/// <summary>
/// Obtém a solução do problema a partir das variáveis de compatibilidade.
/// </summary>
/// <param name="resultCosts">Os custos por componente.</param>
/// <param name="variables">A lista das variáveis escolhidas.</param>
/// <param name="costsMatrices">As matrizes de custos.</param>
/// <returns>A solução.</returns>
private GreedyAlgSolution <CostsType>[] GetSolution(
CostsType[] resultCosts,
List <CoordsElement>[] variables,
List <ILongSparseMathMatrix <CostsType> > costsMatrices)
{
var result = new GreedyAlgSolution <CostsType> [variables.Length];
for (int i = 0; i < result.Length; ++i)
{
var integerSequence = new IntegerSequence();
integerSequence.Add(0, costsMatrices[i].GetLength(0) - 1);
var currentVariables = variables[i];
for (int j = 0; j < currentVariables.Count; ++j)
{
var column = currentVariables[j].Column;
integerSequence.Remove(column);
}
var algSol = new GreedyAlgSolution <CostsType>(integerSequence);
algSol.Cost = resultCosts[i];
result[i] = algSol;
}
return(result);
}
public void Statistics_DicModeAlgTest()
{
var target = new DicModeAlgorithm <int>();
var source = new IntegerSequence();
for (var i = 0; i < 1000; ++i)
{
source.Clear();
source.Add(0, i);
var innerActual = target.Run(source);
Assert.AreEqual(source.Count, innerActual.Count);
innerActual.Sort();
for (var j = 0; j < source.Count; ++j)
{
Assert.AreEqual(source[j], innerActual[j]);
}
}
var arraySource = new int[] { 1, 3, 2, 2, 1, 3, 3, 3, 3, 4, 2 };
var expected = 3;
var actual = target.Run(arraySource);
Assert.AreEqual(1, actual.Count);
Assert.AreEqual(expected, actual[0]);
}
public void Statistics_DicMedianAlgTest()
{
var target = new DicMedianAlgorithm <int>();
var source = new IntegerSequence();
var expected = 1;
for (var i = 1; i < 1000; i += 2)
{
source.Clear();
source.Add(1, i);
var actual = target.Run(source);
Assert.AreEqual(expected, actual.Item1);
Assert.AreEqual(expected, actual.Item2);
++expected;
}
expected = 1;
for (var i = 2; i < 1000; i += 2)
{
source.Clear();
source.Add(1, i);
var actual = target.Run(source);
Assert.AreEqual(expected++, actual.Item1);
Assert.AreEqual(expected, actual.Item2);
}
var arraySource = new int[] { 1, 3, 2, 2, 1, 3, 3, 3, 3, 4, 2 };
expected = 3;
var outerActual = target.Run(arraySource);
Assert.AreEqual(expected, outerActual.Item1);
Assert.AreEqual(expected, outerActual.Item2);
arraySource = new int[] { 1, 3, 2, 2, 1, 3, 3, 3, 4, 2 };
expected = 2;
outerActual = target.Run(arraySource);
Assert.AreEqual(expected++, outerActual.Item1);
Assert.AreEqual(expected, outerActual.Item2);
}
/// <summary>
/// Determina o polinómio característico de uma matriz.
/// </summary>
/// <param name="data">A matriz.</param>
/// <returns>O polinómio característico.</returns>
public UnivariatePolynomialNormalForm <ElementType> Run(ISquareMathMatrix <ElementType> data)
{
if (data == null)
{
return(new UnivariatePolynomialNormalForm <ElementType>(this.variableName));
}
else
{
var lines = data.GetLength(0);
if (lines == 0)
{
return(new UnivariatePolynomialNormalForm <ElementType>(this.variableName));
}
else if (lines == 1)
{
var entry = data[0, 0];
var result = new UnivariatePolynomialNormalForm <ElementType>(
this.ring.MultiplicativeUnity,
1,
this.variableName,
this.ring);
result = result.Add(this.ring.AdditiveInverse(entry), 0, this.ring);
return(result);
}
else if (lines == 2)
{
var variablePol = new UnivariatePolynomialNormalForm <ElementType>(
this.ring.MultiplicativeUnity,
1,
this.variableName,
this.ring);
var firstDiagonalElement = variablePol.Add(
this.ring.AdditiveInverse(data[0, 0]),
this.ring);
var secondDiagonalElement = variablePol.Add(
this.ring.AdditiveInverse(data[1, 1]),
this.ring);
var result = firstDiagonalElement.Multiply(secondDiagonalElement, this.ring);
result = result.Add(
this.ring.AdditiveInverse(this.ring.Multiply(data[0, 1], data[1, 0])),
this.ring);
return(result);
}
else
{
var matrixFactory = new ArrayMathMatrixFactory <ElementType>();
var matrixMultiplicator = new MatrixMultiplicationOperation <ElementType>(
matrixFactory, this.ring, this.ring);
