public static bool TryGaussJordanElimination(NMatrix a, NMatrix b, out NMatrix result)
{
if (a.NoRows != b.NoRows)
throw new ArgumentException();
result = null;
NMatrix lhs = a.Copy();
NMatrix rhs = b.Copy();
int rowCount = lhs.NoRows;
int colCount = rhs.NoCols + lhs.NoCols;
// augment lhs array with rhs array and store in arr2
var matrixArray = new double[rowCount, colCount];
for (int row = 0; row < rowCount; ++row) {
for (int col = 0; col < lhs.NoCols; ++col) {
matrixArray[row, col] = lhs[row, col];
}
for (int col = 0; col < rhs.NoCols; ++col) {
matrixArray[row, lhs.NoCols + col] = rhs[row, col];
}
}
// perform forward elimination to get arr2 in row-echelon form
for (int row = 0; row < rowCount; ++row) {
// run along diagonal, swapping rows to move zeros in working position
// (along the diagonal) downwards
if (IsZero(matrixArray[row, row]))
if (row == (rowCount - 1))
return false; // no solution
for (int insideRow = row + 1; insideRow < rowCount; insideRow++) {
if (!IsZero(matrixArray[insideRow, row])) {
SwapRows(matrixArray, row, insideRow);
break;
}
}
// divide working row by value of working position to get a 1 on the
// diagonal
if (IsZero(matrixArray[row, row]))
return false;
double diagonal = matrixArray[row, row];
for (int col = 0; col < colCount; ++col)
matrixArray[row, col] /= diagonal;
// eliminate value below working position by subtracting a multiple of
// the current row
for (int insideRow = row + 1; insideRow < rowCount; ++insideRow) {
double coefficient = matrixArray[insideRow, insideRow];
for (int col = 0; col < colCount; ++col)
matrixArray[insideRow, col] -= coefficient * matrixArray[insideRow, col];
}
}
// backward substitution steps
for (int dindex = rowCount - 1; dindex >= 0; --dindex) {
// eliminate value above working position by subtracting a multiple of
// the current row
for (int row = dindex - 1; row >= 0; --row) {
double coefficient = matrixArray[row, dindex];
for (int col = 0; col < colCount; ++col)
matrixArray[row, col] -= coefficient * matrixArray[dindex, col];
}
}
result = new NMatrix(matrixArray);
return true;
}
public static bool TryGaussJordanElimination(NMatrix a, NMatrix b, out NMatrix result)
{
if (a.NoRows != b.NoRows)
{
throw new ArgumentException();
}
result = null;
NMatrix lhs = a.Copy();
NMatrix rhs = b.Copy();
int rowCount = lhs.NoRows;
int colCount = rhs.NoCols + lhs.NoCols;
// augment lhs array with rhs array and store in arr2
var matrixArray = new double[rowCount, colCount];
for (int row = 0; row < rowCount; ++row)
{
for (int col = 0; col < lhs.NoCols; ++col)
{
matrixArray[row, col] = lhs[row, col];
}
for (int col = 0; col < rhs.NoCols; ++col)
{
matrixArray[row, lhs.NoCols + col] = rhs[row, col];
}
}
// perform forward elimination to get arr2 in row-echelon form
for (int row = 0; row < rowCount; ++row)
{
// run along diagonal, swapping rows to move zeros in working position
// (along the diagonal) downwards
if (IsZero(matrixArray[row, row]))
{
if (row == (rowCount - 1))
{
return(false); // no solution
}
}
for (int insideRow = row + 1; insideRow < rowCount; insideRow++)
{
if (!IsZero(matrixArray[insideRow, row]))
{
SwapRows(matrixArray, row, insideRow);
break;
}
}
// divide working row by value of working position to get a 1 on the
// diagonal
if (IsZero(matrixArray[row, row]))
{
return(false);
}
double diagonal = matrixArray[row, row];
for (int col = 0; col < colCount; ++col)
{
matrixArray[row, col] /= diagonal;
}
// eliminate value below working position by subtracting a multiple of
// the current row
for (int insideRow = row + 1; insideRow < rowCount; ++insideRow)
{
double coefficient = matrixArray[insideRow, insideRow];
for (int col = 0; col < colCount; ++col)
{
matrixArray[insideRow, col] -= coefficient * matrixArray[insideRow, col];
}
}
}
// backward substitution steps
for (int dindex = rowCount - 1; dindex >= 0; --dindex)
{
// eliminate value above working position by subtracting a multiple of
// the current row
for (int row = dindex - 1; row >= 0; --row)
{
double coefficient = matrixArray[row, dindex];
for (int col = 0; col < colCount; ++col)
{
matrixArray[row, col] -= coefficient * matrixArray[dindex, col];
}
}
}
result = new NMatrix(matrixArray);
return(true);
}