Merge pull request #83 from brocksam/add-cse-kalman-filter-matrix-equ…

…ation

Add new CSE benchmark based on Kalman filter matrix expression

benchmarks/cse.py

@@ -237,3 +237,79 @@ def time_jacobian_cse(self):
     def time_combined_cse(self):
         """Time simultaneous CSE on the lighthouse example and its Jacobian."""
         cse([self.y, self.G])
+
+
+class KalmanFilterMatrixEquationCSE:
+    """Kalman filter example from Matthew Rocklin's SciPy 2013 talk.
+
+    Talk titled: "Matrix Expressions and BLAS/LAPACK; SciPy 2013 Presentation"
+
+    https://pyvideo.org/scipy-2013/matrix-expressions-and-blaslapack-scipy-2013-pr
+
+    Notes
+    =====
+
+    Equations are:
+        new_mu = mu + Sigma*H.T * (R + H*Sigma*H.T).I * (H*mu - data)
+        new_Sigma = Sigma - Sigma*H.T * (R + H*Sigma*H.T).I * H * Sigma
+
+    """
+
+    def setup(self):
+        """Create the 2x2 matrix equations for mu and Sigma."""
+        N = 2
+        mu = ImmutableDenseMatrix(symbols(f'mu:{N}'))
+        Sigma = ImmutableDenseMatrix(symbols(f'Sigma:{N * N}')).reshape(N, N)
+        H = ImmutableDenseMatrix(symbols(f'H:{N * N}')).reshape(N, N)
+        R = ImmutableDenseMatrix(symbols(f'R:{N * N}')).reshape(N, N)
+        data = ImmutableDenseMatrix(symbols(f'data:{N}'))
+        self.new_mu = MatAdd(
+            mu,
+            MatMul(
+                Sigma,
+                Transpose(H),
+                Inverse(MatAdd(R, MatMul(H, Sigma, Transpose(H)))),
+                MatAdd(MatMul(H, mu), MatMul(S.NegativeOne, data)),
+            )
+        )
+        self.new_Sigma = MatAdd(
+            Sigma,
+            MatMul(
+                S.NegativeOne,
+                Sigma,
+                Transpose(H),
+                Inverse(MatAdd(R, MatMul(H, Sigma, Transpose(H)))),
+                H,
+                Sigma,
+            )
+        )
+
+        x0 = MatrixSymbol('x0', N, N)
+        x1 = MatrixSymbol('x1', N, N)
+        replacements_expected = [
+            (x0, Transpose(H)),
+            (x1, Inverse(MatAdd(R, MatMul(H, Sigma, x0)))),
+        ]
+        reduced_exprs_expected = [
+            MatAdd(
+                mu,
+                MatMul(
+                    Sigma,
+                    x0,
+                    x1,
+                    MatAdd(MatMul(H, mu), MatMul(S.NegativeOne, data)),
+                ),
+            ),
+            MatAdd(Sigma, MatMul(S.NegativeOne, Sigma, x0, x1, H, Sigma)),
+        ]
+        self.cse_expr_expected = (replacements_expected, reduced_exprs_expected)
+
+    def test_cse(self):
+        """Expected result from CSE on the Kalman filter example."""
+        cse_expr = cse([self.new_mu, self.new_Sigma])
+        assert cse_expr == self.cse_expr_expected
+
+    def time_cse(self):
+        """Time CSE on the Kalman filter example."""
+        cse([self.new_mu, self.new_Sigma])
+