Add Gaussian Mixture residuals to batch

examples/ex_gaussian_mixture.py

@@ -0,0 +1,91 @@
+from navlie.batch.gaussian_mixtures import (
+    GaussianMixtureResidual,
+    MaxMixtureResidual,
+    SumMixtureResidual,
+    MaxSumMixtureResidual,
+    HessianSumMixtureResidual,
+)
+from navlie.batch.residuals import PriorResidual
+
+from navlie.lib.states import VectorState
+import os
+import matplotlib.pyplot as plt
+import numpy as np
+import seaborn as sns
+from pathlib import Path
+from navlie.batch.problem import Problem
+
+
+def main():
+    key = "x"
+    component_residuals = []
+    stamp = 0.0
+    means = [np.array([0.0]), np.array([0.5]), np.array([1])]
+    covariances = [
+        np.atleast_2d(np.array([2])),
+        np.atleast_2d(np.array([2])),
+        np.atleast_2d(np.array([3])),
+    ]
+    weights = [0.5, 0.5]
+    for lv1 in range(len(means)):
+        prior_state = VectorState(means[lv1], stamp)
+
+        component_residuals.append(PriorResidual([key], prior_state, covariances[lv1]))
+    res_dict = {
+        "Max-Mixture": MaxMixtureResidual(component_residuals, weights),
+        "Sum-Mixture": SumMixtureResidual(component_residuals, weights),
+        "Max-Sum-Mixture": MaxSumMixtureResidual(component_residuals, weights, 10),
+        "Hessian-Sum-Mixture": HessianSumMixtureResidual(
+            component_residuals, weights, True, 0.1
+        ),
+    }
+
+    x0 = VectorState(2, 0.0, "x")
+    plt.figure()
+    for key, res in res_dict.items():
+        x = x0.copy()
+        print(f"Running {key} optimization...")
+        problem = Problem(
+            solver="LM",
+            max_iters=100,
+            step_tol=1e-8,
+            tau=1e-11,
+            verbose=False,
+        )
+        problem.add_residual(res)
+        problem.add_variable("x", x)
+        opt_nv_res = problem.solve()
+        x = np.linspace(-3, 3, 1000)
+        linestyles = ["-", "--", "-.", ":", "-"] * 6
+
+        res: MaxMixtureResidual = res
+        plt.plot(
+            x,
+            np.array([evaluate_log_likelihood(res, val) for val in x]),
+            label=key,
+            linestyle=linestyles[lv1],
+        )
+        plt.scatter(
+            opt_nv_res["variables"]["x"].value,
+            np.sum(res.evaluate([opt_nv_res["variables"]["x"]]) ** 2),
+            marker="o",
+        )
+    plt.xlabel("x")
+    plt.ylabel("Cost Function Value (offset by norm. constants)")
+    plt.legend()
+    plt.show()
+
+
+def evaluate_error(res: GaussianMixtureResidual, val: np.ndarray):
+    error = res.evaluate([VectorState(val.squeeze())])
+    error = np.atleast_1d(error)
+    return error
+
+
+def evaluate_log_likelihood(res: GaussianMixtureResidual, val: np.ndarray):
+    error = evaluate_error(res, np.atleast_1d(val))
+    return np.linalg.norm(error, 2) ** 2
+
+
+if __name__ == "__main__":
+    main()