zrzk
/
px4_autopilot
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
Browse Source

Matrix: convert dual test to gtest

v1.13.0-BW
Matthias Grob 3 years ago
parent
62571b6984
commit
79e8152f05
3 changed files with 342 additions and 312 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 2
      src/lib/matrix/test/CMakeLists.txt
  2. 341
      src/lib/matrix/test/MatrixDualTest.cpp
  3. 311
      src/lib/matrix/test/dual.cpp

2
src/lib/matrix/test/CMakeLists.txt
Unescape View File

@ -23,7 +23,6 @@ set(tests @@ -23,7 +23,6 @@ set(tests
hatvee
least_squares
upperRightTriangle
dual
pseudoInverse
)
@ -43,5 +42,6 @@ endforeach() @@ -43,5 +42,6 @@ endforeach()
px4_add_unit_gtest(SRC MatrixAssignmentTest.cpp)
px4_add_unit_gtest(SRC MatrixAttitudeTest.cpp)
px4_add_unit_gtest(SRC MatrixCopyToTest.cpp)
px4_add_unit_gtest(SRC MatrixDualTest.cpp)
px4_add_unit_gtest(SRC MatrixSparseVectorTest.cpp)
px4_add_unit_gtest(SRC MatrixUnwrapTest.cpp)

341
src/lib/matrix/test/MatrixDualTest.cpp
Unescape View File

@ -0,0 +1,341 @@ @@ -0,0 +1,341 @@
/****************************************************************************
*
* Copyright (C) 2022 PX4 Development Team. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
* 3. Neither the name PX4 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.
*
****************************************************************************/
#include <gtest/gtest.h>
#include <matrix/math.hpp>
#include <iostream>
using namespace matrix;
template <typename Scalar, size_t N>
bool isEqualAll(Dual<Scalar, N> a, Dual<Scalar, N> b)
{
return isEqualF(a.value, b.value) && a.derivative == b.derivative;
}
template <typename T>
T testFunction(const Vector<T, 3> &point)
{
// function is f(x,y,z) = x^2 + 2xy + 3y^2 + z
return point(0) * point(0)
+ 2.f * point(0) * point(1)
+ 3.f * point(1) * point(1)
+ point(2);
}
template <typename Scalar>
Vector<Scalar, 3> positionError(const Vector<Scalar, 3> &positionState,
const Vector<Scalar, 3> &velocityStateBody,
const Quaternion<Scalar> &bodyOrientation,
const Vector<Scalar, 3> &positionMeasurement,
Scalar dt
)
{
return positionMeasurement - (positionState + bodyOrientation.rotateVector(velocityStateBody) * dt);
}
TEST(MatrixDualTest, Dual)
{
const Dual<float, 1> a(3, 0);
const Dual<float, 1> b(6, 0);
{
EXPECT_FLOAT_EQ(a.value, 3.f);
EXPECT_FLOAT_EQ(a.derivative(0), 1.f);
}
{
// addition
Dual<float, 1> c = a + b;
EXPECT_FLOAT_EQ(c.value, 9.f);
EXPECT_FLOAT_EQ(c.derivative(0), 2.f);
Dual<float, 1> d = +a;
EXPECT_TRUE(isEqualAll(d, a));
d += b;
EXPECT_TRUE(isEqualAll(d, c));
Dual<float, 1> e = a;
e += b.value;
EXPECT_FLOAT_EQ(e.value, c.value);
EXPECT_EQ(e.derivative, a.derivative);
Dual<float, 1> f = b.value + a;
EXPECT_TRUE(isEqualAll(f, e));
}
{
// subtraction
Dual<float, 1> c = b - a;
EXPECT_FLOAT_EQ(c.value, 3.f);
EXPECT_FLOAT_EQ(c.derivative(0), 0.f);
Dual<float, 1> d = b;
EXPECT_TRUE(isEqualAll(d, b));
d -= a;
EXPECT_TRUE(isEqualAll(d, c));
Dual<float, 1> e = b;
e -= a.value;
EXPECT_FLOAT_EQ(e.value, c.value);
EXPECT_EQ(e.derivative, b.derivative);
Dual<float, 1> f = a.value - b;
EXPECT_TRUE(isEqualAll(f, -e));
}
{
// multiplication
