Skip to content

Commit 66d2d53

Browse files
Samya-SSamya-S
committed
OT Lab 2
1 parent 69bc752 commit 66d2d53

File tree

3 files changed

+334
-0
lines changed

3 files changed

+334
-0
lines changed

‎OT Lab - 2 (08-08-24)/Assignment 2.pdf

91 KB
Binary file not shown.

‎OT Lab - 2 (08-08-24)/BasicFeasibleSolution.cpp

+172
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,172 @@
1+
#include <bits/stdc++.h>
2+
using namespace std;
3+
4+
long fact(long n){
5+
if(n < 2) return 1;
6+
return n * fact(n-1);
7+
}
8+
long nCr(int n,int r){
9+
return fact(n)/(fact(r)*fact(n-r));
10+
}
11+
12+
bool isDiagonallyDominantMatrix(vector<vector<double>> a) {
13+
int n = a.size();
14+
for (int i = 0; i < n; i++) {
15+
double sum = 0;
16+
for (int j = 0; j < n; j++) {
17+
if (i != j) {
18+
sum += abs(a[i][j]);
19+
}
20+
}
21+
if (sum > abs(a[i][i])) {
22+
return false;
23+
}
24+
}
25+
return true;
26+
}
27+
28+
void reorder(vector<vector<double>> &a, vector<double> &b){
29+
int n = a.size();
30+
31+
vector<vector<double>> a1(n);
32+
vector<double> b1(n);
33+
34+
for(int i=0; i<n; i++){
35+
int maxInd = max_element(a[i].begin(), a[i].end()) - a[i].begin();
36+
a1[maxInd] = a[i];
37+
b1[maxInd] = b[i];
38+
}
39+
40+
a = a1; b = b1;
41+
42+
// cout << "new equations:" << endl;
43+
// for(int i=0; i<n; i++){
44+
// for(int j=0; j<n; j++){
45+
// cout << a[i][j] << "x" << j+1 << " ";
46+
// if(j!=n-1) cout << "+ ";
47+
// else cout << "= ";
48+
// }
49+
// cout << b[i] << endl;
50+
// }
51+
52+
return;
53+
}
54+
55+
void gaussSeidel(vector<vector<double>> &a, vector<double> &b){
56+
int n = a.size();
57+
58+
cout << "Given equations:" << endl;
59+
for(int i=0; i<n; i++){
60+
for(int j=0; j<n; j++){
61+
cout << a[i][j] << "x" << j+1 << " ";
62+
if(j!=n-1) cout << "+ ";
63+
else cout << "= ";
64+
}
65+
cout << b[i] << endl;
66+
}
67+
68+
reorder(a, b);
69+
70+
if (!isDiagonallyDominantMatrix(a)) {
71+
cout << "The matrix is not diagonally dominant." << endl;
72+
cout << "The Gauss-Seidel method may not converge." << endl;
73+
return;
74+
}
75+
76+
vector<double> x(n, 0);
77+
78+
cout << "Enter initial values of x" << endl;
