/// <summary>
/// Calcula as entradas da matriz de multiplicação.
/// </summary>
/// <param name="data">A matriz.</param>
/// <param name="diagonalElement">O elemento na diagonal.</param>
/// <param name="subMatrixSequence">A sequência que define a sub-matriz.</param>
/// <param name="singleValueSequence">A sequência que define o valor.</param>
/// <param name="multiplicator">O objecto responsável pela multiplicação de matrizes.</param>
/// <param name="multiplicationMatrix">A matriz que comporta o resultado da multiplicação.</param>
private void FillMultiplicationMatrix(
IMathMatrix <ElementType> data,
ElementType diagonalElement,
IntegerSequence subMatrixSequence,
IntegerSequence singleValueSequence,
MatrixMultiplicationOperation <ElementType> multiplicator,
IMatrix <ElementType> multiplicationMatrix)
{
var dimension = multiplicationMatrix.GetLength(1);
var rowSubMatrix = data.GetSubMatrix(singleValueSequence, subMatrixSequence);
var columnSubMatrix = data.GetSubMatrix(subMatrixSequence, singleValueSequence);
var mainSubMatrix = data.GetSubMatrix(subMatrixSequence, subMatrixSequence);
for (int i = 0; i < dimension; ++i)
{
multiplicationMatrix[i, i] = this.ring.MultiplicativeUnity;
}
for (int i = 0; i < dimension; ++i)
{
multiplicationMatrix[i + 1, i] = this.ring.AdditiveInverse(diagonalElement);
}
var vectorsMultiply = multiplicator.Multiply(rowSubMatrix, columnSubMatrix);
for (int i = 0; i < dimension - 1; ++i)
{
multiplicationMatrix[i + 2, i] = this.ring.AdditiveInverse(vectorsMultiply[0, 0]);
}
vectorsMultiply = multiplicator.Multiply(rowSubMatrix, mainSubMatrix);
vectorsMultiply = multiplicator.Multiply(vectorsMultiply, columnSubMatrix);
for (int i = 0; i < dimension - 2; ++i)
{
multiplicationMatrix[i + 3, i] = this.ring.AdditiveInverse(vectorsMultiply[0, 0]);
}
var subMatrix = mainSubMatrix;
for (int i = 3; i < dimension; ++i)
{
subMatrix = multiplicator.Multiply(mainSubMatrix, subMatrix);
vectorsMultiply = multiplicator.Multiply(rowSubMatrix, subMatrix);
vectorsMultiply = multiplicator.Multiply(vectorsMultiply, columnSubMatrix);
for (int j = 0; j < dimension - i; ++j)
{
multiplicationMatrix[j + i + 1, j] = this.ring.AdditiveInverse(vectorsMultiply[0, 0]);
}
}
}
/// <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);
}
}
}
