138 lines
3.8 KiB
Plaintext
138 lines
3.8 KiB
Plaintext
private function gailv($weici_arr,$cur_weici,$flag=1){
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$a = file_get_contents('norm.txt');
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$a = $this->shape($a);
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$dim =[33,11];
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$xk = $weici_arr;//[5263,4960,5961,4977]; // 高校录取位次
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$position_student = $cur_weici;//4936; // 学生当年位次
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/**************************************************************/
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$xk_average = array_sum($xk)/count($xk);
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# (1) 当学生位次与高校位次差异较大时，选择不放大“方差因子”以使得求解的概率更大或更小
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if($position_student <$xk_average){
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$distance_factor=$position_student/$xk_average;
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}else{
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$distance_factor=$xk_average/$position_student;
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}
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//echo 'distance_factor='.$distance_factor.' ';
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$enlarge_factor_sigma=$distance_factor*2+1; #方差放大因子在[1,3]之间变化
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# (2)数据的倾斜程度越大，越需要降低直线斜率
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$scale_step=$xk_average/2; #选取合适的x轴尺度
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/*************************************************************/
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// 线性规划预测当年数据
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$xi_vector = [];
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for($i=0;$i<=count($xk)-1;$i++){
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$xi_vector[] = $i*$scale_step+$scale_step;
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}
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$yi_vector = $xk;
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$xi_vector_average = array_sum($xi_vector)/count($xi_vector);
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$yi_vector_average = array_sum($yi_vector)/count($yi_vector);
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$frac_up = 0;$frac_down=0;$a_linear=0;$b_linear=0;
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foreach ($xi_vector as $i => $val) {
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$frac_up = $frac_up+($xi_vector[$i]-$xi_vector_average)*($yi_vector[$i]-$yi_vector_average);
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$frac_down = $frac_down+($xi_vector[$i]-$xi_vector_average)*($xi_vector[$i]-$xi_vector_average);
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$a_linear = $frac_up/$frac_down;
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$b_linear = $yi_vector_average - $a_linear*$xi_vector_average;
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}
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$xk_predicted = $a_linear * (count($xk)+1)+$b_linear;
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$theta_line=abs(atan($a_linear)*180/pi()); #计算直线斜率
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# (2)数据的倾斜程度越大，越需要降低直线斜率
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$beta_a_linear=1 - $theta_line/90;
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//echo 'beta_a_linear='.$beta_a_linear.' ';
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$xk_predicted = $beta_a_linear * $a_linear*($xi_vector[count($xi_vector)-1]+$scale_step)+$b_linear;
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///////////////////////////////////////////////
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$mu = array_sum($xk)/count($xk)*0.99999999; //样本均值
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// 样本方差
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$s = 0;
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foreach ($xk as $val) {
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$s = $s + pow(($val-$mu),2);
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}
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$sigma = sqrt($s/(count($xk)-1))*$enlarge_factor_sigma;
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//echo 'mu='.$mu.' sigma='.$sigma;
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$Z_norm = ($position_student - $mu)/$sigma; // 转换成标准正态分布
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$sign_index = 1;
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if($Z_norm<0){
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$sign_index = -1;
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$Z_norm = abs($Z_norm);
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}
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//使数据不超过表格行的范围
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$Z_norm = $Z_norm>3.19?3.19:$Z_norm;
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// 查表确定Z的值
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for($i=0;$i<$dim[0];$i++){
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if($Z_norm<=$a[$i][0]){
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$m_row = $i-1;
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break;
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}else{
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$m_row = $dim[0]-1;
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}
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}
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$Z_decimal = $Z_norm - $a[$m_row][0];// 获取Z的百分位小数部分
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for($j=0;$j<11;$j++){
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if($Z_decimal<=$a[0][$j]){
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$n_col = $j-1;
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break;
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}else{
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$n_col = $dim[1] - 1;
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}
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}
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//echo 'm_row='.$m_row.' n_col='.$n_col;
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// 均值到Z的概率
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if($n_col<10){
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$x0 = $Z_decimal;
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$xk = $a[0][$n_col];
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$xkk = $a[0][$n_col+1];
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$phi_xk = $a[$m_row][$n_col];
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$phi_xkk = $a[$m_row][$n_col+1];
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}else{
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$x0 = $Z_decimal;
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$xk = $a[0][$n_col];
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$xkk = 0.1;
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$phi_xk = $a[$m_row][$n_col];
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$phi_xkk = $a[$m_row+1][1];
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}
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$P_Z_norm = ($x0-$xk)/($xkk-$xk)*$phi_xkk+($xkk-$x0)/($xkk-$xk)*$phi_xk;// 插值
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//echo 'P_Z_norm='.$P_Z_norm."\r\n";
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// 录取概率
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$P_student = 0.5 -$sign_index*$P_Z_norm;
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//echo '学生的录取概率：'.$P_student;
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return $P_student;
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}
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private function shape($a){
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$arr = explode("\n",$a);
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foreach($arr as $key => $val){
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$_temp = explode(' ', $val);
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$item = [];
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foreach($_temp as $t){
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if(trim($t)==''){
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continue;
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}
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$item[] = trim($t);
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}
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$arr[$key] = $item;
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}
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return $arr;
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} |