.. _sec-manual-varstatic: ***************** Vectors, matrices ***************** Basic structures such as vectors :math:\mathbf{x} or matrices :math:\mathbf{X} are proposed in order to handle constants, measurements or parameters. They are not aimed at representing temporal evolutions contrary to trajectories, presented :ref:in the next section . Note also that they are not involved during the process of constraint propagation, that only relies on domains presented in the next part. .. contents:: .. note:: .. Figure:: ../../img/logo_ibex.jpg :align: right .. Figure:: ../../img/logo_pyibex.jpg :align: right These static variables come from the IBEX library _. They are briefly presented here for the sake of consistency. For more information, please refer to the IBEX documentation _ for C++ use or to the pyIbex manual _ for Python usage. .. _sec-manual-varstatic-vectors: Vectors ------- Vectors of reals, denoted in bold in this manual, are represented by the class Vector. Their use is intuitive: .. tabs:: .. code-tab:: py x1 = [0,1,3] # creates the vector x1=(0;1;3) x2 = [1]*3 # creates the vector x2=(1;1;1) x3 = x1 # creates a copy of x1 .. code-tab:: c++ Vector x1({0,1,3}); // creates the vector x1=(0;1;3) Vector x2(3,1); // creates the vector x2=(1;1;1) Vector x3(x1); // creates a copy of x1 Vector operations are available to handle Vector objects: .. tabs:: .. code-tab:: py # Use default types of Python, or Numpy .. code-tab:: c++ int n = x1.size(); // vector dimension (number of components): 3 x1.resize(5); // updates x1 to (0;1;3;0;0) x3.resize(2); // updates x3 to (0;1) Vector x4 = x1.subvector(2,3); // creates x4=(3;0) x1.put(x2,2); // updates x1 to (0;1;1;4;1) // Access to the ith component: x2[1] = 4; // updates x2 to (1;4;1) Note that these operations are also available for other vector types: :ref:matrices , :ref:boxes , :ref:vectors of trajectories , and :ref:vectors of tubes . Basic arithmetic operations are applicable on vectors such as binary operators: :math:+,-,\cdot,/ .. tabs:: .. code-tab:: py # Use default types of Python, or Numpy .. code-tab:: c++ x1 = 4*x1; // scalar multiplication of a vector x1 *= 4; // same operation (multiplication and assignment) Vector x5 = x3*x4; // dot product .. _sec-manual-varstatic-matrices: Matrices -------- Matrix objects are exactly designed the same way as vectors. Here are listed different ways to build a matrix: .. tabs:: .. code-tab:: py # Use default types of Python, or Numpy .. code-tab:: c++ Matrix m1({{1,2,3},{4,5,6}}); // creates a 2×3 matrix cout << m1 << endl; // Outputs: // ((1 ; 2 ; 3) // (4 ; 5 ; 6)) cout << m1.transpose() << endl; // Outputs: // ((1 ; 4) // (2 ; 5) // (3 ; 6)) Matrix m2 = ones(2,2); // a 2×2 matrix of ones Matrix m3 = eye(3); // a 3×3 identity matrix Other arithmetic operations apply on matrices in the same manner as for vectors.