public function get_complement($data, $i, $j) {
  /* x和y为矩阵data的行数和列数 */
  $x = count($data);
  $y = count($data[0]);
  /* data2为所求剩余矩阵 */
  $data2 =[];
  for ($k = 0; $k < $x -1; $k++) {
    if ($k < $i) {
      for ($kk = 0; $kk < $y -1; $kk++) {
        if ($kk < $j) {
          $data2[$k][$kk] = $data[$k][$kk];
        } else {
          $data2[$k][$kk] = $data[$k][$kk +1];
        }
      }
    } else {
      for ($kk = 0; $kk < $y -1; $kk++) {
        if ($kk < $j) {
          $data2[$k][$kk] = $data[$k +1][$kk];
        } else {
          $data2[$k][$kk] = $data[$k +1][$kk +1];
        }
      }
    }
  }
  return $data2;
}
/* 计算矩阵行列式 */
public function cal_det($data) {
  $ans = 0;
  if (count($data[0]) === 2) {
    $ans = $data[0][0] * $data[1][1] - $data[0][1] * $data[1][0];
  } else {
    for ($i = 0; $i < count($data[0]); $i++) {
      $data_temp = $this->get_complement($data, 0, $i);
      if ($i % 2 === 0) {
        $ans = $ans + $data[0][$i] * ($this->cal_det($data_temp));
      } else {
        $ans = $ans - $data[0][$i] * ($this->cal_det($data_temp));
      }
    }
  }
  return $ans;
}
/*计算矩阵的伴随矩阵*/
public function ajoint($data) {
  $m = count($data);
  $n = count($data[0]);
  $data2 =[];
  for ($i = 0; $i < $m; $i++) {
    for ($j = 0; $j < $n; $j++) {
      if (($i + $j) % 2 === 0) {
        $data2[$i][$j] = $this->cal_det($this->get_complement($data, $i, $j));
      } else {
        $data2[$i][$j] = - $this->cal_det($this->get_complement($data, $i, $j));
      }
    }
  }
  return $this->trans($data2);
}
/*转置矩阵*/
public function trans($data) {
  $i = count($data);
  $j = count($data[0]);
  $data2 =[];
  for ($k2 = 0; $k2 < $j; $k2++) {
    for ($k1 = 0; $k1 < $i; $k1++) {
      $data2[$k2][$k1] = $data[$k1][$k2];
    }
  }
  /*将矩阵转置便可得到伴随矩阵*/
  return $data2;
}
/*求矩阵的逆，输入参数为原矩阵*/
public function inv($data) {
  $m = count($data);
  $n = count($data[0]);
  $data2 =[];
  $det_val = $this->cal_det($data);
  $data2 = $this->ajoint($data);
  for ($i = 0; $i < $m; $i++) {
    for ($j = 0; $j < $n; $j++) {
      $data2[$i][$j] = $data2[$i][$j] / $det_val;
    }
  }
  return $data2;
}
/*求两矩阵的乘积*/
public function getProduct($data1, $data2) {
  /*$data1 为左乘矩阵*/
  $m1 = count($data1);
  $n1 = count($data1[0]);
  $m2 = count($data2);
  $n2 = count($data2[0]);
  $data_new =[];
  if ($n1 !== $m2) {
    return false;
  } else {
    for ($i = 0; $i <= $m1 -1; $i++) {
      for ($k = 0; $k <= $n2 -1; $k++) {
        $data_new[$i][$k] = 0;
        for ($j = 0; $j <= $n1 -1; $j++) {
          $data_new[$i][$k] += $data1[$i][$j] * $data2[$j][$k];
        }
      }
    }
  }
  return $data_new;
}
/*多元线性方程*/
public function getParams($arr_x, $arr_y) {
  $final =[];
  $arr_x_t = $this->trans($arr_x);
  $result = $this->getProduct($this->getProduct($this->inv($this->getProduct($arr_x_t, $arr_x)), $arr_x_t), $arr_y);
  foreach ($result as $key => $val) {
    foreach ($val as $_k => $_v) {
      $final[] = $_v;
    }
  }
  return $final;
}