Adding rewrites involving kronecker product (pymc-devs#975)

* Added rewrite for diag of kronecker product

* Added rewrite for slogdet; added docstrings for  rewrites

* fixed typo

pytensor/tensor/rewriting/linalg.py

@@ -22,7 +22,7 @@
 from pytensor.tensor.blas import Dot22
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle, Elemwise
-from pytensor.tensor.math import Dot, Prod, _matrix_matrix_matmul, log, prod
+from pytensor.tensor.math import Dot, Prod, _matrix_matrix_matmul, log, outer, prod
 from pytensor.tensor.nlinalg import (
     SVD,
     KroneckerProduct,
@@ -818,3 +818,72 @@ def rewrite_slogdet_blockdiag(fgraph, node):
     )
 
     return [prod(sign_sub_matrices), sum(logdet_sub_matrices)]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([ExtractDiag])
+def rewrite_diag_kronecker(fgraph, node):
+    """
+    This rewrite simplifies the diagonal of the kronecker product of 2 matrices by extracting the individual sub matrices and returning their outer product as a vector.
+
+    diag(kron(a,b)) -> outer(diag(a), diag(b))
+
+    Parameters
+    ----------
+    fgraph: FunctionGraph
+        Function graph being optimized
+    node: Apply
+        Node of the function graph to be optimized
+
+    Returns
+    -------
+    list of Variable, optional
+        List of optimized variables, or None if no optimization was performed
+    """
+    # Check for inner kron operation
+    potential_kron = node.inputs[0].owner
+    if not (potential_kron and isinstance(potential_kron.op, KroneckerProduct)):
+        return None
+
+    # Find the matrices
+    a, b = potential_kron.inputs
+    diag_a, diag_b = diag(a), diag(b)
+    outer_prod_as_vector = outer(diag_a, diag_b).flatten()
+
+    return [outer_prod_as_vector]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([slogdet])
+def rewrite_slogdet_kronecker(fgraph, node):
+    """
+    This rewrite simplifies the slogdet of a kronecker-structured matrix by extracting the individual sub matrices and returning the sign and logdet values computed using those
+
+    Parameters
+    ----------
+    fgraph: FunctionGraph
+        Function graph being optimized
+    node: Apply
+        Node of the function graph to be optimized
+
+    Returns
+    -------
+    list of Variable, optional
+        List of optimized variables, or None if no optimization was performed
+    """
+    # Check for inner kron operation
+    potential_kron = node.inputs[0].owner
+    if not (potential_kron and isinstance(potential_kron.op, KroneckerProduct)):
+        return None
+
+    # Find the matrices
+    a, b = potential_kron.inputs
+    signs, logdets = zip(*[slogdet(a), slogdet(b)])
+    sizes = [a.shape[-1], b.shape[-1]]
+    prod_sizes = prod(sizes, no_zeros_in_input=True)
+    signs_final = [signs[i] ** (prod_sizes / sizes[i]) for i in range(2)]
+    logdet_final = [logdets[i] * prod_sizes / sizes[i] for i in range(2)]
+
+    return [prod(signs_final, no_zeros_in_input=True), sum(logdet_final)]

tests/tensor/rewriting/test_linalg.py

@@ -751,3 +751,55 @@ def test_slogdet_blockdiag_rewrite():
         atol=1e-3 if config.floatX == "float32" else 1e-8,
         rtol=1e-3 if config.floatX == "float32" else 1e-8,
     )
+
+
+def test_diag_kronecker_rewrite():
+    a, b = pt.dmatrices("a", "b")
+    kron_prod = pt.linalg.kron(a, b)
+    diag_kron_prod = pt.diag(kron_prod)
+    f_rewritten = function([a, b], diag_kron_prod, mode="FAST_RUN")
+
+    # Rewrite Test
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert not any(isinstance(node.op, KroneckerProduct) for node in nodes)
+
+    # Value Test
+    a_test, b_test = np.random.rand(2, 20, 20)
+    kron_prod_test = np.kron(a_test, b_test)
+    diag_kron_prod_test = np.diag(kron_prod_test)
+    rewritten_val = f_rewritten(a_test, b_test)
+    assert_allclose(
+        diag_kron_prod_test,
+        rewritten_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+
+
+def test_slogdet_kronecker_rewrite():
+    a, b = pt.dmatrices("a", "b")
+    kron_prod = pt.linalg.kron(a, b)
+    sign_output, logdet_output = pt.linalg.slogdet(kron_prod)
+    f_rewritten = function([kron_prod], [sign_output, logdet_output], mode="FAST_RUN")
+
+    # Rewrite Test
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert not any(isinstance(node.op, KroneckerProduct) for node in nodes)
+
+    # Value Test
+    a_test, b_test = np.random.rand(2, 20, 20)
+    kron_prod_test = np.kron(a_test, b_test)
+    sign_output_test, logdet_output_test = np.linalg.slogdet(kron_prod_test)
+    rewritten_sign_val, rewritten_logdet_val = f_rewritten(kron_prod_test)
+    assert_allclose(
+        sign_output_test,
+        rewritten_sign_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+    assert_allclose(
+        logdet_output_test,
+        rewritten_logdet_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )