gaussElim.js

// This code was obtained from the website https://gist.github.com/codecontemplator/6b3db07a29e435940ffc
// Credits to codecontemplator

function print(M, msg) {
    console.log("======" + msg + "=========")
    for(var k=0; k<M.length; ++k) {
      console.log(M[k]);
    }
    console.log("==========================")
  }
  
  function diagonalize(M) {
    var m = M.length;
    var n = M[0].length;
    var i_max;
    for(var k=0; k<Math.min(m,n); ++k) {
      i_max = findPivot(M, k);
      if (A[i_max, k] == 0)
        throw "matrix is singular";
      swap_rows(M, k, i_max);
      for(var i=k+1; i<m; ++i) {
        var c = A[i][k] / A[k][k];
        for(var j=k+1; j<n; ++j) {
          A[i][j] = A[i][j] - A[k][j] * c;
        }
        A[i][k] = 0;
      }
    }
  }
  
  function findPivot(M, k) {
    var i_max = k;
    for(var i=k+1; i<M.length; ++i) {
      if (Math.abs(M[i][k]) > Math.abs(M[i_max][k])) {
        i_max = i;
      }
    }
    return i_max;
  }
  
  function swap_rows(M, i_max, k) {
    if (i_max != k) {
      var temp = A[i_max];
      A[i_max] = A[k];
      A[k] = temp;
    }
  }
  
  function makeM(A, b) {
    for(var i=0; i<A.length; ++i) {
      A[i].push(b[i]);
    }
  }
  
  function substitute(M) {
    var m = M.length;
    for(var i=m-1; i>=0; --i) {
      var x = M[i][m] / M[i][i];
      for(var j=i-1; j>=0; --j) {
        M[j][m] -= x * M[j][i];
        M[j][i] = 0;
      }
      M[i][m] = x;
      M[i][i] = 1;
    }
  }
  
  function extractX(M) {
    var x = [];
    var m = A.length;
    var n = A[0].length;
    for(var i=0; i<m; ++i){
      x.push(A[i][n-1]);
    }
    return x;
  }
  
  function solve(A, b) {
    makeM(A,b);
    diagonalize(A);
    substitute(A);
    var x = extractX(A);
    return x;
  }
   
  A = [
    [1,0,0,1/Math.sqrt(2),1,0,0,0,0,0],
    [0,1,0,1/Math.sqrt(2),0,0,0,0,0,0],
    [0,0,0,-1/Math.sqrt(2),0,1/Math.sqrt(2),1,0,0,0],
    [0,0,0,-1/Math.sqrt(2),0,-1/Math.sqrt(2),0,0,0,0],
    [0,0,0,0,-1,-1/Math.sqrt(2),0,1/Math.sqrt(2),1,0],
    [0,0,0,0,0,1/Math.sqrt(2),0,1/Math.sqrt(2),0,0],
    [0,0,0,0,0,0,-1,-1/Math.sqrt(2),0,1/Math.sqrt(2)],
    [0,0,0,0,0,0,0,-1/Math.sqrt(2),0,-1/Math.sqrt(2)],
    [0,0,0,0,0,0,0,0,-1,-1/Math.sqrt(2)],
    [0,0,1,0,0,0,0,0,0,1/Math.sqrt(2)]
 ];
  
  b = [0,0,0,0,0,20,0,0,0,0];
  
  print(A, " A ");

  print(b, " b ");
  
  var x = solve(A, b);
  console.log(x);