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% GTSAM Copyright 2010, Georgia Tech Research Corporation,
% Atlanta, Georgia 30332-0415
% All Rights Reserved
% Authors: Frank Dellaert, et al. (see THANKS for the full author list)
%
% See LICENSE for the license information
%
% @brief Simple robotics example using the pre-built planar SLAM domain
% @author Alex Cunningham
% @author Frank Dellaert
% @author Chris Beall
% @author Vadim Indelman
% @author Can Erdogan
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import gtsam.*
%% Assumptions
% - All values are axis aligned
% - Robot poses are facing along the X axis (horizontal, to the right in images)
% - We have full odometry for measurements
% - The robot is on a grid, moving 2 meters each step
%% Create graph container and add factors to it
graph = NonlinearFactorGraph;
%% Add prior
% gaussian for prior
priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
priorMean = Pose2(0.0, 0.0, 0.0); % prior at origin
graph.add(PriorFactorPose2(1, priorMean, priorNoise)); % add directly to graph
%% Add odometry
% general noisemodel for odometry
odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
odometry = Pose2(2.0, 0.0, 0.0); % create a measurement for both factors (the same in this case)
graph.add(BetweenFactorPose2(1, 2, odometry, odometryNoise));
graph.add(BetweenFactorPose2(2, 3, odometry, odometryNoise));
%% Add measurements
% general noisemodel for measurements
measurementNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2]);
% print
graph.print('full graph');
%% Initialize to noisy points
initialEstimate = Values;
initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
initialEstimate.insert(2, Pose2(2.3, 0.1,-0.2));
initialEstimate.insert(3, Pose2(4.1, 0.1, 0.1));
initialEstimate.print('initial estimate');
%% set up solver, choose ordering and optimize
params = DoglegParams;
params.setAbsoluteErrorTol(1e-15);
params.setRelativeErrorTol(1e-15);
params.setVerbosity('ERROR');
params.setVerbosityDL('VERBOSE');
params.setOrdering(graph.orderingCOLAMD());
optimizer = DoglegOptimizer(graph, initialEstimate, params);
result = optimizer.optimizeSafely();
result.print('final result');
%% Get the corresponding dense matrix
ord = graph.orderingCOLAMD();
gfg = graph.linearize(result);
denseAb = gfg.augmentedJacobian;
%% Get sparse matrix A and RHS b
IJS = gfg.sparseJacobian_();
Ab=sparse(IJS(1,:),IJS(2,:),IJS(3,:));
A = Ab(:,1:end-1);
b = full(Ab(:,end));
clf
spy(A);
title('Non-zero entries in measurement Jacobian');
