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b8f28cc6a3
* fix deprication version for latest numpy * fix deprication version for latest numpy * fix deprication version for latest numpy * fix deprication version for latest numpy
283 lines
9.0 KiB
Python
283 lines
9.0 KiB
Python
# Copyright (c) 2020 Jeff Irion and contributors
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#
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# This file originated from the `graphslam` package:
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#
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# https://github.com/JeffLIrion/python-graphslam
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r"""A ``Graph`` class that stores the edges and vertices required for Graph SLAM.
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"""
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import warnings
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from collections import defaultdict
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from functools import reduce
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy.sparse import SparseEfficiencyWarning, lil_matrix
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from scipy.sparse.linalg import spsolve
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warnings.simplefilter("ignore", SparseEfficiencyWarning)
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warnings.filterwarnings("ignore", category=SparseEfficiencyWarning)
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# pylint: disable=too-few-public-methods
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class _Chi2GradientHessian:
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r"""A class that is used to aggregate the :math:`\chi^2` error, gradient, and Hessian.
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Parameters
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----------
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dim : int
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The compact dimensionality of the poses
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Attributes
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----------
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chi2 : float
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The :math:`\chi^2` error
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dim : int
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The compact dimensionality of the poses
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gradient : defaultdict
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The contributions to the gradient vector
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hessian : defaultdict
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The contributions to the Hessian matrix
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"""
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def __init__(self, dim):
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self.chi2 = 0.
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self.dim = dim
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self.gradient = defaultdict(lambda: np.zeros(dim))
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self.hessian = defaultdict(lambda: np.zeros((dim, dim)))
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@staticmethod
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def update(chi2_grad_hess, incoming):
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r"""Update the :math:`\chi^2` error and the gradient and Hessian dictionaries.
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Parameters
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----------
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chi2_grad_hess : _Chi2GradientHessian
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The ``_Chi2GradientHessian`` that will be updated
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incoming : tuple
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"""
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chi2_grad_hess.chi2 += incoming[0]
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for idx, contrib in incoming[1].items():
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chi2_grad_hess.gradient[idx] += contrib
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for (idx1, idx2), contrib in incoming[2].items():
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if idx1 <= idx2:
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chi2_grad_hess.hessian[idx1, idx2] += contrib
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else:
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chi2_grad_hess.hessian[idx2, idx1] += np.transpose(contrib)
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return chi2_grad_hess
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class Graph(object):
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r"""A graph that will be optimized via Graph SLAM.
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Parameters
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----------
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edges : list[graphslam.edge.edge_odometry.EdgeOdometry]
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A list of the vertices in the graph
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vertices : list[graphslam.vertex.Vertex]
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A list of the vertices in the graph
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Attributes
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----------
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_chi2 : float, None
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The current :math:`\chi^2` error, or ``None`` if it has not yet been computed
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_edges : list[graphslam.edge.edge_odometry.EdgeOdometry]
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A list of the edges (i.e., constraints) in the graph
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_gradient : numpy.ndarray, None
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The gradient :math:`\mathbf{b}` of the :math:`\chi^2` error, or ``None`` if it has not yet been computed
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_hessian : scipy.sparse.lil_matrix, None
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The Hessian matrix :math:`H`, or ``None`` if it has not yet been computed
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_vertices : list[graphslam.vertex.Vertex]
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A list of the vertices in the graph
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"""
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def __init__(self, edges, vertices):
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# The vertices and edges lists
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self._edges = edges
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self._vertices = vertices
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# The chi^2 error, gradient, and Hessian
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self._chi2 = None
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self._gradient = None
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self._hessian = None
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self._link_edges()
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def _link_edges(self):
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"""Fill in the ``vertices`` attributes for the graph's edges.
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"""
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index_id_dict = {i: v.id for i, v in enumerate(self._vertices)}
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id_index_dict = {v_id: v_index for v_index, v_id in
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index_id_dict.items()}
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# Fill in the vertices' `index` attribute
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for v in self._vertices:
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v.index = id_index_dict[v.id]
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for e in self._edges:
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e.vertices = [self._vertices[id_index_dict[v_id]] for v_id in
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e.vertex_ids]
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def calc_chi2(self):
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r"""Calculate the :math:`\chi^2` error for the ``Graph``.
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Returns
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-------
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float
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The :math:`\chi^2` error
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"""
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self._chi2 = sum((e.calc_chi2() for e in self._edges))
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return self._chi2
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def _calc_chi2_gradient_hessian(self):
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r"""Calculate the :math:`\chi^2` error, the gradient :math:`\mathbf{b}`, and the Hessian :math:`H`.
