feat(11-05): 实现二阶马尔可夫转移概率增强

- 新增 _getTransitionMatrix2ndOrder 方法构建二阶转移矩阵
- 新增 _calcTransitionScore2ndOrder 方法计算二阶转移得分
- getPredictionV3 根据数据量和状态对观察次数自动选择阶数
- 阈值: 历史期数>=200，状态对观察>=5次，比例>=30%
- analysis 返回新增 transition_order、transition_available 字段

application/admin/model/History.php

@@ -2227,12 +2227,49 @@ class History extends Model
         }
         $expectedFreq10 = 10 / 49;
 
-        // ====== 3. 转移概率分析（新增）======
+        // ====== 3. 转移概率分析 ======
-        // 获取转移概率矩阵数据
+        // 根据历史数据量决定使用一阶或二阶马尔可夫
+        // 阈值条件：总期数 >= 200 且 状态对观察次数充足（>=5次的比例>=30%）
+        $minPeriodsThreshold = 200; // 二阶马尔可夫最小历史期数阈值（从100提升到200）
+        $minStatePairCount = 5;      // 状态对最小观察次数
+        $use2ndOrder = false;
+        $secondOrderAvailable = false;
+
+        // 获取一阶转移概率矩阵（始终计算，作为fallback）
         $zoneTransition = $this->_getTransitionMatrix($allHistory, 'zone');
         $tailTransition = $this->_getTransitionMatrix($allHistory, 'tail');
         $headTransition = $this->_getTransitionMatrix($allHistory, 'head');
 
+        // 获取二阶转移概率矩阵（数据充足时）
+        $zoneTransition2nd = null;
+        $tailTransition2nd = null;
+        $headTransition2nd = null;
+        $prev2Zone = 0;
+        $prev2Tail = 0;
+        $prev2Head = 0;
+
+        if (count($allHistory) >= $minPeriodsThreshold && count($allHistory) >= 2) {
+            // 获取前两期号码属性
+            $prev2Special = (int)$allHistory[1]['num7'];
+            $prev2Zone = $this->_getZoneIdx($prev2Special);
+            $prev2Tail = $prev2Special % 10;
+            $prev2Head = $this->_getHeadIdx($prev2Special);
+
+            // 构建二阶转移矩阵
+            $zoneTransition2nd = $this->_getTransitionMatrix2ndOrder($allHistory, 'zone', $minStatePairCount);
+            $tailTransition2nd = $this->_getTransitionMatrix2ndOrder($allHistory, 'tail', $minStatePairCount);
+            $headTransition2nd = $this->_getTransitionMatrix2ndOrder($allHistory, 'head', $minStatePairCount);
+
+            // 检查状态对观察次数是否充足（至少30%的状态对有足够观察）
+            // tail类型状态空间最大(100)，以tail为基准判断
+            if ($tailTransition2nd['total_pairs'] > 0) {
+                $sufficientRatio = $tailTransition2nd['sufficient_pairs'] / $tailTransition2nd['total_pairs'];
+                $secondOrderAvailable = $sufficientRatio >= 0.3; // 至少30%状态对观察>=5次
+            }
+
+            $use2ndOrder = $secondOrderAvailable;
+        }
+
         // 上期号码的各类属性
         $lastZone = $this->_getZoneIdx($lastSpecial);
         $lastTail = $lastSpecial % 10;
@@ -2304,6 +2341,10 @@ class History extends Model
             'oddeven_stats' => $oddevenStats,
             'bigsmall_stats' => $bigsmallStats,
             'trend_direction' => $trendDirection,
+            'transition_order' => $use2ndOrder ? 2 : 1,  // 转移概率阶数
+            'transition_available' => $secondOrderAvailable, // 二阶是否可用
+            'history_count' => count($allHistory),      // 历史期数
+            'min_periods_threshold' => $minPeriodsThreshold, // 二阶阈值
             'last_zone' => $zoneLabels[$lastZone] ?? '',
             'last_tail' => $lastTail,
             'last_head' => $lastHead,
@@ -2339,12 +2380,22 @@ class History extends Model
             $detail['freq_score'] = round($freqScore, 2);
             $totalScore += $freqScore * $weights['freq_regression'];
 
-            // === 转移概率得分（新增）===
+            // === 转移概率得分（根据阶数选择计算方法）===
+            if ($use2ndOrder && $zoneTransition2nd && $tailTransition2nd && $headTransition2nd) {
+                $transScore = $this->_calcTransitionScore2ndOrder(
+                    $num, $lastZone, $prev2Zone, $lastTail, $prev2Tail, $lastHead, $prev2Head,
+                    $zoneTransition2nd, $tailTransition2nd, $headTransition2nd,
+                    $zoneMap, $tailMap, $headMap
+                );
+                $detail['trans_order'] = 2;
+            } else {
                 $transScore = $this->_calcTransitionScore(
                     $num, $lastZone, $lastTail, $lastHead,
                     $zoneTransition, $tailTransition, $headTransition,
                     $zoneMap, $tailMap, $headMap
                 );
+                $detail['trans_order'] = 1;
+            }
             $detail['trans_score'] = round($transScore, 2);
             $totalScore += $transScore * $weights['transition_prob'];
 
