Implement aesara.tensor.matmul

aesara/tensor/math.py

@@ -1,5 +1,6 @@
 import builtins
 import warnings
+from typing import TYPE_CHECKING, Optional
 
 import numpy as np
 
@@ -34,6 +35,7 @@
 from aesara.tensor.shape import shape, specify_broadcastable
 from aesara.tensor.type import (
     DenseTensorType,
+    TensorType,
     complex_dtypes,
     continuous_dtypes,
     discrete_dtypes,
@@ -47,6 +49,9 @@
 from aesara.tensor.var import TensorConstant, _tensor_py_operators
 
 
+if TYPE_CHECKING:
+    from numpy.typing import ArrayLike, DTypeLike
+
 # We capture the builtins that we are going to replace to follow the numpy API
 _abs = builtins.abs
 
@@ -2851,9 +2856,145 @@ def logsumexp(x, axis=None, keepdims=False):
     return log(sum(exp(x), axis=axis, keepdims=keepdims))
 
 
+class MatMul(Op):
+    __props__ = ("dtype",)
+
+    def __init__(self, dtype=None):
+        self.dtype = dtype
+
+    @classmethod
+    def _get_output_shape(cls, x1, x2, shapes, validate=False):
+        x1_shape, x2_shape = shapes
+
+        if x1.ndim == 1 and x2.ndim == 1:
+            if validate and x1_shape[0] != x2_shape[0]:
+                raise ValueError("1d inputs must have the same length.")
+            return ()
+        elif x1.ndim == 1 and x2.ndim > 1:
+            if validate and x1_shape[0] != x2_shape[-2]:
+                raise ValueError(
+                    "length of input 1 must be equal the length "
+                    "of the 2nd-last dimension of input 2"
+                )
+            return x2_shape[:-2] + x2_shape[-1:]
+        elif x1.ndim > 1 and x2.ndim == 1:
+            if validate and x1_shape[-1] != x2_shape[0]:
+                raise ValueError(
+                    "length of input 2 must be equal the length "
+                    "of the last dimension of input 1"
+                )
+            return x1_shape[:-1]
+        elif x1.ndim == 2 and x2.ndim == 2:
+            if validate and x1_shape[-1] != x2_shape[0]:
+                raise ValueError(
+                    "number of columns of input 1 must be equal to "
+                    "the number of rows of input 2"
+                )
+            return x1_shape[:-1] + x2_shape[-1:]
+        elif x1.ndim > 2 and x2.ndim == 2:
+            if validate and x1_shape[-1] != x2_shape[0]:
+                raise ValueError(
+                    "number of rows of input 2 must be equal to "
+                    "the length of the last dimension of input 1"
+                )
+            return x1_shape[:-2] + x1_shape[-2:-1] + x2_shape[-1:]
+        elif x1.ndim == 2 and x2.ndim > 2:
+            if validate and x1_shape[-1] != x2_shape[-2]:
+                raise ValueError(
+                    "number of columns of input 1 must be equal "
+                    "the length of the 2nd-last dimension of input 2"
+                )
+            return x2_shape[:-2] + x1_shape[-2:-1] + x2_shape[-1:]
+        else:
+
+            if validate:
+                from aesara.tensor.random.basic import broadcast_shapes
+
+                bshape = broadcast_shapes(x1_shape[:-2], x2_shape[:-2])