Dual<float, 1> c = a * b;
EXPECT_FLOAT_EQ(c.value, 18.f);
EXPECT_FLOAT_EQ(c.derivative(0), 9.f);
Dual<float, 1> d = a;
EXPECT_TRUE(isEqualAll(d, a));
d *= b;
EXPECT_TRUE(isEqualAll(d, c));
Dual<float, 1> e = a;
e *= b.value;
EXPECT_FLOAT_EQ(e.value, c.value);
EXPECT_EQ(e.derivative, a.derivative * b.value);
Dual<float, 1> f = b.value * a;
EXPECT_TRUE(isEqualAll(f, e));
}
{
// division
Dual<float, 1> c = b / a;
EXPECT_FLOAT_EQ(c.value, 2.f);
EXPECT_FLOAT_EQ(c.derivative(0), -1.f / 3.f);
Dual<float, 1> d = b;
EXPECT_TRUE(isEqualAll(d, b));
d /= a;
EXPECT_TRUE(isEqualAll(d, c));
Dual<float, 1> e = b;
e /= a.value;
EXPECT_FLOAT_EQ(e.value, c.value);
EXPECT_EQ(e.derivative, b.derivative / a.value);
Dual<float, 1> f = a.value / b;
EXPECT_TRUE(isEqualAll(f, 1.f / e));
}
{
Dual<float, 1> blank;
EXPECT_FLOAT_EQ(blank.value, 0.f);
EXPECT_FLOAT_EQ(blank.derivative(0), 0.f);
}
{
// sqrt
EXPECT_FLOAT_EQ(sqrt(a).value, sqrt(a.value));
EXPECT_FLOAT_EQ(sqrt(a).derivative(0), 1.f / sqrt(12.f));
}
{
// abs
EXPECT_TRUE(isEqualAll(a, abs(-a)));
EXPECT_FALSE(isEqualAll(-a, abs(a)));
EXPECT_TRUE(isEqualAll(-a, -abs(a)));
}
{
// ceil
Dual<float, 1> c(1.5, 0);
EXPECT_FLOAT_EQ(ceil(c).value, ceil(c.value));
EXPECT_FLOAT_EQ(ceil(c).derivative(0), 0.f);
}
{
// floor
Dual<float, 1> c(1.5, 0);
EXPECT_FLOAT_EQ(floor(c).value, floor(c.value));
EXPECT_FLOAT_EQ(floor(c).derivative(0), 0.f);
}
{
// fmod
EXPECT_FLOAT_EQ(fmod(a, 0.8f).value, fmod(a.value, 0.8f));
EXPECT_EQ(fmod(a, 0.8f).derivative, a.derivative);
}
{
// max/min
EXPECT_TRUE(isEqualAll(b, max(a, b)));
EXPECT_TRUE(isEqualAll(a, min(a, b)));
}
{
// isnan
EXPECT_FALSE(IsNan(a));
Dual<float, 1> c(sqrt(-1.f), 0);
EXPECT_TRUE(IsNan(c));
}
{
// isfinite/isinf
EXPECT_TRUE(IsFinite(a));
EXPECT_FALSE(IsInf(a));
Dual<float, 1> c(sqrt(-1.f), 0);
EXPECT_FALSE(IsFinite(c));
EXPECT_FALSE(IsInf(c));
Dual<float, 1> d(INFINITY, 0);
EXPECT_FALSE(IsFinite(d));
EXPECT_TRUE(IsInf(d));
}
{
// sin/cos/tan
EXPECT_FLOAT_EQ(sin(a).value, sin(a.value));
EXPECT_FLOAT_EQ(sin(a).derivative(0), cos(a.value)); // sin'(x) = cos(x)
EXPECT_FLOAT_EQ(cos(a).value, cos(a.value));
EXPECT_FLOAT_EQ(cos(a).derivative(0), -sin(a.value)); // cos'(x) = -sin(x)
EXPECT_FLOAT_EQ(tan(a).value, tan(a.value));
EXPECT_FLOAT_EQ(tan(a).derivative(0), 1.f + tan(a.value)*tan(a.value)); // tan'(x) = 1 + tan^2(x)
}
{
// asin/acos/atan
Dual<float, 1> c(0.3f, 0);
EXPECT_FLOAT_EQ(asin(c).value, asin(c.value));
EXPECT_FLOAT_EQ(asin(c).derivative(0), 1.f / sqrt(1.f - 0.3f * 0.3f)); // asin'(x) = 1/sqrt(1-x^2)
EXPECT_FLOAT_EQ(acos(c).value, acos(c.value));
EXPECT_FLOAT_EQ(acos(c).derivative(0), -1.f / sqrt(1.f - 0.3f * 0.3f)); // acos'(x) = -1/sqrt(1-x^2)
EXPECT_FLOAT_EQ(atan(c).value, atan(c.value));
EXPECT_FLOAT_EQ(atan(c).derivative(0), 1.f / (1.f + 0.3f * 0.3f)); // tan'(x) = 1 + x^2
}
{
// atan2
EXPECT_FLOAT_EQ(atan2(a, b).value, atan2(a.value, b.value));
EXPECT_TRUE(isEqualAll(atan2(a, Dual<float, 1>(b.value)), atan(a / b.value))); // atan2'(y, x) = atan'(y/x)
}
{
// partial derivatives
// function is f(x,y,z) = x^2 + 2xy + 3y^2 + z, we need with respect to d/dx and d/dy at the point (0.5, -0.8, 2)
using D = Dual<float, 2>;
