ARCHIVED - PX4-Matrix is now maintained within PX4-Autopilot. https://github.com/PX4/PX4-Autopilot/tree/4a3d64f1d76856d22323d1061ac6e560efda0a05/src/lib/matrix
A simple and efficient template based matrix library.
- (BSD) The Matrix library is licensed under a permissive 3-clause BSD license. Contributions must be made under the same license.
- Compile time size checking.
- Euler angle (321), DCM, Quaternion conversion through constructors.
- High testing coverage.
- No dynamically sized matrices.
-
matrix/math.hpp : Provides matrix math routines.
- Matrix (MxN)
- Square Matrix (MxM, has inverse)
- Vector (Mx1)
- Scalar (1x1)
- Quaternion
- Dcm
- Euler (Body 321)
- Axis Angle
-
matrix/filter.hpp : Provides filtering routines.
- kalman_correct
-
matrix/integrate.hpp : Provides integration routines.
- integrate_rk4 (Runge-Kutta 4th order)
The tests can be executed as following:
mkdir build
cd build
cmake -DTESTING=ON ..
make check
The format can be checked as following:
mkdir build
cd build
cmake -DFORMAT=ON ..
make check_format
See the test directory for detailed examples. Some simple examples are included below:
// define an euler angle (Body 3(yaw)-2(pitch)-1(roll) rotation)
float roll = 0.1f;
float pitch = 0.2f;
float yaw = 0.3f;
Eulerf euler(roll, pitch, yaw);
// convert to quaternion from euler
Quatf q_nb(euler);
// convert to DCM from quaternion
Dcmf dcm(q_nb);
// you can assign a rotation instance that already exist to another rotation instance, e.g.
dcm = euler;
// you can also directly create a DCM instance from euler angles like this
dcm = Eulerf(roll, pitch, yaw);
// create an axis angle representation from euler angles
AxisAngle<float> axis_angle = euler;
// use axis angle to initialize a DCM
Dcmf dcm2(AxisAngle(1, 2, 3));
// use axis angle with axis/angle separated to init DCM
Dcmf dcm3(AxisAngle(Vector3f(1, 0, 0), 0.2));
// do some kalman filtering
const size_t n_x = 5;
const size_t n_y = 3;
// define matrix sizes
SquareMatrix<float, n_x> P;
Vector<float, n_x> x;
Vector<float, n_y> y;
Matrix<float, n_y, n_x> C;
SquareMatrix<float, n_y> R;
SquareMatrix<float, n_y> S;
Matrix<float, n_x, n_y> K;
// define measurement matrix
C = zero<float, n_y, n_x>(); // or C.setZero()
C(0,0) = 1;
C(1,1) = 2;
C(2,2) = 3;
// set x to zero
x = zero<float, n_x, 1>(); // or x.setZero()
// set P to identity * 0.01
P = eye<float, n_x>()*0.01;
// set R to identity * 0.1
R = eye<float, n_y>()*0.1;
// measurement
y(0) = 1;
y(1) = 2;
y(2) = 3;
// innovation
r = y - C*x;
// innovations variance
S = C*P*C.T() + R;
// Kalman gain matrix
K = P*C.T()*S.I();
// S.I() is the inverse, defined for SquareMatrix
// correction
x += K*r;
// slicing
float data[9] = {0, 2, 3,
4, 5, 6,
7, 8, 10
};
SquareMatrix<float, 3> A(data);
// Slice a 3,3 matrix starting at row 1, col 0,
// with size 2 x 3, warning, no size checking
Matrix<float, 2, 3> B(A.slice<2, 3>(1, 0));
// this results in:
// 4, 5, 6
// 7, 8, 10
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