+                if x1_shape[-1] != x2_shape[-2]:
+                    raise ValueError(
+                        "length of the last dimension of input 1 must be equal "
+                        "to the length of the 2nd-last dimension of input 2"
+                    )
+            else:
+                from aesara.tensor.extra_ops import broadcast_shape
+
+                bshape = broadcast_shape(
+                    x1_shape[:-2], x2_shape[:-2], arrays_are_shapes=True
+                )
+            return bshape + x1_shape[-2:-1] + x2_shape[-1:]
+
+    def make_node(self, a, b):
+        a = as_tensor_variable(a)
+        b = as_tensor_variable(b)
+
+        if 0 in {a.ndim, b.ndim}:
+            raise ValueError("inputs to `matmul` cannot be scalar.")
+
+        out_shape = self._get_output_shape(
+            a, b, (a.type.shape, b.type.shape), validate=True
+        )
+        out = TensorType(dtype=self.dtype, shape=out_shape)()
+        return Apply(self, [a, b], [out])
+
+    def perform(self, node, inputs, outputs):
+        x1, x2 = inputs
+        outputs[0][0] = np.matmul(x1, x2, dtype=self.dtype)
+
+    def infer_shape(self, fgraph, node, shapes):
+        x1, x2 = node.inputs
+        return [self._get_output_shape(x1, x2, shapes)]
+
+
+def matmul(x1: "ArrayLike", x2: "ArrayLike", dtype: Optional["DTypeLike"] = None):
+    """Compute the matrix product of two tensor variables.
+
+    Parameters
+    ----------
+    x1, x2
+        Input arrays, scalars not allowed.
+    dtype
+        The desired data-type for the array. If not given, then the type will
+        be determined as the minimum type required to hold the objects in the
+        sequence.
+
+    Returns
+    -------
+    out : ndarray
+        The matrix product of the inputs. This is a scalar only when both
+        `x1`, `x2` are 1-d vectors.
+
+    Raises
+    ------
+    ValueError
+        If the last dimension of `x1` is not the same size as the second-to-last
+        dimension of `x2`. If a scalar value is passed in.
+
+    Notes
+    -----
+    The behavior depends on the arguments in the following way.
+
+    - If both arguments are 2-D they are multiplied like conventional matrices.
+    - If either argument is N-D, N > 2, it is treated as a stack of matrices
+        residing in the last two indexes and broadcast accordingly.
+    - If the first argument is 1-D, it is promoted to a matrix by prepending a
+        1 to its dimensions. After matrix multiplication the prepended 1 is removed.
+    - If the second argument is 1-D, it is promoted to a matrix by appending a
+        1 to its dimensions. After matrix multiplication the appended 1 is removed.
+
+    `matmul` differs from `dot` in two important ways:
+
+    - Multiplication by scalars is not allowed, use `mul` instead.
+    - Stacks of matrices are broadcast together as if the matrices were elements,
+        respecting the signature ``(n, k), (k, m) -> (n, m)``:
+    """
+    return MatMul(dtype=dtype)(x1, x2)
+
+
 __all__ = [
     "max_and_argmax",
     "max",
+    "matmul",
     "argmax",
     "min",
     "argmin",

