/// <summary>
/// Solves <i>A*X = B</i>; returns <i>X</i>.
/// </summary>
/// <param name="B">A Matrix with as many rows as <i>A</i> and any number of columns.</param>
/// <returns><i>X</i> so that <i>L*L'*X = B</i>.</returns>
/// <exception cref="ArgumentException">if <i>B.Rows != A.Rows</i>.</exception>
/// <exception cref="ArgumentException">if <i>!isSymmetricPositiveDefinite()</i>.</exception>
private DoubleMatrix2D XXXsolveBuggy(DoubleMatrix2D B)
{
var F = Cern.Jet.Math.Functions.functions;
if (B.Rows != n)
{
throw new ArgumentException(Cern.LocalizedResources.Instance().Exception_MatrixRowDimensionsMustAgree);
}
if (!isSymmetricPositiveDefinite)
{
throw new ArgumentException(Cern.LocalizedResources.Instance().Exception_MatrixIsNotSymmetricPositiveDefinite);
}
// Copy right hand side.
DoubleMatrix2D X = B.Copy();
int nx = B.Columns;
// precompute and cache some views to avoid regenerating them time and again
DoubleMatrix1D[] Xrows = new DoubleMatrix1D[n];
for (int k = 0; k < n; k++)
{
Xrows[k] = X.ViewRow(k);
}
// Solve L*Y = B;
for (int k = 0; k < n; k++)
{
for (int i = k + 1; i < n; i++)
{
// X[i,j] -= X[k,j]*L[i,k]
Xrows[i].Assign(Xrows[k], F2.MinusMult(mL[i, k]));
}
Xrows[k].Assign(F1.Div(mL[k, k]));
}
// Solve L'*X = Y;
for (int k = n - 1; k >= 0; k--)
{
Xrows[k].Assign(F1.Div(mL[k, k]));
for (int i = 0; i < k; i++)
{
// X[i,j] -= X[k,j]*L[k,i]
Xrows[i].Assign(Xrows[k], F2.MinusMult(mL[k, i]));
}
}
return(X);
}