// set our starting point, requesting partial derivatives of x and y in column 0 and 1
Vector3<D> dualPoint(D(0.5f, 0), D(-0.8f, 1), D(2.f));
Dual<float, 2> dualResult = testFunction(dualPoint);
// compare to a numerical derivative:
Vector<float, 3> floatPoint = collectReals(dualPoint);
float floatResult = testFunction(floatPoint);
float h = 0.0001f;
Vector<float, 3> floatPoint_plusDX = floatPoint;
floatPoint_plusDX(0) += h;
float floatResult_plusDX = testFunction(floatPoint_plusDX);
Vector<float, 3> floatPoint_plusDY = floatPoint;
floatPoint_plusDY(1) += h;
float floatResult_plusDY = testFunction(floatPoint_plusDY);
Vector2f numerical_derivative((floatResult_plusDX - floatResult) / h,
(floatResult_plusDY - floatResult) / h);
EXPECT_EQ(dualResult.value, floatResult);
EXPECT_TRUE(isEqual(dualResult.derivative, numerical_derivative, 1e-2f));
}
{
// jacobian
// get residual of x/y/z with partial derivatives of rotation
Vector3f direct_error;
Matrix<float, 3, 4> numerical_jacobian;
{
Vector3f positionState(5, 6, 7);
Vector3f velocityState(-1, 0, 1);
Quaternionf velocityOrientation(0.2f, -0.1f, 0, 1);
Vector3f positionMeasurement(4.5f, 6.2f, 7.9f);
float dt = 0.1f;
direct_error = positionError(positionState,
velocityState,
velocityOrientation,
positionMeasurement,
dt);
float h = 0.001f;
for (size_t i = 0; i < 4; i++) {
Quaternion<float> h4 = velocityOrientation;
h4(i) += h;
numerical_jacobian.col(i) = (positionError(positionState,
velocityState,
h4,
positionMeasurement,
dt)
- direct_error) / h;
}
}
Vector3f auto_error;
Matrix<float, 3, 4> auto_jacobian;
{
using D4 = Dual<float, 4>;
using Vector3d4 = Vector3<D4>;
Vector3d4 positionState(D4(5), D4(6), D4(7));
Vector3d4 velocityState(D4(-1), D4(0), D4(1));
// request partial derivatives of velocity orientation
// by setting these variables' derivatives in corresponding columns [0...3]
Quaternion<D4> velocityOrientation(D4(0.2f, 0), D4(-0.1f, 1), D4(0, 2), D4(1, 3));
Vector3d4 positionMeasurement(D4(4.5f), D4(6.2f), D4(7.9f));
D4 dt(0.1f);
Vector3d4 error = positionError(positionState,
velocityState,
velocityOrientation,
positionMeasurement,
dt);
auto_error = collectReals(error);
auto_jacobian = collectDerivatives(error);
}
EXPECT_EQ(direct_error, auto_error);
EXPECT_TRUE(isEqual(numerical_jacobian, auto_jacobian, 1e-3f));
}
}

311
src/lib/matrix/test/dual.cpp
Unescape View File

@ -1,311 +0,0 @@ @@ -1,311 +0,0 @@
#include "test_macros.hpp"
#include <matrix/math.hpp>
#include <iostream>
using namespace matrix;
template <typename Scalar, size_t N>
bool isEqualAll(Dual<Scalar, N> a, Dual<Scalar, N> b)
{
return isEqualF(a.value, b.value) && a.derivative == b.derivative;
}
template <typename T>
T testFunction(const Vector<T, 3> &point)
{
// function is f(x,y,z) = x^2 + 2xy + 3y^2 + z
return point(0) * point(0)
+ 2.f * point(0) * point(1)
+ 3.f * point(1) * point(1)
+ point(2);
}
template <typename Scalar>
Vector<Scalar, 3> positionError(const Vector<Scalar, 3> &positionState,
const Vector<Scalar, 3> &velocityStateBody,
const Quaternion<Scalar> &bodyOrientation,
const Vector<Scalar, 3> &positionMeasurement,
Scalar dt
)
{