aesara/tensor/nlinalg.py

@@ -1,4 +1,3 @@
-import logging
 from functools import partial
 from typing import Tuple, Union
 
@@ -14,9 +13,6 @@
 from aesara.tensor.type import dvector, lscalar, matrix, scalar, vector
 
 
-logger = logging.getLogger(__name__)
-
-
 class MatrixPinv(Op):
     __props__ = ("hermitian",)
 

tests/tensor/test_math.py

@@ -35,11 +35,13 @@
 from aesara.tensor.math import (
     Argmax,
     Dot,
+    MatMul,
     MaxAndArgmax,
     Mean,
     Prod,
     ProdWithoutZeros,
     Sum,
+    _allclose,
     _dot,
     abs,
     add,
@@ -80,6 +82,7 @@
     log10,
     logaddexp,
     logsumexp,
+    matmul,
     max,
     max_and_argmax,
     maximum,
@@ -3382,3 +3385,142 @@ def test_log1mexp_grad_lim():
     assert grad_x_fn(-0.0) == -np.inf
     assert grad_x_fn(-1e-309) == -np.inf
     assert grad_x_fn(-1e-308) != -np.inf
+
+
+class TestMatMul(utt.InferShapeTester):
+    def setup_method(self):
+        super().setup_method()
+        self.rng = np.random.default_rng(utt.fetch_seed())
+        self.op = matmul
+        self.op_class = MatMul
+
+    def _validate_output(self, a, b):
+        aesara_sol = self.op(a, b).eval()
+        numpy_sol = np.matmul(a, b)
+        assert _allclose(numpy_sol, aesara_sol)
+
+    @pytest.mark.parametrize(
+        "x1, x2",
+        [
+            # test output when both inputs are vectors
+            (np.arange(3).astype(config.floatX), np.arange(3).astype(config.floatX)),
+            # test output when both inputs are matrices
+            (
+                np.arange(3 * 5).reshape((5, 3)).astype(config.floatX),
+                np.arange(2 * 3).reshape((3, 2)).astype(config.floatX),
+            ),
+            # test behaviour when one of the inputs is has dimension > 2
+            (
+                np.arange(3 * 5).reshape((5, 3)).astype(config.floatX),
+                np.arange(2 * 3 * 5).reshape((2, 3, 5)).astype(config.floatX),
+            ),
+            # test behaviour when one of the inputs is a vector
+            (
+                np.arange(3 * 5).reshape((5, 3)).astype(config.floatX),
+                np.arange(3).astype(config.floatX),
+            ),
+            (
+                np.arange(5).astype(config.floatX),
+                np.arange(3 * 5).reshape((5, 3)).astype(config.floatX),
+            ),
+            # check if behaviour is correct N-D arrays where N > 2.
+            (
+                np.arange(2 * 2 * 4).reshape((2, 2, 4)).astype(config.floatX),
+                np.arange(2 * 2 * 4).reshape((2, 4, 2)).astype(config.floatX),
+            ),
+        ],
+    )
+    def test_op(self, x1, x2):
+        self._validate_output(x1, x2)
+
+    def test_scalar_error(self):
+        with pytest.raises(ValueError, match="cannot be scalar"):
+            self.op(4, [4, 1])
+
+    @pytest.mark.parametrize("dtype", (np.float16, np.float32, np.float64))
+    def test_dtype_param(self, dtype):
+        sol = self.op([1, 2, 3], [3, 2, 1], dtype=dtype)
+        assert sol.eval().dtype == dtype
+
+    @pytest.mark.parametrize(
+        "x1_shape,x2_shape,exp_res,error_regex",
+        [
+            ((1,), (3,), None, "inputs must have the same length"),
+            ((2,), (3, 1), None, "length of input 1.*2nd-last dimension of input 2"),
+            ((2, 5), (3,), None, "length of input 2.*of the last dimension of input 1"),
+            (
+                (2, 5),
+                (3, 4),
+                None,
+                "number of columns of input 1 .* number of rows of input 2",
+            ),
+            (
+                (2, 1, 3),
+                (5, 4),
+                None,
+                "number of rows of input 2 .* last dimension of input 1",
+            ),
+            (
+                (2, 5),
+                (2, 4, 3),
+                None,
+                "number of columns of input 1 .* 2nd-last dimension of input 2",
+            ),
+            (
+                (3, 2, 4, 5),
+                (1, 6, 7),
+                None,
+                "length of the last dimension of input 1 .* 2nd-last dimension of input 2",
+            ),
+            (
+                (4, 5, 4),
+                (3, 2, 2),
+                None,
+                "cannot be broadcast to a single shape",
+            ),
+            (
+                (4, None, 2),
+                (4, 2, None),
+                (4, None, None),
+                None,
+            ),
+        ],
+    )
+    def test_get_output_shape(self, x1_shape, x2_shape, exp_res, error_regex):
+        x1 = tensor(dtype=np.float64, shape=x1_shape)
+        x2 = tensor(dtype=np.float64, shape=x2_shape)
+
+        if error_regex is not None:
+            with pytest.raises(ValueError, match=error_regex):
+                self.op_class._get_output_shape(
+                    x1, x2, (x1_shape, x2_shape), validate=True
+                )
+        else:
+            assert (
+                self.op_class._get_output_shape(
+                    x1, x2, (x1_shape, x2_shape), validate=True
+                )
+                == exp_res
+            )
+
+    def test_infer_shape(self):
+        for shape_x1, shape_x2 in [
+            ((5,), (5,)),
+            ((5,), (2, 5, 3)),
+            ((2, 5, 3), (3,)),
+            ((2, 5), (5, 4)),
+            ((2, 5), (2, 5, 3)),
+            ((2, 1, 3), (3, 4)),
+            ((3, 2, 4, 5), (1, 5, 7)),
+        ]:
+            a = tensor(dtype=config.floatX, shape=shape_x1)
+            b = tensor(dtype=config.floatX, shape=shape_x2)
+            x1 = self.rng.random(shape_x1).astype(config.floatX)
+            x2 = self.rng.random(shape_x2).astype(config.floatX)
+
+            self._compile_and_check(
+                [a, b],
+                [self.op(a, b)],
+                [x1, x2],
+                self.op_class,
+            )