/// <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>
/// <returns>The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</returns>
public virtual Matrix <T> Solve(Matrix <T> input)
{
// Check for proper arguments.
if (input == null)
{
throw new ArgumentNullException("input");
}
if (!ComputeVectors)
{
throw new InvalidOperationException(Resources.SingularVectorsNotComputed);
}
var result = MatrixU.CreateMatrix(MatrixVT.ColumnCount, input.ColumnCount);
Solve(input, result);
return(result);
}
/// <summary>Returns the singular values as a diagonal <see cref="Matrix{T}"/>.</summary>
/// <returns>The singular values as a diagonal <see cref="Matrix{T}"/>.</returns>
public Matrix <T> W()
{
var rows = MatrixU.RowCount;
var columns = MatrixVT.ColumnCount;
var result = MatrixU.CreateMatrix(rows, columns);
for (var i = 0; i < rows; i++)
{
for (var j = 0; j < columns; j++)
{
if (i == j)
{
result.At(i, i, VectorS[i]);
}
}
}
return(result);
}