return positionMeasurement - (positionState + bodyOrientation.rotateVector(velocityStateBody) * dt);
}
int main()
{
const Dual<float, 1> a(3, 0);
const Dual<float, 1> b(6, 0);
{
TEST(isEqualF(a.value, 3.f));
TEST(isEqualF(a.derivative(0), 1.f));
}
{
// addition
Dual<float, 1> c = a + b;
TEST(isEqualF(c.value, 9.f));
TEST(isEqualF(c.derivative(0), 2.f));
Dual<float, 1> d = +a;
TEST(isEqualAll(d, a));
d += b;
TEST(isEqualAll(d, c));
Dual<float, 1> e = a;
e += b.value;
TEST(isEqualF(e.value, c.value));
TEST(isEqual(e.derivative, a.derivative));
Dual<float, 1> f = b.value + a;
TEST(isEqualAll(f, e));
}
{
// subtraction
Dual<float, 1> c = b - a;
TEST(isEqualF(c.value, 3.f));
TEST(isEqualF(c.derivative(0), 0.f));
Dual<float, 1> d = b;
TEST(isEqualAll(d, b));
d -= a;
TEST(isEqualAll(d, c));
Dual<float, 1> e = b;
e -= a.value;
TEST(isEqualF(e.value, c.value));
TEST(isEqual(e.derivative, b.derivative));
Dual<float, 1> f = a.value - b;
TEST(isEqualAll(f, -e));
}
{
// multiplication
Dual<float, 1> c = a * b;
TEST(isEqualF(c.value, 18.f));
TEST(isEqualF(c.derivative(0), 9.f));
Dual<float, 1> d = a;
TEST(isEqualAll(d, a));
d *= b;
TEST(isEqualAll(d, c));
Dual<float, 1> e = a;
e *= b.value;
TEST(isEqualF(e.value, c.value));
TEST(isEqual(e.derivative, a.derivative * b.value));
Dual<float, 1> f = b.value * a;
TEST(isEqualAll(f, e));
}
{
// division
Dual<float, 1> c = b / a;
TEST(isEqualF(c.value, 2.f));
TEST(isEqualF(c.derivative(0), -1.f / 3.f));
Dual<float, 1> d = b;
TEST(isEqualAll(d, b));
d /= a;
TEST(isEqualAll(d, c));
Dual<float, 1> e = b;
e /= a.value;
TEST(isEqualF(e.value, c.value));
TEST(isEqual(e.derivative, b.derivative / a.value));
Dual<float, 1> f = a.value / b;
TEST(isEqualAll(f, 1.f / e));
}
{
Dual<float, 1> blank;
TEST(isEqualF(blank.value, 0.f));
TEST(isEqualF(blank.derivative(0), 0.f));
}
{
// sqrt
TEST(isEqualF(sqrt(a).value, sqrt(a.value)));
TEST(isEqualF(sqrt(a).derivative(0), 1.f / sqrt(12.f)));
}
{
// abs
TEST(isEqualAll(a, abs(-a)));
TEST(!isEqualAll(-a, abs(a)));
TEST(isEqualAll(-a, -abs(a)));
}
{
// ceil
Dual<float, 1> c(1.5, 0);
TEST(isEqualF(ceil(c).value, ceil(c.value)));
TEST(isEqualF(ceil(c).derivative(0), 0.f));
}
{
// floor
Dual<float, 1> c(1.5, 0);
TEST(isEqualF(floor(c).value, floor(c.value)));
TEST(isEqualF(floor(c).derivative(0), 0.f));
}
{
// fmod
TEST(isEqualF(fmod(a, 0.8f).value, fmod(a.value, 0.8f)));
TEST(isEqual(fmod(a, 0.8f).derivative, a.derivative));
}
{
// max/min
TEST(isEqualAll(b, max(a, b)));
TEST(isEqualAll(a, min(a, b)));
}
{
// isnan
TEST(!IsNan(a));
Dual<float, 1> c(sqrt(-1.f), 0);
TEST(IsNan(c));
}
{
// isfinite/isinf
TEST(IsFinite(a));
TEST(!IsInf(a));
Dual<float, 1> c(sqrt(-1.f), 0);
TEST(!IsFinite(c));
TEST(!IsInf(c));
Dual<float, 1> d(INFINITY, 0);
TEST(!IsFinite(d));
TEST(IsInf(d));
}
{
// sin/cos/tan
TEST(isEqualF(sin(a).value, sin(a.value)));
TEST(isEqualF(sin(a).derivative(0), cos(a.value))); // sin'(x) = cos(x)
TEST(isEqualF(cos(a).value, cos(a.value)));
TEST(isEqualF(cos(a).derivative(0), -sin(a.value))); // cos'(x) = -sin(x)
TEST(isEqualF(tan(a).value, tan(a.value)));
TEST(isEqualF(tan(a).derivative(0), 1.f + tan(a.value)*tan(a.value))); // tan'(x) = 1 + tan^2(x)
}
{
// asin/acos/atan
