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--- tools:matrix:start [2017/02/15 21:30] – graf
+++ tools:matrix:start [2022/04/20 13:29] (current) – [Logging Matrices] ursgraf
@@ Line 2: / Line 2: @@
 The blocks in the control system are connected among each other with the aid of signals. As described in [[eeros_architecture:control_system: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:
 <code cpp>
-  Vector<3, double> v;
+Vector<3, double> v;
-  v << 1.5, -2, 0;
 </code>
 The declaration could be simplified to
 <code cpp>
-  Vector3<> v;
+Vector3<> v;
-  v << 1.5, -2, 0;
 </code>
-as ''Vector3'' is a predefined type with three dimensions and the default element type is ''double''. A matrix of 3 times 3 with element type ''int'' could be defined as
+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
 <code cpp>
-  Matrix<3, 3, int> m;
+v = {1.5, -2, 0}
-  m << 1, 4, 7,
+v << 1.5, -2, 0; // or with input operator
-, 5, 8,
+Vector3 v{1,2,3}; // or directly upon declaration
-, 6, 9;
+</code>
+A matrix of 3 times 3 with element type ''int'' could be defined as
+<code cpp>
+Matrix<3, 3, int> m;
+m << 1, 2, 3,
+, 5, 6,
+, 8, 9;
+</code>
+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
+<code cpp>
+Matrix<3, 3, int> m{1, 4, 7, 2, 5, 8, 3, 6, 9};
+</code>
+===== Accessing Elements =====
+You can access rows, columns or single elements of matrices with the following methods:
+<code cpp>
+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]]
+</code>
+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
+<code cpp>
+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
+</code>
+===== Logging Matrices =====
+A matrix can be logged simply by writing
+<code cpp>
+log.info() << m;
+</code>
+With the 3 x 3 matrix from above we would get
+<code>
+-09-16 17:36:53:929    I:  [ [1 4 7]' [2 5 8]' [3 6 9]' ]
+</code>
+The matrix is plotted colon per colon. To give some more examples:
+<code cpp>
+Matrix<1,1> m1{1};
+Matrix<2,1> m2{1,2};
+Matrix<1,2> m3{1,2};
+</code>
+This matrices will be printed as
+<code>
+-09-16 17:37:18:122    I:  [1]'
+-09-16 17:37:18:122    I:  [1 2]'         // one colon with two rows
+-09-16 17:37:18:122    I:  [ [1]' [2]' ]' // one row with two colons
+</code>
+===== Matrix Operations =====
+Some examples show basic matrix operations.
+<code cpp>
+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]'
 </code>