// For steps 25-33 in stage one
private static Matrix NAPTStageOneHelper2(Matrix CAP, Matrix SRG, Matrix FA1, Matrix UA11, Matrix REL, Vector AOC, int stage, int networkid)
{
// 25. Generate a Non-Aggression matrix NAG
Matrix NAG = new Matrix(FA1.Rows, FA1.Cols);
for (int i = 0; i < FA1.Rows; i++)
{
for (int j = 0; j < FA1.Cols; j++)
{
if (FA1[i, j] == 2)
NAG[i, j] = 1;
else
NAG[i, j] = 0;
}
}
Vector NAG_vec = new Vector(NAG.Rows);
for (int i = 0; i < NAG_vec.Size; i++)
{
NAG_vec[i] = NAG.GetRowSum(i);
}
// 26. Generate an Allies Attractiveness matrix AAT = DP1 * UA11
// Calculate the sum row entry
Matrix AAT = new Matrix(UA11.Rows, UA11.Cols);
/*
for (int i = 0; i < DP1.Rows; i++)
for (int j = 0; j < UA11.Cols; j++)
AAT[i, j] = DP1[i, j] * UA11[i, j];
*/
//FA1.Binarize();
for (int i = 0; i < FA1.Rows; i++)
for (int j = 0; j < FA1.Cols; j++)
if (FA1[i, j] != 1)
FA1[i, j] = 0;
// Generate the vector DEF for Output Matrix
Vector DEF = new Vector(FA1.Rows);
for (int i = 0; i < DEF.Size; i++)
{
DEF[i] = FA1.GetRowSum(i);
}
// follows the excel instructions
for (int i = 0; i < FA1.Rows; i++)
{
for (int j = 0; j < UA11.Cols; j++)
{
//AAT[i, j] = (FA1[i, j] == 1 ? 1 : 0) * UA11[i, j];
AAT[i, j] = FA1[i, j] * UA11[i, j];
}
}
// 27. Generate the attractiveness coefficient atc for each row
/*
double[] atc = new double[AAT.Rows];
for (int i = 0; i < AAT.Rows; i++)
atc[i] = AAT.GetRowSum(i) * DP1.GetRowSum(i);
*/
// follow excel instructions
//double[] ATC = new double[AAT.Rows];
Vector ATC = new Vector(AAT.Rows);
for (int i = 0; i < AAT.Rows; i++)
{
if (FA1.GetRowSum(i) > 0)
ATC[i] = AAT.GetRowSum(i) / FA1.GetRowSum(i);
else
ATC[i] = 0;
}
// 28. Generate an Allies Reliability matrix ARE = BFA1 * REL (where BAF1 is the binarized FA1 matrix)
//FA1.Binarize();
Matrix ARE = new Matrix(FA1.Rows, REL.Cols);
if (stage == 1)
{
for (int i = 0; i < FA1.Rows; i++)
for (int j = 0; j < REL.Cols; j++)
ARE[i, j] = FA1[i, j] * REL[i, i]; // may need to be changed to [j, j]
}
else
{
for (int i = 0; i < FA1.Rows; i++)
for (int j = 0; j < REL.Cols; j++)
ARE[i, j] = NAG[i, j] * REL[j, j];
}
Vector REC = new Vector(ARE.Rows);
if (stage == 1)
{
for (int i = 0; i < REC.Size; i++)
{
if ((DEF[i] + NAG_vec[i]) > 0)
REC[i] = ARE.GetRowSum(i) / (DEF[i] + NAG_vec[i]);
else
REC[i] = 0;
}
}
else
{
for (int i = 0; i < REC.Size; i++)
{
REC[i] = ARE.GetRowAverage(i);
}
}
// 29. Generate an alliance capabilities matrix defined as AC1 = DP1 * CAP
/*
Matrix AC1 = new Matrix(DP1.Rows, CAP.Cols);
for (int i = 0; i < DP1.Rows; i++)
for (int j = 0; j < CAP.Cols; j++)
AC1[i, j] = DP1[i, j] * CAP[i, i];
*/
// follow excel instructions
Matrix AC1 = new Matrix(FA1.Rows, CAP.Cols);
for (int i = 0; i < FA1.Rows; i++)
{
for (int j = 0; j < CAP.Cols; j++)
{
if (i == j)
AC1[i, j] = CAP[j, j];
else
AC1[i, j] = FA1[i, j] * CAP[j, j];
}
}
// 30. Generate a cumulative alliance capability vector CAL
Vector CAL = new Vector(AC1.Rows);
for (int i = 0; i < AC1.Rows; i++)
CAL[i] = AC1.GetRowSum(i);
// 31. Generate a finals SRG capabilities matrix SRGC1
