Home > matpower6.0 > extras > sdp_pf > mat2vec.m

mat2vec

PURPOSE ^

MAT2VEC Converts a SDP matrix into a a list form used in the matrix

SYNOPSIS ^

function [sdpvec]=mat2vec(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq)

DESCRIPTION ^

MAT2VEC Converts a SDP matrix into a a list form used in the matrix
completion decomposition.
   [SDPVEC] = MAT2VEC(SDPMAT, WREF_DD, WREF_QQ, WREF_DQ, MATIDX_DD,MATIDX_QQ, MATIDX_DQ)

   Used in the formation of the matrix completion decomposition for the
   semidefinite programming relaxation of the optimal power flow. Converts
   a 2*nbus by 2*nbus symmetric matrix sdpmat into a list form. For each
   nonzero element of sdpmat, the list form in sdpvec gives the
   appropriate matrix, the location in the matrix, and the value for that
   element.

   Inputs:
       SDPMAT : Symmetric 2*nbus by 2*nbus matrix (intended to be Yk, Yk_,
           Mk, Ylineft, Ylinetf, Y_lineft, Y_linetf from the semidefinite
           programming relaxation).
       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.

   Outputs:
       SDPVEC : A matrix with four columns, with a row for each nonzero
           element of sdpmat. The first column gives the index of the
           decomposed matrix. The second and third columns give the row
           and column, respectively, of the appropriate entry of the
           decomposed matrix. The fourth column is the value of the entry.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [sdpvec]=mat2vec(sdpmat, Wref_dd, Wref_qq, Wref_dq, matidx_dd, matidx_qq, matidx_dq)
0002 %MAT2VEC Converts a SDP matrix into a a list form used in the matrix
0003 %completion decomposition.
0004 %   [SDPVEC] = MAT2VEC(SDPMAT, WREF_DD, WREF_QQ, WREF_DQ, MATIDX_DD,MATIDX_QQ, MATIDX_DQ)
0005 %
0006 %   Used in the formation of the matrix completion decomposition for the
0007 %   semidefinite programming relaxation of the optimal power flow. Converts
0008 %   a 2*nbus by 2*nbus symmetric matrix sdpmat into a list form. For each
0009 %   nonzero element of sdpmat, the list form in sdpvec gives the
0010 %   appropriate matrix, the location in the matrix, and the value for that
0011 %   element.
0012 %
0013 %   Inputs:
0014 %       SDPMAT : Symmetric 2*nbus by 2*nbus matrix (intended to be Yk, Yk_,
0015 %           Mk, Ylineft, Ylinetf, Y_lineft, Y_linetf from the semidefinite
0016 %           programming relaxation).
0017 %       WREF_DD : Matrix with three columns. The first column is a
0018 %           numbering 1:size(Wref_dd,1). The second and third columns
0019 %           indicate the row and column indices of the elements of the
0020 %           matrix sdpmat, with the row of Wref_dd corresponding to the
0021 %           index of matidx_dd. That is, the element of sdpmat located in
0022 %           row Wref_dd(i,1), column Wref_dd(i,2) corresponds to
0023 %           matidx_dd(i).
0024 %       WREF_QQ : Similar to Wref_dd, except for the qq entries of sdpmat.
0025 %       WREF_DQ : Similar to Wref_dd, except for the dq entries of sdpmat.
0026 %       MATIDX_DD : Matrix with three columns. Row i of matidx_dd indicates
0027 %           the location of sdpmat(Wref_dd(i,1), Wref_dd(i,2)). The first
0028 %           column indicates the index of the corresponding matrix. The
0029 %           second and third columns indicate the row and column,
0030 %           respectively, of the corresponding matrix.
0031 %       MATIDX_QQ : Similar to matidx_dd, except corresponding to the qq
0032 %           entries of sdpmat.
0033 %       MATIDX_DQ : Similar to matidx_dd, except corresponding to the dq
0034 %           entries of sdpmat.
0035 %
0036 %   Outputs:
0037 %       SDPVEC : A matrix with four columns, with a row for each nonzero
0038 %           element of sdpmat. The first column gives the index of the
0039 %           decomposed matrix. The second and third columns give the row
0040 %           and column, respectively, of the appropriate entry of the
0041 %           decomposed matrix. The fourth column is the value of the entry.
0042 
0043 %   MATPOWER
0044 %   Copyright (c) 2013-2016, Power Systems Engineering Research Center (PSERC)
