public void Restore(LinearProgram linearProgram, double[] originalCoeficients, int[] originalIndices)
{
var newObjective = new double[linearProgram.ObjectiveCoefficients.Length];
for (var i = 1; i < originalIndices.Length; i++)
{
var originalIndice = originalIndices[i];
var originalCoef = originalCoeficients[i];
if (linearProgram.NonBasicIndices.Contains(originalIndice))
{
var index = Array.FindIndex(linearProgram.NonBasicIndices, n => n == originalIndice);
var ttmp = new double[linearProgram.ObjectiveCoefficients.Length];
ttmp[index] = originalCoef;
AddArray(newObjective, ttmp);
}
else
{
var index = Array.FindIndex(linearProgram.BasicIndices, b => b == originalIndice);
var tmp = new double[linearProgram.ObjectiveCoefficients.Length];
linearProgram.Coefficients[index].CopyTo(tmp, 0);
AddArray(newObjective, tmp, originalCoef);
}
}
linearProgram.ObjectiveCoefficients = newObjective;
}
public LinearProgamSolution Solve(LinearProgram linearProgram)
{
//check if needs initialization
bool needsInit = linearProgram.Coefficients.Any(c => c[0] < 0);
if (needsInit)
{
//solve dual
var dual = _mapPrimalToDual.Map(linearProgram);
var dualSol = SolveSingle(dual);
//todo: check if feasbile
if (dualSol.SolutionType != LinearProgramSolutionType.Solved)
{
return(new LinearProgamSolution(0, 0, LinearProgramSolutionType.Infeasible));
}
//map back to primal
var primal = _mapDualToPrimal.Map(dual);
//restore objective
_restoreObjective.Restore(primal, dual.OriginalObjectiveCoefficients, dual.OriginalNonBasicIndices);
//solve
var primalSol = SolveSingle(primal);
return(primalSol);
}
else
{
return(SolveSingle(linearProgram));
}
}
private LinearProgamSolution SolveSingle(LinearProgram linearProgram)
{
var pivotCount = 0;
while (true)
{
//do this until no entering, or stop if unbounded
_analyze.Analyze(linearProgram);
//no entering, must be solved
if (_analyze.Entering == 0)
{
break;
}
//if unbounded
if (_analyze.Leaving == 0)
{
return(new LinearProgamSolution(0, 0, LinearProgramSolutionType.Unbounded));
}
//if here, we can pivot
++pivotCount;
_pivotor.Pivot(_analyze.Entering, _analyze.Leaving, linearProgram);
}
return(new LinearProgamSolution(linearProgram.ObjectiveValue, pivotCount, LinearProgramSolutionType.Solved));
}
private int GetEntering(LinearProgram linearProgram)
{
var objectiveCoefficients = linearProgram.ObjectiveCoefficients;
var nonbasic = linearProgram.NonBasicIndices;
var n = linearProgram.N;
//pick entering var (coeff > 0)
var enteringPos = int.MaxValue;
for (var j = 1; j <= n; j++)
{
if (objectiveCoefficients[j] > 0.0)
{
if (enteringPos == int.MaxValue ||
nonbasic[j] < nonbasic[enteringPos])
{
enteringPos = j;
}
}
}
if (enteringPos == int.MaxValue)
{
return(0);
}
_enteringPos = enteringPos;
return(nonbasic[enteringPos]);
}
public void Analyze(LinearProgram linearProgram)
{
Entering = GetEntering(linearProgram);
//if unbounded
if (Entering == 0)
{
return;
}
Leaving = GetLeaving(linearProgram);
}
public LinearProgram Read(string fileName)
{
var lp = new LinearProgram();
var lines = File.ReadAllLines(fileName);
var sizeVars = GetInts(lines[0]);
lp.M = sizeVars[0];
lp.N = sizeVars[1];
var basic = GetInts(lines[1]);
lp.BasicIndices = new int[basic.Length + 1];
basic.CopyTo(lp.BasicIndices, 1);
var nonBasic = GetInts(lines[2]);
lp.NonBasicIndices = new int[nonBasic.Length + 1];
nonBasic.CopyTo(lp.NonBasicIndices, 1);
var bVars = GetDoubles(lines[3]);
lp.Coefficients = new double[bVars.Length + 1][];
int m = 0;
for (int i = 4; i < lines.Length; i++)
{
var values = GetDoubles(lines[i]);
if (i == lines.Length - 1)
{
lp.ObjectiveCoefficients = values;
}
else
{
if (m == 0)
{
lp.Coefficients[m] = new double[values.Length + 1];
}
++m;
lp.Coefficients[m] = new double[values.Length + 1];
lp.Coefficients[m][0] = bVars[m - 1];
values.CopyTo(lp.Coefficients[m], 1);
}
}
return(lp);
}
public void Pivot(int entering, int leaving, LinearProgram linearProgram)
{
var enteringPos = Array.FindIndex(linearProgram.NonBasicIndices, i => i == entering);
var leavingPos = Array.FindIndex(linearProgram.BasicIndices, i => i == leaving);