var subMatrixSequence = new IntegerSequence();
var singleValueSequence = new IntegerSequence();
IMatrix <ElementType> multiplicationMatrix = new ArrayMathMatrix <ElementType>(
lines + 1,
lines,
this.ring.AdditiveUnity);
subMatrixSequence.Add(1, lines - 1);
singleValueSequence.Add(0);
this.FillMultiplicationMatrix(
data,
data[0, 0],
subMatrixSequence,
singleValueSequence,
matrixMultiplicator,
multiplicationMatrix);
var currentDimension = 1;
while (currentDimension < lines - 1)
{
subMatrixSequence.Clear();
singleValueSequence.Clear();
subMatrixSequence.Add(currentDimension + 1, lines - 1);
singleValueSequence.Add(currentDimension);
var otherLines = lines - currentDimension;
var otherMultiplicationMatrix = new ArrayMathMatrix <ElementType>(
otherLines + 1,
otherLines,
this.ring.AdditiveUnity);
this.FillMultiplicationMatrix(
data,
data[currentDimension, currentDimension],
subMatrixSequence,
singleValueSequence,
matrixMultiplicator,
otherMultiplicationMatrix);
multiplicationMatrix = matrixMultiplicator.Multiply(
multiplicationMatrix,
otherMultiplicationMatrix);
++currentDimension;
}
var lastOtherMultiplicationMatrix = new ArrayMathMatrix <ElementType>(
2,
1,
this.ring.AdditiveUnity);
lastOtherMultiplicationMatrix[0, 0] = this.ring.MultiplicativeUnity;
lastOtherMultiplicationMatrix[1, 0] = this.ring.AdditiveInverse(data[currentDimension, currentDimension]);
multiplicationMatrix = matrixMultiplicator.Multiply(
multiplicationMatrix,
lastOtherMultiplicationMatrix);
var result = new UnivariatePolynomialNormalForm <ElementType>(
multiplicationMatrix[0, 0],
lines,
this.variableName,
this.ring);
for (int i = 1; i <= lines; ++i)
{
result = result.Add(multiplicationMatrix[i, 0], lines - i, this.ring);
}
return(result);
}
}
}
/// <summary>
/// Obtém uma solução a partir duma aproximação inicial.
/// </summary>
/// <param name="approximateMedians">As medianas.</param>
/// <param name="costs">Os custos.</param>
/// <param name="niter">O número máximo melhoramentos a serem aplicados à solução encontrada.</param>
/// <returns>A solução construída a partir da aproximação.</returns>
public GreedyAlgSolution <CoeffType> Run(
CoeffType[] approximateMedians,
ILongSparseMathMatrix <CoeffType> costs,
int niter)
{
if (approximateMedians == null)
{
throw new ArgumentNullException("approximateMedians");
}
else if (costs == null)
{
throw new ArgumentNullException("costs");
}
else if (approximateMedians.Length != costs.GetLength(1))
{
throw new ArgumentException("The number of medians must match the number of columns in costs matrix.");
}
else
{
var settedSolutions = new IntegerSequence();
var approximateSolutions = new List <int>();
var sum = this.coeffsField.AdditiveUnity;
for (int i = 0; i < approximateMedians.Length; ++i)
{
var currentMedian = approximateMedians[i];
if (!this.coeffsField.IsAdditiveUnity(currentMedian))
{
sum = this.coeffsField.Add(sum, approximateMedians[i]);
if (this.converter.CanApplyDirectConversion(currentMedian))
{
var converted = this.converter.DirectConversion(currentMedian);
if (converted == 1)
{
settedSolutions.Add(i);
}
else
{
throw new OdmpProblemException(string.Format(
"The median {0} at position {1} of medians array can't be converted to the unity.",
currentMedian,
i));
}
}
else
{
approximateSolutions.Add(i);
}
}
}
if (this.converter.CanApplyDirectConversion(sum))
{
var convertedSum = this.converter.DirectConversion(sum);
if (convertedSum <= 0 || convertedSum > approximateMedians.Length)
{
throw new IndexOutOfRangeException(string.Format(
"The medians sum {0} is out of bounds. It must be between 1 and the number of elements in medians array.",
convertedSum));
}
var solutionBoard = new CoeffType[approximateMedians.Length];
var marked = new BitArray(approximateMedians.Length, false);
if (settedSolutions.Count == convertedSum)
{
var result = new GreedyAlgSolution <CoeffType>(settedSolutions);
result.Cost = this.ComputeCost(settedSolutions, costs, solutionBoard, marked);
return(result);
}
else
{
// Partição das mediana em dois conjuntos: as que vão falzer parte da solução e as restantes
// entre as soluções aproximadas.