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"""
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n = len(self._vertices)
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dim = len(self._vertices[0].pose.to_compact())
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chi2_gradient_hessian = reduce(_Chi2GradientHessian.update,
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(e.calc_chi2_gradient_hessian()
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for e in self._edges),
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_Chi2GradientHessian(dim))
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self._chi2 = chi2_gradient_hessian.chi2
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# Fill in the gradient vector
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self._gradient = np.zeros(n * dim, dtype=float)
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for idx, cont in chi2_gradient_hessian.gradient.items():
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self._gradient[idx * dim: (idx + 1) * dim] += cont
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# Fill in the Hessian matrix
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self._hessian = lil_matrix((n * dim, n * dim), dtype=float)
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for (row_idx, col_idx), cont in chi2_gradient_hessian.hessian.items():
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x_start = row_idx * dim
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x_end = (row_idx + 1) * dim
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y_start = col_idx * dim
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y_end = (col_idx + 1) * dim
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self._hessian[x_start:x_end, y_start:y_end] = cont
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if row_idx != col_idx:
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x_start = col_idx * dim
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x_end = (col_idx + 1) * dim
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y_start = row_idx * dim
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y_end = (row_idx + 1) * dim
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self._hessian[x_start:x_end, y_start:y_end] = \
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np.transpose(cont)
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def optimize(self, tol=1e-4, max_iter=20, fix_first_pose=True):
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r"""Optimize the :math:`\chi^2` error for the ``Graph``.
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Parameters
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----------
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tol : float
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If the relative decrease in the :math:`\chi^2` error between iterations is less than ``tol``, we will stop
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max_iter : int
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The maximum number of iterations
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fix_first_pose : bool
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If ``True``, we will fix the first pose
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"""
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n = len(self._vertices)
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dim = len(self._vertices[0].pose.to_compact())
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# Previous iteration's chi^2 error
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chi2_prev = -1.
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# For displaying the optimization progress
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print("\nIteration chi^2 rel. change")
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print("--------- ----- -----------")
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for i in range(max_iter):
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self._calc_chi2_gradient_hessian()
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# Check for convergence (from the previous iteration); this avoids having to calculate chi^2 twice
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if i > 0:
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rel_diff = (chi2_prev - self._chi2) / (
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chi2_prev + np.finfo(float).eps)
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print(
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"{:9d} {:20.4f} {:18.6f}".format(i, self._chi2, -rel_diff))
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if self._chi2 < chi2_prev and rel_diff < tol:
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return
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else:
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print("{:9d} {:20.4f}".format(i, self._chi2))
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# Update the previous iteration's chi^2 error
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chi2_prev = self._chi2
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# Hold the first pose fixed
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if fix_first_pose:
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self._hessian[:dim, :] = 0.
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self._hessian[:, :dim] = 0.
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self._hessian[:dim, :dim] += np.eye(dim)
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self._gradient[:dim] = 0.
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# Solve for the updates
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dx = spsolve(self._hessian, -self._gradient)
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# Apply the updates
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for v, dx_i in zip(self._vertices, np.split(dx, n)):
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v.pose += dx_i
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# If we reached the maximum number of iterations, print out the final iteration's results
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self.calc_chi2()
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rel_diff = (chi2_prev - self._chi2) / (chi2_prev + np.finfo(float).eps)
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print("{:9d} {:20.4f} {:18.6f}".format(
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max_iter, self._chi2, -rel_diff))
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def to_g2o(self, outfile):
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"""Save the graph in .g2o format.
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Parameters
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----------
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outfile : str
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The path where the graph will be saved
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"""
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with open(outfile, 'w') as f:
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for v in self._vertices:
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f.write(v.to_g2o())
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for e in self._edges:
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f.write(e.to_g2o())
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def plot(self, vertex_color='r', vertex_marker='o', vertex_markersize=3,
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edge_color='b', title=None):
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"""Plot the graph.
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Parameters
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----------
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vertex_color : str
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The color that will be used to plot the vertices
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vertex_marker : str
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The marker that will be used to plot the vertices
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vertex_markersize : int
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The size of the plotted vertices
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edge_color : str
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The color that will be used to plot the edges
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title : str, None
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The title that will be used for the plot
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"""
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plt.figure()
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for e in self._edges:
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e.plot(edge_color)
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for v in self._vertices:
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v.plot(vertex_color, vertex_marker, vertex_markersize)
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if title:
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plt.title(title)
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plt.show()
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