79+
for (int i = 0; i < n; i++) {
80+
cout << "x:[" << i << "] = ";
81+
cin >> x[i];
82+
}
83+
84+
// cout << endl << "Enter the allowed error: ";
85+
double delta = 0.01;
86+
// cin >> delta;
87+
cout << endl;
88+
89+
double error;
90+
do {
91+
vector<double> prev, y(n);
92+
prev = x;
93+
for (int i = 0; i < n; i++) {
94+
y[i] = (b[i] / a[i][i]);
95+
for (int j = 0; j < n; j++) {
96+
if (j != i)
97+
y[i] = y[i] - ((a[i][j] / a[i][i]) * x[j]);
98+
}
99+
x[i] = y[i];
100+
cout << "x" << i + 1 << " = " << fixed << setprecision(6) << y[i] << " ";
101+
// cout << "x" << i + 1 << " = " << y[i] << " ";
102+
}
103+
cout << endl;
104+
105+
error = 0;
106+
for (int i = 0; i < n; i++) {
107+
error += pow(prev[i]-x[i], 2);
108+
}
109+
} while(sqrtl(error) > delta);
110+
111+
cout << endl;
112+
cout << "The final solution is:" << endl;
113+
for (int i = 0; i < n; i++) {
114+
cout << "x[" << i << "] = " << x[i] << endl;
115+
}
116+
cout << endl;
117+
118+
return;
119+
}
120+
121+
int main() {
122+
// cout << "Enter the number of variables: ";
123+
int n; cin >> n;
124+
// cout << endl;
125+
126+
// cout << "Enter the number of equations: ";
127+
int m; cin >> m;
128+
// cout << endl;
129+
130+
vector<vector<double>> a(m, vector<double>(n, 0));
131+
vector<double> b(m, 0);
132+
133+
for (int i = 0; i < m; i++) {
134+
for (int j = 0; j < n; j++) {
135+
// cout << "a[" << i << ", " << j << "] = ";
136+
cin >> a[i][j];
137+
}
138+
}
139+
140+
for (int i = 0; i < m; i++) {
141+
// cout << "b[" << i << "] = ";
142+
cin >> b[i];
143+
}
144+
// cout << endl;
145+
146+
vector<int> perm(n,0);
147+
for(int i=0; i<m; i++) perm[i] = 1;
148+
sort(perm.begin(), perm.end());
149+
150+
do{
151+
for(int i=0; i<n; i++){
152+
cout << "x" << i+1 << "=";
153+
if(perm[i]) cout << "? ";
154+
else cout << "0 ";
155+
}
156+
cout << endl;
157+
158+
vector<vector<double>> a1(m);
159+
160+
for(int i=0; i<m; i++){
161+
for(int j=0; j<n; j++){
162+
if(perm[j]==1) a1[i].push_back(a[i][j]);
163+
}
164+
}
165+
166+
gaussSeidel(a1, b);
167+
168+
cout << endl;
169+
} while(next_permutation(perm.begin(), perm.end()));
170+
171+
return 0;
172+
}

