/// <summary>
/// Solves a system of linear equations, <b>AX = B</b>, with A SVD 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)
{
// The solution X should have the same number of columns as B
if (input.ColumnCount != result.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
}
// The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows
if (EigenValues.Count != input.RowCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
}
// The solution X row dimension is equal to the column dimension of A
if (EigenValues.Count != result.RowCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
}
if (IsSymmetric)
{
var order = EigenValues.Count;
var tmp = new Complex[order];
for (var k = 0; k < order; k++)
{
for (var j = 0; j < order; j++)
{
Complex value = 0.0;
if (j < order)
{
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(i, j).Conjugate() * input.At(i, k);
}
value /= EigenValues[j].Real;
}
tmp[j] = value;
}
for (var j = 0; j < order; j++)
{
Complex value = 0.0;
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(j, i) * tmp[i];
}
result.At(j, k, value);
}
}
}
else
{
throw new ArgumentException(Resources.ArgumentMatrixSymmetric);
}
}
/// <summary>
/// Solves a system of linear equations, <b>AX = B</b>, with A SVD 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 <float> input, Matrix <float> result)
{
// The solution X should have the same number of columns as B
if (input.ColumnCount != result.ColumnCount)
{
throw new ArgumentException("Matrix column dimensions must agree.");
}
// The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows
if (EigenValues.Count != input.RowCount)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
// The solution X row dimension is equal to the column dimension of A
if (EigenValues.Count != result.RowCount)
{
throw new ArgumentException("Matrix column dimensions must agree.");
}
if (IsSymmetric)
{
var order = EigenValues.Count;
var tmp = new float[order];
for (var k = 0; k < order; k++)
{
for (var j = 0; j < order; j++)
{
float value = 0;
if (j < order)
{
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(i, j) * input.At(i, k);
}
value /= (float)EigenValues[j].Real;
}
tmp[j] = value;
}
for (var j = 0; j < order; j++)
{
float value = 0;
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(j, i) * tmp[i];
}
result.At(j, k, value);
}
}
}
else
{
throw new ArgumentException("Matrix must be symmetric.");
}
}
/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>, with A EVD 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)
{
// Ax=b where A is an m x m matrix
// Check that b is a column vector with m entries
if (EigenValues.Count != input.Count)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
// Check that x is a column vector with n entries
if (EigenValues.Count != result.Count)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(EigenValues, result);
}
if (IsSymmetric)
{
// Symmetric case -> x = V * inv(λ) * VH * b;
var order = EigenValues.Count;
var tmp = new Complex[order];
Complex value;
for (var j = 0; j < order; j++)
{
value = 0;
if (j < order)
{
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(i, j).Conjugate() * input[i];
}
value /= EigenValues[j].Real;
}
tmp[j] = value;
}
for (var j = 0; j < order; j++)
{
value = 0;
for (int i = 0; i < order; i++)
{
value += EigenVectors.At(j, i) * tmp[i];
}
result[j] = value;
}
}
else
{
throw new ArgumentException(Resources.ArgumentMatrixSymmetric);
}
}
/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>, with A EVD 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 <float> input, Vector <float> result)
{
// Ax=b where A is an m x m matrix
// Check that b is a column vector with m entries
if (EigenValues.Count != input.Count)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
// Check that x is a column vector with n entries
if (EigenValues.Count != result.Count)
{
throw new ArgumentException("Matrix dimensions must agree.");
}
if (IsSymmetric)
{
// Symmetric case -> x = V * inv(λ) * VT * b;
var order = EigenValues.Count;
var tmp = new float[order];
float value;
for (var j = 0; j < order; j++)
{
value = 0;
if (j < order)
{
for (var i = 0; i < order; i++)
{
value += EigenVectors.At(i, j) * input[i];
}
value /= (float)EigenValues[j].Real;
}
tmp[j] = value;
}
for (var j = 0; j < order; j++)
{
value = 0;
for (int i = 0; i < order; i++)
{
value += EigenVectors.At(j, i) * tmp[i];
}
result[j] = value;
}
}
else
{
throw new ArgumentException("Matrix must be symmetric.");
}
}