#!/usr/bin/env python
from __future__ import print_function
import gtsam
import numpy as np

# Create an empty nonlinear factor graph
graph = gtsam.NonlinearFactorGraph()

# Add a prior on the first pose, setting it to the origin
# A prior factor consists of a mean and a noise model (covariance matrix)
priorMean = gtsam.Pose2(0.0, 0.0, 0.0)  # prior at origin
priorNoise = gtsam.noiseModel.Diagonal.Sigmas(np.array([0.3, 0.3, 0.1]))
graph.add(gtsam.PriorFactorPose2(1, priorMean, priorNoise))

# Add odometry factors
odometry = gtsam.Pose2(2.0, 0.0, 0.0)
# For simplicity, we will use the same noise model for each odometry factor
odometryNoise = gtsam.noiseModel.Diagonal.Sigmas(np.array([0.2, 0.2, 0.1]))
# Create odometry (Between) factors between consecutive poses
graph.add(gtsam.BetweenFactorPose2(1, 2, odometry, odometryNoise))
graph.add(gtsam.BetweenFactorPose2(2, 3, odometry, odometryNoise))
graph.print("\nFactor Graph:\n")

# Create the data structure to hold the initialEstimate estimate to the solution
# For illustrative purposes, these have been deliberately set to incorrect values
initial = gtsam.Values()
initial.insert(1, gtsam.Pose2(0.5, 0.0, 0.2))
initial.insert(2, gtsam.Pose2(2.3, 0.1, -0.2))
initial.insert(3, gtsam.Pose2(4.1, 0.1, 0.1))
initial.print("\nInitial Estimate:\n")

# optimize using Levenberg-Marquardt optimization
params = gtsam.LevenbergMarquardtParams()
optimizer = gtsam.LevenbergMarquardtOptimizer(graph, initial, params)
result = optimizer.optimize()
result.print("\nFinal Result:\n")