Adds functions to rewrite cholesky decomposition of identity and diagonal matrices (pymc-devs#925)

* fixed merge conflicts

* fixed failing tests and added rewrite for pt.diag

* minor changes; added test to not apply rewrite

* added test for batched case and more cases of not applying rewrite

* minor changes

Author: tanish1729

pytensor/tensor/rewriting/linalg.py

@@ -887,3 +887,82 @@ def rewrite_slogdet_kronecker(fgraph, node):
     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)]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_remove_useless_cholesky(fgraph, node):
+    """
+     This rewrite takes advantage of the fact that the cholesky decomposition 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 Cholesky.
+
+    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
+    """
+    # Find whether cholesky op is being applied
+    if not isinstance(node.op.core_op, Cholesky):
+        return None
+
+    # Check whether input to Cholesky 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 hasattr(potential_eye.owner.inputs[-1], "data")
+        and potential_eye.owner.inputs[-1].data.item() == 0
+    ):
+        return None
+    return [potential_eye]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_cholesky_diag_to_sqrt_diag(fgraph, node):
+    # Find whether cholesky op is being applied
+    if not isinstance(node.op.core_op, Cholesky):
+        return None
+
+    [input] = node.inputs
+    # Check for use of pt.diag first
+    if (
+        input.owner
+        and isinstance(input.owner.op, AllocDiag)
+        and AllocDiag.is_offset_zero(input.owner)
+    ):
+        diag_input = input.owner.inputs[0]
+        cholesky_val = pt.diag(diag_input**0.5)
+        return [cholesky_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(input)
+    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
+
+    # Now, we can simply return the matrix consisting of sqrt values of the original diagonal elements
+    # 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_input = non_eye_input.diagonal(axis1=-1, axis2=-2)
+        if eye_input.type.ndim > 2:
+            non_eye_input = pt.shape_padaxis(non_eye_input, -2)
+
+    return [eye_input * (non_eye_input**0.5)]

tests/tensor/rewriting/test_linalg.py

@@ -803,3 +803,106 @@ def test_slogdet_kronecker_rewrite():
         atol=1e-3 if config.floatX == "float32" else 1e-8,
         rtol=1e-3 if config.floatX == "float32" else 1e-8,
     )
+
+
+def test_cholesky_eye_rewrite():
+    x = pt.eye(10)
+    L = pt.linalg.cholesky(x)
+    f_rewritten = function([], L, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+
+    # Rewrite Test
+    assert not any(isinstance(node.op, Cholesky) for node in nodes)
+
+    # Value Test
+    x_test = np.eye(10)
+    L = np.linalg.cholesky(x_test)
+    rewritten_val = f_rewritten()
+
+    assert_allclose(
+        L,
+        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"],
+)
+def test_cholesky_diag_from_eye_mul(shape):
+    # Initializing x based on scalar/vector/matrix
+    x = pt.tensor("x", shape=shape)
+    y = pt.eye(7) * x
+    # Performing cholesky decomposition using pt.linalg.cholesky
+    z_cholesky = pt.linalg.cholesky(y)
+
+    # REWRITE TEST
+    f_rewritten = function([x], z_cholesky, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert not any(isinstance(node.op, Cholesky) 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
+    cholesky_val = np.linalg.cholesky(x_test_matrix)
+    rewritten_val = f_rewritten(x_test)
+
+    assert_allclose(
+        cholesky_val,
+        rewritten_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+
+
+def test_cholesky_diag_from_diag():
+    x = pt.dvector("x")
+    x_diag = pt.diag(x)
+    x_cholesky = pt.linalg.cholesky(x_diag)
+
+    # REWRITE TEST
+    f_rewritten = function([x], x_cholesky, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+
+    assert not any(isinstance(node.op, Cholesky) for node in nodes)
+
+    # NUMERIC VALUE TEST
+    x_test = np.random.rand(10)
+    x_test_matrix = np.eye(10) * x_test
+    cholesky_val = np.linalg.cholesky(x_test_matrix)
+    rewritten_cholesky = f_rewritten(x_test)
+
+    assert_allclose(
+        cholesky_val,
+        rewritten_cholesky,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+
+
+def test_rewrite_cholesky_diag_to_sqrt_diag_not_applied():
+    # Case 1 : y is not a diagonal matrix because of k = -1
+    x = pt.tensor("x", shape=(7, 7))
+    y = pt.eye(7, k=-1) * x
+    z_cholesky = pt.linalg.cholesky(y)
+
+    # REWRITE TEST (should not be applied)
+    f_rewritten = function([x], z_cholesky, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert any(isinstance(node.op, Cholesky) for node in nodes)
+
+    # Case 2 : eye is degenerate
+    x = pt.scalar("x")
+    y = pt.eye(1) * x
+    z_cholesky = pt.linalg.cholesky(y)
+    f_rewritten = function([x], z_cholesky, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert any(isinstance(node.op, Cholesky) for node in nodes)