/// <summary>
/// Brings the MatrixD into upper triangular form using elementary row operations.
/// </summary>
/// <param name="value">The MatrixD to put into upper triangular form.</param>
/// <param name="result">When the method completes, contains the upper triangular MatrixD.</param>
/// <remarks>
/// If the MatrixD is not invertible (i.e. its determinant is zero) than the result of this
/// method may produce Single.Nan and Single.Inf values. When the MatrixD represents a system
/// of linear equations, than this often means that either no solution exists or an infinite
/// number of solutions exist.
/// </remarks>
public static void UpperTriangularForm(ref MatrixD value, out MatrixD result)
{
//Adapted from the row echelon code.
result = value;
int lead = 0;
int rowcount = 4;
int columncount = 4;
for (int r = 0; r < rowcount; ++r)
{
if (columncount <= lead)
return;
int i = r;
while (MathUtilD.IsZero(result[i, lead]))
{
i++;
if (i == rowcount)
{
i = r;
lead++;
if (lead == columncount)
return;
}
}
if (i != r)
{
result.ExchangeRows(i, r);
}
double multiplier = 1d / result[r, lead];
for (; i < rowcount; ++i)
{
if (i != r)
{
result[i, 0] -= result[r, 0] * multiplier * result[i, lead];
result[i, 1] -= result[r, 1] * multiplier * result[i, lead];
result[i, 2] -= result[r, 2] * multiplier * result[i, lead];
result[i, 3] -= result[r, 3] * multiplier * result[i, lead];
}
}
lead++;
}
}
/// <summary>
/// Brings the MatrixD into row echelon form using elementary row operations;
/// </summary>
/// <param name="value">The MatrixD to put into row echelon form.</param>
/// <param name="result">When the method completes, contains the row echelon form of the MatrixD.</param>
public static void RowEchelonForm(ref MatrixD value, out MatrixD result)
{
//Source: Wikipedia pseudo code
//Reference: http://en.wikipedia.org/wiki/Row_echelon_form#Pseudocode
result = value;
int lead = 0;
int rowcount = 4;
int columncount = 4;
for (int r = 0; r < rowcount; ++r)
{
if (columncount <= lead)
return;
int i = r;
while (MathUtilD.IsZero(result[i, lead]))
{
i++;
if (i == rowcount)
{
i = r;
lead++;
if (lead == columncount)
return;
}
}
if (i != r)
{
result.ExchangeRows(i, r);
}
double multiplier = 1d / result[r, lead];
result[r, 0] *= multiplier;
result[r, 1] *= multiplier;
result[r, 2] *= multiplier;
result[r, 3] *= multiplier;
for (; i < rowcount; ++i)
{
if (i != r)
{
result[i, 0] -= result[r, 0] * result[i, lead];
result[i, 1] -= result[r, 1] * result[i, lead];
result[i, 2] -= result[r, 2] * result[i, lead];
result[i, 3] -= result[r, 3] * result[i, lead];
}
}
lead++;
}
}