FUNCTION SUMMARY: Subroutine EQRODAssignment is called in symbolic LU factorization, this subroutine is specifically used to identify the pointers of equivalent branches spanning the boundary buses. The equivalent branches are the fills in the factorization process of rows and columns of the external buses. [CindxU,ERPU,MinNod,Switch,ChainFlag] = EQRODAssignment(ERP,CIndx,CindxU,ERPU,MinNod,Switch,SelfRef,RowIndex,Chain,MinNod1) INPUT DATA: ERP - (N_node+1)*1 array containning the end of row pointer data CIndx - N*1 array containning the column index of the rows, N is the number of non-zeros elements in the input data CIndxU- N*1 array containning the column index of rows in the U matrix. The length N dedpends on the number of non-zero elements in previous rows on right of diagonal. ERPU - N_dim*1 array containing end of row pointer of all rows except the last row which doesn have any off diagonal element, N_dim is the dimension of the input matrix A in the original Ax = b problem Switch- N*1 array which is used to record the index off diagonal element in CIndxU and avoid keep the indices disjoint SelfRef-scalar, data value in the self refertial link also is the pointer point to next position in the self referential link RowIndex-scalar, the index of the row in processing Chain- 1*n array, if the MinNod got from this cycle (MinNod1) is different to the previous one and the previous one is not inf, then Chain(MinNod1) will record the value of Link(MinNod1) MinNod -scalar, store the minimum index of non-zero element on the right of the diagonal MinNod1 -scalar, MinNod value recorded in the last cycle OUTPUT DATA: ERPU - N_dim*1 array containing end of row pointer of all rows except the last row which doesn have any off diagonal element, N_dim is the dimension of the input matrix A in the original Ax = b problem CIndxU - N*1 array containing the column index of off diagonal element in each row in the U matrix. The length N depends on the number of native plus filled non-zero elements in the off diagonal position in U matrix. CIndxU is ordered. MinNod - scalar, store the minimum index of non-zero element on the right of the diagonal Switch- N*1 array which is used to record the index off diagonal element in CIndxU and avoid keep the indices disjoint ChainFlag- scalar, indicate if the MinNod is changed NOTE: in output data, ERPU, CIndxU, MinNod and Switch are updated in the subroutine. The output will return the updated arrays. NOTE: This subroutine is only used to generate the equivalent line indices.

- PartialSymLU FUNCTION SUMMARY:

