backwardSub.h

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#pragma once
#include "../utils.h"
#include <iostream>
#include <vector>
 
Matrix<double> backwardSub(const Matrix<double>& R, const Matrix<double>& b) {
  size_t m  = R.rows();
  size_t n  = R.columns();
  size_t v  = b.rows();
  size_t nv = b.columns();
  if(v != m) {
    // Error, cannot compute
    std::cout << "Matrix vector dimension miss match, error!\n";
    return Matrix<double>();
  }
  if(m != n) {
    // Error, cannot compute
    std::cout << "Matrix not squared. Dimension miss match, error!\n";
    return Matrix<double>();
  }
 
  auto x = zeros(v, nv);
 
  if(R(m - 1, n - 1) != 0) { x.SetRow(v - 1, b(v - 1) * (1 / R(m - 1, n - 1))); }
 
  for(int j = (int)m - 2; j >= 0; j--) {
    double s_k = 0.0f;
    for(size_t k = j + 1; k < m; k++) { s_k += (R(j, k) * x(k, 0)); }
    for(size_t i = 0; i < nv; ++i) { x(j, i) = (b(j, i) - s_k) / R(j, j); }
  }
 
  return x;
}