vector< vector<Fraction> > SLESolver::BringToRowEchelonForm(std::vector< std::vector<Fraction> > augmentedMatrix)
{
int rowLength = augmentedMatrix.size();
int columnLength = augmentedMatrix[0].size();
int lastPivotIndex = 0;
for (int j = 0; j < columnLength; j++) {
Fraction currentFraction = augmentedMatrix[lastPivotIndex][j];
bool pivotFound = false;
int nextLineIndex = lastPivotIndex + 1;
if (currentFraction.GetNumerator() == 0) {
int nonZeroRowIndex = 0;
for (int k = nextLineIndex; k < rowLength; k++) {
if (augmentedMatrix[k][j].GetNumerator() != 0) {
nonZeroRowIndex = k;
pivotFound = true;
break;
}
}
if (pivotFound) {
_solutionWriter->WriteLine("R" + to_string(lastPivotIndex + 1) + "<->" + "R" + to_string(nonZeroRowIndex + 1));
for (int k = j; k < columnLength; k++) {
Fraction temp = augmentedMatrix[lastPivotIndex][k];
augmentedMatrix[lastPivotIndex][k] = augmentedMatrix[nonZeroRowIndex][k];
augmentedMatrix[nonZeroRowIndex][k] = temp;
}
PrintMatrix(augmentedMatrix);
}
}
else {
pivotFound = true;
}
if (pivotFound) {
for (int k = nextLineIndex; k < rowLength; k++) {
Fraction fractionToCheck = augmentedMatrix[k][j];
if (fractionToCheck.GetNumerator() != 0) {
int newNumerator = -fractionToCheck.GetNumerator() * augmentedMatrix[lastPivotIndex][j].GetDenominator();
int newDenominator = fractionToCheck.GetDenominator() * augmentedMatrix[lastPivotIndex][j].GetNumerator();
Fraction fractionToMultiplyBy(newNumerator, newDenominator);
_solutionWriter->WriteLine("R" + to_string(lastPivotIndex + 1) + "*(" + fractionToMultiplyBy.GetString() + ") + " + "R" + to_string(k + 1));
for (int t = j; t < columnLength; t++) {
Fraction fractionToAdd(augmentedMatrix[lastPivotIndex][t]);
fractionToAdd.Multiply(fractionToMultiplyBy);
augmentedMatrix[k][t].Add(fractionToAdd);
}
PrintMatrix(augmentedMatrix);
}
}
lastPivotIndex++;
if (lastPivotIndex == rowLength) {
break;
}
}
}
return augmentedMatrix;
}
const Fraction operator*(const Fraction& term1, const Fraction& term2) {
//Turned into improper fractions and then mulitplied through
Fraction result;
result.SetNumerator(((term1.GetWhole() * term1.GetDenominator()) + term1.GetNumerator()) * ((term2.GetWhole() * term2.GetDenominator()) + term2.GetNumerator()));
result.SetDenominator(term1.GetDenominator() * term2.GetDenominator());
result.Normalize();
return result;
}
const Fraction operator/(const Fraction& term1, const Fraction& term2) {
//Multiplies by the reciprocal of term2
Fraction result;
result.SetNumerator(((term1.GetWhole() * term1.GetDenominator()) + term1.GetNumerator()) * term2.GetDenominator());
result.SetDenominator(term1.GetDenominator() * ((term2.GetWhole() * term2.GetDenominator()) + term2.GetNumerator()));
result.Normalize();
return result;
}
const Fraction operator-(const Fraction& term1, const Fraction& term2) {
//Finds least commons denominator, turns into improper fraction and then subtracted
Fraction frac1(0, ((term1.GetWhole() * term1.GetDenominator() * term2.GetDenominator()) + (term1.GetNumerator() * term2.GetDenominator())), (term1.GetDenominator() * term2.GetDenominator()));
Fraction frac2(0, ((term2.GetWhole() * term2.GetDenominator() * term1.GetDenominator()) + (term2.GetNumerator() * term1.GetDenominator())), (term1.GetDenominator() * term2.GetDenominator()));
Fraction result(0, (frac1.GetNumerator() - frac2.GetNumerator()), frac1.GetDenominator());
result.Normalize();
return result;
}
