/// <summary>
/// Solves a system of linear equations, <c>Ax = b</c>, with A LU factorized.
/// </summary>
/// <param name="input">The right hand side vector, <c>b</c>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <c>x</c>.</param>
public override void Solve(Vector <float> input, Vector <float> result)
{
// Check for proper arguments.
if (input == null)
{
throw new ArgumentNullException(nameof(input));
}
if (result == null)
{
throw new ArgumentNullException(nameof(result));
}
// Check for proper dimensions.
if (input.Count != result.Count)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
if (input.Count != Factors.RowCount)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(input, Factors);
}
// Copy the contents of input to result.
input.CopyTo(result);
for (var i = 0; i < Pivots.Length; i++)
{
if (Pivots[i] == i)
{
continue;
}
var p = Pivots[i];
(result[p], result[i]) = (result[i], result[p]);
}
var order = Factors.RowCount;
// Solve L*Y = P*B
for (var k = 0; k < order; k++)
{
for (var i = k + 1; i < order; i++)
{
result[i] -= result[k] * Factors.At(i, k);
}
}
// Solve U*X = Y;
for (var k = order - 1; k >= 0; k--)
{
result[k] /= Factors.At(k, k);
for (var i = 0; i < k; i++)
{
result[i] -= result[k] * Factors.At(i, k);
}
}
}
/// <summary>
/// Solves a system of linear equations, <c>AX = B</c>, with A LU factorized.
/// </summary>
/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <c>B</c>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <c>X</c>.</param>
public override void Solve(Matrix <Complex32> input, Matrix <Complex32> result)
{
// Check for proper arguments.
if (input == null)
{
throw new ArgumentNullException(nameof(input));
}
if (result == null)
{
throw new ArgumentNullException(nameof(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 != Factors.RowCount)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(input, Factors);
}
// Copy the contents of input to result.
input.CopyTo(result);
for (var i = 0; i < Pivots.Length; i++)
{
if (Pivots[i] == i)
{
continue;
}
var p = Pivots[i];
for (var j = 0; j < result.ColumnCount; j++)
{
var temp = result.At(p, j);
result.At(p, j, result.At(i, j));
result.At(i, j, temp);
}
}
var order = Factors.RowCount;
// Solve L*Y = P*B
for (var k = 0; k < order; k++)
{
for (var i = k + 1; i < order; i++)
{
for (var j = 0; j < result.ColumnCount; j++)
{
var temp = result.At(k, j) * Factors.At(i, k);
result.At(i, j, result.At(i, j) - temp);
}
}
}
// Solve U*X = Y;
for (var k = order - 1; k >= 0; k--)
{
for (var j = 0; j < result.ColumnCount; j++)
{
result.At(k, j, (result.At(k, j) / Factors.At(k, k)));
}
for (var i = 0; i < k; i++)
{
for (var j = 0; j < result.ColumnCount; j++)
{
var temp = result.At(k, j) * Factors.At(i, k);
result.At(i, j, result.At(i, j) - temp);
}
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="UserLU"/> class. This object will compute the
/// LU 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>
public UserLU(Matrix <Complex32> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
// Create an array for the pivot indices.
var order = matrix.RowCount;
Factors = matrix.Clone();
Pivots = new int[order];
// Initialize the pivot matrix to the identity permutation.
for (var i = 0; i < order; i++)
{
Pivots[i] = i;
}
var vectorLUcolj = new Complex32[order];
for (var j = 0; j < order; j++)
{
// Make a copy of the j-th column to localize references.
for (var i = 0; i < order; i++)
{
vectorLUcolj[i] = Factors.At(i, j);
}
// Apply previous transformations.
for (var i = 0; i < order; i++)
{
var kmax = Math.Min(i, j);
var s = Complex32.Zero;
for (var k = 0; k < kmax; k++)
{
s += Factors.At(i, k) * vectorLUcolj[k];
}
vectorLUcolj[i] -= s;
Factors.At(i, j, vectorLUcolj[i]);
}
// Find pivot and exchange if necessary.
var p = j;
for (var i = j + 1; i < order; i++)
{
if (vectorLUcolj[i].Magnitude > vectorLUcolj[p].Magnitude)
{
p = i;
}
}
if (p != j)
{
for (var k = 0; k < order; k++)
{
var temp = Factors.At(p, k);
Factors.At(p, k, Factors.At(j, k));
Factors.At(j, k, temp);
}
Pivots[j] = p;
}
// Compute multipliers.
if (j < order & Factors.At(j, j) != 0.0f)
{
for (var i = j + 1; i < order; i++)
{
Factors.At(i, j, (Factors.At(i, j) / Factors.At(j, j)));
}
}
}
}
