// matrix A
let matrixA = [
  [6, -2, -3],
  [-2, 5, -2],
  [-3, -2, 8],
];


// Generate L and U using matrix A length
let matrixL = Array(matrixA.length)
  .fill()
  .map(() => Array(matrixA.length).fill(0));
let matrixU = Array(matrixA.length)
  .fill()
  .map(() => Array(matrixA.length).fill(0));

crout = () => {
  // assign matrix A length to a variable
  let n = matrixA.length;

  // loop in to index
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      // if j is less than i change value of matrixL to 0 with its corresponding indexes
      if (j < i) matrixL[j][i] = 0;

      else {
        // the first column of matrix L is equal to the first column of matrix A
        matrixL[j][i] = matrixA[j][i];
        //  loop the values excluding the first column and top row
        for (k = 0; k < i; k++) {
          matrixL[j][i] = matrixL[j][i] - matrixL[j][k] * matrixU[k][i];
        }
      }
    }
    // loop in to index
    for (j = 0; j < n; j++) {
      // if j is less than i change value of martixU to 0 with its corresponding indexes
      if (j < i) matrixU[i][j] = 0;
      // if j is equal to i the change value to 1
      //  result to a diagonal values of 1
      else if (j == i) matrixU[i][j] = 1;

      else {
        // get index of the first rows of matrixU
        matrixU[i][j] = matrixA[i][j] / matrixL[i][i];
        // loop to get values excluding the first rows, 1's and 0's
        for (k = 0; k < i; k++) {
          matrixU[i][j] =
            matrixU[i][j] - (matrixL[i][k] * matrixU[k][j]) / matrixL[i][i];
        }
      }
    }
  }
  //  print in console
  console.log("matrixA:\n", matrixA, "\n\nmatrixL:\n", matrixL, "\n\nmatrixU:\n", matrixU);

};
crout();