.Modelica_LinearSystems2.Math.Matrices.Internal.symMatMul

Information

This function is used to efficiently calculate the matrix X from equation

         T
X = A*B*A + C,

with B and C being symmetric matrices. They hold

B = Bu + Bl   and    C = Cu + Cl,

where Bu and Cu with

       T               T
Bu = Bl   and   Cu = Cl

are upper triangular matrices. Furthermore, the matrices are defined such that i.e.,

        | bij/2  for i = j
bu,ij = |
        | bij   else

and cu,ij respectively.

Finally, X is given by the sum of a upper triangular matrix and its transposes

               T                   T         T                 T              T     T        T
X = A*(Bu+Bl)*A + (Cu+Cl) =  A*Bu*A + A*Bl*A + (Cu+Cl) = A*Bu*A + Cu + (A*Bu*A + Cu) =  E + E

Since, X also has to be symmetric, only the upper triangle of X is computed by calculatiing the upper triangle of matrix E and adding the upper triangle of E'.

The calculation employs the BLAS functions dtrmm and dgemm.

Note, that only the upper triangle is calculated. The complete solution could be achieved by the command

X := symmetric(X)

Interface

function symMatMul
  extends Modelica.Icons.Function;
  import Modelica_LinearSystems2.Math.Matrices.LAPACK;
  input Real A[:, :];
  input Real B[size(A, 2), size(A, 2)];
  input Real C[size(A, 1), size(A, 1)];
  input Boolean add = true "Value is true if a==1, false if a==0";
  output Real M[size(A, 1), size(A, 1)];
end symMatMul;

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