Add rewrite to merge multiple SVD Ops with different settings (#769)

Co-authored-by: Ricardo Vieira <[email protected]>

pytensor/tensor/rewriting/linalg.py

@@ -4,20 +4,25 @@
 
 from pytensor import Variable
 from pytensor.graph import Apply, FunctionGraph
-from pytensor.graph.rewriting.basic import copy_stack_trace, node_rewriter
+from pytensor.graph.rewriting.basic import (
+    copy_stack_trace,
+    node_rewriter,
+)
 from pytensor.tensor.basic import TensorVariable, diagonal
 from pytensor.tensor.blas import Dot22
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle
 from pytensor.tensor.math import Dot, Prod, _matrix_matrix_matmul, log, prod
 from pytensor.tensor.nlinalg import (
+    SVD,
     KroneckerProduct,
     MatrixInverse,
     MatrixPinv,
     det,
     inv,
     kron,
     pinv,
+    svd,
 )
 from pytensor.tensor.rewriting.basic import (
     register_canonicalize,
@@ -377,3 +382,59 @@ def local_lift_through_linalg(
                 return [block_diag(*inner_matrices)]
             else:
                 raise NotImplementedError  # pragma: no cover
+
+
+@register_canonicalize
+@register_stabilize
+@register_specialize
+@node_rewriter([Blockwise])
+def svd_uv_merge(fgraph, node):
+    """If we have more than one `SVD` `Op`s and at least one has keyword argument
+    `compute_uv=True`, then we can change `compute_uv = False` to `True` everywhere
+    and allow `pytensor` to re-use the decomposition outputs instead of recomputing.
+    """
+    if not isinstance(node.op.core_op, SVD):
+        return
+
+    (x,) = node.inputs
+
+    if node.op.core_op.compute_uv:
+        # compute_uv=True returns [u, s, v].
+        # if at least u or v is used, no need to rewrite this node.
+        if (
+            len(fgraph.clients[node.outputs[0]]) > 0
+            or len(fgraph.clients[node.outputs[2]]) > 0
+        ):
+            return
+
+        # Else, has to replace the s of this node with s of an SVD Op that compute_uv=False.
+        # First, iterate to see if there is an SVD Op that can be reused.
+        for cl, _ in fgraph.clients[x]:
+            if cl == "output":
+                continue
+            if isinstance(cl.op, Blockwise) and isinstance(cl.op.core_op, SVD):
+                if not cl.op.core_op.compute_uv:
+                    return {
+                        node.outputs[1]: cl.outputs[0],
+                    }
+
+        # If no SVD reusable, return a new one.
+        return {
+            node.outputs[1]: svd(
+                x, full_matrices=node.op.core_op.full_matrices, compute_uv=False
+            ),
+        }
+
+    else:
+        # compute_uv=False returns [s].
+        # We want rewrite if there is another one with compute_uv=True.
+        # For this case, just reuse the `s` from the one with compute_uv=True.
+        for cl, _ in fgraph.clients[x]:
+            if cl == "output":
+                continue
+            if isinstance(cl.op, Blockwise) and isinstance(cl.op.core_op, SVD):
+                if cl.op.core_op.compute_uv and (
+                    len(fgraph.clients[cl.outputs[0]]) > 0
+                    or len(fgraph.clients[cl.outputs[2]]) > 0
+                ):
+                    return [cl.outputs[1]]

tests/tensor/rewriting/test_linalg.py

@@ -15,11 +15,13 @@
 from pytensor.tensor.elemwise import DimShuffle
 from pytensor.tensor.math import _allclose, dot, matmul
 from pytensor.tensor.nlinalg import (
+    SVD,
     Det,
     KroneckerProduct,
     MatrixInverse,
     MatrixPinv,
     matrix_inverse,
+    svd,
 )
 from pytensor.tensor.rewriting.linalg import inv_as_solve
 from pytensor.tensor.slinalg import (
@@ -390,3 +392,67 @@ def test_local_lift_through_linalg(constructor, f_op, f, g_op, g):
     test_vals = [x @ np.swapaxes(x, -1, -2) for x in test_vals]
 
     np.testing.assert_allclose(f1(*test_vals), f2(*test_vals), atol=1e-8)
+
+
+def test_svd_uv_merge():
+    a = matrix("a")
+    s_1 = svd(a, full_matrices=False, compute_uv=False)
+    _, s_2, _ = svd(a, full_matrices=False, compute_uv=True)
+    _, s_3, _ = svd(a, full_matrices=True, compute_uv=True)
+    u_4, s_4, v_4 = svd(a, full_matrices=True, compute_uv=True)
+    # `grad` will introduces an SVD Op with compute_uv=True
+    # full_matrices = True is not supported for grad of svd
+    gs = pt.grad(pt.sum(s_1), a)
+
+    # 1. compute_uv=False needs rewriting with compute_uv=True
+    f_1 = pytensor.function([a], gs)
+    nodes = f_1.maker.fgraph.apply_nodes
+    svd_counter = 0
+    for node in nodes:
+        if isinstance(node.op, SVD):
+            assert node.op.compute_uv
+            svd_counter += 1
+    assert svd_counter == 1
+
+    # 2. compute_uv=True needs rewriting with compute=False, reuse node
+    f_2 = pytensor.function([a], [s_1, s_2])
+    nodes = f_2.maker.fgraph.apply_nodes
+    svd_counter = 0
+    for node in nodes:
+        if isinstance(node.op, SVD):
+            assert not node.op.compute_uv
+            svd_counter += 1
+    assert svd_counter == 1
+
+    # 3. compute_uv=True needs rewriting with compute=False, create new node
+    # full_matrices needs to retain the value
+    f_3 = pytensor.function([a], [s_2])
+    nodes = f_3.maker.fgraph.apply_nodes
+    svd_counter = 0
+    for node in nodes:
+        if isinstance(node.op, SVD):
+            assert not node.op.compute_uv
+            svd_counter += 1
+    assert svd_counter == 1
+
+    # Case 2 of 3. for a different full_matrices
+    f_4 = pytensor.function([a], [s_3])
+    nodes = f_4.maker.fgraph.apply_nodes
+    svd_counter = 0
+    for node in nodes:
+        if isinstance(node.op, SVD):
+            assert not node.op.compute_uv
+            assert node.op.full_matrices
+            svd_counter += 1
+    assert svd_counter == 1
+
+    # 4. No rewrite should happen
+    f_5 = pytensor.function([a], [u_4])
+    nodes = f_5.maker.fgraph.apply_nodes
+    svd_counter = 0
+    for node in nodes:
+        if isinstance(node.op, SVD):
+            assert node.op.full_matrices
+            assert node.op.compute_uv
+            svd_counter += 1
+    assert svd_counter == 1