/// <summary>
/// Solves the specified linear system of equations <i>Ax=b</i>.
/// </summary>
/// <param name="matrixA">The matrix A.</param>
/// <param name="initialX">
/// The initial guess for x. If this value is <see langword="null"/>, a zero vector will be used
/// as initial guess.
/// </param>
/// <param name="vectorB">The vector b.</param>
/// <returns>The solution vector x.</returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentNullException">
/// <paramref name="vectorB"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is not a square matrix.
/// </exception>
/// <exception cref="ArgumentException">
/// The number of elements of <paramref name="initialX"/> does not match.
/// </exception>
public override VectorF Solve(MatrixF matrixA, VectorF initialX, VectorF vectorB)
{
NumberOfIterations = 0;
if (matrixA == null)
{
throw new ArgumentNullException("matrixA");
}
if (vectorB == null)
{
throw new ArgumentNullException("vectorB");
}
if (matrixA.IsSquare == false)
{
throw new ArgumentException("Matrix A must be a square matrix.", "matrixA");
}
if (matrixA.NumberOfRows != vectorB.NumberOfElements)
{
throw new ArgumentException("The number of rows of A and b do not match.");
}
if (initialX != null && initialX.NumberOfElements != vectorB.NumberOfElements)
{
throw new ArgumentException("The number of elements of the initial guess for x and b do not match.");
}
VectorF xOld = initialX ?? new VectorF(vectorB.NumberOfElements);
VectorF xNew = new VectorF(vectorB.NumberOfElements);
bool isConverged = false;
// Make iterations until max iteration count or the result has converged.
for (int i = 0; i < MaxNumberOfIterations && !isConverged; i++)
{
for (int j = 0; j < vectorB.NumberOfElements; j++)
{
float delta = 0;
for (int k = 0; k < j; k++)
{
delta += matrixA[j, k] * xNew[k];
}
for (int k = j + 1; k < vectorB.NumberOfElements; k++)
{
delta += matrixA[j, k] * xOld[k];
}
delta = (vectorB[j] - delta) / matrixA[j, j];
xNew[j] = xOld[j] + RelaxationFactor * (delta - xOld[j]);
}
// Test convergence
isConverged = VectorF.AreNumericallyEqual(xOld, xNew, Epsilon);
xOld = xNew.Clone();
NumberOfIterations = i + 1;
}
return(xNew);
}
/// <summary>
/// Solves the specified linear system of equations <i>Ax=b</i>.
/// </summary>
/// <param name="matrixA">The matrix A.</param>
/// <param name="initialX">
/// The initial guess for x. If this value is <see langword="null"/>, a zero vector will be used
/// as initial guess.
/// </param>
/// <param name="vectorB">The vector b.</param>
/// <returns>The solution vector x.</returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentNullException">
/// <paramref name="vectorB"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is not a square matrix.
/// </exception>
/// <exception cref="ArgumentException">
/// The number of elements of <paramref name="initialX"/> does not match.
/// </exception>
public override VectorF Solve(MatrixF matrixA, VectorF initialX, VectorF vectorB)
{
// TODO: We can possible improve the method by reordering after each step.
// This can be done randomly or we sort by the "convergence" of the elements.
// See book Physics-Based Animation.
NumberOfIterations = 0;
if (matrixA == null)
throw new ArgumentNullException("matrixA");
if (vectorB == null)
throw new ArgumentNullException("vectorB");
if (matrixA.IsSquare == false)
throw new ArgumentException("Matrix A must be a square matrix.", "matrixA");
if (matrixA.NumberOfRows != vectorB.NumberOfElements)
throw new ArgumentException("The number of rows of A and b do not match.");
if (initialX != null && initialX.NumberOfElements != vectorB.NumberOfElements)
throw new ArgumentException("The number of elements of the initial guess for x and b do not match.");
VectorF xOld = initialX ?? new VectorF(vectorB.NumberOfElements);
VectorF xNew = new VectorF(vectorB.NumberOfElements);
bool isConverged = false;
// Make iterations until max iteration count or the result has converged.
for (int i = 0; i < MaxNumberOfIterations && !isConverged; i++)
{
for (int j = 0; j < vectorB.NumberOfElements; j++)
{
float delta = 0;
for (int k = 0; k < j; k++)
delta += matrixA[j, k] * xNew[k];
for (int k = j + 1; k < vectorB.NumberOfElements; k++)
delta += matrixA[j, k] * xOld[k];
xNew[j] = (vectorB[j] - delta) / matrixA[j, j];
}
// Test convergence
isConverged = VectorF.AreNumericallyEqual(xOld, xNew, Epsilon);
xOld = xNew.Clone();
NumberOfIterations = i + 1;
}
return xNew;
}
/// <summary>
/// Solves the specified linear system of equations <i>Ax=b</i>.