var recoveredMedians = new List <int>();
var unrecoveredMedians = new List <int>();
var innerComparer = new InnerComparer(approximateMedians, this.comparer);
approximateSolutions.Sort(innerComparer);
var count = convertedSum - settedSolutions.Count;
var i = 0;
for (; i < count; ++i)
{
recoveredMedians.Add(approximateSolutions[i]);
settedSolutions.Add(approximateSolutions[i]);
}
for (; i < approximateSolutions.Count; ++i)
{
unrecoveredMedians.Add(approximateSolutions[i]);
}
var currentCost = this.ComputeCost(settedSolutions, costs, solutionBoard, marked);
// Processa as melhorias de uma forma simples caso seja possível
if (unrecoveredMedians.Count > 0 && niter > 0)
{
var exchangeSolutionBoard = new CoeffType[solutionBoard.Length];
var currentBestBoard = new CoeffType[solutionBoard.Length];
for (i = 0; i < niter; ++i)
{
var itemToExchange = -1;
var itemToExchangeIndex = -1;
var itemToExchangeWith = -1;
var itemToExchangeWithIndex = -1;
var minimumCost = this.coeffsField.AdditiveUnity;
for (int j = 0; j < recoveredMedians.Count; ++j)
{
for (int k = 0; k < unrecoveredMedians.Count; ++k)
{
var replacementCost = this.ComputeReplacementCost(
unrecoveredMedians[k],
recoveredMedians[j],
settedSolutions,
costs,
solutionBoard,
exchangeSolutionBoard);
if (this.comparer.Compare(replacementCost, minimumCost) < 0)
{
// Aceita a troca
itemToExchange = recoveredMedians[j];
itemToExchangeIndex = j;
itemToExchangeWith = unrecoveredMedians[k];
itemToExchangeWithIndex = k;
minimumCost = replacementCost;
var swapBestBoard = currentBestBoard;
currentBestBoard = exchangeSolutionBoard;
exchangeSolutionBoard = swapBestBoard;
}
}
}
if (itemToExchange == -1 || itemToExchangeWith == -1)
{
i = niter - 1;
}
else
{
// Efectua a troca
var swapSolutionBoard = solutionBoard;
solutionBoard = currentBestBoard;
currentBestBoard = swapSolutionBoard;
currentCost = this.coeffsField.Add(currentCost, minimumCost);
settedSolutions.Remove(itemToExchange);
settedSolutions.Add(itemToExchangeWith);
var swap = recoveredMedians[itemToExchangeIndex];
recoveredMedians[itemToExchangeIndex] = unrecoveredMedians[itemToExchangeWithIndex];
unrecoveredMedians[itemToExchangeWithIndex] = swap;
}
}
}
return(new GreedyAlgSolution <CoeffType>(settedSolutions)
{
Cost = currentCost
});
}
}
else
{
throw new OdmpProblemException("The sum of medians can't be converted to an integer.");
}
}
}
public void Statistcs_EnumGeneralizeMeanAlgorithmTest()
{
var integerNumb = new IntegerDomain();
var target = new EnumGeneralizedMeanAlgorithm <int, double, int>(
i => i,
d => d,
(d, i) => d / i,
new DoubleField(),
integerNumb);
var integerSequence = new IntegerSequence();
for (var i = 1; i < 5000; ++i)
{
integerSequence.Add(i);
var expected = (i + 1) / 2.0;
var actual = target.Run(integerSequence);
Assert.AreEqual(expected, actual);
}
integerSequence = new IntegerSequence();
var n = 1000000;
integerSequence.Add(1, n);
var outerExpected = (n + 1) / 2.0;
var outerActual = target.Run(integerSequence);
Assert.AreEqual(outerExpected, outerActual);
var bigIntegerDomain = new BigIntegerDomain();
var fractionField = new FractionField <BigInteger>(bigIntegerDomain);
var fractionTarget = new EnumGeneralizedMeanAlgorithm <int, Fraction <BigInteger>, int>(
i => new Fraction <BigInteger>(i, 1, bigIntegerDomain),
d => d,
(d, i) => d.Divide(i, bigIntegerDomain),
fractionField,
integerNumb);
var fractionExpected = new Fraction <BigInteger>(n + 1, 2, bigIntegerDomain);
var fractionActual = fractionTarget.Run(integerSequence);
Assert.AreEqual(fractionExpected, fractionActual);
// Teste com alteração da função directa
fractionTarget.DirectFunction = i => new Fraction <BigInteger>(new BigInteger(i) * i, 1, bigIntegerDomain);
