/// <summary>
/// Solves the linear equation A × X = B for symmetric matrices A.
/// <para>
/// This method only finds exact linear solutions, i.e. solutions for
/// which ||A × X - B|| is exactly 0.
/// </para>
/// </summary>
/// <param name="b">Right-hand side of the equation A × X = B.</param>
/// <returns>Vector X that minimizes the two norm of A × X - B.</returns>
/// <exception cref=DimensionMismatchException""> if the matrices dimensions do not
/// match.</exception>
/// <exception cref="SingularMatrixException"> if the decomposed matrix is singular.
/// </exception>
public RealVector solve(RealVector b)
{
if (!isNonSingular())
{
throw new SingularMatrixException();
}
int m = realEigenvalues.Length;
if (b.getDimension() != m)
{
throw new DimensionMismatchException(b.getDimension(), m);
}
double[] bp = new double[m];
for (int i = 0; i < m; ++i)
{
ArrayRealVector v = eigenvectors[i];
double[] vData = v.getDataRef();
double s = v.dotProduct(b) / realEigenvalues[i];
for (int j = 0; j < m; ++j)
{
bp[j] += s * vData[j];
}
}
return(new ArrayRealVector(bp, false));
}
/// <inheritdoc/>
public RealMatrix solve(RealMatrix b)
{
if (!isNonSingular())
{
throw new SingularMatrixException();
}
int m = realEigenvalues.Length;
if (b.getRowDimension() != m)
{
throw new DimensionMismatchException(b.getRowDimension(), m);
}
int nColB = b.getColumnDimension();
double[][] bp = new double[m][];
double[] tmpCol = new double[m];
for (int k = 0; k < nColB; ++k)
{
for (int i = 0; i < m; ++i)
{
tmpCol[i] = b.getEntry(i, k);
bp[i][k] = 0;
}
for (int i = 0; i < m; ++i)
{
ArrayRealVector v = eigenvectors[i];
double[] vData = v.getDataRef();
double s = 0;
for (int j = 0; j < m; ++j)
{
s += v.getEntry(j) * tmpCol[j];
}
s /= realEigenvalues[i];
for (int j = 0; j < m; ++j)
{
bp[j][k] += s * vData[j];
}
}
}
return(new Array2DRowRealMatrix(bp, false));
}