Rewriting the kron function using JAX implementation (#684)

* Update the kron function to use numpy implementation and move the function to `tensor.nlinalg.py`

Author: tanish1729

pytensor/tensor/nlinalg.py

@@ -1010,6 +1010,40 @@ def tensorsolve(a, b, axes=None):
     return TensorSolve(axes)(a, b)
 
 
+def kron(a, b):
+    """Kronecker product.
+
+    Same as np.kron(a, b)
+
+    Parameters
+    ----------
+    a: array_like
+    b: array_like
+
+    Returns
+    -------
+    array_like with a.ndim + b.ndim - 2 dimensions
+    """
+    a = as_tensor_variable(a)
+    b = as_tensor_variable(b)
+    if a.ndim + b.ndim <= 2:
+        raise TypeError(
+            "kron: inputs dimensions must sum to 3 or more. "
+            f"You passed {int(a.ndim)} and {int(b.ndim)}."
+        )
+
+    if a.ndim < b.ndim:
+        a = ptb.expand_dims(a, tuple(range(b.ndim - a.ndim)))
+    elif b.ndim < a.ndim:
+        b = ptb.expand_dims(b, tuple(range(a.ndim - b.ndim)))
+    a_reshaped = ptb.expand_dims(a, tuple(range(1, 2 * a.ndim, 2)))
+    b_reshaped = ptb.expand_dims(b, tuple(range(0, 2 * b.ndim, 2)))
+    out_shape = tuple(a.shape * b.shape)
+    output_out_of_shape = a_reshaped * b_reshaped
+    output_reshaped = output_out_of_shape.reshape(out_shape)
+    return output_reshaped
+
+
 __all__ = [
     "pinv",
     "inv",
@@ -1025,4 +1059,5 @@ def tensorsolve(a, b, axes=None):
     "norm",
     "tensorinv",
     "tensorsolve",
+    "kron",
 ]

pytensor/tensor/slinalg.py

@@ -15,7 +15,7 @@
 from pytensor.tensor import basic as ptb
 from pytensor.tensor import math as ptm
 from pytensor.tensor.blockwise import Blockwise
-from pytensor.tensor.nlinalg import matrix_dot
+from pytensor.tensor.nlinalg import kron, matrix_dot
 from pytensor.tensor.shape import reshape
 from pytensor.tensor.type import matrix, tensor, vector
 from pytensor.tensor.variable import TensorVariable
@@ -559,51 +559,6 @@ def eigvalsh(a, b, lower=True):
     return Eigvalsh(lower)(a, b)
 
 
-def kron(a, b):
-    """Kronecker product.
-
-    Same as scipy.linalg.kron(a, b).
-
-    Parameters
-    ----------
-    a: array_like
-    b: array_like
-
-    Returns
-    -------
-    array_like with a.ndim + b.ndim - 2 dimensions
-
-    Notes
-    -----
-    numpy.kron(a, b) != scipy.linalg.kron(a, b)!
-    They don't have the same shape and order when
-    a.ndim != b.ndim != 2.
-
-    """
-    a = as_tensor_variable(a)
-    b = as_tensor_variable(b)
-    if a.ndim + b.ndim <= 2:
-        raise TypeError(
-            "kron: inputs dimensions must sum to 3 or more. "
-            f"You passed {int(a.ndim)} and {int(b.ndim)}."
-        )
-    o = ptm.outer(a, b)
-    o = o.reshape(ptb.concatenate((a.shape, b.shape)), ndim=a.ndim + b.ndim)
-    shf = o.dimshuffle(0, 2, 1, *range(3, o.ndim))
-    if shf.ndim == 3:
-        shf = o.dimshuffle(1, 0, 2)
-        o = shf.flatten()
-    else:
-        o = shf.reshape(
-            (
-                o.shape[0] * o.shape[2],
-                o.shape[1] * o.shape[3],
-                *(o.shape[i] for i in range(4, o.ndim)),
-            )
-        )
-    return o
-
-
 class Expm(Op):
     """
     Compute the matrix exponential of a square array.
@@ -1021,7 +976,6 @@ def block_diag(*matrices: TensorVariable):
     "cholesky",
     "solve",
     "eigvalsh",
-    "kron",
     "expm",
     "solve_discrete_lyapunov",
     "solve_continuous_lyapunov",

