TinneyOne

 Subroutine TinneyOne applied Tinney 1 optimal ordering to the input data
 in order to reduce the fills generated in the partial LU factorization
 process. 

   [PivOrd,PivInd] = TinneyOne(ERP,PivInd,PivOrd,ExBus)

 INPUT DATA:
   ERP: 1*n array, includes end of row pointer of input addmittance matrix
   PivInd: 1*n array, includes bus ordering after pivotting
   PivOrd: 1*n array, includes bus indices after pivotting
   ExBus: 1*n array, includes bus indices of external buses

 OUTPUT DATA:
   PivInd: 1*n array, includes bus ordering after pivotting by Tinney 1
   ordering
   PivOrd: 1*n array, includes bus indices after pivotting by Tinney 1
   ordering

 NOTE:
   This subroutine does not pivot any data but output an array includes
   ordering of buses. Pivoting will be done in the subroutine PivotData.

0001 function [PivOrd,PivInd] = TinneyOne(ERP,PivInd,PivOrd,ExBus)
0002 % Subroutine TinneyOne applied Tinney 1 optimal ordering to the input data
0003 % in order to reduce the fills generated in the partial LU factorization
0004 % process.
0005 %
0006 %   [PivOrd,PivInd] = TinneyOne(ERP,PivInd,PivOrd,ExBus)
0007 %
0008 % INPUT DATA:
0009 %   ERP: 1*n array, includes end of row pointer of input addmittance matrix
0010 %   PivInd: 1*n array, includes bus ordering after pivotting
0011 %   PivOrd: 1*n array, includes bus indices after pivotting
0012 %   ExBus: 1*n array, includes bus indices of external buses
0013 %
0014 % OUTPUT DATA:
0015 %   PivInd: 1*n array, includes bus ordering after pivotting by Tinney 1
0016 %   ordering
0017 %   PivOrd: 1*n array, includes bus indices after pivotting by Tinney 1
0018 %   ordering
0019 %
0020 % NOTE:
0021 %   This subroutine does not pivot any data but output an array includes
0022 %   ordering of buses. Pivoting will be done in the subroutine PivotData.
0023 
0024 %   MATPOWER
0025 %   Copyright (c) 2014-2016, Power Systems Engineering Research Center (PSERC)
0026 %   by Yujia Zhu, PSERC ASU
0027 %
0028 %   This file is part of MATPOWER/mx-reduction.
0029 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0030 %   See https://github.com/MATPOWER/mx-reduction/ for more info.
0031 
0032 %% Extract the external bus part
0033 ExLen = length(ExBus);
0034 ERP_E = ERP(1:ExLen+1);
0035 %%
0036 RowLen = ERP_E;
0037 for i = 1:ExLen
0038     RowLen(i)=ERP_E(i+1)-ERP_E(i); % calculate the number of non-zero entry in each row
0039 end
0040 RowLen(end)=[];
0041 [RowLen,RowOrd] = sort(RowLen);
0042 for i =1:ExLen
0043     RowOrdO(RowOrd(i))=i;
0044 end
0045 PivInd(1:ExLen)=PivInd(RowOrdO);
0046 for i = 1:ExLen
0047     PivOrd(PivInd(i))=i;
0048 end
0049 
0050 end