"Gaussian Elimination" Implementation in C++ #555
There are no files selected for viewing
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,187 @@ | ||
| #include <iostream> | ||
| #include <algorithm> | ||
| #include <stdexcept> | ||
| #include <vector> | ||
| #include <cmath> | ||
| using namespace std; | ||
|
|
||
| class EquationSolver | ||
|
There was a problem hiding this comment. There really is no need in making a class for solving Gaussian elimination. There was a problem hiding this comment. So, should I just define each function individually, because I thought encapsulating it would make it more user-friendly and show how it can be used to solve equations. |
||
| { | ||
| private: | ||
|
|
||
| // subtract row from another row after multiplcation | ||
| void subRow(vector<long double> &toBeSubtracted, const vector<long double> &toSubtract, | ||
|
There was a problem hiding this comment. There is no need of making this function if it's used in one place. There was a problem hiding this comment. Since the row subtraction function was being showcased in the documentation, I thought a special mention would be necessary. |
||
| long double mult, int start) | ||
| { | ||
| for (int i = start; i < toBeSubtracted.size(); i++) | ||
| toBeSubtracted[i] -= mult * toSubtract[i]; | ||
| } | ||
| // A start variable is given since if we know all values are 0, we don't need | ||
| // to subtract. | ||
|
|
||
|
|
||
| // swap two rows | ||
| void swapRow(vector<long double> &eqn1, vector<long double> &eqn2, int start) | ||
| { | ||
| for (int i = start; i < eqn1.size(); i++) | ||
| swap(eqn1[i], eqn2[i]); | ||
| } | ||
| // A start variable is given since if we know all values are 0, we don't need | ||
| // to swap. | ||
|
|
||
|
|
||
| int gaussianElimination(vector<vector<long double>> &eqns, int varc) | ||
| { | ||
| // 'eqns' is the matrix, 'varc' is no. of vars | ||
| int err = 0; // marker for if matrix is singular | ||
| for (int i = 0; i < varc - 1; i++) | ||
| { | ||
| long double pivot = fabsl(eqns[i][i]); | ||
| int newRow = i; | ||
| for (int j = i + 1; j < varc; j++) | ||
| { | ||
| if (fabsl(eqns[j][i]) > pivot) | ||
| { | ||
| pivot = fabsl(eqns[j][i]); | ||
| newRow = j; | ||
| } | ||
| } | ||
|
|
||
| if (pivot == 0.0) | ||
| { | ||
| err = 1; // Marking that matrix is singular | ||
| continue; | ||
| } | ||
| if (newRow != i) | ||
| swapRow(eqns[newRow], eqns[i], i); | ||
|
|
||
| for (int j = i + 1; j < varc; j++) | ||
| if (eqns[j][i]) | ||
| subRow(eqns[j], eqns[i], (eqns[j][i] / eqns[i][i]), i); | ||
| } | ||
|
|
||
| if (eqns[varc - 1][varc - 1] == 0 || err) | ||
| { | ||
| if (eqns[varc - 1][varc] == 0 || err) | ||
| return 1; // Error code: Singular matrix | ||
| else | ||
| return 2; // Error code: No solutions | ||
| // Cannot solve since final equation is '0*xn = c' | ||
| } | ||
| return 0; // Successful | ||
| } | ||
|
|
||
|
|
||
| void gaussJordan(vector<vector<long double>> &eqns, int varc) | ||
| { | ||
| // 'eqns' is the (Row-echelon) matrix, 'varc' is no. of vars | ||
| for (int i = varc - 1; i >= 0; i--) | ||
| { | ||
| eqns[i][varc] /= eqns[i][i]; | ||
| eqns[i][i] = 1; // We know that the only entry in this row is 1 | ||
|
|
||
| for (int j = i - 1; j >= 0; j--) // subtracting rows from below | ||
