Add a SolveTriangular Op

`Solve` has also been changed to match SciPy.

Author: fshart

aesara/tensor/slinalg.py

@@ -1,5 +1,6 @@
 import logging
 import warnings
+from typing import Union
 
 import numpy as np
 import scipy.linalg
@@ -11,6 +12,7 @@
 from aesara.tensor import basic as aet
 from aesara.tensor import math as atm
 from aesara.tensor.type import matrix, tensor, vector
+from aesara.tensor.var import TensorVariable
 
 
 logger = logging.getLogger(__name__)
@@ -259,93 +261,52 @@ def cho_solve(c_and_lower, b, check_finite=True):
     return CholeskySolve(lower=lower, check_finite=check_finite)(A, b)
 
 
-class Solve(Op):
-    """
-    Solve a system of linear equations.
-
-    For on CPU and GPU.
-    """
+class SolveBase(Op):
+    """Base class for `scipy.linalg` matrix equation solvers."""
 
     __props__ = (
-        "assume_a",
         "lower",
-        "check_finite",  # "transposed"
+        "check_finite",
     )
 
     def __init__(
         self,
-        assume_a="gen",
         lower=False,
-        check_finite=True,  # transposed=False
+        check_finite=True,
     ):
-        if assume_a not in ("gen", "sym", "her", "pos"):
-            raise ValueError(f"{assume_a} is not a recognized matrix structure")
-        self.assume_a = assume_a
         self.lower = lower
         self.check_finite = check_finite
-        # self.transposed = transposed
 
-    def __repr__(self):
-        return "Solve{%s}" % str(self._props())
+    def perform(self, node, inputs, outputs):
+        pass
 
     def make_node(self, A, b):
         A = as_tensor_variable(A)
         b = as_tensor_variable(b)
-        assert A.ndim == 2
-        assert b.ndim in [1, 2]
 
-        # infer dtype by solving the most simple
-        # case with (1, 1) matrices
+        if A.ndim != 2:
+            raise ValueError(f"`A` must be a matrix; got {A.type} instead.")
+        if b.ndim not in [1, 2]:
+            raise ValueError(f"`b` must be a matrix or a vector; got {b.type} instead.")
+
+        # Infer dtype by solving the most simple case with 1x1 matrices
         o_dtype = scipy.linalg.solve(
             np.eye(1).astype(A.dtype), np.eye(1).astype(b.dtype)
         ).dtype
         x = tensor(broadcastable=b.broadcastable, dtype=o_dtype)
         return Apply(self, [A, b], [x])
 
-    def perform(self, node, inputs, output_storage):
-        A, b = inputs
-
-        if self.assume_a != "gen":
-            # if self.transposed:
-            #     if self.assume_a == "her":
-            #         trans = "C"
-            #     else:
-            #         trans = "T"
-            # else:
-            #     trans = "N"
-
-            rval = scipy.linalg.solve_triangular(
-                A,
-                b,
-                lower=self.lower,
-                check_finite=self.check_finite,
-                # trans=trans
-            )
-        else:
-            rval = scipy.linalg.solve(
-                A,
-                b,
-                assume_a=self.assume_a,
-                lower=self.lower,
-                check_finite=self.check_finite,
-                # transposed=self.transposed,
-            )
-
-        output_storage[0][0] = rval
-
-    # computes shape of x where x = inv(A) * b
     def infer_shape(self, fgraph, node, shapes):
         Ashape, Bshape = shapes
         rows = Ashape[1]
-        if len(Bshape) == 1:  # b is a Vector
+        if len(Bshape) == 1:
             return [(rows,)]
         else:
-            cols = Bshape[1]  # b is a Matrix
+            cols = Bshape[1]
             return [(rows, cols)]
 
     def L_op(self, inputs, outputs, output_gradients):
-        r"""
-        Reverse-mode gradient updates for matrix solve operation :math:`c = A^{-1} b`.
+        r"""Reverse-mode gradient updates for matrix solve operation :math:`c = A^{-1} b`.
 
         Symbolic expression for updates taken from [#]_.
 
@@ -364,31 +325,148 @@ def L_op(self, inputs, outputs, output_gradients):
         # We need to return (dC/d[inv(A)], dC/db)
         c_bar = output_gradients[0]
 
-        trans_solve_op = Solve(
-            assume_a=self.assume_a,
-            check_finite=self.check_finite,
-            lower=not self.lower,
+        trans_solve_op = type(self)(
+            **{
+                k: (not getattr(self, k) if k == "lower" else getattr(self, k))
+                for k in self.__props__
+            }
         )
         b_bar = trans_solve_op(A.T, c_bar)
         # force outer product if vector second input
         A_bar = -atm.outer(b_bar, c) if c.ndim == 1 else -b_bar.dot(c.T)
 
-        if self.assume_a != "gen":
-            if self.lower:
-                A_bar = aet.tril(A_bar)
-            else:
-                A_bar = aet.triu(A_bar)
-
         return [A_bar, b_bar]
 