fractionExpected = new Fraction <BigInteger>(
(new BigInteger(n) + BigInteger.One) * (2 * new BigInteger(n) + 1), 6, bigIntegerDomain);
fractionActual = fractionTarget.Run(integerSequence);
Assert.AreEqual(fractionExpected, fractionActual);
// Teste com transformação
var transformedTarget = new EnumGeneralizedMeanAlgorithm <BigInteger, Fraction <BigInteger>, int>(
i => new Fraction <BigInteger>(i, 1, bigIntegerDomain),
d => d,
(d, i) => d.Divide(i, bigIntegerDomain),
fractionField,
integerNumb);
var transformedSeq = new TransformEnumerable <int, BigInteger>(
integerSequence,
i => new BigInteger(i) * i);
var transformedExpected = new Fraction <BigInteger>(
(new BigInteger(n) + BigInteger.One) * (2 * new BigInteger(n) + 1), 6, bigIntegerDomain);
var transformedActual = transformedTarget.Run(transformedSeq);
Assert.AreEqual(transformedExpected, transformedActual);
}
public void Statistcs_EnumGeneralizeMeanBlockAlgorithmTest()
{
var integerNumb = new IntegerDomain();
var target = new EnumGeneralizedMeanAlgorithm <int, double, int>(
i => i,
d => d,
(d, i) => d / i,
new DoubleField(),
integerNumb);
var blockNumber = 2500;
var integerSequence = new IntegerSequence();
for (var i = 1; i < 5500; ++i)
{
integerSequence.Add(i);
var expected = (i + 1) / 2.0;
var actual = target.Run <double>(
integerSequence,
blockNumber,
(j, k) => j / (double)k,
(d1, d2) => d1 * d2);
Assert.IsTrue(Math.Abs(expected - actual) < 0.0001);
}
integerSequence = new IntegerSequence();
var n = 1000500;
integerSequence.Add(1, n);
var outerExpected = (n + 1) / 2.0;
var outerActual = target.Run <double>(
integerSequence,
blockNumber,
(j, k) => j / (double)k,
(d1, d2) => d1 * d2);
Assert.AreEqual(outerExpected, outerActual);
var integerDomain = new BigIntegerDomain();
var fractionField = new FractionField <BigInteger>(integerDomain);
var fracTarget = new EnumGeneralizedMeanAlgorithm <int, Fraction <BigInteger>, int>(
i => new Fraction <BigInteger>(i, 1, integerDomain),
d => d,
(d, i) => d.Divide(i, integerDomain),
fractionField,
integerNumb);
var fractionExpected = new Fraction <BigInteger>(n + 1, 2, integerDomain);
var fractionActual = fracTarget.Run <Fraction <BigInteger> >(
integerSequence,
blockNumber,
(j, k) => new Fraction <BigInteger>(j, k, integerDomain),
(d1, d2) => d1.Multiply(d2, integerDomain));
Assert.AreEqual(fractionExpected, fractionActual);
// Teste com alteração da função directa
fracTarget.DirectFunction = i => new Fraction <BigInteger>(new BigInteger(i) * i, 1, integerDomain);
fractionExpected = new Fraction <BigInteger>(
(new BigInteger(n) + BigInteger.One) * (2 * new BigInteger(n) + 1), 6, integerDomain);
fractionActual = fracTarget.Run <Fraction <BigInteger> >(
integerSequence,
blockNumber,
(j, k) => new Fraction <BigInteger>(j, k, integerDomain),
(d1, d2) => d1.Multiply(d2, integerDomain));
// Teste com transformação
var transformedTarget = new EnumGeneralizedMeanAlgorithm <BigInteger, Fraction <BigInteger>, int>(
i => new Fraction <BigInteger>(i, 1, integerDomain),
d => d,
(d, i) => d.Divide(i, integerDomain),
fractionField,
integerNumb);
var transformedSeq = new TransformEnumerable <int, BigInteger>(
integerSequence,
i => new BigInteger(i) * i);
var transformedExpected = new Fraction <BigInteger>(
(new BigInteger(n) + BigInteger.One) * (2 * new BigInteger(n) + 1), 6, integerDomain);
var transformedActual = transformedTarget.Run <Fraction <BigInteger> >(
transformedSeq,
blockNumber,
(j, k) => new Fraction <BigInteger>(j, k, integerDomain),
(d1, d2) => d1.Multiply(d2, integerDomain));
Assert.AreEqual(transformedExpected, transformedActual);
}