tests/tensor/test_nlinalg.py

@@ -17,6 +17,7 @@
     det,
     eig,
     eigh,
+    kron,
     lstsq,
     matrix_dot,
     matrix_inverse,
@@ -580,3 +581,42 @@ def test_eval(self):
         t_binv1 = tf_b1(self.b1)
         assert _allclose(t_binv, n_binv)
         assert _allclose(t_binv1, n_binv1)
+
+
+class TestKron(utt.InferShapeTester):
+    rng = np.random.default_rng(43)
+
+    def setup_method(self):
+        self.op = kron
+        super().setup_method()
+
+    @pytest.mark.parametrize("shp0", [(2,), (2, 3), (2, 3, 4), (2, 3, 4, 5)])
+    @pytest.mark.parametrize("shp1", [(6,), (6, 7), (6, 7, 8), (6, 7, 8, 9)])
+    def test_perform(self, shp0, shp1):
+        if len(shp0) + len(shp1) == 2:
+            pytest.skip("Sum of shp0 and shp1 must be more than 2")
+        x = tensor(dtype="floatX", shape=(None,) * len(shp0))
+        a = np.asarray(self.rng.random(shp0)).astype(config.floatX)
+        y = tensor(dtype="floatX", shape=(None,) * len(shp1))
+        f = function([x, y], kron(x, y))
+        b = self.rng.random(shp1).astype(config.floatX)
+        out = f(a, b)
+        # Using the np.kron to compare outputs
+        np_val = np.kron(a, b)
+        np.testing.assert_allclose(out, np_val)
+
+    @pytest.mark.parametrize(
+        "i, shp0, shp1",
+        [(0, (2, 3), (6, 7)), (1, (2, 3), (4, 3, 5)), (2, (2, 4, 3), (4, 3, 5))],
+    )
+    def test_kron_commutes_with_inv(self, i, shp0, shp1):
+        if (pytensor.config.floatX == "float32") & (i == 2):
+            pytest.skip("Half precision insufficient for test 3 to pass")
+        x = tensor(dtype="floatX", shape=(None,) * len(shp0))
+        a = np.asarray(self.rng.random(shp0)).astype(config.floatX)
+        y = tensor(dtype="floatX", shape=(None,) * len(shp1))
+        b = self.rng.random(shp1).astype(config.floatX)
+        lhs_f = function([x, y], pinv(kron(x, y)))
+        rhs_f = function([x, y], kron(pinv(x), pinv(y)))
+        atol = 1e-4 if config.floatX == "float32" else 1e-12
+        np.testing.assert_allclose(lhs_f(a, b), rhs_f(a, b), atol=atol)

tests/tensor/test_slinalg.py

@@ -20,7 +20,6 @@
     cholesky,
     eigvalsh,
     expm,
-    kron,
     solve,
     solve_continuous_lyapunov,
     solve_discrete_are,
@@ -512,46 +511,6 @@ def test_expm_grad_3():
     utt.verify_grad(expm, [A], rng=rng)
 
 
-class TestKron(utt.InferShapeTester):
-    rng = np.random.default_rng(43)
-
-    def setup_method(self):
-        self.op = kron
-        super().setup_method()
-
-    def test_perform(self):
-        for shp0 in [(2,), (2, 3), (2, 3, 4), (2, 3, 4, 5)]:
-            x = tensor(dtype="floatX", shape=(None,) * len(shp0))
-            a = np.asarray(self.rng.random(shp0)).astype(config.floatX)
-            for shp1 in [(6,), (6, 7), (6, 7, 8), (6, 7, 8, 9)]:
-                if len(shp0) + len(shp1) == 2:
-                    continue
-                y = tensor(dtype="floatX", shape=(None,) * len(shp1))
-                f = function([x, y], kron(x, y))
-                b = self.rng.random(shp1).astype(config.floatX)
-                out = f(a, b)
-                # Newer versions of scipy want 4 dimensions at least,
-                # so we have to add a dimension to a and flatten the result.
-                if len(shp0) + len(shp1) == 3:
-                    scipy_val = scipy.linalg.kron(a[np.newaxis, :], b).flatten()
-                else:
-                    scipy_val = scipy.linalg.kron(a, b)
-                np.testing.assert_allclose(out, scipy_val)
-
-    def test_numpy_2d(self):
-        for shp0 in [(2, 3)]:
-            x = tensor(dtype="floatX", shape=(None,) * len(shp0))
-            a = np.asarray(self.rng.random(shp0)).astype(config.floatX)
-            for shp1 in [(6, 7)]:
-                if len(shp0) + len(shp1) == 2:
-                    continue
-                y = tensor(dtype="floatX", shape=(None,) * len(shp1))
-                f = function([x, y], kron(x, y))
-                b = self.rng.random(shp1).astype(config.floatX)
-                out = f(a, b)
-                assert np.allclose(out, np.kron(a, b))
-
-
 def test_solve_discrete_lyapunov_via_direct_real():
     N = 5
     rng = np.random.default_rng(utt.fetch_seed())