// Generate a SRG capability vector SRGC
Matrix SRGC1 = new Matrix(FA1.Rows, FA1.Cols);
for (int i = 0; i < FA1.Rows; i++)
{
for (int j = 0; j < FA1.Cols; j++)
{
if (SRG[i, j] == 1 && FA1[i, j] == 0)
SRGC1[i, j] = CAP[j, j];
else
SRGC1[i, j] = 0;
}
}
Vector SRGC_vec = new Vector(SRGC1.Rows);
for (int i = 0; i < SRGC1.Rows; i++)
SRGC_vec[i] = SRGC1.GetRowSum(i);
// 32. Generate a revised AOC1 vector
Vector AOC1 = new Vector(SRGC_vec.Size);
for (int i = 0; i < SRGC_vec.Size; i++)
{
if (CAL[i] >= SRGC_vec[i])
AOC1[i] = 0;
else
AOC1[i] = SRGC_vec[i] - CAL[i];
}
// 33. Save output
Matrix Output = new Matrix(FA1.Rows, 9);
string[] colNames = {"Node", "DEF", "NAG", "CAP", "CAL", "AOC0", "AOC1", "ATC", "REC"};
//Output.NetworkId = 101 + stage;
Output.NetworkId = int.Parse(networkid + "0" + stage);
for (int i = 0; i < colNames.Length; i++)
Output.ColLabels[i] = colNames[i];
for (int i = 0; i < Output.Rows; i++)
{
//Output.RowLabels[i] = (101 + stage).ToString();
Output.RowLabels[i] = (int.Parse(networkid + "0" + stage)).ToString();
Output[i, 0] = i + 1;
}
Output.SetColVector(1, DEF);
Output.SetColVector(2, NAG_vec);
for (int i = 0; i < CAP.Rows; i++)
Output[i, 3] = CAP[i, i];
Output.SetColVector(4, CAL);
Output.SetColVector(5, AOC);
Output.SetColVector(6, AOC1);
Output.SetColVector(7, ATC);
Output.SetColVector(8, REC);
return Output;
}
private static Matrix SimulateNAPTStageTwo(Matrix FA1, Matrix SRG1, Matrix DP1, Matrix CAP, Matrix REL, Matrix UA11, int rowColSize, Matrix output, ref Matrix SRGOutput, ref Matrix EAOutput, int stage, string EAOutputFile, string outputfile, bool overwrite, bool EADyadic, bool outputDyadic, int networkid)
{
//int networkid = SRG1.NetworkId;
// 2. Generate Allies of Enemies matrix AE2 = SRG1 x DP1
Matrix AE2 = SRG1 * DP1;
// 3. Generate SRG2
Matrix SRG2 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < SRG2.Rows; i++)
{
for (int j = 0; j < SRG2.Cols; j++)
{
if (FA1[i, j] > 0)
SRG2[i, j] = 0;
else if (SRG1[i, j] == 1 || AE2[i, j] > 0)
SRG2[i, j] = 1;
else
SRG2[i, j] = 0;
}
}
// 4. Generate an Allies Capabilities Matrix AC20 = DP1 * C. Sum over rows of AC20
// Method from excel sheet
Matrix AC20 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < rowColSize; i++)
{
for (int j = 0; j < rowColSize; j++)
{
if (i == j || FA1[i, j] == 1)
AC20[i, j] = CAP[j, j];
else
AC20[i, j] = 0;
}
}
// 5. Generate an SRG Capabilities Matrix SRGC20 = SRGC * C. Sum across rows
Matrix SRGC20 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < rowColSize; i++)
{
for (int j = 0; j < rowColSize; j++)
{
SRGC20[i, j] = SRG2[i, j] * CAP[j, j];
}
}
// 6. Generate an Alliance Opportunity Cost Vector AOC20
Vector AOC20 = new Vector(rowColSize);
for (int i = 0; i < rowColSize; i++)
{
if (AC20.GetRowSum(i) >= SRGC20.GetRowSum(i))
AOC20[i] = 0;
else
AOC20[i] = SRGC20.GetRowSum(i) - AC20.GetRowSum(i);
}
// 7. Generate a Potential Alliance Network T2 PAN2
// method from excel sheet
Matrix PAN2 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < rowColSize; i++)
