Detailed explanation of simulation curve algorithm based on PHP

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; }