+    def __repr__(self):
+        return f"{type(self).__name__}{self._props()}"
+
+
+class SolveTriangular(SolveBase):
+    """Solve a system of linear equations."""
+
+    __props__ = (
+        "lower",
+        "trans",
+        "unit_diagonal",
+        "check_finite",
+    )
+
+    def __init__(
+        self,
+        trans=0,
+        lower=False,
+        unit_diagonal=False,
+        check_finite=True,
+    ):
+        super().__init__(lower=lower, check_finite=check_finite)
+        self.trans = trans
+        self.unit_diagonal = unit_diagonal
+
+    def perform(self, node, inputs, outputs):
+        A, b = inputs
+        outputs[0][0] = scipy.linalg.solve_triangular(
+            A,
+            b,
+            lower=self.lower,
+            trans=self.trans,
+            unit_diagonal=self.unit_diagonal,
+            check_finite=self.check_finite,
+        )
+
+    def L_op(self, inputs, outputs, output_gradients):
+        res = super().L_op(inputs, outputs, output_gradients)
+
+        if self.lower:
+            res[0] = aet.tril(res[0])
+        else:
+            res[0] = aet.triu(res[0])
+
+        return res
+
+
+solvetriangular = SolveTriangular()
+
+
+def solve_triangular(
+    a: TensorVariable,
+    b: TensorVariable,
+    trans: Union[int, str] = 0,
+    lower: bool = False,
+    unit_diagonal: bool = False,
+    check_finite: bool = True,
+) -> TensorVariable:
+    """Solve the equation `a x = b` for `x`, assuming `a` is a triangular matrix.
+
+    Parameters
+    ----------
+    a
+        Square input data
+    b
+        Input data for the right hand side.
+    lower : bool, optional
+        Use only data contained in the lower triangle of `a`. Default is to use upper triangle.
+    trans: {0, 1, 2, ‘N’, ‘T’, ‘C’}, optional
+        Type of system to solve:
+        trans       system
+        0 or 'N'    a x = b
+        1 or 'T'    a^T x = b
+        2 or 'C'    a^H x = b
+    unit_diagonal: bool, optional
+        If True, diagonal elements of `a` are assumed to be 1 and will not be referenced.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+    """
+    return SolveTriangular(
+        lower=lower,
+        trans=trans,
+        unit_diagonal=unit_diagonal,
+        check_finite=check_finite,
+    )(a, b)
+
+
+class Solve(SolveBase):
+    """
+    Solve a system of linear equations.
+
+    For on CPU and GPU.
+    """
+
+    __props__ = (
+        "assume_a",
+        "lower",
+        "check_finite",
+    )
+
+    def __init__(
+        self,
+        assume_a="gen",
+        lower=False,
+        check_finite=True,
+    ):
+        if assume_a not in ("gen", "sym", "her", "pos"):
+            raise ValueError(f"{assume_a} is not a recognized matrix structure")
+
+        super().__init__(lower=lower, check_finite=check_finite)
+        self.assume_a = assume_a
+
+    def perform(self, node, inputs, outputs):
+        a, b = inputs
+        outputs[0][0] = scipy.linalg.solve(
+            a=a,
+            b=b,
+            lower=self.lower,
+            check_finite=self.check_finite,
+            assume_a=self.assume_a,
+        )
+
 
 solve = Solve()
 
 
 def solve(a, b, assume_a="gen", lower=False, check_finite=True):
-    """
-    Solves the linear equation set ``a * x = b`` for the unknown ``x``
-    for square ``a`` matrix.
+    """Solves the linear equation set ``a * x = b`` for the unknown ``x`` for square ``a`` matrix.
 
     If the data matrix is known to be a particular type then supplying the
     corresponding string to ``assume_a`` key chooses the dedicated solver.
@@ -432,8 +510,8 @@ def solve(a, b, assume_a="gen", lower=False, check_finite=True):
 
 
 # TODO: These are deprecated; emit a warning
-solve_lower_triangular = Solve(assume_a="sym", lower=True)
-solve_upper_triangular = Solve(assume_a="sym", lower=False)
+solve_lower_triangular = SolveTriangular(lower=True)
+solve_upper_triangular = SolveTriangular(lower=False)
 solve_symmetric = Solve(assume_a="sym")
 
 # TODO: Optimizations to replace multiplication by matrix inverse

tests/link/test_numba.py

@@ -2174,6 +2174,31 @@ def test_Cholesky(x, lower, exc):
             "gen",
             None,
         ),
+    ],
+)
+def test_Solve(A, x, lower, exc):
+    g = slinalg.Solve(lower)(A, x)
+
+    if isinstance(g, list):
+        g_fg = FunctionGraph(outputs=g)
+    else:
+        g_fg = FunctionGraph(outputs=[g])
+
+    cm = contextlib.suppress() if exc is None else pytest.warns(exc)
+    with cm:
+        compare_numba_and_py(
+            g_fg,
+            [
+                i.tag.test_value
+                for i in g_fg.inputs
+                if not isinstance(i, (SharedVariable, Constant))
+            ],
+        )
+
+
+@pytest.mark.parametrize(
+    "A, x, lower, exc",
+    [
         (
             set_test_value(
                 aet.dmatrix(),
@@ -2185,8 +2210,8 @@ def test_Cholesky(x, lower, exc):
         ),
     ],
 )
-def test_Solve(A, x, lower, exc):
-    g = slinalg.Solve(lower)(A, x)
+def test_SolveTriangular(A, x, lower, exc):
+    g = slinalg.SolveTriangular(lower)(A, x)
 
     if isinstance(g, list):
         g_fg = FunctionGraph(outputs=g)