{
for (int j = 0; j < rowColSize; j++)
{
if (i == j || FA1[i, j] > 0)
PAN2[i, j] = 0;
else
PAN2[i, j] = 1 - SRG2[i, j];
}
}
// 8. Generate a Utility for Potential Ally matrix UA21 = PAN2 * UA11. Calulate the max row for UA21
/*
Matrix UA21 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < rowColSize; i++)
{
for (int j = 0; j < rowColSize; j++)
{
if (i != j)
UA21[i, j] = PAN2[i, j] * UA11[i, j];
else
UA21[i, j] = 0;
}
}
*/
Matrix UA21 = new Matrix(UA11);
// 9. Calculate the Potential Ally Capabilities matrix CUA21
// method from excel sheet
Matrix CUA21 = new Matrix(rowColSize, rowColSize);
for (int i = 0; i < rowColSize; i++)
{
for (int j = 0; j < rowColSize; j++)
{
if (i != j && UA21[i, j] == UA21.GetMaxInRow(i))
CUA21[i, j] = CAP[j, j];
else
CUA21[i, j] = 0;
}
}
Matrix DP2 = new Matrix(rowColSize, rowColSize);
Matrix FA2 = new Matrix(rowColSize, rowColSize);
NAPTStageOneHelper1(CAP, SRG2, SRGC20, PAN2, UA21, CUA21, AOC20, ref DP2, ref FA2, stage, AC20);
if (stage >= 10)
FA2.NetworkId = int.Parse(networkid + "" + stage);
else
FA2.NetworkId = int.Parse(networkid + "0" + stage);
for (int i = 0; i < FA1.Rows; i++)
{
FA2.RowLabels[i] = FA1.RowLabels[i];
FA2.ColLabels[i] = FA1.ColLabels[i];
}
// write FA2 to matrix file
// Set network ID and row and col labels first
if (!EADyadic)
MatrixWriter.WriteMatrixToMatrixFile(FA2, EAOutputFile, overwrite);
else
MatrixWriter.WriteMatrixToDyadicFile(FA2, EAOutputFile, overwrite);
//overwrite = false;
Matrix M2 = FA2 - FA1;
if (M2.IsAllZero)
{
// done?
EAOutput = FA2;
for (int i = 0; i < output.Rows; i++)
{
output.RowLabels[i] = (int.Parse(networkid + "0" + stage)).ToString();
}
if (!outputDyadic)
MatrixWriter.WriteMatrixToMatrixFile(output, outputfile, overwrite);
else
MatrixWriter.WriteMatrixToDyadicFile(output, outputfile, overwrite);
return output; // for now
}
else
{
// need to unbinarize FA2 first
Matrix Temp = new Matrix(FA2);
// argument needs to be UA11 and not UA12 (according to excel)
Matrix new_output = NAPTStageOneHelper2(CAP, SRG2, FA2, UA11, REL, AOC20, stage, networkid);
// write new_output to matrix file
if (!outputDyadic)
MatrixWriter.WriteMatrixToMatrixFile(new_output, outputfile, overwrite);
else
MatrixWriter.WriteMatrixToDyadicFile(new_output, outputfile, overwrite);
// Copy the data from SRG2 to SRGOutput
SRGOutput.Clear();
for (int i = 0; i < SRG2.Rows; i++)
for (int j = 0; j < SRG2.Cols; j++)
SRGOutput[i, j] = SRG2[i, j];
SRGOutput.NetworkId = new_output.NetworkId;
FA2.Clear();
Temp.CloneTo(FA2);
return SimulateNAPTStageTwo(FA2, SRG1, DP2, CAP, REL, UA11, rowColSize, new_output, ref SRGOutput, ref EAOutput, stage + 1, EAOutputFile, outputfile, overwrite, EADyadic, outputDyadic, networkid);
}
}
// for steps 13-24 in stage one
private static void NAPTStageOneHelper1(Matrix CAP, Matrix SRG, Matrix SRGC, Matrix PAN, Matrix UA11, Matrix CUA11, Vector AOC,
ref Matrix DP1, ref Matrix FA1, int stage, Matrix AC)
{
// 13. Calculate the expected alliance matrix A11
// Sum across rows of A11?
