* Replace mention of Aesara with Theano as Aesara is discontinued and Theano is the better-known library.

* Also remove fork of Theano.

* Mention PyMC.

When replacing the Shared RNG variables, the input order of the FunctionGraph was not explicitly aligned with the input storage of the function being compiled.

The provided output could be silently ignored and replaced by the new output of the vectorized node.

The changes also avoid vectorizing multiple-output nodes when none of the unreplaced outputs are needed.

* Copy `block_diag` and support functions from `pymc.math`

* Evaluate output in sphinx code example
Co-authored-by: Ricardo Vieira <28983449+ricardoV94@users.noreply.github.com>

* Test type equivalence with `isinstance` instead of `==`
Co-authored-by: Ricardo Vieira <28983449+ricardoV94@users.noreply.github.com>

* Typo in test function

* Split `block_diag` into sparse and dense version

Closely follow scipy function signature for `block_diag`

* Use `as_sparse_or_tensor_variable` in `SparseBlockDiagonalMatrix` to allow sparse matrix inputs to `pytensor.sparse.block_diag`

* Test sparse and dense inputs to `pytensor.sparse.block_diag`

* Add numba overload for `pytensor.tensor.slinalg.block_diag`

* add jax overload for `pytensor.tensor.slinalg.block_diag`

* Move stand-alone `block_diag_grad` function into `grad` method

* Add `format` prop to `SparseBlockDiagonalMatrix`

* Use `compare_numba_and_py` in `numba\test_slinalg.py::test_block_diag`

* Add support for Blockwise to `slinalg.block_diag`

* Add gradient test

Remove `Matrix` from `BlockDiagonal` and `SparseBlockDiagonal` `Op` names

Correct errors in docstrings

Move input validation to a shared class method

* Remove `gufunc_signature` from `__props__`
Co-authored-by: Ricardo Vieira <28983449+ricardoV94@users.noreply.github.com>

* Implement correct `__props__` for subclasses of `BaseBlockMatrix`

---------
Co-authored-by: Ricardo Vieira <28983449+ricardoV94@users.noreply.github.com>

* Use `solve_triangular` instead of in `psd_solve_with_chol`

* Add unittest for `psd_solve_with_chol`

* Specify `mode=FAST_RUN` in test

* Relax `test_psd_solve_with_chol` `atol` and `rtol` for half-precision tests

Also refactors shared logic for other batch axed Ops

All types of axis arguments are supported by max_and_argmax

This reverts commit 0fc2cd8e.

This rewrites replaces a batched matmul by a core matmul by raveling the batched dimensions of the batched input, doing a 2D matmul and then unravelling the batched dimensions of the output.

This sidesteps the Blockwise Dot operation and allows specialization into BLAS routines.

The idea was taken from these two discussions:
https://github.com/numpy/numpy/issues/7569
https://github.com/numpy/numpy/issues/8957

Bumps [actions/download-artifact](https://github.com/actions/download-artifact) from 3 to 4.
- [Release notes](https://github.com/actions/download-artifact/releases)
- [Commits](https://github.com/actions/download-artifact/compare/v3...v4)

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updated-dependencies:
- dependency-name: actions/download-artifact
  dependency-type: direct:production
  update-type: version-update:semver-major
...
Signed-off-by: dependabot[bot] <support@github.com>

Docstring still uses old name of `vectorize`

Bumps [actions/setup-python](https://github.com/actions/setup-python) from 4 to 5.
- [Release notes](https://github.com/actions/setup-python/releases)
- [Commits](https://github.com/actions/setup-python/compare/v4...v5)

---
updated-dependencies:
- dependency-name: actions/setup-python
  dependency-type: direct:production
  update-type: version-update:semver-major
...
Signed-off-by: dependabot[bot] <support@github.com>

* feat(numpy logical aliases): add aliases for logical function equivalents in NumPy (#462)

* fix(logical): bitwise and logical are distinct operators

* doc(aliases): Document the new NumPy inequality aliases in the same style as existing bitwise ones.

* refactor(numpy-aliases): collect all NumPy aliases in one block at the end of the file

* Change `import pytensor.tensor as at` to `as pt` everywhere in the docs

* Change `import pytensor.tensor as at` to `as pt` everywhere

Change `import pytensor.scalar as aes` to `as ps` everywhere

Change `import pytensor.tensor.random as aer` to `as ptr` everywhere

Change test variables with `_at` suffix or `at_` prefix to `_pt` and `pt_`, respectively

* More renaming

* Rename remaining instances of `aes` and `aer`

When size is not provided, the batch shapes of the parameters were being broadcasted twice, and the second time, wrongly, due to mixing static shape of the original parameters and the potentially larger shape of the just broadcasted parameters.

Fixes #542

Also prevent Alloc from constant_folding when it's used by Elemwise and Blockwise to avoid creating useless large arrays

Also adds better static shapes

The Op now always expects rank 3 inputs, and any dimshuffles are added explicitly by the helper function

It now supports an arbitrary number of batched dimensions of b, by raveling them together

Also return matmul for respective vectorize of dot, to avoid creating redundant Blockwise Ops

Also extend eager rewrite to more Ops

The Blockwise MatrixInverse grad test became more sensitive in float32, because desired stabilization rewrites (mainly `inv_as_solve`) that target Dot of Blockwise{MatrixInverse} are now triggered in the default blockwise grad but not in the non-default non-blockwise grad

Rewrite was already tagged as "shape_unsafe"