/// <summary>
/// Testa a solução do sistema de equações.
/// </summary>
/// <param name="matrix">A matriz dos coeficientes das variáveis.</param>
/// <param name="independent">O vector dos coeficientes independentes.</param>
/// <param name="solution">A solução do sistema simétrico.</param>
private void TestSolution(
IMathMatrix <CoeffType> matrix,
IMathMatrix <CoeffType> independent,
LinearSystemSolution <CoeffType> solution)
{
if (solution.Vector != null)
{
var vec = solution.Vector;
var lines = matrix.GetLength(0);
var columns = matrix.GetLength(1);
for (var i = 0; i < lines; ++i)
{
var sum = this.ring.AdditiveUnity;
for (var j = 0; j < columns; ++j)
{
var value = this.ring.Multiply(
matrix[i, j],
vec[j]);
sum = this.ring.Add(
sum,
value);
}
if (!this.ring.Equals(sum, independent[i, 0]))
{
solution.Vector = null;
solution.VectorSpaceBasis.Clear();
}
}
}
}
/// <summary>
/// Determina a solução de um sistema linear de equações.
/// </summary>
/// <remarks>
/// A matriz e o vector independente são alterados durante o processo.
/// </remarks>
/// <param name="coefficientsMatrix">A matriz dos coeficientes.</param>
/// <param name="independentVector">O vector independente.</param>
/// <returns>A solução do sistema.</returns>
public LinearSystemSolution <ElementType> Run(
IMathMatrix <ElementType> coefficientsMatrix,
IMathMatrix <ElementType> independentVector)
{
this.condensationAlgorithm.Run(coefficientsMatrix, independentVector);
var result = new LinearSystemSolution <ElementType>();
var matrixLines = coefficientsMatrix.GetLength(0);
var matrixColumns = coefficientsMatrix.GetLength(1);
var currentPivotLine = 0;
var currentPivotColumn = 0;
var lastNonZeroColumn = -1;
var independentSolutionVector = new ArrayMathVector <ElementType>(matrixColumns, this.field.AdditiveUnity);
while (currentPivotLine < matrixLines && currentPivotColumn < matrixColumns)
{
var pivotValue = coefficientsMatrix[currentPivotLine, currentPivotColumn];
if (this.field.IsAdditiveUnity(pivotValue))
{
if (this.field.IsAdditiveUnity(independentSolutionVector[currentPivotLine]))
{
var basisVector = new ArrayMathVector <ElementType>(matrixColumns, this.field.AdditiveUnity);
basisVector[currentPivotColumn] = this.field.AdditiveInverse(
this.field.MultiplicativeUnity);
var i = currentPivotLine - 1;
var j = lastNonZeroColumn;
while (i >= 0 && j >= 0)
{
var linePivotValue = coefficientsMatrix[i, j];
if (this.field.IsMultiplicativeUnity(linePivotValue))
{
basisVector[j] = coefficientsMatrix[i, currentPivotColumn];
--i;
}
--j;
}
result.VectorSpaceBasis.Add(basisVector);
}
else
{
result.Vector = null;
result.VectorSpaceBasis.Clear();
return(result);
}
}
else
{
lastNonZeroColumn = currentPivotColumn;
independentSolutionVector[currentPivotColumn] = independentVector[currentPivotLine, 0];
++currentPivotLine;
}
++currentPivotColumn;
}
result.Vector = independentSolutionVector;
return(result);
}
/// <summary>
/// Executa o algorimtmo que permite determinar a solução do sistema simétrico
/// com base na decomposição LDL^T.
/// </summary>
/// <param name="first">A matriz dos coeficientes das variáveis.</param>
/// <param name="second">O vector dos coeficientes independentes.</param>
/// <returns>A solução do sistema.</returns>
public LinearSystemSolution <CoeffType> Run(
ISquareMathMatrix <CoeffType> first,
IMathMatrix <CoeffType> second)
{
if (first == null)
{
throw new ArgumentNullException("first");
}
else if (second == null)
{
throw new ArgumentNullException("second");
}
else
{
var size = first.GetLength(0);
if (second.GetLength(0) != size)
{
throw new ArgumentException(
"The number of columns in coefficients matrix must equal the number of lines in independent vector.");
}
else
{
var result = new LinearSystemSolution <CoeffType>();
var decompRes = this.decompositionAlgorithm.Run(
first);
var indSol = this.ProcessFirstMatrix(
decompRes.UpperTriangularMatrix,
second,
size);
if (this.ProcessDiagonal(decompRes.DiagonalMatrix, indSol, size))
{
this.ProcessRemainingMatrices(
decompRes.UpperTriangularMatrix,
decompRes.DiagonalMatrix,
indSol,
size,
result);
}
return(result);
}
}
}
/// <summary>
/// Processa as restantes matrizes.
