recoverFromW

RECOVERFROMW Carries out a trace operation on the decomposed matrices
   [QUANTITY] = RECOVERFROMW(SDPMAT, WREF_DD, WREF_QQ, WREF_DQ, MATIDX_DD, MATIDX_QQ, MATIDX_DQ, W, SDPVAR, MAXCLIQUE)

   Calculates trace(sdpmat*W) for the decomposed matrices.

   Inputs:
       SDPMAT : A 2*nbus by 2*nbus matrix.
       WREF_DD : Matrix with three columns. The first column is a 
           numbering 1:size(Wref_dd,1). The second and third columns 
           indicate the row and column indices of the elements of the 
           matrix sdpmat, with the row of Wref_dd corresponding to the 
           index of matidx_dd. That is, the element of sdpmat located in 
           row Wref_dd(i,1), column Wref_dd(i,2) corresponds to 
           matidx_dd(i).
       WREF_QQ : Similar to Wref_dd, except for the qq entries of sdpmat.
       WREF_DQ : Similar to Wref_dd, except for the dq entries of sdpmat.
       MATIDX_DD : Matrix with three columns. Row i of matidx_dd indicates
           the location of sdpmat(Wref_dd(i,1), Wref_dd(i,2)). The first
           column indicates the index of the corresponding matrix. The
           second and third columns indicate the row and column,
           respectively, of the corresponding matrix. 
       MATIDX_QQ : Similar to matidx_dd, except corresponding to the qq 
           entries of sdpmat.
       MATIDX_DQ : Similar to matidx_dd, except corresponding to the dq 
           entries of sdpmat.
       W : Cell array of decomposed W matrices corresponding to maxclique.
       SDPVAR : SDP variable (sdpvar) that will be multiplied by sdpmat
           and added to the decomposed A matrices.
       MAXCLIQUE : Cell array of the buses in each maximal clique.

   Outputs:
       QUANTITY : trace(sdpmat*W), the equivalent to a trace operation on
           the 2*nbus by 2*nbus W matrix using the decomposed matrices.

0001 function [quantity] = recoverFromW(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq, W, maxclique)
0002 %RECOVERFROMW Carries out a trace operation on the decomposed matrices
0003 %   [QUANTITY] = RECOVERFROMW(SDPMAT, WREF_DD, WREF_QQ, WREF_DQ, MATIDX_DD, MATIDX_QQ, MATIDX_DQ, W, SDPVAR, MAXCLIQUE)
0004 %
0005 %   Calculates trace(sdpmat*W) for the decomposed matrices.
0006 %
0007 %   Inputs:
0008 %       SDPMAT : A 2*nbus by 2*nbus matrix.
0009 %       WREF_DD : Matrix with three columns. The first column is a
0010 %           numbering 1:size(Wref_dd,1). The second and third columns
0011 %           indicate the row and column indices of the elements of the
0012 %           matrix sdpmat, with the row of Wref_dd corresponding to the
0013 %           index of matidx_dd. That is, the element of sdpmat located in
0014 %           row Wref_dd(i,1), column Wref_dd(i,2) corresponds to
0015 %           matidx_dd(i).
0016 %       WREF_QQ : Similar to Wref_dd, except for the qq entries of sdpmat.
0017 %       WREF_DQ : Similar to Wref_dd, except for the dq entries of sdpmat.
0018 %       MATIDX_DD : Matrix with three columns. Row i of matidx_dd indicates
0019 %           the location of sdpmat(Wref_dd(i,1), Wref_dd(i,2)). The first
0020 %           column indicates the index of the corresponding matrix. The
0021 %           second and third columns indicate the row and column,
0022 %           respectively, of the corresponding matrix.
0023 %       MATIDX_QQ : Similar to matidx_dd, except corresponding to the qq
0024 %           entries of sdpmat.
0025 %       MATIDX_DQ : Similar to matidx_dd, except corresponding to the dq
0026 %           entries of sdpmat.
0027 %       W : Cell array of decomposed W matrices corresponding to maxclique.
0028 %       SDPVAR : SDP variable (sdpvar) that will be multiplied by sdpmat
0029 %           and added to the decomposed A matrices.
0030 %       MAXCLIQUE : Cell array of the buses in each maximal clique.
0031 %
0032 %   Outputs:
0033 %       QUANTITY : trace(sdpmat*W), the equivalent to a trace operation on
0034 %           the 2*nbus by 2*nbus W matrix using the decomposed matrices.
0035 
0036 %   MATPOWER
0037 %   Copyright (c) 2013-2019, Power Systems Engineering Research Center (PSERC)
0038 %   by Daniel Molzahn, PSERC U of Wisc, Madison
0039 %
0040 %   This file is part of MATPOWER/mx-sdp_pf.
0041 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0042 %   See https://github.com/MATPOWER/mx-sdp_pf/ for more info.
0043 
0044 [Ykvec] = mat2vec(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq);
0045 
0046 Wmats = unique(Ykvec(:,1));
0047 quantity = 0;
0048 for m=1:length(Wmats)
0049     Ykvec_rows = find(Ykvec(:,1) == Wmats(m));
0050     quantity = quantity + trace(W{Wmats(m)} * sparse(Ykvec(Ykvec_rows,2),Ykvec(Ykvec_rows,3),Ykvec(Ykvec_rows,4),2*length(maxclique{Wmats(m)}),2*length(maxclique{Wmats(m)})));
0051 end