/// </summary>
/// <param name="matrixA">The matrix A.</param>
/// <param name="initialX">
/// The initial guess for x. If this value is <see langword="null"/>, a zero vector will be used
/// as initial guess.
/// </param>
/// <param name="vectorB">The vector b.</param>
/// <returns>The solution vector x.</returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentNullException">
/// <paramref name="vectorB"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is not a square matrix.
/// </exception>
/// <exception cref="ArgumentException">
/// The number of elements of <paramref name="initialX"/> does not match.
/// </exception>
public override VectorF Solve(MatrixF matrixA, VectorF initialX, VectorF vectorB)
{
NumberOfIterations = 0;
if (matrixA == null)
throw new ArgumentNullException("matrixA");
if (vectorB == null)
throw new ArgumentNullException("vectorB");
if (matrixA.IsSquare == false)
throw new ArgumentException("Matrix A must be a square matrix.", "matrixA");
if (matrixA.NumberOfRows != vectorB.NumberOfElements)
throw new ArgumentException("The number of rows of A and b do not match.");
if (initialX != null && initialX.NumberOfElements != vectorB.NumberOfElements)
throw new ArgumentException("The number of elements of the initial guess for x and b do not match.");
VectorF xOld = initialX ?? new VectorF(vectorB.NumberOfElements);
VectorF xNew = new VectorF(vectorB.NumberOfElements);
bool isConverged = false;
// Make iterations until max iteration count or the result has converged.
for (int i = 0; i < MaxNumberOfIterations && !isConverged; i++)
{
for (int j=0; j<vectorB.NumberOfElements; j++)
{
float delta = 0;
for (int k=0; k < j; k++)
delta += matrixA[j, k] * xNew[k];
for (int k=j+1; k < vectorB.NumberOfElements; k++)
delta += matrixA[j, k] * xOld[k];
delta = (vectorB[j] - delta) / matrixA[j, j];
xNew[j] = xOld[j] + RelaxationFactor * (delta - xOld[j]);
}
// Test convergence
isConverged = VectorF.AreNumericallyEqual(xOld, xNew, Epsilon);
xOld = xNew.Clone();
NumberOfIterations = i + 1;
}
return xNew;
}
public void CloneTest()
{
VectorF v = new VectorF(new List<float>(new float[] { 1, 2, 3, 4, 5 }));
VectorF clonedVector = v.Clone();
Assert.AreEqual(v, clonedVector);
}
/// <summary>
/// Solves the specified linear system of equations <i>Ax=b</i>.
/// </summary>
/// <param name="matrixA">The matrix A.</param>
/// <param name="initialX">
/// The initial guess for x. If this value is <see langword="null"/>, a zero vector will be used
/// as initial guess.
/// </param>
/// <param name="vectorB">The vector b.</param>
/// <returns>The solution vector x.</returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentNullException">
/// <paramref name="vectorB"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is not a square matrix.
/// </exception>
/// <exception cref="ArgumentException">
/// The number of elements of <paramref name="initialX"/> does not match.
/// </exception>
public override VectorF Solve(MatrixF matrixA, VectorF initialX, VectorF vectorB)
{
// TODO: We can possible improve the method by reordering after each step.
// This can be done randomly or we sort by the "convergence" of the elements.
// See book Physics-Based Animation.
NumberOfIterations = 0;
if (matrixA == null)
{
throw new ArgumentNullException("matrixA");
}
if (vectorB == null)
{
throw new ArgumentNullException("vectorB");
}
if (matrixA.IsSquare == false)
{
throw new ArgumentException("Matrix A must be a square matrix.", "matrixA");
}
if (matrixA.NumberOfRows != vectorB.NumberOfElements)
{
throw new ArgumentException("The number of rows of A and b do not match.");
}
if (initialX != null && initialX.NumberOfElements != vectorB.NumberOfElements)
{
throw new ArgumentException("The number of elements of the initial guess for x and b do not match.");
}
VectorF xOld = initialX ?? new VectorF(vectorB.NumberOfElements);
VectorF xNew = new VectorF(vectorB.NumberOfElements);
bool isConverged = false;
// Make iterations until max iteration count or the result has converged.
for (int i = 0; i < MaxNumberOfIterations && !isConverged; i++)
{
for (int j = 0; j < vectorB.NumberOfElements; j++)
{
float delta = 0;
for (int k = 0; k < j; k++)
{
delta += matrixA[j, k] * xNew[k];
}
for (int k = j + 1; k < vectorB.NumberOfElements; k++)
{
delta += matrixA[j, k] * xOld[k];
}
xNew[j] = (vectorB[j] - delta) / matrixA[j, j];
}
// Test convergence
isConverged = VectorF.AreNumericallyEqual(xOld, xNew, Epsilon);
xOld = xNew.Clone();
NumberOfIterations = i + 1;
}
return(xNew);
}
