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

Also cover cases of AdvancedIncSubtensor with batch indices that were not supported before

* Skip slow numba pad tests

* Reduce number of Second tests

* Update test.yml

Also implemented tests as suggested by ricardoV94

They don't simplify shape inference, since the operation is never meaningful shape-wise

* Add `concat_with_broadcast` helper function

Use new helper in xt.concat
Co-authored-by: Ricardo <ricardo.vieira1994@gmail.com>

* block_diag dot rewrite
Co-authored-by: Ricardo <ricardo.vieira1994@gmail.com>

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Co-authored-by: Ricardo <ricardo.vieira1994@gmail.com>

* Implemented allow_cast in PatternNodeRewriter
to allow rewrites that would otherwise fail when the new and old dtype differ.
Example:
`np.array(1., "float64") - sigmoid(x)` cannot be rewritten as
`sigmoid(-x)` (where x is an fmatrix) because the type would change.
This commit allows an automatic cast to be added so the expression
is rewritten as `cast(sigmoid(-x), "float64")`.
Relevant tests added.

* Added test cases for which issue #1497 fails

* Changed PatternNodeRewriter::transform to allow types that do not contain dtype
like MyType in the tests

* Address #1497 by changing instances of np.isclose to a function isclose, which uses 10 ULPs by default

* Addressed failed tests (with older python/numpy versions)

* Addressed feedback by ricardoV94

* Test PatternNodeRewriter doesn't support multi-output nodes in pattern

But it's fine if they're just root inputs

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Co-authored-by: Luca Citi <lciti@ieee.org>
Co-authored-by: Ricardo Vieira <ricardo.vieira1994@gmail.com>

The marked xfail test was failing because Ger wasn't introduced, not because of the complex dtype.

New rewrite is added to convert unpaired batched row/column matvec or vec products as equivalent matmul products.

This reduces the number of rewrite passes, by avoiding constant fold of cast/expand_dims/alloc

* Refactor QR

* Update JAX QR dispatch

* Update Torch QR dispatch

* Update numba QR dispatch

Also remove broadcast which is not a method in Xarray