Hi,
I am having the following equation, wich I want to simplify to have less iterations in a python code:
the w's are each scalar values, R is a second order orthogonal tensor, dependent on the index r, and C is a fourth order tensor, dependent on the index q (It is symmetrical, but I think this information is not required for my question.) So basically it is a summation over several transformations on fourth order tensors. In Einstein summation convention this equation would look like this:
Note that I have set the dependencies in superscripts.
My question now is:
Is it reasonable to simplify the equation to this Version:
and finally in the tensor notation:
I already implemented it into the code and both equations give the same results. Just to be sure, I wanted some kind of mathematical justification, that this is possible.
Thanks in advance and kind regards,
Noah
I am having the following equation, wich I want to simplify to have less iterations in a python code:
the w's are each scalar values, R is a second order orthogonal tensor, dependent on the index r, and C is a fourth order tensor, dependent on the index q (It is symmetrical, but I think this information is not required for my question.) So basically it is a summation over several transformations on fourth order tensors. In Einstein summation convention this equation would look like this:
Note that I have set the dependencies in superscripts.
My question now is:
Is it reasonable to simplify the equation to this Version:
and finally in the tensor notation:
I already implemented it into the code and both equations give the same results. Just to be sure, I wanted some kind of mathematical justification, that this is possible.
Thanks in advance and kind regards,
Noah