public SimplexResult Solve(SimplexTuple tuple)
{
var multiplier = 1;
if (tuple.Type == ObjectiveFunctionType.Min) multiplier *= -1;
var standartTuple = (new SimplexInputBuilder()).ConvertToStandartForm(tuple);
var bInternal = InitializeSimplex(tuple);
iteration = 0;
var columns = Enumerable.Range(0, tuple.ObjFuncCoeffs.Count).ToArray();
var AB = standartTuple.EqualityCoeffs.Extract(bInternal.InequalityIndexes, columns);
var bB = standartTuple.FreeTerms.Extract(bInternal.InequalityIndexes);
var vector = SolveInternal(standartTuple.EqualityCoeffs, standartTuple.FreeTerms, standartTuple.ObjFuncCoeffs,
bInternal, AB, bB);
//Multiply result to -1 if we have min function at start
var optimalValue = multiplier*(standartTuple.ObjFuncCoeffs.ToRowMatrix()*vector)[0];
return new SimplexResult {OptimalValue = optimalValue, OptimalVector = vector, Iteration = iteration};
}
internal StartingBasis InitializeSimplex(SimplexTuple tuple)
{
var negativeCount = tuple.FreeTerms.Count(x => x < 0);
int varCount = tuple.ObjFuncCoeffs.Count;
var startingEq = new List<int>(varCount);
for (int i = 0; i < tuple.EqualityCoeffs.RowCount; i++)
{
var row = tuple.EqualityCoeffs.Row(i);
if (row.Count(x => x.FloatEquals(-1)) == 1
&& row.Count(x => x.FloatEquals(0)) == (varCount - 1)
&& startingEq.Count < varCount)
startingEq.Add(i);
}
//If min index > 0 -> all free terms are positive.
//This means that basis just zero variables and indexes of that inequalities
if (negativeCount == 0)
{
return new StartingBasis
{
InequalityIndexes = startingEq.ToArray(),
FeasibleBasis = new double[varCount]
};
}
//Create auxilary problem
var auxObjFunc = new List<double>(varCount + negativeCount);
auxObjFunc.AddRange(tuple.ObjFuncCoeffs.Select(ofc => 0).Select(dummy => (double) dummy));
var auxA = tuple.EqualityCoeffs.Clone();
var auxb = tuple.FreeTerms.Clone();
int rowCount = tuple.EqualityCoeffs.RowCount;
//for each negative index we should go with added slack variable
//TODO: work with Dense/Sparse vectors
for (int i = 0; i < tuple.EqualityCoeffs.RowCount; i++)
{
if (tuple.FreeTerms[i] >= 0) continue;
//add a new slack variable to obj function with coeff -1
auxObjFunc.Add(-1);
//add new column for that variable
var zeroVector = new DenseVector(rowCount);
zeroVector[i] = -1;
auxA = auxA.InsertColumn(varCount++, zeroVector);
//add new row for this variable
var nonNegativeRow = new DenseVector(varCount);
nonNegativeRow[varCount - 1] = -1;
auxA = auxA.InsertRow(rowCount, nonNegativeRow);
var zeroFreeTerm = new DenseVector(new[] {0.0});
auxb = auxb.ToColumnMatrix().InsertRow(rowCount, zeroFreeTerm).Column(0);
rowCount++;
//add top constraint to this variable
var freeTermRow = new DenseVector(varCount);
freeTermRow[varCount - 1] = 1;
auxA = auxA.InsertRow(rowCount, freeTermRow);
var newFreeTerm = new DenseVector(new[] {-tuple.FreeTerms[i]});
auxb = auxb.ToColumnMatrix().InsertRow(rowCount, newFreeTerm).Column(0);
startingEq.Add(rowCount);
rowCount++;
}
var auxBasis = new StartingBasis
{
InequalityIndexes = startingEq.ToArray(),
FeasibleBasis = new double[varCount]
};
iteration = 0;
var columns = Enumerable.Range(0, varCount).ToArray();
//TODO: work with Dense/Sparse vectors
var auxAb = ((DenseMatrix) auxA).Extract(startingEq.ToArray(), columns);
var auxbB = ((DenseVector) auxb).Extract(startingEq.ToArray());
Vector vector = SolveInternal((DenseMatrix) auxA, (DenseVector) auxb, new DenseVector(auxObjFunc.ToArray()),
auxBasis, auxAb, auxbB);
for (int k = tuple.ObjFuncCoeffs.Count; k < varCount; k++)
if (!vector[k].FloatEquals(0))
throw new SimplexException("Problem is unsolvable");
var basis = vector.Take(tuple.ObjFuncCoeffs.Count).ToArray();
var indexes =
auxBasis.InequalityIndexes.Where(x => x < tuple.EqualityCoeffs.RowCount).Take(tuple.ObjFuncCoeffs.Count).ToArray();
return new StartingBasis
{
InequalityIndexes = indexes,
FeasibleBasis = basis
};
}
public SimplexTuple ConvertToStandartForm(SimplexTuple tuple)
{
if (tuple.Type == ObjectiveFunctionType.Min)
{
tuple.ObjFuncCoeffs *= -1;
tuple.ObjFuncFreeTerm *= -1;
tuple.Type = ObjectiveFunctionType.Max;
}
int length = tuple.EquationTypes.Count;
for (int i = 0; i < length; i++)
{
var equation = tuple.EquationTypes[i];
if (equation == EquationType.MoreOrEqual)
{
tuple.EqualityCoeffs.SetRow(i, -1*tuple.EqualityCoeffs.Row(i));
tuple.FreeTerms[i] *= -1;
tuple.EquationTypes[i] = EquationType.LessOrEqual;
}
if (equation == EquationType.Equal)
{
tuple.EquationTypes[i] = EquationType.LessOrEqual;
var additionalRow = tuple.EqualityCoeffs.Row(i).Clone();
tuple.EqualityCoeffs = (DenseMatrix) tuple.EqualityCoeffs.InsertRow(i + 1, additionalRow);
tuple.EquationTypes.Insert(i + 1, EquationType.MoreOrEqual);
var val = tuple.FreeTerms[i];
var freeTerms = tuple.FreeTerms.ToList();
freeTerms.Insert(i + 1, val);
tuple.FreeTerms = new DenseVector(freeTerms.ToArray());
length++;
}
}
return tuple;
}