Matrix A11 = new Matrix(CUA11.Rows, CUA11.Cols);
if (stage == 1)
{
for (int i = 0; i < CUA11.Rows; i++)
{
for (int j = 0; j < CUA11.Cols; j++)
{
if (i == j)
A11[i, j] = CAP[i, i];
else if (CUA11[i, j] == CUA11.GetMaxInRow(i))
A11[i, j] = CAP[j, j];
else
A11[i, j] = 0;
}
}
}
else // stage 2 is different
{
for (int i = 0; i < CUA11.Rows; i++)
{
for (int j = 0; j < CUA11.Cols; j++)
{
if (AC[i, j] > 0)
A11[i, j] = AC[i, j];
else if (CUA11[i, j] > 0)
A11[i, j] = CUA11[i, j];
else
A11[i, j] = 0;
}
}
}
/*
// 14. Update the AOC vector to AOC11
Vector AOC11 = new Vector(AOC.Size);
for (int i = 0; i < A11.Rows; i++)
{
if (A11.GetRowSum(i) >= AOC[i])
AOC11[i] = 0;
else
AOC11[i] = AOC[i] - A11.GetRowSum(i);
}
*/
// 14. Update the AOC vector to AOC11
// (modified to compare to SRG CAP instead of AOC) -------- this one is correct ------
Vector AOC11 = new Vector(AOC.Size);
for (int i = 0; i < A11.Rows; i++)
{
if (A11.GetRowSum(i) >= SRGC.GetRowSum(i))
AOC11[i] = 0;
else
AOC11[i] = SRGC.GetRowSum(i) - A11.GetRowSum(i);
}
// 17. Subtract Sum(AOC12) - Sum(AOC11). If result is equal to zero, stop run and go back to step #x
// If the result is less than zero, repeat steps 11-16 by calculating UA13, CUA13, A13, AOC13
//
// This method incorporates steps 15-16
Matrix new_A = UpdateAOC(UA11, CUA11, AOC11, CAP, SRGC, A11, PAN, stage);
// 18. Generate an aliiance offer matrix AO1 which is a binarized version of A1x (where x is the number
// of the last A matrix
//new_A.Binarize();
// Recently updated as of 3:59AM 7/17/2012 (subject to change)
Matrix AO1 = new Matrix(new_A.Rows, new_A.Cols);
for (int i = 0; i < AO1.Rows; i++)
{
for (int j = 0; j < AO1.Cols; j++)
{
if (i == j)
AO1[i, j] = 0;
else if (new_A[i, j] > 0)
AO1[i, j] = 1;
else
AO1[i, j] = 0;
}
}
// 19. Transpose AO1
Matrix AO1_T = AO1.GetTranspose();
// 20. Generate a Defence Pacts matrix DP1 = AO1 * AO1'
DP1 = new Matrix(AO1.Rows, AO1_T.Cols);
for (int i = 0; i < AO1.Rows; i++)
for (int j = 0; j < AO1_T.Cols; j++)
DP1[i, j] = AO1[i, j] * AO1_T[i, j];
// 21. Generate an Allies of Enemies AE1 matrix AE1 = SRG x DP1
Matrix AE1 = SRG * DP1;
// 22. Generate a Prevention matrix PV1
/*
Matrix PV1 = new Matrix(AE1.Rows, AE1.Cols);
for (int i = 0; i < AE1.Rows; i++)
{
for (int j = 0; j < AE1.Cols; j++)
{
if (DP1[i, j] == 0 && AE1[i, j] == 0)
PV1[i, j] = 0;
else if (DP1[i, j] == 1 && AE1[i, j] == 0)
PV1[i, j] = 1;
else if (DP1[i, j] == 0 && AE1[i, j] > 0)
PV1[i, j] = 2;
}
}
*/
// New implementation which uses excel formula instead of pdf
Matrix PV1 = new Matrix(AE1.Rows, AE1.Cols);
for (int i = 0; i < AE1.Rows; i++)
{
for (int j = 0; j < AE1.Cols; j++)
{
if (i == j)
PV1[i, j] = 0;
else if (stage == 1)
{
if (AE1[i, j] == 1)
PV1[i, j] = 1;
else if (AE1[i, j] > 0 && SRG[i, j] == 0)
PV1[i, j] = 2;
else
PV1[i, j] = 0;
}
else
{
if (DP1[i, j] == 1)
PV1[i, j] = 1;
else if (AE1[i, j] > 0 && SRG[i, j] == 0)