‎OT Lab - 2 (08-08-24)/p3.cpp

+162
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,162 @@
1+
#include <bits/stdc++.h>
2+
#include <vector>
3+
#include <cmath>
4+
using namespace std;
5+
void combinations(vector<int> &elements , int k , vector<vector<int>> &result,vector<int> &current , int start ){
6+
if(k==0){
7+
result.push_back(current);
8+
return;
9+
}
10+
for(int i = start ;i<=elements.size()-k ;i++){
11+
current.push_back(elements[i]);
12+
combinations(elements,k-1,result,current,i+1);
13+
current.pop_back();
14+
}
15+
}
16+
17+
const double TOLERANCE = 0.001;
18+
const int MAX_ITERATIONS = 1000;
19+
20+
bool isDiagonallyDominant(const vector<vector<double>>& A) {
21+
int n = A.size();
22+
for (int i = 0; i < n; ++i) {
23+
double diag = fabs(A[i][i]);
24+
double sum = 0.0;
25+
for (int j = 0; j < n; ++j) {
26+
if (i != j) {
27+
sum += fabs(A[i][j]);
28+
}
29+
}
30+
if (diag <= sum) {
31+
return false;
32+
}
33+
}
34+
return true;
35+
}
36+
37+
void gaussSeidel(const vector<vector<double>>& A, const vector<double>& b, vector<double>& x) {
38+
int n = A.size();
39+
vector<double> x_old(n);
40+
41+
for (int k = 0; k < MAX_ITERATIONS; ++k) {
42+
x_old = x;
43+
44+
for (int i = 0; i < n; ++i) {
45+
double sum = 0.0;
46+
47+
for (int j = 0; j < n; ++j) {
48+
if (i != j) {
49+
sum += A[i][j] * x[j];
50+
}
51+
}
52+
53+
x[i] = (b[i] - sum) / A[i][i];
54+
}
55+
56+
double max_diff = 0.0;
57+
for (int i = 0; i < n; ++i) {
58+
max_diff = max(max_diff, fabs(x[i] - x_old[i]));
59+
}
60+
61+
if (max_diff < TOLERANCE) {
62+
// cout << "Converged after " << k + 1 << " iterations." << endl;
63+
return;
64+
}
65+
}
66+
67+
//cout << "Maximum number of iterations reached." << endl;
68+
}
69+
70+
int main(){
71+
int n,m;
72+
73+
cout << "Enter value of n and m : ";
74+
cin >> n>>m;
75+
int ineq;
76+
cout << "type 1 if it is a inequality else type 0: ";
77+
cin>>ineq;
78+
int add = 0 ;
79+
if(ineq) add = m;
80+
81+
82+
vector<vector<double>> A(m, vector<double>(n+add,0));
83+
vector<double> b(m);
84+
cout << "Enter the augmented matrix (coefficients):" << endl;
85+
for (int i = 0; i < m; ++i) {
86+
for (int j = 0; j < n; ++j) {
87+
cin >> A[i][j];
88+
}
89+
90+
}
91+
int tmp = n;
92+
if(ineq){
93+
for(int i = 0 ;i<m;i++) {A[i][tmp] =1;tmp++;}
94+
}
95+
cout << "Enter the values of vector b " << endl;
96+
for(int i = 0 ;i<m;i++) cin >> b[i];
97+
if(ineq) cout<<"WE WILL USE SLACK VARIABLES HERE"<<endl;
98+
99+
vector<int> indices(n+add);
100+
iota(indices.begin(),indices.end(),0);
101+
vector<vector<int>> combo;
102+
vector<int> curr;
103+
combinations(indices,m,combo,curr,0);
104+
for(auto c:combo){
105+
vector<vector<double>> AA(m, vector<double>(m));
106+
vector<double> x(m,0.0);
107+
for (int i = 0; i < m; ++i) {
108+
for (int j = 0; j < m; ++j) {
109+
AA[i][j] = A[i][c[j]];
110+
}
111+
112+
}
113+
114+
if (isDiagonallyDominant(AA)) {
115+
// cout << "The matrix is diagonally dominant." << endl;
116+
gaussSeidel(AA, b, x);
117+
118+
cout << "Solution:" << endl;
119+
int cnt = 0;
120+
for(int i = 0 ;i<m;i++){
121+
if(c[i]>=n && x[i]<0){
122+
cout<<"slack variable can't be nagative"<<endl;
123+
continue;
124+
}
125+
}
126+
for (int i = 0; i < m; ++i) {
127+
cout << "x" << c[i] + 1 << " = " << x[i] << endl;
128+
129+
}
130+
cout<<"other variables are taken as 0"<<endl;
131+
132+
bool flag = 0;
133+
for(int i = 0 ;i<m;i++){
134+
if(x[i]<0){ flag = 1;}
135+
if(x[i]==0.0) cnt++;
136+
}
137+
if((cnt+ n+add - m) ==m) {
138+
if(flag==1) cout << "This is a nondegenerate basic solution but not feasible." << endl;
139+
else cout << "This is a nondegenerate basic solution and feasible." << endl;
140+
}
141+
else if(cnt){
142+
if(flag==1) cout << "This is a degenerate basic solution but not feasible." << endl;
143+
else cout << "This is a degenerate basic solution and feasible." << endl;
144+
}
145+
else {
146+
if(flag==1) cout << "This is a basic solution but not feasible." << endl;
147+
else cout << "This is a basic solution and feasible." << endl;
148+
}
149+
150+
151+
152+
153+
} else {
154+
cout << "The matrix is not diagonally dominant." << endl;
155+
}
156+
157+
158+
159+
}
160+
return 0 ;
161+
162+
}

0 commit comments

Comments
 (0)