function [quantity] = recoverFromW(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq, W, maxclique)
%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.

%   MATPOWER
%   Copyright (c) 2013-2016 by Power System Engineering Research Center (PSERC)
%   by Daniel Molzahn, PSERC U of Wisc, Madison
%
%   This file is part of MATPOWER.
%   Covered by the 3-clause BSD License (see LICENSE file for details).
%   See http://www.pserc.cornell.edu/matpower/ for more info.

[Ykvec] = mat2vec(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq);

Wmats = unique(Ykvec(:,1));
quantity = 0;
for m=1:length(Wmats)
    Ykvec_rows = find(Ykvec(:,1) == Wmats(m));
    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)})));
end
