functionsymMatMul_C

Calculate the upper triangle of A*B*A'+a*C with B and C symmetric

Extends from Modelica.Icons.Function (Icon for functions).

Information

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

           T
  X = A*B*A + C.

with B and C are 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 trinagle of E'.
The calculation employs the BLAS functions dtrmm and dgemm.

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

X := symmetric(X)

In contrast to function symMatMul this function is implemented in C-code

Inputs

Type	Name	Default	Description
Real[:,:]	A
Real[size(A, 2),size(A, 2)]	B
Real[size(A, 1),size(A, 1)]	C
Boolean	add	true	Value is true if a==1, false if a==0

Outputs

Type	Name	Default	Description
Real[size(A, 1),size(A, 1)]	M	C

Revisions

Date	Author	Comment
2010-05-31	Marcus Baur, DLR-RM	Realization