public Matrix SolveFor(Matrix mRight)
{
Debug.Assert(mRight.NumRows == m_nNumColumns);
Debug.Assert(m_nNumColumns == m_nNumRows);
Matrix mRet = new Matrix(m_nNumColumns, mRight.NumColumns);
LUDecompositionResults resDecomp = LUDecompose();
int[] nP = resDecomp.PivotArray;
Matrix mL = resDecomp.L;
Matrix mU = resDecomp.U;
double dSum = 0.0;
for (int k = 0; k < mRight.NumColumns; k++)
{
Matrix D = new Matrix(m_nNumRows, 1);
D[0, 0] = mRight[nP[0], k] / mL[0, 0];
for (int i = 1; i < m_nNumRows; i++)
{
dSum = 0.0;
for (int j = 0; j < i; j++)
{
dSum += mL[i, j] * D[j, 0];
}
D[i, 0] = (mRight[nP[i], k] - dSum) / mL[i, i];
}
mRet[m_nNumRows - 1, k] = D[m_nNumRows - 1, 0];
for (int i = m_nNumRows - 2; i >= 0; i--)
{
dSum = 0.0;
for (int j = i + 1; j < m_nNumRows; j++)
{
dSum += mU[i, j] * mRet[j, k];
}
mRet[i, k] = D[i, 0] - dSum;
}
}
return(mRet);
}
private LUDecompositionResults LUDecompose()
{
Debug.Assert(m_nNumColumns == m_nNumRows);
LUDecompositionResults resRet = new LUDecompositionResults();
int[] nP = new int[m_nNumRows]; //Pivot matrix.
Matrix mU = new Matrix(m_nNumRows, m_nNumColumns);
Matrix mL = new Matrix(m_nNumRows, m_nNumColumns);
Matrix mUWorking = Clone();
Matrix mLWorking = new Matrix(m_nNumRows, m_nNumColumns);
for (int i = 0; i < m_nNumRows; i++)
{
nP[i] = i;
}
for (int i = 0; i < m_nNumRows; i++)
{
double dMaxRowRatio = double.NegativeInfinity;
int nMaxRow = -1;
int nMaxPosition = -1;
for (int j = i; j < m_nNumRows; j++)
{
double dRowSum = 0.0;
for (int k = i; k < m_nNumColumns; k++)
{
dRowSum += Math.Abs(mUWorking[nP[j], k]);
}
if (Math.Abs(mUWorking[nP[j], i] / dRowSum) > dMaxRowRatio)
{
dMaxRowRatio = Math.Abs(mUWorking[nP[j], i] / dRowSum);
nMaxRow = nP[j];
nMaxPosition = j;
}
}
if (nMaxRow != nP[i])
{
int nHold = nP[i];
nP[i] = nMaxRow;
nP[nMaxPosition] = nHold;
}
double dRowFirstElementValue = mUWorking[nP[i], i];
for (int j = 0; j < m_nNumRows; j++)
{
if (j < i)
{
mUWorking[nP[i], j] = 0.0;
}
else if (j == i)
{
mLWorking[nP[i], j] = dRowFirstElementValue;
mUWorking[nP[i], j] = 1.0;
}
else
{
mUWorking[nP[i], j] /= dRowFirstElementValue;
mLWorking[nP[i], j] = 0.0;
}
}
for (int k = i + 1; k < m_nNumRows; k++)
{
dRowFirstElementValue = mUWorking[nP[k], i];
for (int j = 0; j < m_nNumRows; j++)
{
if (j < i)
{
mUWorking[nP[k], j] = 0.0;
}
else if (j == i)
{
mLWorking[nP[k], j] = dRowFirstElementValue;
mUWorking[nP[k], j] = 0.0;
}
else
{
mUWorking[nP[k], j] = mUWorking[nP[k], j] - dRowFirstElementValue * mUWorking[nP[i], j];
}
}
}
}
for (int i = 0; i < m_nNumRows; i++)
{
for (int j = 0; j < m_nNumRows; j++)
{
mU[i, j] = mUWorking[nP[i], j];
mL[i, j] = mLWorking[nP[i], j];
}
}
resRet.U = mU;
resRet.L = mL;
resRet.PivotArray = nP;
return(resRet);
}
