Shruti, MATPOWER does use “\” operator for the linear solves. However note that, internally, MATLAB does perform some sort of matrix reordering to reduce the fill-ins in the factored matrix. For instance, UMFPACK uses an approximate minimum degree reordering scheme by default.
Shri From: Shruti Rao <[email protected]<mailto:[email protected]>> Reply-To: MATPOWER discussion forum <[email protected]<mailto:[email protected]>> Date: Sunday, October 18, 2015 at 8:31 PM To: MATPOWER discussion forum <[email protected]<mailto:[email protected]>> Subject: Re: Question about sparsity-based implementation in MATPower Thank you Dr. Abhyakar, My main aim was to confirm that MATPower uses the inbuilt "\" to solve the matrix equations and not Tinney or some other form of reordering and then LU factorization followed by forward,backward substitutions. From your response I assume that it is true that MATpower uses "\" right? Thank you for your response. On Sun, Oct 18, 2015 at 6:27 PM, Abhyankar, Shrirang G. <[email protected]<mailto:[email protected]>> wrote: Hi Shruti, The direct linear solver used by MATLAB depends on the symmetry of the Jacobian matrix. For MATPOWER test cases that have symmetric Jacobians (due to inactive taps), a Cholesky factorization is used (LL^T = A). For cases that lead to non-symmetric Jacobian, MATLAB uses UMFPACK for performing the linear solve. Shri From: Shruti Rao <[email protected]<mailto:[email protected]>> Reply-To: MATPOWER discussion forum <[email protected]<mailto:[email protected]>> Date: Sunday, October 18, 2015 at 5:37 PM To: MATPOWER discussion forum <[email protected]<mailto:[email protected]>> Subject: Question about sparsity-based implementation in MATPower Greetings MATPower community, I had a question about the way sparsity-based techniques are used in the Newton-Raphson solver of the power flow algorithm in MATPower. I ran the code step-by-step and from my understanding, the way the sparsity of the Jacobian matrix is exploited is that it is created as a MATLAB "sparse" matrix wherein only the non-zeros are stored with the respective matrix positions and then the MATLAB operator "\" is invoked while calculating dx = -(J \ F); where J is the Jacobian and F is the vector of mismatches. MATLAB "\" by default exploits the sparsity of the matrix by using a LU solver. The kind of solver "\" uses actually depends on the matrix structure if it is diagonal/tridiagonal/banded and so on (Flowchart obtained from Mathworks website attached in the email). I assume based on the typical structure of the Jacobian that an LU solver is most likely to be chosen. Is my understanding correct or am I missing something out? Thank you for your time and effort. -- Best Regards, Shruti Dwarkanath Rao Graduate Research Assistant School of Electrical, Computer and Energy Engineering Arizona State University Tempe, AZ, 85281 650 996 0116<tel:650%20996%200116> -- Best Regards, Shruti Dwarkanath Rao Graduate Research Assistant School of Electrical, Computer and Energy Engineering Arizona State University Tempe, AZ, 85281 650 996 0116
