Gradient checking cleanup and local parameterization bugfix
Change the Ceres gradient checking API to make is useful for
unit testing, clean up code duplication and fix interaction between
gradient checking and local parameterizations.
There were two gradient checking implementations, one being used
when using the check_gradients flag in the Solver, the other
being a standalone class. The standalone version was restricted
to cost functions with fixed parameter sizes at compile time, which
is being lifted here. This enables it to be used inside the
GradientCheckingCostFunction as well.
In addition, this installs new hooks in the Solver to ensure
that Solve will fail if any incorrect gradients are detected. This
way, you can set the check_gradient flags to true and detect
errors in an automated way, instead of just printing error information
to the log. The error log is now also returned in the Solver summary
instead of being printed directly. The user can then decide what to
do with it. The existing hooks for user callbacks are used for
this purpose to keep the internal API changes minimal and non-invasive.
The last and biggest change is the way the the interaction between
local parameterizations and the gradient checker works. Before,
local parameterizations would be ignored by the checker. However,
if a cost function does not compute its Jacobian along the null
space of the local parameterization, this wil not have any effect
on the solver, but would result in a gradient checker error.
With this change, the Jacobians are multiplied by the Jacobians
of the respective local parameterization and thus being compared
in the tangent space only.
The typical use case for this are quaternion parameters, where
a cost function will typically assume that the quaternion is
always normalized, skipping the correct computation of the Jacobian
along the normal to save computation cost.
Change-Id: I5e1bb97b8a899436cea25101efe5011b0bb13282
diff --git a/internal/ceres/is_close.cc b/internal/ceres/is_close.cc
new file mode 100644
index 0000000..a91a174
--- /dev/null
+++ b/internal/ceres/is_close.cc
@@ -0,0 +1,59 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2016 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Authors: keir@google.com (Keir Mierle), dgossow@google.com (David Gossow)
+
+#include "ceres/is_close.h"
+
+#include <algorithm>
+#include <cmath>
+
+namespace ceres {
+namespace internal {
+bool IsClose(double x, double y, double relative_precision,
+ double *relative_error,
+ double *absolute_error) {
+ double local_absolute_error;
+ double local_relative_error;
+ if (!absolute_error) {
+ absolute_error = &local_absolute_error;
+ }
+ if (!relative_error) {
+ relative_error = &local_relative_error;
+ }
+ *absolute_error = std::fabs(x - y);
+ *relative_error = *absolute_error / std::max(std::fabs(x), std::fabs(y));
+ if (x == 0 || y == 0) {
+ // If x or y is exactly zero, then relative difference doesn't have any
+ // meaning. Take the absolute difference instead.
+ *relative_error = *absolute_error;
+ }
+ return *relative_error < std::fabs(relative_precision);
+}
+} // namespace internal
+} // namespace ceres