0045 %   by Daniel Molzahn, PSERC U of Wisc, Madison
0046 %
0047 %   This file is part of MATPOWER.
0048 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0049 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0050 
0051 %% Setup
0052 
0053 nbus = size(sdpmat,1) / 2;
0054 [matrow, matcol, matval] = find(triu(sdpmat));
0055 
0056 % To speed up this function, rather than search throuh the entire Wref_dd,
0057 % Wref_qq, Wref_dq vectors every time we look up a nonzero entry of sdpmat,
0058 % filter out the entries that will actually be used in the rest of the
0059 % function.
0060 
0061 dd_buses = unique([matrow(matrow <= nbus); matcol(matcol <= nbus)]);
0062 dd_rows = [];
0063 for i=1:length(dd_buses)
0064     dd_rows = [dd_rows; find(Wref_dd(:,2) == dd_buses(i) | Wref_dd(:,3) == dd_buses(i))];
0065 end
0066 Wref_dd = Wref_dd(dd_rows,:);
0067 
0068 qq_buses = unique([matrow(matrow > nbus); matcol(matcol > nbus)]) - nbus;
0069 qq_rows = [];
0070 for i=1:length(qq_buses)
0071     qq_rows = [qq_rows; find(Wref_qq(:,2) == qq_buses(i) | Wref_qq(:,3) == qq_buses(i))];
0072 end
0073 Wref_qq = Wref_qq(qq_rows,:);
0074 
0075 dq_buses = unique([matrow(matrow > nbus)-nbus; matcol(matcol > nbus)-nbus; matrow(matrow <= nbus); matcol(matcol <= nbus)]);
0076 dq_rows = [];
0077 for i=1:length(dq_buses)
0078     dq_rows = [dq_rows; find(Wref_dq(:,2) == dq_buses(i) | Wref_dq(:,3) == dq_buses(i))];
0079 end
0080 Wref_dq = Wref_dq(dq_rows,:);
0081 
0082 
0083 %% Form sdpvec
0084 
0085 sdpvec = zeros(2*length(matrow),4);
0086 idx = 0;
0087 for m = 1:length(matrow);
0088     idx = idx + 1;
0089     if matrow(m) <= nbus && matcol(m) <= nbus % In the dd section of the W matrix
0090         Wref_dd_row = find( (Wref_dd(:,2) == matrow(m) & Wref_dd(:,3) == matcol(m)) | ... 
0091                             (Wref_dd(:,3) == matrow(m) & Wref_dd(:,2) == matcol(m)), 1);
0092         sdpvec(idx,:) = [matidx_dd(Wref_dd(Wref_dd_row,1),1) matidx_dd(Wref_dd(Wref_dd_row,1),2) matidx_dd(Wref_dd(Wref_dd_row,1),3) matval(m)];
0093         idx = idx + 1;
0094         sdpvec(idx,:) = [matidx_dd(Wref_dd(Wref_dd_row,1),1) matidx_dd(Wref_dd(Wref_dd_row,1),3) matidx_dd(Wref_dd(Wref_dd_row,1),2) matval(m)];
0095     elseif matrow(m) > nbus && matcol(m) > nbus % In the qq section of the W matrix
0096         Wref_qq_row = find( (Wref_qq(:,2) == (matrow(m)-nbus) & Wref_qq(:,3) == (matcol(m))-nbus) | ...
0097                             (Wref_qq(:,3) == (matrow(m)-nbus) & Wref_qq(:,2) == (matcol(m)-nbus)), 1);
0098         sdpvec(idx,:) = [matidx_qq(Wref_qq(Wref_qq_row,1),1) matidx_qq(Wref_qq(Wref_qq_row,1),2) matidx_qq(Wref_qq(Wref_qq_row,1),3) matval(m)];
0099         idx = idx + 1;
0100         sdpvec(idx,:) = [matidx_qq(Wref_qq(Wref_qq_row,1),1) matidx_qq(Wref_qq(Wref_qq_row,1),3) matidx_qq(Wref_qq(Wref_qq_row,1),2) matval(m)];
0101     elseif (matrow(m) > nbus && matcol(m) <= nbus) % In the dq section of the W matrix
0102         Wref_dq_row = find(Wref_dq(:,3) == (matrow(m)-nbus) & Wref_dq(:,2) == matcol(m), 1);
0103         
0104         sdpvec(idx,:) = [matidx_dq(Wref_dq(Wref_dq_row,1),1) matidx_dq(Wref_dq(Wref_dq_row,1),2) matidx_dq(Wref_dq(Wref_dq_row,1),3) matval(m)];
0105         idx = idx + 1;
0106         sdpvec(idx,:) = [matidx_dq(Wref_dq(Wref_dq_row,1),1) matidx_dq(Wref_dq(Wref_dq_row,1),3) matidx_dq(Wref_dq(Wref_dq_row,1),2) matval(m)];
0107     elseif (matrow(m) <= nbus && matcol(m) > nbus) % In the dq section of the W matrix
0108         Wref_dq_row = find(Wref_dq(:,2) == matrow(m) & Wref_dq(:,3) == (matcol(m)-nbus), 1);
0109         
0110         sdpvec(idx,:) = [matidx_dq(Wref_dq(Wref_dq_row,1),1) matidx_dq(Wref_dq(Wref_dq_row,1),2) matidx_dq(Wref_dq(Wref_dq_row,1),3) matval(m)];
0111         idx = idx + 1;
0112         sdpvec(idx,:) = [matidx_dq(Wref_dq(Wref_dq_row,1),1) matidx_dq(Wref_dq(Wref_dq_row,1),3) matidx_dq(Wref_dq(Wref_dq_row,1),2) matval(m)];
0113     else
0114         error('mat2vec: Invalid matrow or matcol for bus %i',k);
0115     end
0116 end
0117 
0118 sdpvec = unique(sdpvec,'rows'); % Don't double count diagonals

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