PV1[i, j] = 2;
else
PV1[i, j] = 0;
}
}
}
// 23. Transpose PV1
Matrix PV1_T = PV1.GetTranspose();
// 24. Generate a final alliance matrix at T1 (FA1)
FA1 = new Matrix(PV1.Rows, PV1.Cols);
for (int i = 0; i < PV1.Rows; i++)
{
for (int j = 0; j < PV1.Cols; j++)
{
// PDF implementation
/*
if (PV1[i, j] == 0 && PV1_T[i, j] == 0)
FA1[i, j] = 0;
else
FA1[i, j] = (PV1[i, j] > PV1_T[i, j]) ? PV1[i, j] : PV1_T[i, j]; // max value of the two
*/
// Excel Implementation
if (PV1[i, j] > 0 && PV1_T[i, j] > 0)
FA1[i, j] = (PV1[i, j] > PV1_T[i, j]) ? PV1[i, j] : PV1_T[i, j]; // max value of the two
else
FA1[i, j] = 0;
}
}
}
/// <summary>
/// Simulates stage two of the realist network formation simulation.
/// </summary>
/// <param name="C">Capability matrix for stage two</param>
/// <param name="R">Policy relevance matrix (SRG)</param>
/// <param name="EAF">EAF matrix from stage one</param>
/// <param name="M">MID matrix</param>
/// <returns>Expected alliance matrix</returns>
/// <returns>EA matrix for stage two</returns>
private static Matrix UpdateSimplifiedRealistStageTwo(Matrix C, Matrix R, Matrix M, Matrix BEA, string outputFile, double br)
{
int n = C.Rows;
Matrix AE = M * BEA;
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
{
if (R[i, j] == 1 || AE[i, j] > 0 ) R[i, j] = 1;
else R[i, j] = 0;
}
R.ZeroDiagonal();
Matrix SRC = R * C;
Vector SRGC = new Vector(n);
for (int i = 0; i < n; ++i)
SRGC[i] = SRC.GetRowSum(i) * br;
Matrix EAC = BEA * C;
Vector AOC = new Vector(n);
for (int i = 0; i < n; ++i)
{
if (EAC.GetRowSum(i) + C[i, i] >= SRGC[i]) AOC[i] = 0;
else AOC[i] = 1 - ((EAC.GetRowSum(i) + C[i, i]) / SRGC[i]);
}
Matrix F = Matrix.Ones(n, n);
F.ZeroDiagonal();
Matrix PAN = F - R;
Matrix PAC = PAN * C;
Matrix EE = M * M;
EE.ZeroDiagonal();
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EE[i, j] != 0) EE[i, j] = 1;
Matrix EEC = EE * C;
Vector EEM = new Vector(n);
for (int i = 0; i < n; ++i)
EEM[i] = Algorithms.MaxValue<double>(EEC.GetRowEnumerator(i));
Matrix EA = new Matrix(n, n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EAC[i, j] > 0 || AOC[i] <= 0)
EA[i, j] = EAC[i, j];
else if (PAN[i, j] > 0 && EEC[i, j] == EEM[i])
EA[i, j] = EEC[i, j];
else
EA[i, j] = 0;
//Copied from Stage 1
Vector SEA = new Vector(n);
Matrix previousEA = new Matrix(n);
Matrix TempEEC = new Matrix(n);
EEC.CloneTo(TempEEC);
do
{
EA.CloneTo(previousEA);
for (int i = 0; i < n; ++i)
SEA[i] = EA.GetRowSum(i) + C[i, i];
for (int i = 0; i < n; ++i)
{
if (SRGC[i] <= SEA[i]) AOC[i] = 0;
else AOC[i] = 1 - SEA[i] / SRGC[i];
}
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EEC[i, j] == EEM[i]) EEC[i, j] = 0;
for (int i = 0; i < n; ++i)
EEM[i] = Algorithms.MaxValue<double>(EEC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
{
if (AOC[i] == 0 || EA[i, j] != 0) ;
else if (PAN[i, j] > 0 && EEC[i, j] == EEM[i])
EA[i, j] = EEC[i, j];
else EA[i, j] = 0;
