Add more invariants and documentation to manifold_test.cc
Change-Id: I62e040679cc4fd4c5a7486885ebb4ad1a08b7b45
diff --git a/internal/ceres/manifold_test.cc b/internal/ceres/manifold_test.cc
index 23c59af..a3777ae 100644
--- a/internal/ceres/manifold_test.cc
+++ b/internal/ceres/manifold_test.cc
@@ -38,7 +38,7 @@
#include "ceres/dynamic_numeric_diff_cost_function.h"
#include "ceres/internal/eigen.h"
#include "ceres/numeric_diff_options.h"
-#include "ceres/random.h"
+#include "ceres/rotation.h"
#include "ceres/types.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
@@ -50,7 +50,17 @@
// helpful to expose them as testing utilities which can be used by the user
// when implementing their own manifold objects.
-constexpr int kNumTrials = 100;
+// The tests in this file are in two parts.
+//
+// 1. Manifold::Plus is doing what is expected. This requires per manifold
+// logic.
+// 2. The other methods of the manifold have mathematical properties that
+// make it compatible with Plus, as described in
+// https://arxiv.org/pdf/1107.1119.pdf. These tests are implemented using
+// generic matchers defined below which can all be called by the macro
+// EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y)
+
+constexpr int kNumTrials = 1000;
constexpr double kEpsilon = 1e-9;
// Checks that the invariant Plus(x, 0) == x holds.
@@ -60,7 +70,7 @@
Vector actual = Vector::Zero(ambient_size);
Vector zero = Vector::Zero(tangent_size);
- arg.Plus(x.data(), zero.data(), actual.data());
+ EXPECT_TRUE(arg.Plus(x.data(), zero.data(), actual.data()));
const double n = (actual - x).norm();
const double d = x.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
@@ -78,7 +88,7 @@
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector actual = Vector::Zero(tangent_size);
- arg.Minus(x.data(), x.data(), actual.data());
+ EXPECT_TRUE(arg.Minus(x.data(), x.data(), actual.data()));
const double diffnorm = actual.norm();
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() //
@@ -124,10 +134,11 @@
Matrix expected = Matrix::Zero(ambient_size, tangent_size);
double* jacobians[1] = {expected.data()};
- CHECK(cost_function.Evaluate(parameters, x_plus_zero.data(), jacobians));
+ EXPECT_TRUE(
+ cost_function.Evaluate(parameters, x_plus_zero.data(), jacobians));
Matrix actual = Matrix::Random(ambient_size, tangent_size);
- arg.PlusJacobian(x.data(), actual.data());
+ EXPECT_TRUE(arg.PlusJacobian(x.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
@@ -143,13 +154,13 @@
}
// Checks that the invariant Minus(Plus(x, delta), x) == delta holds.
-MATCHER_P2(HasCorrectMinusAt, x, delta, "") {
+MATCHER_P2(MinusPlusIsIdentityAt, x, delta, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector x_plus_delta = Vector::Zero(ambient_size);
- arg.Plus(x.data(), delta.data(), x_plus_delta.data());
+ EXPECT_TRUE(arg.Plus(x.data(), delta.data(), x_plus_delta.data()));
Vector actual = Vector::Zero(tangent_size);
- arg.Minus(x_plus_delta.data(), x.data(), actual.data());
+ EXPECT_TRUE(arg.Minus(x_plus_delta.data(), x.data(), actual.data()));
const double n = (actual - delta).norm();
const double d = delta.norm();
@@ -165,6 +176,31 @@
return true;
}
+// Checks that the invariant Plus(Minus(y, x), x) == y holds.
+MATCHER_P2(PlusMinusIsIdentityAt, x, y, "") {
+ const int ambient_size = arg.AmbientSize();
+ const int tangent_size = arg.TangentSize();
+
+ Vector y_minus_x = Vector::Zero(tangent_size);
+ EXPECT_TRUE(arg.Minus(y.data(), x.data(), y_minus_x.data()));
+
+ Vector actual = Vector::Zero(ambient_size);
+ EXPECT_TRUE(arg.Plus(x.data(), y_minus_x.data(), actual.data()));
+
+ const double n = (actual - y).norm();
+ const double d = y.norm();
+ const double diffnorm = (d == 0.0) ? n : (n / d);
+ if (diffnorm > kEpsilon) {
+ *result_listener << "\nx: " << x.transpose()
+ << "\nexpected: " << y.transpose()
+ << "\nactual:" << actual.transpose()
+ << "\ndiff:" << (y - actual).transpose()
+ << "\ndiffnorm: " << diffnorm;
+ return false;
+ }
+ return true;
+}
+
// Helper struct to curry Minus(., x) so that it can be numerically
// differentiated.
