public void SolveLinear(SimpleMatrix vec)
{
if (xDim != yDim || yDim != vec.yDim)
{
throw (new InvalidOperationException
("Matrix not quadratic or vector dimension mismatch"));
}
for (int y = 0; y < (yDim - 1); ++y)
{
int yMaxIndex = y;
double yMaxValue = Math.Abs(values[y, y]);
for (int py = y; py < yDim; ++py)
{
if (Math.Abs(values[py, y]) > yMaxValue)
{
yMaxValue = Math.Abs(values[py, y]);
yMaxIndex = py;
}
}
SwapRow(y, yMaxIndex);
vec.SwapRow(y, yMaxIndex);
for (int py = y + 1; py < yDim; ++py)
{
double elimMul = values[py, y] / values[y, y];
for (int x = 0; x < xDim; ++x)
{
values[py, x] -= elimMul * values[y, x];
}
vec[py, 0] -= elimMul * vec[y, 0];
}
}
for (int y = yDim - 1; y >= 0; --y)
{
double solY = vec[y, 0];
for (int x = xDim - 1; x > y; --x)
{
solY -= values[y, x] * vec[x, 0];
}
vec[y, 0] = solY / values[y, y];
}
}
// The vector 'vec' is used both for input/output purposes. As input, it
// contains the vector v, and after this method finishes it contains x,
// the solution in the formula
// this * x = v
// This matrix might get row-swapped, too.
public void SolveLinear(SimpleMatrix vec)
{
if (xDim != yDim || yDim != vec.yDim)
{
throw (new InvalidOperationException
("Matrix not quadratic or vector dimension mismatch"));
}
// Gaussian Elimination Algorithm, as described by
// "Numerical Methods - A Software Approach", R.L. Johnston
// Forward elimination with partial pivoting
for (int y = 0; y < (yDim - 1); ++y)
{
// Searching for the largest pivot (to get "multipliers < 1.0 to
// minimize round-off errors")
int yMaxIndex = y;
double yMaxValue = Math.Abs(values[y, y]);
for (int py = y; py < yDim; ++py)
{
if (Math.Abs(values[py, y]) > yMaxValue)
{
yMaxValue = Math.Abs(values[py, y]);
yMaxIndex = py;
}
}
// if a larger row has been found, swap with the current one
SwapRow(y, yMaxIndex);
vec.SwapRow(y, yMaxIndex);
// Now do the elimination left of the diagonal
for (int py = y + 1; py < yDim; ++py)
{
// always <= 1.0
double elimMul = values[py, y] / values[y, y];
for (int x = 0; x < xDim; ++x)
{
values[py, x] -= elimMul * values[y, x];
}
// FIXME: do we really need this?
vec[py, 0] -= elimMul * vec[y, 0];
}
}
// Back substitution
for (int y = yDim - 1; y >= 0; --y)
{
double solY = vec[y, 0];
for (int x = xDim - 1; x > y; --x)
{
solY -= values[y, x] * vec[x, 0];
}
vec[y, 0] = solY / values[y, y];
}
}