Solve Ax = b, A = lower triangular matrix in c++

Question

I`m trying to do this function that solves linear systems, A*x = b, where A = lower triangular matrix, linear independent matrix and with only one solution. But the results always show 0 0 0 0 ... I have printed the sum, s, and it always shows 0 as well...

 #include  <iostream>
 using namespace std;

void solve(int n, float a[][MAX], float b[], float x[]){
 int i,j;
 float s;

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

            s = s + a[i][j]*x[j];
            cout<<s<<endl;
        }
    x[i] = (b[i] - s)/a[i][i];
 }
}

no, it has to be in c++, with "simple libraries and packs"... — , Mar 06 '14 at 22:20
This is a famous algorithm. It's called back substitution. Try google for a bit. I'm quite sure you will find it step by step :) If you're still stuck scream for help. — Wilmer E. Henao, Mar 06 '14 at 22:23
back substitution isn`t working :(. But yes, @lizusek, we can use a upper triangular — , Mar 06 '14 at 22:50
@LVL what do you mean, what is not working? do you refer to my answer or someone else or back substitution algorithm? — 4pie0, Mar 06 '14 at 22:53
@LVL it is working, really. Have you tried my version posted below? Note the range of sumation — 4pie0, Mar 06 '14 at 22:56

4pie0 · Accepted Answer · 2014-03-07T00:01:31.447

3

void solve(int n, float a[][MAX], float b[], float x[]){
  int i,j;
  float s;

  for(i = 0; i < n; i++) {
        s = 0;
        for(j = 0; j < i; j++) {
                       ^
            s = s + a[ i][ j] * x[ j];
        }
        x[ i] = ( b[ i] - s) / a[ i][ i];
   }
}

BackSubstitution.pdf

compiled example

edited Mar 07 '14 at 00:01

answered Mar 06 '14 at 22:44

4pie0

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the compiled example does not work (=not robust) for certain input. For instance, I enter $a[3][3]={0.2,-0.2,0,0,0.3,-0.2,0,0,0.25}$ and $b[3]={3,3,3}$. The codes compiles but leads to an incorrect answer as 15,10,12. Is it a way to fix the codes? – math101 Mar 12 '20 at 15:49

score 2 · Answer 2 · answered Mar 06 '14 at 22:40

2

This line:

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

Should be:

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

Then it works fine - assuming your pivots are always non zero.

answered Mar 06 '14 at 22:40

sbabbi

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@lizusek Err... no? For instance when i=1 s should be A[1][0]*x[0] while in your code is simply 0. You have to sum all the A[i][j]*x[j] **on the left** of the diagonal, so basically for i < j. – sbabbi Mar 06 '14 at 23:15

Solve Ax = b, A = lower triangular matrix in c++

2 Answers2