0001 function [CindxU,ERPU,MinNod,Switch,ChainFlag] = EQRODAssignment(ERP,CIndx,CindxU,ERPU,MinNod,Switch,SelfRef,RowIndex,Chain,MinNod1) 0002 %FUNCTION SUMMARY: 0003 % Subroutine EQRODAssignment is called in symbolic LU factorization, this 0004 % subroutine is specifically used to identify the pointers of equivalent 0005 % branches spanning the boundary buses. The equivalent branches are the 0006 % fills in the factorization process of rows and columns of the external 0007 % buses. 0008 % 0009 % [CindxU,ERPU,MinNod,Switch,ChainFlag] = EQRODAssignment(ERP,CIndx,CindxU,ERPU,MinNod,Switch,SelfRef,RowIndex,Chain,MinNod1) 0010 % 0011 % INPUT DATA: 0012 % ERP - (N_node+1)*1 array containning the end of row pointer data 0013 % CIndx - N*1 array containning the column index of the rows, N is the 0014 % number of non-zeros elements in the input data 0015 % CIndxU- N*1 array containning the column index of rows in the U matrix. 0016 % The length N dedpends on the number of non-zero elements in 0017 % previous rows on right of diagonal. 0018 % ERPU - N_dim*1 array containing end of row pointer of all rows except 0019 % the last row which doesn have any off diagonal element, N_dim is 0020 % the dimension of the input matrix A in the original Ax = b 0021 % problem 0022 % Switch- N*1 array which is used to record the index off diagonal 0023 % element in CIndxU and avoid keep the indices disjoint 0024 % SelfRef-scalar, data value in the self refertial link also is the pointer 0025 % point to next position in the self referential link 0026 % RowIndex-scalar, the index of the row in processing 0027 % Chain- 1*n array, if the MinNod got from this cycle (MinNod1) is 0028 % different to the previous one and the previous one is not inf, then Chain(MinNod1) will 0029 % record the value of Link(MinNod1) 0030 % MinNod -scalar, store the minimum index of non-zero element on the 0031 % right of the diagonal 0032 % MinNod1 -scalar, MinNod value recorded in the last cycle 0033 % 0034 % OUTPUT DATA: 0035 % ERPU - N_dim*1 array containing end of row pointer of all rows except 0036 % the last row which doesn have any off diagonal element, N_dim is 0037 % the dimension of the input matrix A in the original Ax = b 0038 % problem 0039 % CIndxU - N*1 array containing the column index of off diagonal element 0040 % in each row in the U matrix. The length N depends on the 0041 % number of native plus filled non-zero elements in the off 0042 % diagonal position in U matrix. CIndxU is ordered. 0043 % MinNod - scalar, store the minimum index of non-zero element on the 0044 % right of the diagonal 0045 % Switch- N*1 array which is used to record the index off diagonal 0046 % element in CIndxU and avoid keep the indices disjoint 0047 % ChainFlag- scalar, indicate if the MinNod is changed 0048 % NOTE: in output data, ERPU, CIndxU, MinNod and Switch are updated in the 0049 % subroutine. The output will return the updated arrays. 0050 % 0051 % NOTE: This subroutine is only used to generate the equivalent line 0052 % indices. 0053 0054 % MATPOWER 0055 % Copyright (c) 2014-2016, Power Systems Engineering Research Center (PSERC) 0056 % by Yujia Zhu, PSERC ASU 0057 % 0058 % This file is part of MATPOWER. 0059 % Covered by the 3-clause BSD License (see LICENSE file for details). 0060 % See http://www.pserc.cornell.edu/matpower/ for more info. 0061 0062 %% to assign value to ROD position 0063 RowLen = ERP(SelfRef+1)-ERP(SelfRef); % number of non-zero element in current row 0064 RowColInd = CIndx(ERP(SelfRef)+1:ERP(SelfRef+1)); 0065 % Initiate the ERPU to be the end of last row 0066 if ERPU(RowIndex+1)==0 0067 ERPU(RowIndex+1)=ERPU(RowIndex); % In the loop every time read one ROD element ERPU(RowColInd)+1 0068 end 0069 ChainFlag=0; 0070 RowColInd2=RowColInd(RowColInd>RowIndex); 0071 for i = 1:RowLen % dealing with each non-zero native non-zero element first 0072 if RowColInd(i)>RowIndex&&(Switch(RowColInd(i))~=RowIndex) % check if current element is on ROD 0073 CindxU(ERPU(RowIndex+1)+1)=RowColInd(i); 0074 ERPU(RowIndex+1)=ERPU(RowIndex+1)+1; % increase 1 after reading one non-zero number; 0075 % Update the MinNod if MinNod greater than current column 0076 % index RowColInd(i) 0077 if MinNod>RowColInd(i) 0078 MinNod = RowColInd(i); % update the MinNod 0079 end 0080 % Update the Switch list 0081 Switch(RowColInd(i))=RowIndex; 0082 elseif Chain(RowColInd(i))~=0&&RowColInd(i)>RowIndex 0083 if MinNod>RowColInd(i) 0084 MinNod = RowColInd(i); % update the MinNod 0085 end 0086 end 0087 end 0088 if ~isempty(RowColInd2) 0089 if (min(RowColInd2)==MinNod1)&&(MinNod~=MinNod1) 0090 ChainFlag=1; 0091 MinNod=inf; 0092 end 0093 end 0094 end

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