}
//for (int i = 0; i < n; ++i)
// for (int j = 0; j < n; ++j)
// {
// if (AOC[i] == 0 || EA[i, j] > 0) ;
// else if (EEC[i, j] == EEM[i]) EA[i, j] = EEC[i, j];
// else EA[i, j] = 0;
// }
} while ((!previousEA.IsSameAs(EA)) && !EEC.IsAllZero && !AOC.IsZeroVector);
if (!AOC.IsZeroVector)
{
//for (int i = 0; i < n; ++i)
// for (int j = 0; j < n; ++j)
// if (PAC[i, j] > 0 && TempEEC[i, j] != 0) PAC[i, j] = 0;
//PAC.CopyLabelsFrom(C);
//MatrixWriter.WriteMatrixToMatrixFile(PAC, outputFile);
Vector PAM = new Vector(n);
for (int i = 0; i < n; ++i)
PAM[i] = Algorithms.MaxValue<double>(PAC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (AOC[i] != 0 && PAC[i, j] == PAM[i] && EA[i, j] == 0)
EA[i, j] = PAC[i, j];
do
{
EA.CloneTo(previousEA);
for (int i = 0; i < n; ++i)
SEA[i] = EA.GetRowSum(i) + C[i, i];
for (int i = 0; i < n; ++i)
{
if (SRGC[i] <= SEA[i]) AOC[i] = 0;
else AOC[i] = 1 - SEA[i] / SRGC[i];
}
//Matrix output = new Matrix(n, n + 4);
//for (int i = 0; i < n; i++)
// for (int j = 0; j < n; j++)
// output[i, j] = EA[i, j];
//for (int i = 0; i < n; ++i)
// output[i, n] = SEA[i];
//for (int i = 0; i < n; ++i)
// output[i, n + 1] = SRGC[i];
//for (int i = 0; i < n; ++i)
// output[i, n + 2] = AOC[i];
//for (int i = 0; i < n; ++i)
// output[i, n + 3] = 1111;
//output.CopyLabelsFrom(C);
//MatrixWriter.WriteMatrixToMatrixFile(output, outputFile);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (PAC[i, j] == PAM[i]) PAC[i, j] = 0;
//PAC.CopyLabelsFrom(C);
//MatrixWriter.WriteMatrixToMatrixFile(PAC, outputFile);
for (int i = 0; i < n; ++i)
PAM[i] = Algorithms.MaxValue<double>(PAC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (AOC[i] != 0 && PAC[i, j] == PAM[i] && EA[i, j] == 0)
EA[i, j] = PAC[i, j];
} while ((!previousEA.IsSameAs(EA)) && !PAC.IsAllZero && !AOC.IsZeroVector);
}//if AOC is not all zero
Matrix EAT = EA.GetTranspose();
Matrix EAF = new Matrix(n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
EAF[i, j] = EA[i, j] * EAT[i, j];
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
{
if (EAF[i, j] != 0) BEA[i, j] = 1;
else BEA[i, j] = 0;
}
return BEA;
}
private static Vector UpdateEAMatrix(Vector AO, Matrix Q, Matrix EA)
{
int n = AO.Size;
Vector MQ = new Vector(n);
Vector SEA = Vector.Zero(n);
Vector RS = null;
while (true)
{
for (int i = 0; i < SEA.Size; ++i)
SEA[i] = EA.GetRowSum(i);
RS = AO - SEA;
for (int i = 0; i < MQ.Size; ++i)
MQ[i] = Algorithms.MaxValue<double>(Q.GetRowEnumerator(i));
for (int i = 0; i < EA.Rows; ++i)
{
if (RS[i] < double.Epsilon)
continue;
for (int j = 0; j < EA.Cols; ++j)
if (EA[i, j] == 0 && Q[i, j] == MQ[i])
EA[i, j] = Q[i, j];
}
for (int i = 0; i < Q.Rows; ++i)
for (int j = 0; j < Q.Cols; ++j)
if (Q[i, j] == MQ[i])
Q[i, j] = 0;
if (Algorithms.MaxValue<double>(RS) < double.Epsilon)
break;
if (Algorithms.MaxValue<double>(MQ) < double.Epsilon)
break;
}
return RS;
}
