/// <summary>
/// Divide um número complexo corrente por outro.
/// </summary>
/// <param name="right">O número a ser dividido.</param>
/// <param name="field">O corpo responsável pelas operações.</param>
/// <returns>O resultado da divisão.</returns>
/// <exception cref="ArgumentNullException">Se algum dos argumentos for nulo.</exception>
/// <exception cref="DivideByZeroException">Se ocorrer uma divisão por zero.</exception>
public ComplexNumber <ObjectType> Divide(ComplexNumber <ObjectType> right, IField <ObjectType> field)
{
if (field == null)
{
throw new ArgumentNullException("field");
}
else if (right == null)
{
throw new ArgumentNullException("right");
}
else if (right.IsZero(field))
{
throw new DivideByZeroException("Can't divide by the zero complex number.");
}
else
{
var quadReal = field.Multiply(right.realPart, right.realPart);
var quadImaginary = field.Multiply(right.imaginaryPart, right.imaginaryPart);
var denom = field.Add(quadReal, quadImaginary);
var resReal = field.Multiply(this.realPart, right.realPart);
resReal = field.Add(
resReal,
field.Multiply(this.imaginaryPart, right.imaginaryPart));
resReal = field.Multiply(
resReal,
field.MultiplicativeInverse(denom));
var resImg = field.Multiply(this.realPart, right.imaginaryPart);
resImg = field.AdditiveInverse(resImg);
resImg = field.Add(
resImg,
field.Multiply(this.imaginaryPart, right.realPart));
resImg = field.Multiply(
resImg,
field.MultiplicativeInverse(denom));
var result = new ComplexNumber <ObjectType>();
result.realPart = resReal;
result.imaginaryPart = resImg;
return(result);
}
}
/// <summary>
/// Obtém uma base ortogonalizada a partir da base actual.
/// </summary>
/// <param name="coefficientsField">O corpo responsável pelas operações sobre os coeficientes.</param>
/// <param name="vectorSpace">O espaço responsável pela multiplicação de um escalar com um vector.</param>
/// <param name="scalarProduct">O produto escalar.</param>
/// <returns>A base ortogonalizada.</returns>
/// <exception cref="ArgumentNullException">Se algum dos argumentos for nulo.</exception>
public VectorSpaceGenerator <CoeffType> GetOrthogonalizedBase(
IField <CoeffType> coefficientsField,
IVectorSpace <CoeffType, IMathVector <CoeffType> > vectorSpace,
IScalarProductSpace <IMathVector <CoeffType>, CoeffType> scalarProduct)
{
if (coefficientsField == null)
{
throw new ArgumentNullException("coefficientsField");
}
else if (vectorSpace == null)
{
throw new ArgumentNullException("vectorSpace");
}
else if (scalarProduct == null)
{
throw new ArgumentNullException("scalarProduct");
}
else
{
var result = new List <IMathVector <CoeffType> >();
// Mantém a lista de resultados intermédios
var intermediaryResults = new List <CoeffType>();
if (this.basisVectors.Count > 0)
{
var basisCount = this.basisVectors.Count;
var i = -1;
var control = 0;
while (control < basisCount)
{
var currentVector = this.basisVectors[control];
if (!currentVector.IsNull(coefficientsField))
{
i = control;
control = basisCount;
}
else
{
++control;
}
}
if (i != -1)
{
--basisCount;
var currentVector = this.basisVectors[i];
result.Add(currentVector);
if (i < basisCount)
{
var denom = scalarProduct.Multiply(currentVector, currentVector);
intermediaryResults.Add(denom);
++i;
for (; i < basisCount; ++i)
{
currentVector = this.basisVectors[i];
for (int j = 0; j < result.Count; ++j)
{
denom = intermediaryResults[j];
if (!coefficientsField.IsAdditiveUnity(denom))
{
var orthoVector = result[j];
var num = scalarProduct.Multiply(currentVector, orthoVector);
if (!coefficientsField.IsAdditiveUnity(num))
{
var scalar = coefficientsField.Multiply(
num,
coefficientsField.MultiplicativeInverse(denom));
scalar = coefficientsField.AdditiveInverse(scalar);
if (!coefficientsField.IsMultiplicativeUnity(scalar))
