Gaussian elimination [repost]

[jgg2002]

(Note: this is a repost from a post I posted 3 days ago but it got no replies, so I am reposting it. I hope I don't get banned)

Hello there. So, for the last 2-2,5 hours I've been writing this code for the Gaussian elimination for solving matrix equations in the form Ax = b. Obviously, somewhere in my code, or algorithm, there's a logic error. I've commented on some important parts on the code to further explain what I am trying to do.

Thanks in advance

#include<iostream>
#include<cmath>
#include<fstream>

using namespace std;

ofstream fout ("output matrix gauss.txt");

double matrix[1000][1000];

//class for a position variable
typedef class{
public:
int i=0;
int j=0;
void create(int a, int b){
i = a;
j = b;
}
// (I've written some currently useless functions, left them in, I might need them)
void update(){
i++;
j++;
}
void manual_update(int increase, string type){
if (type=="both"){
    i+=increase;
    j+=increase;
}
else if (type=="i"){
    i+=increase;
}
else if (type=="j"){
    j+=increase;
}
}
}Position;

void updateRow (int row, Position compare, double times, int dimension, string type){
if (type=="else"){
 for (int i=0; i<=dimension; i++){
   matrix[row][i] -= times * (matrix[compare.j][i]);
 }
}
else if (type=="main"){
    for (int i=0; i<=dimension; i++){
        matrix[row][i] *= times;
    }
}
}

double findTimes (Position current, Position compare, string type){
double times;
    if (type=="main"){
  times = 1 / matrix[current.i][current.j];
    }
else if (type=="else"){
    times = matrix[current.i][current.j] / matrix[compare.i][compare.j];
}
return times;
}

bool hasFinished (int i, int j){
bool finished = false;
if (matrix[i][j]==1 && i==j){
    finished = true;
}
else if (matrix[i][j]==0 && i!=j){
    finished = true;
}
return finished;
}

int main(){
int n;
cin>>n;



for (int i=0; i<n; i++){          //reads the matrix
    for (int j=0; j<n; j++){
        cin>>matrix[i][j];
    }
    cin>>matrix[i][n];
}
for (int j=0; j<n; j++){
    for (int i=0; i<n; i++){
        Position current;            //current position
        current.create(i, j);
        Position compare;           //position from where the updateRow() will be substracting
        if (i!=n-1){
            compare.create(i+1, j);
        }
        else{
            compare.create(i-1, j);
        }
        if (hasFinished (j, i)==false && i==j){
        updateRow(i, compare, findTimes(compare, current, "main"), n, "main");  //checks whether it should update or not
        }
        else if (hasFinished(j, i)==false && i!=j){
            updateRow(i, compare, findTimes(compare, current, "else"), n, "else");
        }
        for (int i=0; i<n; i++){
            for (int j=0; j<n+1; j++){
                fout<<matrix[i][j]<<" ";   //I outputed each step to a file to debug, never mind this
            }
            fout<<"\n";
        }
        fout<<"\n";
    }
}
for (int i=0; i<n; i++){
    cout<<matrix[i][n]<<"\n";           //Print result
}
}

[jlb]

Obviously, somewhere in my code, or algorithm, there's a logic error.

Why is it obvious?

I suggest that you throughly describe your problem. Then show what you inputted into the program, what the program outputted with that input and what you expected the output to be.

[jgg2002]

It is obvious because if there wasn't I wouldn't be posting this here.

As the problem description, well I forgot to mention that. It is a program to solve equation systems with equations in the form Ax = b using Gaussian Elimination. You are given an integer N, specifying the number of variables, and therefore, number of equations. Then N lines, each with N integers, specifying each the coeffiecient of each variable and another integer specifying the sum of those variables.

Output should be the value of each variable.

Example for (x=1, y=2, z=3)
Input:
3
1 1 1 6
1 1 2 9
1 2 1 8

Output:
1
2
3

My program for the same input outputs:
2
-14,5
8

[keskiverto]

Your matrix is double but input is all int. Would ints suffice?

[jgg2002]

I put double because some row operations might return a decimal value at some point. I've changed a bit the code, I will now edit the post to the new one. (It still returns wrong ouput though)

[jgg2002]

The program should, at the end, after all the row operations modify the matrix like this(for the example above):

1 0 0 1
0 1 0 2
0 0 1 3

So it wouldn't matter if in a step a decimal value popped up.

You have to take decimal value into consideration because then the program would crash.

[jgg2002]

Never mind I solved it finally. Phew, this one was hard.

#include<iostream>
#include<cmath>
#include<algorithm>

using namespace std;

double matrix[1000][1000];

typedef class{
public:
    int row;
    int column;
void createPos(int a, int b){
row = a;
column = b;
}
}Position;

string findType (Position current){
string type;
if (current.row==current.column){
    type = "main";
}
else if (current.row!=current.column){
    type = "else";
}
return type;
}

bool hasFinished (Position current){
bool finished = false;
if (current.row==current.column && matrix[current.row][current.column]==1){
    finished = true;
}
else if (current.row!=current.column && matrix[current.row][current.column]==0){
    finished = true;
}
return finished;
}

Position findPos (Position current, int n){
Position compare;
int row = 0;
int column = current.column;
for (int i=0; i<n; i++){
    if (matrix[i][column]!=0 && i!=current.row){
        row = i;
    }
}
compare.createPos(row, column);
return compare;
}

double findTimes (Position current, Position compare, string type){
double times;
if (type=="main"){
    times = 1 / matrix[current.row][current.column];
}
else if (type=="else"){
    times = matrix[current.row][current.column] / matrix[compare.row][compare.column];
}
return times;
}

void updateRow (Position current, Position compare, double times, string type, int n){
if (type=="main"){
for (int column = 0; column<=n; column++){
    matrix[current.row][column] *= times;
}
}
else if (type=="else"){
    for (int column = 0; column<=n; column++){
        matrix[current.row][column] -= times * matrix[compare.row][column];
    }
}
}

int main(){
int n;
cin>>n;
for (int row = 0; row < n; row ++){
    for (int column = 0; column < n; column ++){
        cin >> matrix[row][column];
    }
    cin>>matrix[row][n];
}
for (int column = 0; column<n; column++){
    for (int row = 0; row<n; row++){
        Position current, compare;
        string type;
        current.createPos(row, column);
        if (hasFinished(current)==false){
            compare = findPos(current, n);
            type = findType (current);
            updateRow(current, compare, findTimes(current, compare, type), type, n);
        }
    }
}
for (int row = 0; row<n; row++){
    for (int column = 0; column<n; column++){
        cout<<matrix[row][column]<<" ";
    }
    cout<<"\n";
}
cout<<"final answer: \n";
for (int row = 0; row<n; row++){
    cout << matrix[row][n]<<"\n";
}
}