private static Matrix UpdateAOC(Matrix _UA, Matrix _CUA, Vector _AOC, Matrix CAP, Matrix SRGC, Matrix _A, Matrix PAN, int stage)
{
double sum1 = 0;
double sum2 = 0;
// Calculate sum for AOC11
for (int i = 0; i < _AOC.Size; i++)
sum1 += _AOC[i];
// Update the UA11 matrix into UA12 matrix
Matrix UA = new Matrix(_CUA.Rows, _CUA.Cols);
for (int i = 0; i < _CUA.Rows; i++)
{
for (int j = 0; j < _CUA.Cols; j++)
{
if (_CUA[i, j] == _CUA.GetMaxInRow(i))
UA[i, j] = 0;
else
{
// excel sheet assigns value from _UA instead of _CUA
//UA[i, j] = _CUA[i, j];
UA[i, j] = _UA[i, j];
}
}
}
// Generate a matrix CUA11
Matrix CUA = new Matrix(UA.Rows, UA.Cols);
if (stage == 1)
{
for (int i = 0; i < UA.Rows; i++)
{
for (int j = 0; j < UA.Cols; j++)
{
if (UA[i, j] != UA.GetMaxInRow(i))
CUA[i, j] = 0;
else if (UA[i, j] == UA.GetMaxInRow(i) && PAN[i, j] > 0 && i != j) // needs PAN and i!=j conditions
CUA[i, j] = CAP[j, j];
}
}
}
else // for the other stages
{
for (int i = 0; i < UA.Rows; i++)
{
for (int j = 0; j < UA.Cols; j++)
{
if (UA[i, j] != UA.GetMaxInRow(i))
CUA[i, j] = 0;
else if (UA[i, j] == UA.GetMaxInRow(i) && UA[i, j] > 0 && i != j) // needs PAN and i!=j conditions
CUA[i, j] = CAP[j, j];
}
}
}
// Calculate the expected alliance matrix A11
//
// ****** Calculated completely different in excel sheet ******
//
/*
Matrix A = new Matrix(CUA.Rows, CUA.Cols);
for (int i = 0; i < CUA.Rows; i++)
{
for (int j = 0; j < CUA.Cols; j++)
{
if (i == j)
A[i, j] = CAP[i, i];
else if (CUA[i, j] == CUA.GetMaxInRow(i))
A[i, j] = CAP[j, j];
else
A[i, j] = 0;
}
}
*/
// This version may be wrong; might need to use above version
Matrix A = new Matrix(CUA.Rows, CUA.Cols);
if (stage == 1)
{
for (int i = 0; i < CUA.Rows; i++)
{
for (int j = 0; j < CUA.Cols; j++)
{
if (_A[i, j] > 0 || _AOC[i] == 0)
A[i, j] = _A[i, j];
else
{
if (CUA[i, j] > 0)
A[i, j] = CUA[i, j];
else
A[i, j] = 0;
}
}
}
}
else
{
for (int i = 0; i < CUA.Rows; i++)
{
for (int j = 0; j < CUA.Cols; j++)
{
if (_A[i, j] > 0)
A[i, j] = _A[i, j];
else if (CUA[i, j] > 0)
A[i, j] = CUA[i, j];
else
A[i, j] = 0;
}
}
}
/*
// Update the AOC vector to AOC11
Vector AOC = new Vector(_AOC.Rows);
for (int i = 0; i < A.Rows; i++)
{
if (A.GetRowSum(i) >= _AOC[i])
AOC[i] = 0;
else
AOC[i] = _AOC[i] - A.GetRowSum(i);
}
*/
// Update the AOC vector to AOC11 --------- this one is correct ---------
Vector AOC = new Vector(_AOC.Size);
for (int i = 0; i < A.Rows; i++)
{
if (A.GetRowSum(i) >= SRGC.GetRowSum(i))
AOC[i] = 0;
else
AOC[i] = SRGC.GetRowSum(i) - A.GetRowSum(i);
}
// Calculate sum for AOC12
for (int i = 0; i < AOC.Size; i++)
sum2 += AOC[i];
if ((sum2 - sum1) > 0)
throw new Exception("The difference of sum cannot be greater than zero!");
if ((sum2 - sum1) < 0)
return UpdateAOC(UA, CUA, AOC, CAP, SRGC, A, PAN, stage);
else
return A;
}
/// <summary>
/// Simulates stage one of the SIMPLIFIED realist network formation simulation.
