Linear mapping

Linear combination mapping.

Collaboration diagram for Linear mapping:

Implements a linear combination mapping. The sim object takes two inputs \(u\), \(v\) and maps them to the output \(y\).

\(y=C_u u + C_v v\)

The dimensions of the output vector and the inputs \(u\) and \(u\) are derived from the sizes of the input matrices \(C_u\) and \(C_v\). The matrices are defined as a list of comma-separated row vectors, which in turn are separated by ";". The number of rows in these matrices must be equal, i.e. the dimension of the output.

The input matrices,

\(c_{u}=\begin{bmatrix}0 & 1 & 2\\0 & -2 & -3\end{bmatrix}\) and \(c_{v}=\begin{bmatrix}1 & 2\\3 & 2\end{bmatrix}\)

and the inputs,

\(u=\begin{bmatrix}3\\2\\1\end{bmatrix}\) and \(v=\begin{bmatrix}2\\2\end{bmatrix}\)

yields the following linear mapping:

\(y=\begin{bmatrix}0 & 1 & 2\\0 & -2 & -3\end{bmatrix} \cdot \begin{bmatrix}3\\2\\1\end{bmatrix} + \begin{bmatrix}1 & 2\\3 & 2\end{bmatrix}\ \cdot \begin{bmatrix}2\\2\end{bmatrix} = \begin{bmatrix}10\\3\end{bmatrix}\)

Example configuration excerpt

<Lib
  LibName    = "fhsim_base"
  SimObject  = "Math/LinearMapping"
  Name       = "LinearMap"
  Cu         = "0,1,2;0,-2,-3"
  Cv         = "1,2;3,2"
/>
...
...
<Connection
  LinearMap.InU = "3,2,1"
  LinearMap.InV = "2,2"
/>

Dimension of vectors and matrices are: \(y : M\), \(u: K\), \(v: K\), \(C_u : M \times K\), \(C_v : M \times L\).

Input Ports

Name	Width	Description
InU	K	The first input signal.
InV	L	The second input signal.

Output Ports

Name	Width	Description
Out	M	The output vector \(y\).
Out1 .. Out<M>	1	De-muxed output \(y_i\).

Configuration parameters

Name	Width	Description
Cu	MxK	Matrix \(C_u\).
Cv	MxL	Matrix \(C_v\).

Full example file

<Contents>
  <OBJECTS>
    <Lib
      LibName    = "fhsim_base"
      SimObject  = "Math/LinearMapping"
      Name       = "LinearMap"
      Cu         = "0,1,2;0,-2,-3"
      Cv         = "1,2;3,2"
    />
  </OBJECTS>
 
  <INTERCONNECTIONS>
    <Connection
        LinearMap.InU = "3,2,1"
        LinearMap.InV = "2,2"
    />
  </INTERCONNECTIONS>
 
  <INITIALIZATION>
    <InitialCondition
    />
  </INITIALIZATION>
 
  <INTEGRATION>
    <Engine
      IntegratorMethod           = "2"
      NumCores                   = "1"
      TOutput                    = "0, 5, 10"
      LogStates                  = "1"
      stepsize                   = "0"
      HMax                       = "0.002"
      HMin                       = "0.00000001"
      AbsTol                     = "1e-3"
      RelTol                     = "1e-3"
      UseRSSNormInsteadOfInfNorm = "0"
      FileOutput                 = "objects:all"
    />
  </INTEGRATION>
</Contents>

This SimObject is referred to as Math/LinearMapping