var a = linearProgram.ObjectiveCoefficients;
var b = linearProgram.Coefficients[leavingPos];
var m = a[enteringPos];
var n = b[enteringPos];
var objValue = a[0] + m * b[0] / -n;
linearProgram.ObjectiveCoefficients[0] = objValue;
}
public void Pivot(int entering, int leaving, LinearProgram linearProgram)
{
var enteringPos = Array.FindIndex(linearProgram.NonBasicIndices, i => i == entering);
var leavingPos = Array.FindIndex(linearProgram.BasicIndices, i => i == leaving);
var a = linearProgram.ObjectiveCoefficients;
var b = linearProgram.Coefficients[leavingPos];
//update leaving row:
// - calculate new coefficients
var n = b[enteringPos];
b[enteringPos] = -1.0;
var multiplier = 1 / -n;
MultiplyArray(b, multiplier);
//update other rows
for (var i = 1; i < linearProgram.Coefficients.Length; i++)
{
//already updated leaving row
if (i == leavingPos)
{
continue;
}
//the row to update
var bb = linearProgram.Coefficients[i];
//the coefficient in this row
var c = bb[enteringPos];
//reset coefficient for array addition
bb[enteringPos] = 0.0;
AddArray(bb, b, c);
}
//update objective row
var oc = a[enteringPos];
a[enteringPos] = 0;
AddArray(a, b, oc);
//update basic / non-basic indices
linearProgram.BasicIndices[leavingPos] = entering;
linearProgram.NonBasicIndices[enteringPos] = leaving;
}
private int GetLeaving(LinearProgram linearProgram)
{
var coefficients = linearProgram.Coefficients;
var m = linearProgram.M;
var basic = linearProgram.BasicIndices;
var enteringPos = _enteringPos;
//pick leaving var (coeff <= 0, value within constraints)
var leavingPos = int.MaxValue;
var leavingValue = double.MaxValue;
for (var i = 1; i <= m; i++)
{
var c = coefficients[i][enteringPos];
if (c < 0)
{
var value = coefficients[i][0] / -c;
if (value < leavingValue)
{
leavingValue = value;
leavingPos = i;
}
else if (Math.Abs(value - leavingValue) < .00001)
{
if (basic[i] < basic[leavingPos])
{
leavingPos = i;
}
}
}
}
if (leavingPos == int.MaxValue)
{
return(0);
}
return(basic[leavingPos]);
}
//[Line 1] m n
//[Line 2] B1 B2 ... Bm [the list of basic indices m integers]
//[Line 3] N1 N2 ... Nn [the list of non-basic indices n integers]
//[Line 4] b1 .. bm (m floating point numbers)
//[Line 5] a11 ... a1n (first row coefficients. See dictionary notation above.)
//....
//[Line m+4] am1 ... amn (mth row coefficients. See dictionary notation above.)
//[Line m+5] z0 c1 .. cn (objective coefficients (n+1 floating point numbers))
public DualLinearProgram Map(LinearProgram primal)
{
var dual = new DualLinearProgram();
dual.M = primal.N;
dual.N = primal.M;
dual.OriginalObjectiveCoefficients = primal.ObjectiveCoefficients;
dual.OriginalNonBasicIndices = primal.NonBasicIndices;
dual.BasicIndices = new int[primal.NonBasicIndices.Length];
dual.NonBasicIndices = new int[primal.BasicIndices.Length];
dual.Coefficients = new double[primal.Coefficients[0].Length][];
dual.ObjectiveCoefficients = new double[primal.BasicIndices.Length];
//map primal coefficients to dual coefficients
var a = primal.Coefficients.Length;
for (var i = 0; i < dual.Coefficients.Length; i++)
{
dual.Coefficients[i] = new double[a];//empty row for 1-based indexes
if (i == 0)
{
continue;
}
for (var k = 1; k < primal.Coefficients.Length; k++)
{
dual.Coefficients[i][k] = -primal.Coefficients[k][i];
}
}
//map 1 to dual coefficients b-value
for (var i = 1; i < primal.ObjectiveCoefficients.Length; i++)
{
dual.Coefficients[i][0] = 1;
}
//map primal b values to dual objective coefficients
for (var i = 1; i < primal.Coefficients.Length; i++)
{
dual.ObjectiveCoefficients[i] = -primal.Coefficients[i][0];
}
//set basic / non basic indices
var y = 0;
for (var i = 1; i < dual.BasicIndices.Length; i++)
{
dual.BasicIndices[i] = ++y;
}
for (var i = 1; i < dual.NonBasicIndices.Length; i++)
{
dual.NonBasicIndices[i] = ++y;
}
//set complements
dual.Complements = new int[2][];
dual.Complements[0] = primal.NonBasicIndices.Skip(1).Concat(primal.BasicIndices.Skip(1)).ToArray();
dual.Complements[1] = dual.NonBasicIndices.Skip(1).Concat(dual.BasicIndices.Skip(1)).ToArray();
return(dual);
}