Dual<float, 1> c(0.3f, 0);
TEST(isEqualF(asin(c).value, asin(c.value)));
TEST(isEqualF(asin(c).derivative(0), 1.f / sqrt(1.f - 0.3f * 0.3f))); // asin'(x) = 1/sqrt(1-x^2)
TEST(isEqualF(acos(c).value, acos(c.value)));
TEST(isEqualF(acos(c).derivative(0), -1.f / sqrt(1.f - 0.3f * 0.3f))); // acos'(x) = -1/sqrt(1-x^2)
TEST(isEqualF(atan(c).value, atan(c.value)));
TEST(isEqualF(atan(c).derivative(0), 1.f / (1.f + 0.3f * 0.3f))); // tan'(x) = 1 + x^2
}
{
// atan2
TEST(isEqualF(atan2(a, b).value, atan2(a.value, b.value)));
TEST(isEqualAll(atan2(a, Dual<float, 1>(b.value)), atan(a / b.value))); // atan2'(y, x) = atan'(y/x)
}
{
// partial derivatives
// function is f(x,y,z) = x^2 + 2xy + 3y^2 + z, we need with respect to d/dx and d/dy at the point (0.5, -0.8, 2)
using D = Dual<float, 2>;
// set our starting point, requesting partial derivatives of x and y in column 0 and 1
Vector3<D> dualPoint(D(0.5f, 0), D(-0.8f, 1), D(2.f));
Dual<float, 2> dualResult = testFunction(dualPoint);
// compare to a numerical derivative:
Vector<float, 3> floatPoint = collectReals(dualPoint);
float floatResult = testFunction(floatPoint);
float h = 0.0001f;
Vector<float, 3> floatPoint_plusDX = floatPoint;
floatPoint_plusDX(0) += h;
float floatResult_plusDX = testFunction(floatPoint_plusDX);
Vector<float, 3> floatPoint_plusDY = floatPoint;
floatPoint_plusDY(1) += h;
float floatResult_plusDY = testFunction(floatPoint_plusDY);
Vector2f numerical_derivative((floatResult_plusDX - floatResult) / h,
(floatResult_plusDY - floatResult) / h);
TEST(isEqualF(dualResult.value, floatResult, 0.0f));
TEST(isEqual(dualResult.derivative, numerical_derivative, 1e-2f));
}
{
// jacobian
// get residual of x/y/z with partial derivatives of rotation
Vector3f direct_error;
Matrix<float, 3, 4> numerical_jacobian;
{
Vector3f positionState(5, 6, 7);
Vector3f velocityState(-1, 0, 1);
Quaternionf velocityOrientation(0.2f, -0.1f, 0, 1);
Vector3f positionMeasurement(4.5f, 6.2f, 7.9f);
float dt = 0.1f;
direct_error = positionError(positionState,
velocityState,
velocityOrientation,
positionMeasurement,
dt);
float h = 0.001f;
for (size_t i = 0; i < 4; i++) {
Quaternion<float> h4 = velocityOrientation;
h4(i) += h;
numerical_jacobian.col(i) = (positionError(positionState,
velocityState,
h4,
positionMeasurement,
dt)
- direct_error) / h;
}
}
Vector3f auto_error;
Matrix<float, 3, 4> auto_jacobian;
{
using D4 = Dual<float, 4>;
using Vector3d4 = Vector3<D4>;
Vector3d4 positionState(D4(5), D4(6), D4(7));
Vector3d4 velocityState(D4(-1), D4(0), D4(1));
// request partial derivatives of velocity orientation
// by setting these variables' derivatives in corresponding columns [0...3]
Quaternion<D4> velocityOrientation(D4(0.2f, 0), D4(-0.1f, 1), D4(0, 2), D4(1, 3));
Vector3d4 positionMeasurement(D4(4.5f), D4(6.2f), D4(7.9f));
D4 dt(0.1f);
Vector3d4 error = positionError(positionState,
velocityState,
velocityOrientation,
positionMeasurement,
dt);
auto_error = collectReals(error);
auto_jacobian = collectDerivatives(error);
}
TEST(isEqual(direct_error, auto_error, 0.0f));
TEST(isEqual(numerical_jacobian, auto_jacobian, 1e-3f));
}
return 0;
}
Write Preview
Loading…
Cancel
Save