struct MinusFunctor {
@@ -199,10 +235,10 @@
Matrix expected = Matrix::Zero(tangent_size, ambient_size);
double* jacobians[1] = {expected.data()};
- CHECK(cost_function.Evaluate(parameters, y_minus_x.data(), jacobians));
+ EXPECT_TRUE(cost_function.Evaluate(parameters, y_minus_x.data(), jacobians));
Matrix actual = Matrix::Random(tangent_size, ambient_size);
- arg.MinusJacobian(x.data(), actual.data());
+ EXPECT_TRUE(arg.MinusJacobian(x.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
@@ -217,6 +253,34 @@
return true;
}
+// Checks that D_delta Minus(Plus(x, delta), x) at delta = 0 is an identity
+// matrix.
+MATCHER_P(MinusPlusJacobianIsIdentityAt, x, "") {
+ const int ambient_size = arg.AmbientSize();
+ const int tangent_size = arg.TangentSize();
+
+ Matrix plus_jacobian(ambient_size, tangent_size);
+ EXPECT_TRUE(arg.PlusJacobian(x.data(), plus_jacobian.data()));
+ Matrix minus_jacobian(tangent_size, ambient_size);
+ EXPECT_TRUE(arg.MinusJacobian(x.data(), minus_jacobian.data()));
+
+ const Matrix actual = minus_jacobian * plus_jacobian;
+ const Matrix expected = Matrix::Identity(tangent_size, tangent_size);
+
+ const double n = (actual - expected).norm();
+ const double d = expected.norm();
+ const double diffnorm = n / d;
+ if (diffnorm > kEpsilon) {
+ *result_listener << "\nx: " << x.transpose() << "\nexpected: \n"
+ << expected << "\nactual:\n"
+ << actual << "\ndiff:\n"
+ << expected - actual << "\ndiffnorm: " << diffnorm;
+
+ return false;
+ }
+ return true;
+}
+
// Verify that the output of RightMultiplyByPlusJacobian is ambient_matrix *
// plus_jacobian.
MATCHER_P(HasCorrectRightMultiplyByPlusJacobianAt, x, "") {
@@ -227,14 +291,14 @@
constexpr int kMaxNumRows = 3;
for (int num_rows = kMinNumRows; num_rows <= kMaxNumRows; ++num_rows) {
Matrix plus_jacobian = Matrix::Random(ambient_size, tangent_size);
- arg.PlusJacobian(x.data(), plus_jacobian.data());
+ EXPECT_TRUE(arg.PlusJacobian(x.data(), plus_jacobian.data()));
Matrix ambient_matrix = Matrix::Random(num_rows, ambient_size);
Matrix expected = ambient_matrix * plus_jacobian;
Matrix actual = Matrix::Random(num_rows, tangent_size);
- arg.RightMultiplyByPlusJacobian(
- x.data(), num_rows, ambient_matrix.data(), actual.data());
+ EXPECT_TRUE(arg.RightMultiplyByPlusJacobian(
+ x.data(), num_rows, ambient_matrix.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
@@ -251,14 +315,17 @@
return true;
}
-#define EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta) \
- Vector zero_tangent = Vector::Zero(manifold.TangentSize()); \
- EXPECT_THAT(manifold, XPlusZeroIsXAt(x)); \
- EXPECT_THAT(manifold, XMinusXIsZeroAt(x)); \
- EXPECT_THAT(manifold, HasCorrectMinusAt(x, delta)); \
- EXPECT_THAT(manifold, HasCorrectMinusAt(x, zero_tangent)); \
- EXPECT_THAT(manifold, HasCorrectPlusJacobianAt(x)); \
- EXPECT_THAT(manifold, HasCorrectMinusJacobianAt(x)); \
+#define EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y) \
+ Vector zero_tangent = Vector::Zero(manifold.TangentSize()); \
+ EXPECT_THAT(manifold, XPlusZeroIsXAt(x)); \
+ EXPECT_THAT(manifold, XMinusXIsZeroAt(x)); \
+ EXPECT_THAT(manifold, MinusPlusIsIdentityAt(x, delta)); \
+ EXPECT_THAT(manifold, MinusPlusIsIdentityAt(x, zero_tangent)); \
+ EXPECT_THAT(manifold, PlusMinusIsIdentityAt(x, x)); \
+ EXPECT_THAT(manifold, PlusMinusIsIdentityAt(x, y)); \
+ EXPECT_THAT(manifold, HasCorrectPlusJacobianAt(x)); \
+ EXPECT_THAT(manifold, HasCorrectMinusJacobianAt(x)); \
+ EXPECT_THAT(manifold, MinusPlusJacobianIsIdentityAt(x)); \
