/// <summary>
/// Solves a system of linear equations, <b>AX = B</b>, with A Cholesky factorized.
/// </summary>
/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
public override void Solve(Matrix <Complex> input, Matrix <Complex> result)
{
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
// Check for proper dimensions.
if (result.RowCount != input.RowCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
}
if (result.ColumnCount != input.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
}
if (input.RowCount != CholeskyFactor.RowCount)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(input, CholeskyFactor);
}
input.CopyTo(result);
var order = CholeskyFactor.RowCount;
for (var c = 0; c < result.ColumnCount; c++)
{
// Solve L*Y = B;
Complex sum;
for (var i = 0; i < order; i++)
{
sum = result.At(i, c);
for (var k = i - 1; k >= 0; k--)
{
sum -= CholeskyFactor.At(i, k) * result.At(k, c);
}
result.At(i, c, sum / CholeskyFactor.At(i, i));
}
// Solve L'*X = Y;
for (var i = order - 1; i >= 0; i--)
{
sum = result.At(i, c);
for (var k = i + 1; k < order; k++)
{
sum -= CholeskyFactor.At(k, i).Conjugate() * result.At(k, c);
}
result.At(i, c, sum / CholeskyFactor.At(i, i));
}
}
}
/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>, with A Cholesky factorized.
/// </summary>
/// <param name="input">The right hand side vector, <b>b</b>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
public override void Solve(Vector <Complex> input, Vector <Complex> result)
{
// Check for proper arguments.
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
// Check for proper dimensions.
if (input.Count != result.Count)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (input.Count != CholeskyFactor.RowCount)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(input, CholeskyFactor);
}
input.CopyTo(result);
var order = CholeskyFactor.RowCount;
// Solve L*Y = B;
Complex sum;
for (var i = 0; i < order; i++)
{
sum = result[i];
for (var k = i - 1; k >= 0; k--)
{
sum -= CholeskyFactor.At(i, k) * result[k];
}
result[i] = sum / CholeskyFactor.At(i, i);
}
// Solve L'*X = Y;
for (var i = order - 1; i >= 0; i--)
{
sum = result[i];
for (var k = i + 1; k < order; k++)
{
sum -= CholeskyFactor.At(k, i).Conjugate() * result[k];
}
result[i] = sum / CholeskyFactor.At(i, i);
}
}
/// <summary>
/// Initializes a new instance of the <see cref="UserCholesky"/> class. This object will compute the
/// Cholesky factorization when the constructor is called and cache it's factorization.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not positive definite.</exception>
public UserCholesky(Matrix <Complex> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
// Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
CholeskyFactor = matrix.Clone();
var tmpColumn = new Complex[CholeskyFactor.RowCount];
// Main loop - along the diagonal
for (var ij = 0; ij < CholeskyFactor.RowCount; ij++)
{
// "Pivot" element
var tmpVal = CholeskyFactor.At(ij, ij);
if (tmpVal.Real > 0.0)
{
tmpVal = tmpVal.SquareRoot();
CholeskyFactor.At(ij, ij, tmpVal);
tmpColumn[ij] = tmpVal;
// Calculate multipliers and copy to local column
// Current column, below the diagonal
for (var i = ij + 1; i < CholeskyFactor.RowCount; i++)
{
CholeskyFactor.At(i, ij, CholeskyFactor.At(i, ij) / tmpVal);
tmpColumn[i] = CholeskyFactor.At(i, ij);
}
// Remaining columns, below the diagonal
DoCholeskyStep(CholeskyFactor, CholeskyFactor.RowCount, ij + 1, CholeskyFactor.RowCount, tmpColumn, Control.NumberOfParallelWorkerThreads);
}
else
{
throw new ArgumentException(Resources.ArgumentMatrixPositiveDefinite);
}
for (var i = ij + 1; i < CholeskyFactor.RowCount; i++)
{
CholeskyFactor.At(ij, i, Complex.Zero);
}
}
}
