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.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 % $Id: mat2vec.m 2272 2014-01-17 14:15:47Z ray $ 0045 % by Daniel Molzahn, PSERC U of Wisc, Madison 0046 % Copyright (c) 2013-2014 by Power System Engineering Research Center (PSERC) 0047 % 0048 % This file is part of MATPOWER. 0049 % See http://www.pserc.cornell.edu/matpower/ for more info. 0050 % 0051 % MATPOWER is free software: you can redistribute it and/or modify 0052 % it under the terms of the GNU General Public License as published 0053 % by the Free Software Foundation, either version 3 of the License, 0054 % or (at your option) any later version. 0055 % 0056 % MATPOWER is distributed in the hope that it will be useful, 0057 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0058 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0059 % GNU General Public License for more details. 0060 % 0061 % You should have received a copy of the GNU General Public License 0062 % along with MATPOWER. If not, see <http://www.gnu.org/licenses/>. 0063 % 0064 % Additional permission under GNU GPL version 3 section 7 0065 % 0066 % If you modify MATPOWER, or any covered work, to interface with 0067 % other modules (such as MATLAB code and MEX-files) available in a 0068 % MATLAB(R) or comparable environment containing parts covered 0069 % under other licensing terms, the licensors of MATPOWER grant 0070 % you additional permission to convey the resulting work. 0071 0072 %% Setup 0073 0074 nbus = size(sdpmat,1) / 2; 0075 [matrow, matcol, matval] = find(triu(sdpmat)); 0076 0077 % To speed up this function, rather than search throuh the entire Wref_dd, 0078 % Wref_qq, Wref_dq vectors every time we look up a nonzero entry of sdpmat, 0079 % filter out the entries that will actually be used in the rest of the 0080 % function. 0081 0082 dd_buses = unique([matrow(matrow <= nbus); matcol(matcol <= nbus)]); 0083 dd_rows = []; 0084 for i=1:length(dd_buses) 0085 dd_rows = [dd_rows; find(Wref_dd(:,2) == dd_buses(i) | Wref_dd(:,3) == dd_buses(i))]; 0086 end 0087 Wref_dd = Wref_dd(dd_rows,:); 0088 0089 qq_buses = unique([matrow(matrow > nbus); matcol(matcol > nbus)]) - nbus; 0090 qq_rows = []; 0091 for i=1:length(qq_buses) 0092 qq_rows = [qq_rows; find(Wref_qq(:,2) == qq_buses(i) | Wref_qq(:,3) == qq_buses(i))]; 0093 end 0094 Wref_qq = Wref_qq(qq_rows,:); 0095 0096 dq_buses = unique([matrow(matrow > nbus)-nbus; matcol(matcol > nbus)-nbus; matrow(matrow <= nbus); matcol(matcol <= nbus)]); 0097 dq_rows = []; 0098 for i=1:length(dq_buses) 0099 dq_rows = [dq_rows; find(Wref_dq(:,2) == dq_buses(i) | Wref_dq(:,3) == dq_buses(i))]; 0100 end 0101 Wref_dq = Wref_dq(dq_rows,:); 0102 0103 0104 %% Form sdpvec 0105 0106 sdpvec = zeros(2*length(matrow),4); 0107 idx = 0; 0108 for m = 1:length(matrow); 0109 idx = idx + 1; 0110 if matrow(m) <= nbus && matcol(m) <= nbus % In the dd section of the W matrix 0111 Wref_dd_row = find( (Wref_dd(:,2) == matrow(m) & Wref_dd(:,3) == matcol(m)) | ... 0112 (Wref_dd(:,3) == matrow(m) & Wref_dd(:,2) == matcol(m)), 1); 0113 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)]; 0114 idx = idx + 1; 0115 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)]; 0116 elseif matrow(m) > nbus && matcol(m) > nbus % In the qq section of the W matrix 0117 Wref_qq_row = find( (Wref_qq(:,2) == (matrow(m)-nbus) & Wref_qq(:,3) == (matcol(m))-nbus) | ... 0118 (Wref_qq(:,3) == (matrow(m)-nbus) & Wref_qq(:,2) == (matcol(m)-nbus)), 1); 0119 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)]; 0120 idx = idx + 1; 0121 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)]; 0122 elseif (matrow(m) > nbus && matcol(m) <= nbus) % In the dq section of the W matrix 0123 Wref_dq_row = find(Wref_dq(:,3) == (matrow(m)-nbus) & Wref_dq(:,2) == matcol(m), 1); 0124 0125 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)]; 0126 idx = idx + 1; 0127 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)]; 0128 elseif (matrow(m) <= nbus && matcol(m) > nbus) % In the dq section of the W matrix 0129 Wref_dq_row = find(Wref_dq(:,2) == matrow(m) & Wref_dq(:,3) == (matcol(m)-nbus), 1); 0130 0131 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)]; 0132 idx = idx + 1; 0133 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)]; 0134 else 0135 error('mat2vec: Invalid matrow or matcol for bus %i',k); 0136 end 0137 end 0138 0139 sdpvec = unique(sdpvec,'rows'); % Don't double count diagonals