{
orthoVector = vectorSpace.MultiplyScalar(scalar, orthoVector);
currentVector = vectorSpace.Add(currentVector, orthoVector);
}
}
}
}
// Já foi calculado o vector ortogonal
denom = scalarProduct.Multiply(currentVector, currentVector);
if (coefficientsField.IsAdditiveUnity(denom))
{
if (!currentVector.IsNull(coefficientsField))
{
intermediaryResults.Add(denom);
result.Add(currentVector);
}
}
else
{
intermediaryResults.Add(denom);
result.Add(currentVector);
}
}
// Na útlima iteração não é necessário calcular o produto escalar
currentVector = this.basisVectors[i];
for (int j = 0; j < result.Count; ++j)
{
denom = intermediaryResults[j];
if (!coefficientsField.IsAdditiveUnity(denom))
{
var orthoVector = result[j];
var num = scalarProduct.Multiply(currentVector, orthoVector);
if (!coefficientsField.IsAdditiveUnity(num))
{
var scalar = coefficientsField.Multiply(
num,
coefficientsField.MultiplicativeInverse(denom));
scalar = coefficientsField.AdditiveInverse(scalar);
if (!coefficientsField.IsMultiplicativeUnity(scalar))
{
orthoVector = vectorSpace.MultiplyScalar(scalar, orthoVector);
currentVector = vectorSpace.Add(currentVector, orthoVector);
}
}
}
}
// Já foi calculado o vector ortogonal
if (!currentVector.IsNull(coefficientsField))
{
result.Add(currentVector);
}
}
}
}
return(new VectorSpaceGenerator <CoeffType>(
this.vectorSpaceDimension,
result));
}
}
/// <summary>
/// Determina a inversa da matriz correspondente à decomposição especificada.
/// </summary>
/// <param name="decompositionResult">A decomposição.</param>
/// <param name="matrixFactory">A fábrica responsável pela criação da matriz resultante.</param>
/// <param name="field">O corpo responsável pelas operações sobre os objectos.</param>
/// <returns>A inversa da matriz associada à decomposição.</returns>
/// <exception cref="ArgumentNullException">Se algums dos argumentos for nulo.</exception>
public IMathMatrix <CoeffType> Run(
TriangDiagSymmMatrixDecompResult <CoeffType> decompositionResult,
ISquareMatrixFactory <CoeffType> matrixFactory,
IField <CoeffType> field)
{
if (field == null)
{
throw new ArgumentNullException("field");
}
else if (matrixFactory == null)
{
throw new ArgumentNullException("matrixFactory");
}
else if (decompositionResult == null)
{
throw new ArgumentNullException("decompositionResult");
}
else
{
var dimension = decompositionResult.UpperTriangularMatrix.GetLength(0);
for (var i = 0; i < dimension; ++i)
{
var d = decompositionResult.DiagonalMatrix[i, i];
if (field.IsAdditiveUnity(d))
{
throw new MathematicsException("The provided decomposition has no inverse.");
}
}
var result = matrixFactory.CreateMatrix(dimension);
for (int j = dimension - 1; j >= 0; --j)
{
// Elemento na diagonal.
var i = j;
var diagonalValue = field.MultiplicativeInverse(
decompositionResult.DiagonalMatrix[i, j]);
var k = i + 1;
for (; k < dimension; ++k)
{
var product = field.Multiply(
decompositionResult.UpperTriangularMatrix[i, k],
result[i, k]);
diagonalValue = field.Add(
diagonalValue,
field.AdditiveInverse(product));
}
result[i, j] = diagonalValue;
--i;
while (i >= 0)
{
k = i + 1;
var upperValue = field.Multiply(
decompositionResult.UpperTriangularMatrix[i, k],
result[k, j]);
upperValue = field.AdditiveInverse(upperValue);
++k;
for (; k <= j; ++k)
{
var product = field.Multiply(
decompositionResult.UpperTriangularMatrix[i, k],
result[k, j]);
upperValue = field.Add(
upperValue,
field.AdditiveInverse(product));
}
// Como a matriz é simétrica, inverte a orientação.
for (; k < dimension; ++k)
{
var product = field.Multiply(
decompositionResult.UpperTriangularMatrix[i, k],
result[j, k]);
upperValue = field.Add(
upperValue,
field.AdditiveInverse(product));
}
result[i, j] = upperValue;
--i;
}
}
this.SetLowerTerms(result);
return(result);
}
}