with the quadratically scaling memory requirements and the number of print lines for large contractions.

Small fixes for the `dp` path and support for a new mars backend.

**New Features**

- [\109](https://github.com/dgasmith/opt_einsum/pull/109) Adds mars backend support.

**Enhancements**

- [\110](https://github.com/dgasmith/opt_einsum/pull/110) New `auto-hq` and `'random-greedy-128'` paths.
- [\119](https://github.com/dgasmith/opt_einsum/pull/119) Fixes several edge cases in the `dp` path.

**Bug fixes**

- [\127](https://github.com/dgasmith/opt_einsum/pull/127) Fixes an issue where Python 3.6 features are required while Python 3.5 is `opt_einsum`'s stated minimum version.

Adds a new dynamic programming algorithm to the suite of paths.

**New Features**

- [\102](https://github.com/dgasmith/opt_einsum/pull/102) Adds new `dp` path.

This release moves `opt_einsum` to be backend agnostic while adding support
additional backends such as Jax and Autograd. Support for Python 2.7 has been dropped and Python 3.5 will become the new minimum version, a Python deprecation policy equivalent to NumPy's has been adopted.


**New Features**

- [\78](https://github.com/dgasmith/opt_einsum/pull/78) A new random-optimizer has been implemented which uses Boltzmann weighting to explore alternative near-minimum paths using greedy-like schemes. This provides a fairly large path performance enhancements with a linear path time overhead.
- [\78](https://github.com/dgasmith/opt_einsum/pull/78) A new PathOptimizer class has been implemented to provide a framework for building new optimizers. An example is that now custom cost functions can now be provided in the greedy formalism for building custom optimizers without a large amount of additional code.
- [\81](https://github.com/dgasmith/opt_einsum/pull/81) The `backend="auto"` keyword has been implemented for `contract` allowing automatic detection of the correct backend to use based off provided tensors in the contraction.
- [\88](https://github.com/dgasmith/opt_einsum/pull/88) Autograd and Jax support have been implemented.
- [\96](https://github.com/dgasmith/opt_einsum/pull/96) Deprecates Python 2 functionality and devops improvements.

**Enhancements**

- [\84](https://github.com/dgasmith/opt_einsum/pull/84) The `contract_path` function can now accept shape tuples rather than full tensors.
- [\84](https://github.com/dgasmith/opt_einsum/pull/84) The `contract_path` automated path algorithm decision technology has been refactored to a standalone function.

This release primarily focuses on expanding the suite of available path
technologies to provide better optimization characistics for 4-20 tensors while
decreasing the time to find paths for 50-200+ tensors. See `Path Overview <path_finding.htmlperformance-comparison>`_ for more information.

**New Features**

- [\60](https://github.com/dgasmith/opt_einsum/pull/60) A new `greedy` implementation has been added which is up to two orders of magnitude faster for 200 tensors.
- [\73](https://github.com/dgasmith/opt_einsum/pull/73) Adds a new `branch` path that uses `greedy` ideas to prune the `optimal` exploration space to provide a better path than `greedy` at sub `optimal` cost.
- [\73](https://github.com/dgasmith/opt_einsum/pull/73) Adds a new `auto` keyword to the `opt_einsum.contract` `path` option. This keyword automatically chooses the best path technology that takes under 1ms to execute.

**Enhancements**

- [\61](https://github.com/dgasmith/opt_einsum/pull/61) The `opt_einsum.contract` `path` keyword has been changed to `optimize` to more closely match NumPy. `path` will be deprecated in the future.
- [\61](https://github.com/dgasmith/opt_einsum/pull/61) The `opt_einsum.contract_path` now returns a `opt_einsum.contract.PathInfo` object that can be queried for the scaling, flops, and intermediates of the path. The print representation of this object is identical to before.
- [\61](https://github.com/dgasmith/opt_einsum/pull/61) The default `memory_limit` is now unlimited by default based on community feedback.
- [\66](https://github.com/dgasmith/opt_einsum/pull/66) The Torch backend will now use `tensordot` when using a version of Torch which includes this functionality.
- [\68](https://github.com/dgasmith/opt_einsum/pull/68) Indices can now be any hashable object when provided in the `"Interleaved Input" <input_format.html#interleaved-input>`_ syntax.
- [\74](https://github.com/dgasmith/opt_einsum/pull/74) Allows the default `transpose` operation to be overridden to take advantage of more advanced tensor transpose libraries.
- [\73](https://github.com/dgasmith/opt_einsum/pull/73) The `optimal` path is now significantly faster.
- [\81](https://github.com/dgasmith/opt_einsum/pull/81) A documentation pass for v3.0.

**Bug fixes**

- [\72](https://github.com/dgasmith/opt_einsum/pull/72) Fixes the `"Interleaved Input" <input_format.html#interleaved-input>`_ syntax and adds documentation.