Added rewrite for matrix inv(inv(x)) -> x (#893)

Author: tanish1729

pytensor/tensor/rewriting/linalg.py

@@ -569,3 +569,45 @@ def svd_uv_merge(fgraph, node):
                     or len(fgraph.clients[cl.outputs[2]]) > 0
                 ):
                     return [cl.outputs[1]]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_inv_inv(fgraph, node):
+    """
+    This rewrite takes advantage of the fact that if there are two consecutive inverse operations (inv(inv(input))), we get back our original input without having to compute inverse once.
+
+    Here, we check for direct inverse operations (inv/pinv)  and allows for any combination of these "inverse" nodes to be simply rewritten.
+
+    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
+    """
+    valid_inverses = (MatrixInverse, MatrixPinv)
+    # Check if its a valid inverse operation (either inv/pinv)
+    # In case the outer operation is an inverse, it directly goes to the next step of finding inner operation
+    # If the outer operation is not a valid inverse, we do not apply this rewrite
+    if not isinstance(node.op.core_op, valid_inverses):
+        return None
+
+    potential_inner_inv = node.inputs[0].owner
+    if potential_inner_inv is None or potential_inner_inv.op is None:
+        return None
+
+    # Check if inner op is blockwise and and possible inv
+    if not (
+        potential_inner_inv
+        and isinstance(potential_inner_inv.op, Blockwise)
+        and isinstance(potential_inner_inv.op.core_op, valid_inverses)
+    ):
+        return None
+    return [potential_inner_inv.inputs[0]]

tests/tensor/rewriting/test_linalg.py

@@ -10,6 +10,7 @@
 from pytensor import tensor as pt
 from pytensor.compile import get_default_mode
 from pytensor.configdefaults import config
+from pytensor.graph.rewriting.utils import rewrite_graph
 from pytensor.tensor import swapaxes
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle
@@ -554,3 +555,16 @@ def test_svd_uv_merge():
             assert node.op.compute_uv
             svd_counter += 1
     assert svd_counter == 1
+
+
+@pytest.mark.parametrize("inv_op_1", ["inv", "pinv"])
+@pytest.mark.parametrize("inv_op_2", ["inv", "pinv"])
+def test_inv_inv_rewrite(inv_op_1, inv_op_2):
+    def get_pt_function(x, op_name):
+        return getattr(pt.linalg, op_name)(x)
+
+    x = pt.matrix("x")
+    op1 = get_pt_function(x, inv_op_1)
+    op2 = get_pt_function(op1, inv_op_2)
+    rewritten_out = rewrite_graph(op2)
+    assert rewritten_out == x