/// </summary>
/// <param name="upperTriangMatrix">A matriz triangular superior.</param>
/// <param name="diagMatrix">A matriz diagonal.</param>
/// <param name="independent">O vector independente.</param>
/// <param name="size">O tamanho das matrizes.</param>
/// <param name="solution">A solução do sistema.</param>
private void ProcessRemainingMatrices(
IMathMatrix <CoeffType> upperTriangMatrix,
IMathMatrix <CoeffType> diagMatrix,
IMathVector <CoeffType> independent,
int size,
LinearSystemSolution <CoeffType> solution)
{
var field = this.decompositionAlgorithm.Field;
var innerSize = size - 1;
for (var i = innerSize; i >= 0; --i)
{
var diagValue = diagMatrix[i, i];
if (field.IsAdditiveUnity(diagValue))
{
var basisVector = this.basisVectorFactory.Invoke(
size,
field.AdditiveUnity);
var basisVal = field.MultiplicativeUnity;
basisVector[i] = basisVal;
for (var j = i - 1; j >= 0; --j)
{
if (!field.IsAdditiveUnity(diagMatrix[j, j]))
{
var curr = upperTriangMatrix[j, i];
curr = field.Multiply(
curr,
basisVal);
curr = field.AdditiveInverse(curr);
basisVector[j] = field.Add(
basisVector[j],
curr);
}
}
solution.VectorSpaceBasis.Add(basisVector);
}
else
{
var value = independent[i];
if (!field.IsAdditiveUnity(value))
{
for (var j = i - 1; j >= 0; --j)
{
if (!field.IsAdditiveUnity(diagMatrix[j, j]))
{
var curr = upperTriangMatrix[j, i];
curr = field.Multiply(
curr,
value);
curr = field.AdditiveInverse(curr);
independent[j] = field.Add(
independent[j],
curr);
}
}
}
var basis = solution.VectorSpaceBasis;
var basisCount = basis.Count;
for (var k = 0; k < basisCount; ++k)
{
var vec = basis[k];
var basisVal = vec[i];
if (!field.IsAdditiveUnity(basisVal))
{
for (var j = i - 1; j >= 0; --j)
{
if (!field.IsAdditiveUnity(diagMatrix[j, j]))
{
var curr = upperTriangMatrix[j, i];
curr = field.Multiply(
curr,
basisVal);
curr = field.AdditiveInverse(curr);
vec[j] = field.Add(
vec[j],
curr);
}
}
}
}
}
}
solution.Vector = independent;
}
/// <summary>
/// Obtém os valores da solução.
/// </summary>
/// <param name="solution">A solução do sistema modular.</param>
/// <param name="matrixList">A matriz.</param>
/// <param name="primesList">A lista dos números primos da base.</param>
/// <param name="innerData">O número que está a ser factorizado.</param>
/// <returns>Os factores.</returns>
private Tuple <NumberType, NumberType> GetSolution(
LinearSystemSolution <int> solution,
List <int[]> matrixList,
List <int> primesList,
NumberType innerData)
{
var innerDataModularField = this.modularFieldFactory.CreateInstance(innerData);
var countFactors = primesList.Count - 1;
foreach (var solutionBase in solution.VectorSpaceBasis)
{
var firstValue = this.integerNumber.MultiplicativeUnity;
var factorsCount = new Dictionary <int, int>();
for (int i = 0; i < matrixList.Count; ++i)
{
var currentMatrixLine = matrixList[i];
if (solutionBase[i] == 1)
{
firstValue = innerDataModularField.Multiply(
firstValue,
this.integerNumber.GetNorm(this.integerNumber.MapFrom(currentMatrixLine[currentMatrixLine.Length - 1])));
for (int j = 0; j < countFactors; ++j)
{
if (currentMatrixLine[j] != 0)
{
var countValue = 0;
if (factorsCount.TryGetValue(primesList[j], out countValue))
{
countValue += currentMatrixLine[j];
factorsCount[primesList[j]] = countValue;
}
else
{
factorsCount.Add(primesList[j], currentMatrixLine[j]);
}
}
}
}
}
var secondValue = this.integerNumber.MultiplicativeUnity;
foreach (var factorCountKvp in factorsCount)
{
var primePower = MathFunctions.Power(
this.integerNumber.MapFrom(factorCountKvp.Key),
factorCountKvp.Value / 2,
innerDataModularField);
secondValue = innerDataModularField.Multiply(
secondValue,
primePower);
}
if (!this.integerNumber.Equals(firstValue, secondValue))
{
var firstFactor = MathFunctions.GreatCommonDivisor(
innerData,
this.integerNumber.GetNorm(this.integerNumber.Add(firstValue, this.integerNumber.AdditiveInverse(secondValue))),
this.integerNumber);
if (!this.integerNumber.IsMultiplicativeUnity(firstFactor))
{
var secondFactor = this.integerNumber.Quo(innerData, firstFactor);
return(Tuple.Create(firstFactor, secondFactor));
}
}
}
return(Tuple.Create(this.integerNumber.MultiplicativeUnity, innerData));
}
