# Vectors and Matrices

The blocks in the control system are connected among each other with the aid of signals. As described in Signals they carry a timestamp and a value. The value could be a simple type such as an integer or float. Quite often it will consist of a vector or a matrix. A three dimensional vector of type `double`

can be declared and initialized as follows:

Vector<3, double> v;

The declaration could be simplified to

Vector3<> v;

as `Vector3`

is a predefined type with three dimensions and the default element type is `double`

. A `Vector3`

is identical to the type `Matrix<3,1,double>`

. The vector could be initialized as follows

v = {1.5, -2, 0} v << 1.5, -2, 0; // or with input operator Vector3 v{1,2,3}; // or directly upon declaration

A matrix of 3 times 3 with element type `int`

could be defined as

Matrix<3, 3, int> m; m << 1, 2, 3, 4, 5, 6, 7, 8, 9;

The first three numbers will be filled into the first row. While the internal representation is simply a one dimensional vector, the matrix could be visualized as

col0 | col1 | col2 | |
---|---|---|---|

row0 | 1 | 2 | 3 |

row1 | 4 | 5 | 6 |

row2 | 7 | 8 | 9 |

When declaring and initializing a matrix, the values must be given colon per colon. The same matrix as given above would be initialized as follows

Matrix<3, 3, int> m{1, 4, 7, 2, 5, 8, 3, 6, 9};

## Accessing Elements

You can access rows, columns or single elements of matrices with the following methods:

m.get(0,0); // returns element, 1 m.get(1,0); // returns element, 4 m.getRow(1); // returns row, [4,5,6] m.getCol(0); // returns column, [1,4,7]' m.getSubMatrix<2,2>(0,1); // returns matrix [[2,5][3,6]]

Single elements, rows or columns can be written with the methods *set()*, *setRow()*, or *setCol()*.

The operators () and [] work as well as can be seen by the following example

m(3); // returns element or sets element with index 3 m[3]; // returns element or sets element with index 3 m(2,1); // returns element or sets element with index 7 m[2,1]; // does not work, as the [] operator cannot be defined for two parameters

## Logging Matrices

A matrix can be logged simply by writing

log.info() << m;

With the 3 x 3 matrix from above we would get

2021-09-16 17:36:53:929 I: [ [1 4 7]' [2 5 8]' [3 6 9]' ]

The matrix is plotted colon per colon. To give some more examples:

Matrix<1,1> m1{1}; Matrix<2,1> m2{1,2}; Matrix<1,2> m3{1,2};

This matrices will be printed as

2021-09-16 17:37:18:122 I: [1]' 2021-09-16 17:37:18:122 I: [1 2]' // one colon with two rows 2021-09-16 17:37:18:122 I: [ [1]' [2]' ]' // one row with two colons

## Matrix Operations

Some examples show basic matrix operations.

Vector2 v1{1,2}; Matrix<1,2> v2{3,4}; log.info() << v1 * v2; // will print [ [3 6]' [4 8]' ] log.info() << v2 * v1; // will print [11]' Matrix<2,2,double> m1{1,1.5,-1,2}; log.info() << v2 * m1; // will print [ [9]' [5]' ] log.info() << v1.transpose() * m1;// will print [ [4]' [3]' ] auto x = v2 * m1; Vector2 v4 = x.transpose(); log.info() << v4; // will print [9 5]'