added rewrites for inv(diag(x)) and inv(eye) (#898)

* updated tests

* updated rewrites

* paramterized tests and added batch case

* minor changes

pytensor/tensor/rewriting/linalg.py

@@ -3,6 +3,7 @@
 from typing import cast
 
 from pytensor import Variable
+from pytensor import tensor as pt
 from pytensor.graph import Apply, FunctionGraph
 from pytensor.graph.rewriting.basic import (
     copy_stack_trace,
@@ -48,6 +49,7 @@
 
 
 logger = logging.getLogger(__name__)
+ALL_INVERSE_OPS = (MatrixInverse, MatrixPinv)
 
 
 def is_matrix_transpose(x: TensorVariable) -> bool:
@@ -592,11 +594,10 @@ def rewrite_inv_inv(fgraph, node):
     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):
+    if not isinstance(node.op.core_op, ALL_INVERSE_OPS):
         return None
 
     potential_inner_inv = node.inputs[0].owner
@@ -607,7 +608,96 @@ def rewrite_inv_inv(fgraph, node):
     if not (
         potential_inner_inv
         and isinstance(potential_inner_inv.op, Blockwise)
-        and isinstance(potential_inner_inv.op.core_op, valid_inverses)
+        and isinstance(potential_inner_inv.op.core_op, ALL_INVERSE_OPS)
     ):
         return None
     return [potential_inner_inv.inputs[0]]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_inv_eye_to_eye(fgraph, node):
+    """
+     This rewrite takes advantage of the fact that the inverse of an identity matrix is the matrix itself
+    The presence of an identity matrix is identified by checking whether we have k = 0 for an Eye Op inside an inverse op.
+    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
+    """
+    core_op = node.op.core_op
+    if not (isinstance(core_op, ALL_INVERSE_OPS)):
+        return None
+
+    # Check whether input to inverse is Eye and the 1's are on main diagonal
+    potential_eye = node.inputs[0]
+    if not (
+        potential_eye.owner
+        and isinstance(potential_eye.owner.op, Eye)
+        and getattr(potential_eye.owner.inputs[-1], "data", -1).item() == 0
+    ):
+        return None
+    return [potential_eye]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_inv_diag_to_diag_reciprocal(fgraph, node):
+    """
+     This rewrite takes advantage of the fact that for a diagonal matrix, the inverse is a diagonal matrix with the new diagonal entries as reciprocals of the original diagonal elements.
+     This function deals with diagonal matrix arising from the multiplicaton of eye with a scalar/vector/matrix
+
+    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
+    """
+    core_op = node.op.core_op
+    if not (isinstance(core_op, ALL_INVERSE_OPS)):
+        return None
+
+    inputs = node.inputs[0]
+    # Check for use of pt.diag first
+    if (
+        inputs.owner
+        and isinstance(inputs.owner.op, AllocDiag)
+        and AllocDiag.is_offset_zero(inputs.owner)
+    ):
+        inv_input = inputs.owner.inputs[0]
+        inv_val = pt.diag(1 / inv_input)
+        return [inv_val]
+
+    # Check if the input is an elemwise multiply with identity matrix -- this also results in a diagonal matrix
+    inputs_or_none = _find_diag_from_eye_mul(inputs)
+    if inputs_or_none is None:
+        return None
+
+    eye_input, non_eye_inputs = inputs_or_none
+
+    # Dealing with only one other input
+    if len(non_eye_inputs) != 1:
+        return None
+
+    non_eye_input = non_eye_inputs[0]
+
+    # For a matrix, we have to first extract the diagonal (non-zero values) and then only use those
+    if non_eye_input.type.broadcastable[-2:] == (False, False):
+        non_eye_diag = non_eye_input.diagonal(axis1=-1, axis2=-2)
+        non_eye_input = pt.shape_padaxis(non_eye_diag, -2)
+
+    return [eye_input / non_eye_input]

tests/tensor/rewriting/test_linalg.py

@@ -41,6 +41,9 @@
 from tests.test_rop import break_op
 
 
+ATOL = RTOL = 1e-3 if config.floatX == "float32" else 1e-8
+
+
 def test_rop_lop():
     mx = matrix("mx")
     mv = matrix("mv")
@@ -557,14 +560,105 @@ def test_svd_uv_merge():
     assert svd_counter == 1
 
 
+def get_pt_function(x, op_name):
+    return getattr(pt.linalg, op_name)(x)
+
+
 @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
+
+
+@pytest.mark.parametrize("inv_op", ["inv", "pinv"])
+def test_inv_eye_to_eye(inv_op):
+    x = pt.eye(10)
+    x_inv = get_pt_function(x, inv_op)
+    f_rewritten = function([], x_inv, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+
+    # Rewrite Test
+    valid_inverses = (MatrixInverse, MatrixPinv)
+    assert not any(isinstance(node.op, valid_inverses) for node in nodes)
+
+    # Value Test
+    x_test = np.eye(10)
+    x_inv_val = np.linalg.inv(x_test)
+    rewritten_val = f_rewritten()
+
+    assert_allclose(
+        x_inv_val,
+        rewritten_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+
+
+@pytest.mark.parametrize(
+    "shape",
+    [(), (7,), (7, 7), (5, 7, 7)],
+    ids=["scalar", "vector", "matrix", "batched"],
+)
+@pytest.mark.parametrize("inv_op", ["inv", "pinv"])
+def test_inv_diag_from_eye_mul(shape, inv_op):
+    # Initializing x based on scalar/vector/matrix
+    x = pt.tensor("x", shape=shape)
+    x_diag = pt.eye(7) * x
+    # Calculating inverse using pt.linalg.inv
+    x_inv = get_pt_function(x_diag, inv_op)
+
+    # REWRITE TEST
+    f_rewritten = function([x], x_inv, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+
+    valid_inverses = (MatrixInverse, MatrixPinv)
+    assert not any(isinstance(node.op, valid_inverses) for node in nodes)
+
+    # NUMERIC VALUE TEST
+    if len(shape) == 0:
+        x_test = np.array(np.random.rand()).astype(config.floatX)
+    elif len(shape) == 1:
+        x_test = np.random.rand(*shape).astype(config.floatX)
+    else:
+        x_test = np.random.rand(*shape).astype(config.floatX)
+    x_test_matrix = np.eye(7) * x_test
+    inverse_matrix = np.linalg.inv(x_test_matrix)
+    rewritten_inverse = f_rewritten(x_test)
+
+    assert_allclose(
+        inverse_matrix,
+        rewritten_inverse,
+        atol=ATOL,
+        rtol=RTOL,
+    )
+
+
+@pytest.mark.parametrize("inv_op", ["inv", "pinv"])
+def test_inv_diag_from_diag(inv_op):
+    x = pt.dvector("x")
+    x_diag = pt.diag(x)
+    x_inv = get_pt_function(x_diag, inv_op)
+
+    # REWRITE TEST
+    f_rewritten = function([x], x_inv, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+
+    valid_inverses = (MatrixInverse, MatrixPinv)
+    assert not any(isinstance(node.op, valid_inverses) for node in nodes)
+
+    # NUMERIC VALUE TEST
+    x_test = np.random.rand(10)
+    x_test_matrix = np.eye(10) * x_test
+    inverse_matrix = np.linalg.inv(x_test_matrix)
+    rewritten_inverse = f_rewritten(x_test)
+
+    assert_allclose(
+        inverse_matrix,
+        rewritten_inverse,
+        atol=ATOL,
+        rtol=RTOL,
+    )