Can someone explain the last part of this code?

Question

I am a newbie at C++. I have been writing some code for the past 2 hours. It's about finding a solution to a tridiagonal system.

#include<iostream>
#include<cmath>
using namespace std;

int main()
{
    float mat[100][100];
    int n;
    cout << "Enter the dimention of the matrix: ";
    cin >> n;
    cout << "Enter the matrix: ";
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            cin >> mat[i][j];
        }
    }
    float d[100];
    cout << "Enter the values of di's: ";
    for (int i = 0; i < n; i++)
    {
        cin >> d[i];
    }
    for (int i = 0; i < n; i++)
    {
        cout << "The value of d" << i + 1 << " is" << d[i];
    }
    cout << " \n";

    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)

            cout << mat[i][j] << " ";
        {
            cout << endl;
        }

    }

    float a[100], b[100], c[100];
    for (int i = 0; i < n + 1; i++)
    {
        b[i] = mat[i][i];
    }
    for (int l = 0; l < n; l++)
    {
        cout << "The value of b" << l + 1 << " is " << b[l] << " " << endl;
    }
    cout << "\n";

    for (int j = 0; j < n; j++)
    {
        a[j] = mat[j][j - 1];
    }

    for (int i = 1; i < n - 1; i++)
    {
        cout << "The value of a" << i + 1 << " is: " << a[i] << " " << endl;
    }
    cout << "\n";
    for (int k = 0; k < n - 1; k++)
    {
        c[k] = mat[k][k + 1];
    }
    for (int i = 0; i < n - 1; i++)
    {
        cout << "The value of c" << i + 1 << " is: " << c[i] << " " << endl;
    }
//to find alpha
    cout << "\n";
    float alpha[100];
    alpha[0] = b[0];
    for (int i = 1; i < n; i++)
    {
        alpha[i] = b[i] - ((a[i] * c[i - 1]) / alpha[i - 1]);
    }
    for (int i = 0; i < n; i++)
    {
        cout << "The value of alpha" << i + 1 << " is: " << alpha[i] << endl;
    }
    cout << "\n";
//to find beta
    float beta[100];
    beta[0] = (d[0] / b[0]);
    for (int i = 1; i < n; i++)
    {
        beta[i] = ((d[i] - a[i] * beta[i - 1]) / alpha[i]);
    }
    for (int i = 0; i < n; i++)
    {
        cout << " The value of beta" << i + 1 << " is: " << beta[i] << "\n";
    }

    //finding the solutions
    float x[100];
    x[n - 1] = beta[n - 1];
    for (int i = n - 2; i > 0; i--)
    {
        x[i] = beta[i] - ((c[i] * x[i + 1]) / alpha[i]);
    }
    cout << "the solutions are ";
    for (int i = 0; i < n - 1; i++)
    {
        cout << x[i] << "\t";
    }
    cout << beta[n - 1] << "\t";
}

Output:

PS C:\Users\jitub\desktop> ./a.exe
Enter the dimention of the matrix: 4                                                                           
Enter the matrix: 3 -1 0 0 -1 3 -1 0 0 -1 3 -1 0 0 -1 3
Enter the values of di's: -5 10 -15 15
The value of d1 is-5The value of d2 is10The value of d3 is-15The value of d4 is15 
3 -1 0 0 
-1 3 -1 0 
0 -1 3 -1 
0 0 -1 3 
The value of b1 is 3 
The value of b2 is 3 
The value of b3 is 3 
The value of b4 is 3 

The value of a2 is: -1
The value of a3 is: -1 

The value of c1 is: -1
The value of c2 is: -1
The value of c3 is: -1

The value of alpha1 is: 3
The value of alpha2 is: 2.66667
The value of alpha3 is: 2.625
The value of alpha4 is: 2.61905

 The value of beta1 is: -1.66667
 The value of beta2 is: 3.125
 The value of beta3 is: -4.52381
 The value of beta4 is: 4
 the solutions are 0     2       -3      4

Using Thomas's algorithm, I have to find the solution. If I do this by hand, the solution I get is {-1, 2, -3, 4}. But the output I get is always x1=0, which is not true.

The algorithm says beta4=x4, and the other values of xi's are in the for loop. I have tried many ways to print that value. Still, I couldn't find any way that works.

Also, the value of ai's should start from a2. In the last part of this program, I need to print out the values of xi's from backward.

I applied a consistent indentation scheme and at least one possible bug became immediately apparent. In a program the unusual is often a bug, so the more regular you code is, the more easily you can spot irregularities. — user4581301, Aug 23 '21 at 19:01
The programmers secret weapon is the debugger. With a debugger you can step through the code in varying grains and see what the compiler made of your code. Typical usage is to quickly advance to where you believe the problem is with a breakpoint and then step through the code looking for the unexpected, stuff like taking the wrong path or storing the wrong value. Often you wind up having to backtrack and retrace the steps a few times to see exactly what led up to the visible error, but it's almost always faster than fumbling around in the dark or asking a SO question. — user4581301, Aug 23 '21 at 19:06

score 1 · Accepted Answer · edited Aug 23 '21 at 19:58

I think the error is in your implementation of one of the formulas:

Particularly this one:

beta[i] = ((d[i] - a[i] * beta[i - 1]) / alpha[i]);

The correct expression should be (keep reading for another issue):

beta[i] = d[i] - (a[i] * beta[i - 1] / alpha[i]);

This one is also wrong:

x[i] = beta[i] - ((c[i] * x[i + 1]) / alpha[i]);

It should be:

x[i] = (beta[i] - c[i] * x[i + 1]) / alpha[i];

Note how I rearranged the parentheses.

With that fixed, there is something else you may want to check. I don't think you are using the correct indices. It may be just some particularity of your solution but it is my understanding that the expressions should be:

// using a[i-1] instead of a[i]
alpha[i] = b[i] - (a[i-1] * c[i - 1] / alpha[i - 1]);

// using a[1-1] instead of a[i]
beta[i] = d[i] - (a[i-1] * beta[i - 1]) / alpha[i]);

// just for completeness, didn't change the indices
x[i] = (beta[i] - c[i] * x[i + 1]) / alpha[i];

Can someone explain the last part of this code?

1 Answers1