/// </summary>
/// <param name="C">Capability matrix</param>
/// <param name="R">Policy relevance matrix (SRG)</param>
/// <param name="M">MID matrix</param>
/// <returns>Expected alliance matrix</returns>
private static Matrix SimulateSimplifiedRealistStageOne(Matrix C, Matrix R, Matrix M, string outputFile, double br)
{
int n = C.Rows;
Matrix SRC = R * C;
Vector SRGC = new Vector(n);
for (int i = 0; i < n; ++i)
SRGC[i] = SRC.GetRowSum(i) * br;
Vector AOC = new Vector(n);
for (int i = 0; i < n; ++i)
{
if (SRGC[i] <= C[i, i]) AOC[i] = 0;
else AOC[i] = 1 - C[i, i] / SRGC[i];
}
Matrix F = Matrix.Ones(n, n);
F.ZeroDiagonal();
Matrix PAN = F - R;
Matrix PAC = PAN * C;
Matrix EE = M * M;
EE.ZeroDiagonal();
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EE[i, j] != 0) EE[i, j] = 1;
Matrix EEC = EE * C;
Vector EEM = new Vector(n);
for (int i = 0; i < n; ++i)
EEM[i] = Algorithms.MaxValue<double>(EEC.GetRowEnumerator(i));
Matrix EA = new Matrix(n, n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EEC[i, j] == EEM[i] && PAN[i, j] == 1 && AOC[i] != 0)
EA[i, j] = EEC[i, j];
else
EA[i, j] = 0;
Vector SEA = new Vector(n);
Matrix previousEA = new Matrix(n);
do
{
EA.CloneTo(previousEA);
for (int i = 0; i < n; ++i)
SEA[i] = EA.GetRowSum(i) + C[i, i];
for (int i = 0; i < n; ++i)
{
if (SRGC[i] <= SEA[i]) AOC[i] = 0;
else AOC[i] = 1 - SEA[i] / SRGC[i];
}
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (EEC[i, j] == EEM[i]) EEC[i, j] = 0;
for (int i = 0; i < n; ++i)
EEM[i] = Algorithms.MaxValue<double>(EEC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
{
//if (AOC[i] != 0 && EEC[i, j] == EEM[i] && EA[i, j] == 0)
// EA[i, j] = EEC[i, j];
if (AOC[i] == 0 || EA[i, j] != 0);
else if (PAN[i, j] > 0 && EEC[i, j] == EEM[i])
EA[i, j] = EEC[i, j];
else EA[i, j] = 0;
}
} while ((!previousEA.IsSameAs(EA)) && !EEC.IsAllZero && !AOC.IsZeroVector);
if (!AOC.IsZeroVector)
{
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (PAC[i, j] > 0 && EEC[i, j] != 0) PAC[i, j] = 0;
Vector PAM = new Vector(n);
for (int i = 0; i < n; ++i)
PAM[i] = Algorithms.MaxValue<double>(PAC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (AOC[i] != 0 && PAC[i, j] == PAM[i] && EA[i, j] == 0)
EA[i, j] = PAC[i, j];
EA.CopyLabelsFrom(C);
do
{
EA.CloneTo(previousEA);
for (int i = 0; i < n; ++i)
SEA[i] = EA.GetRowSum(i) + C[i, i];
for (int i = 0; i < n; ++i)
{
if (SRGC[i] <= SEA[i]) AOC[i] = 0;
else AOC[i] = 1 - SEA[i] / SRGC[i];
}
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (PAC[i, j] == PAM[i]) PAC[i, j] = 0;
for (int i = 0; i < n; ++i)
PAM[i] = Algorithms.MaxValue<double>(PAC.GetRowEnumerator(i));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (AOC[i] != 0 && PAC[i, j] == PAM[i] && EA[i, j] == 0)
EA[i, j] = PAC[i, j];
EA.CopyLabelsFrom(C);
} while ((!previousEA.IsSameAs(EA)) && !PAC.IsAllZero && !AOC.IsZeroVector);
}//if AOC is not all zero
Matrix EAT = EA.GetTranspose();
Matrix EAF = new Matrix(n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
EAF[i, j] = EA[i, j] * EAT[i, j];
Matrix BEA = new Matrix(n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
{
if (EAF[i, j] != 0) BEA[i, j] = 1;
else BEA[i, j] = 0;
}
return BEA;
}
