matrix

A simple and efficient template based matrix library.

License

• (BSD) The Matrix library is licensed under a permissive 3-clause BSD license. Contributions must be made under the same license.

Features

• Compile time size checking.
• Euler angle (321), DCM, Quaternion conversion through constructors.
• High testing coverage.

Limitations

• No dynamically sized matrices.

Library Overview

• matrix/math.hpp : Provides matrix math routines.

  • Matrix (MxN)
  • Square Matrix (MxM, has inverse)
  • Vector (Mx1)
  • Scalar (1x1)
  • Quaternion
  • Dcm
  • Euler (Body 321)

• matrix/filter.hpp : Provides filtering routines.

  • kalman_correct

• matrix/integrate.hpp : Provides integration routines.

  • integrate_rk4 (Runge-Kutta 4th order)

Example

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);

	// 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