EXPECT_THAT(manifold, HasCorrectRightMultiplyByPlusJacobianAt(x));
TEST(EuclideanManifold, NormalFunctionTest) {
@@ -269,6 +336,7 @@
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
+ const Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
Vector x_plus_delta = Vector::Zero(manifold.AmbientSize());
@@ -276,21 +344,22 @@
EXPECT_NEAR(
(x_plus_delta - x - delta).norm() / (x + delta).norm(), 0.0, kEpsilon);
- EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta);
+ EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
TEST(SubsetManifold, EmptyConstantParameters) {
SubsetManifold manifold(3, {});
for (int trial = 0; trial < kNumTrials; ++trial) {
- Vector x = Vector::Random(3);
+ const Vector x = Vector::Random(3);
+ const Vector y = Vector::Random(3);
Vector delta = Vector::Random(3);
Vector x_plus_delta = Vector::Zero(3);
manifold.Plus(x.data(), delta.data(), x_plus_delta.data());
EXPECT_NEAR(
(x_plus_delta - x - delta).norm() / (x + delta).norm(), 0.0, kEpsilon);
- EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta);
+ EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
@@ -314,9 +383,11 @@
for (int i = 0; i < kAmbientSize; ++i) {
SubsetManifold manifold_with_ith_parameter_constant(kAmbientSize, {i});
-
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(kAmbientSize);
+ Vector y = Vector::Random(kAmbientSize);
+ // x and y must have the same i^th coordinate to be on the manifold.
+ y[i] = x[i];
Vector delta = Vector::Random(kTangentSize);
Vector x_plus_delta = Vector::Zero(kAmbientSize);
@@ -333,7 +404,7 @@
}
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(
- manifold_with_ith_parameter_constant, x, delta);
+ manifold_with_ith_parameter_constant, x, delta, y);
}
}
}
@@ -389,7 +460,7 @@
ProductManifold manifold(manifold1, manifold2, manifold3, manifold4);
for (int trial = 0; trial < kNumTrials; ++trial) {
- Vector x = Vector::Random(manifold.AmbientSize());
+ const Vector x = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
Vector x_plus_delta = Vector::Zero(manifold.AmbientSize());
Vector x_plus_delta_expected = Vector::Zero(manifold.AmbientSize());
@@ -427,7 +498,7 @@
EXPECT_EQ(x_plus_delta[i], x_plus_delta_expected[i]);
}
- EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta);
+ EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, x_plus_delta);
}
}
@@ -439,7 +510,9 @@
EXPECT_EQ(manifold.TangentSize(), 2);
for (int trial = 0; trial < kNumTrials; ++trial) {
- Vector x = Vector::Random(3);
+ const Vector x = Vector::Random(3);
+ Vector y = Vector::Random(3);
+ y[0] = x[0];
Vector delta = Vector::Random(2);
Vector x_plus_delta = Vector::Zero(3);
@@ -449,7 +522,7 @@
EXPECT_EQ(x_plus_delta[1], x[1] + delta[0]);
EXPECT_EQ(x_plus_delta[2], x[2] + delta[1]);
- EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta);
+ EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
@@ -461,17 +534,17 @@
EXPECT_EQ(manifold.TangentSize(), 2);
for (int trial = 0; trial < kNumTrials; ++trial) {
- Vector x = Vector::Random(3);
+ const Vector x = Vector::Random(3);
+ Vector y = Vector::Random(3);
+ y[2] = x[2];
Vector delta = Vector::Random(2);
Vector x_plus_delta = Vector::Zero(3);
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), x_plus_delta.data()));
-
EXPECT_EQ(x_plus_delta[0], x[0] + delta[0]);
EXPECT_EQ(x_plus_delta[1], x[1] + delta[1]);
EXPECT_EQ(x_plus_delta[2], x[2]);
-
- EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta);
+ EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