| { | ||
| eqns[j][varc] -= eqns[j][i] * eqns[i][varc]; | ||
| eqns[j][i] = 0; // We also set all the other values in row to 0 directly | ||
| } | ||
| } | ||
| } | ||
|
|
||
|
|
||
| vector<long double> backSubs(vector<vector<long double>> &eqns, int varc) | ||
| { | ||
| // 'eqns' is matrix, 'varc' is no. of variables | ||
| vector<long double> ans(varc); | ||
| for (int i = varc - 1; i >= 0; i--) | ||
| { | ||
| long double sum = 0; | ||
| for (int j = i + 1; j < varc; j++) | ||
| sum += eqns[i][j] * ans[j]; | ||
|
|
||
| ans[i] = (eqns[i][varc] - sum) / eqns[i][i]; | ||
| } | ||
| return ans; | ||
| } | ||
|
|
||
| public: | ||
| vector<long double> solveByGaussJordan(vector< vector<long double> > eqns, int varc) | ||
| { | ||
| int status = this->gaussianElimination(eqns, varc); | ||
| switch (status) | ||
| { | ||
| case 0: | ||
| break; | ||
|
|
||
| case 1: | ||
| throw runtime_error("Singular matrix"); | ||
|
|
||
| case 2: | ||
| throw runtime_error("No solutions"); | ||
| } | ||
|
|
||
| this->gaussJordan(eqns, varc); | ||
|
|
||
| vector<long double> ans(varc); | ||
| for (int i = 0; i < varc; i++) | ||
| ans[i] = eqns[i][varc]; | ||
| return ans; | ||
| } | ||
|
|
||
| vector<long double> solveByBacksubs(vector< vector<long double> > eqns, int varc) | ||
| { | ||
| int status = this->gaussianElimination(eqns, varc); | ||
| switch (status) | ||
| { | ||
| case 0: | ||
| break; | ||
|
|
||
| case 1: | ||
| throw runtime_error("Singular matrix"); | ||
|
|
||
| case 2: | ||
| throw runtime_error("No solutions"); | ||
| } | ||
|
|
||
| vector<long double> ans = this->backSubs(eqns, varc); | ||
| return ans; | ||
| } | ||
| }; | ||
|
|
||
| int main() { | ||
| int varc = 3; | ||
| vector< vector<long double> > equations { { 2, 3, 4, 6 }, | ||
|
There was a problem hiding this comment. why use |
||
| { 1, 2, 3, 4 }, | ||
| { 3, -4, 0, 10 }}; | ||
| EquationSolver solver; | ||
| vector<long double> ans; | ||
| try | ||
| { | ||
| ans = solver.solveByGaussJordan(equations, varc); | ||
| } | ||
| catch(runtime_error &e) | ||
|
There was a problem hiding this comment. Not a big fan of try catch. |
||
| { | ||
| cout << "Error found: " << e.what() << endl; | ||
| return -1; | ||
| } | ||
|
|
||
|
There was a problem hiding this comment. Print the matrix after the eliminations. |
||
| cout << "The solution is (by Gauss-Jordan)," << endl | ||
| << "x == " << ans[0] << endl | ||
| << "y == " << ans[1] << endl | ||
| << "z == " << ans[2] << endl << endl; | ||
|
|
||
| try | ||
| { | ||
| ans = solver.solveByBacksubs(equations, varc); | ||
| } | ||
| catch (runtime_error &e) | ||
| { | ||
| cout << "Error found: " << e.what() << endl; | ||
| return -1; | ||
| } | ||
|
|
||
| cout << "The solution is (by Backsubstitution)," << endl | ||
| << "x == " << ans[0] << endl | ||
| << "y == " << ans[1] << endl | ||
| << "z == " << ans[2] << endl; | ||
| } | ||
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
I don't think the use of
using namespace stdis a good idea for the philosophy of AAA is. The idea is for the AAA to be used by new comers to the language to learn, also for people to use the algorithm in real work cases and show case the algorithm. I don't believe thatusing namespace stdachieves this.