@@ -2541,6 +2592,124 @@ class History extends Model
         ];
     }
 
+    /**
+     * 构建二阶马尔可夫转移矩阵
+     * 考虑前两期状态联合决定当前转移概率
+     *
+     * 状态空间说明:
+     * - 一阶马尔可夫: N个状态 (zone:5, tail:10, head:5)
+     * - 二阶马尔可夫: N^2个状态对 (zone:25, tail:100, head:25)
+     * - 状态键格式: "prev1-prev2"，如 "2-3" 表示前一期区域2、前两期区域3
+     *
+     * 数据量阈值说明:
+     * - 建议历史数据 >= 200期以获得稳定的二阶概率估计
+     * - 状态对观察次数 >= 5 才使用该状态对的二阶概率
+     * - 观察次数不足时返回 state_pair_insufficient 标志，供调用者回退一阶
+     *
+     * @param array $history 历史数据（降序，最新在前）
+     * @param string $type 类型：zone/tail/head
+     * @param int $minStatePairCount 状态对最小观察次数，默认5
+     * @return array {matrix: [], prob_matrix: [], state_totals: [], num_categories: int, sufficient_pairs: int, total_pairs: int, min_threshold: int}
+     */
+    private function _getTransitionMatrix2ndOrder($history, $type, $minStatePairCount = 5)
+    {
+        // 升序排列（从旧到新）
+        $historyAsc = array_reverse($history);
+
+        // 确定类别数量和索引函数
+        switch ($type) {
+            case 'zone':
+                $numCategories = 5;
+                $getIdx = function ($num) {
+                    if ($num <= 10) return 0;
+                    if ($num <= 20) return 1;
+                    if ($num <= 30) return 2;
+                    if ($num <= 40) return 3;
+                    return 4;
+                };
+                break;
+            case 'tail':
+                $numCategories = 10;
+                $getIdx = function ($num) { return $num % 10; };
+                break;
+            case 'head':
+                $numCategories = 5;
+                $getIdx = function ($num) {
+                    if ($num <= 9) return 0;
+                    if ($num <= 19) return 1;
+                    if ($num <= 29) return 2;
+                    if ($num <= 39) return 3;
+                    return 4;
+                };
+                break;
+            default:
+                return [
+                    'matrix' => [],
+                    'prob_matrix' => [],
+                    'state_totals' => [],
+                    'num_categories' => 0,
+                    'sufficient_pairs' => 0,
+                    'total_pairs' => 0,
+                    'min_threshold' => $minStatePairCount
+                ];
+        }
+
+        // 状态空间: (prev1, prev2) -> current，共 numCategories^2 个前置状态
+        $matrix = [];
+        $stateTotals = [];
+
+        // 初始化矩阵结构
+        for ($i = 0; $i < $numCategories; $i++) {
+            for ($j = 0; $j < $numCategories; $j++) {
+                $stateKey = $i . '-' . $j;
+                $matrix[$stateKey] = array_fill(0, $numCategories, 0);
+                $stateTotals[$stateKey] = 0;
+            }
+        }
+
+        // 统计二阶转移
+        for ($i = 0; $i < count($historyAsc) - 2; $i++) {
+            $prev1 = $getIdx((int)$historyAsc[$i]['num7']);
+            $prev2 = $getIdx((int)$historyAsc[$i + 1]['num7']);
+            $current = $getIdx((int)$historyAsc[$i + 2]['num7']);
+
+            if ($prev1 < 0 || $prev2 < 0 || $current < 0) continue;
+
+            $stateKey = $prev1 . '-' . $prev2;
+            $matrix[$stateKey][$current]++;
+            $stateTotals[$stateKey]++;
+        }
+
+        // 统计充分观察的状态对数量（观察次数 >= minStatePairCount）
+        $sufficientPairs = 0;
+        $totalPairs = $numCategories * $numCategories;
+        foreach ($stateTotals as $stateKey => $count) {
+            if ($count >= $minStatePairCount) {
+                $sufficientPairs++;
+            }
+        }
+
+        // 拉普拉斯平滑处理
+        $probMatrix = [];
+        foreach ($matrix as $stateKey => $counts) {
+            $smoothTotal = $stateTotals[$stateKey] + $numCategories;
+            $probMatrix[$stateKey] = [];
+            for ($j = 0; $j < $numCategories; $j++) {
+                $probMatrix[$stateKey][$j] = ($counts[$j] + 1) / $smoothTotal;
+            }
+        }
+
+        return [
+            'matrix' => $matrix,
+            'prob_matrix' => $probMatrix,
+            'state_totals' => $stateTotals,
+            'num_categories' => $numCategories,
+            'sufficient_pairs' => $sufficientPairs,
+            'total_pairs' => $totalPairs,
+            'min_threshold' => $minStatePairCount
+        ];
+    }
+
     /**
      * 分析单双规律
      * @param array $history 历史数据（降序）
@@ -3090,6 +3259,68 @@ class History extends Model
         return min(100, $score);
     }
 
+    /**
+     * 计算二阶转移概率得分
+     *
+     * 计算方法:
+     * - 综合区域、尾号、首号三个维度的二阶转移概率
+     * - 各维度权重: 区域40%、尾号35%、首号25%
+     * - 得分范围: 0-100
+     *
+     * @param int $num 当前号码
+     * @param int $prev1Zone 前一期区域索引
+     * @param int $prev2Zone 前两期区域索引
+     * @param int $prev1Tail 前一期尾号索引
+     * @param int $prev2Tail 前两期尾号索引
+     * @param int $prev1Head 前一期首号索引
+     * @param int $prev2Head 前两期首号索引
+     * @param array $zoneTrans2nd 二阶区域转移矩阵
+     * @param array $tailTrans2nd 二阶尾号转移矩阵
+     * @param array $headTrans2nd 二阶首号转移矩阵
+     * @param array $zoneMap 号码区域映射
+     * @param array $tailMap 号码尾号映射
+     * @param array $headMap 号码首号映射
+     * @return float 综合转移得分 (0-100)
+     */
+    private function _calcTransitionScore2ndOrder(
+        $num,
+        $prev1Zone, $prev2Zone,
+        $prev1Tail, $prev2Tail,
+        $prev1Head, $prev2Head,
+        $zoneTrans2nd, $tailTrans2nd, $headTrans2nd,
+        $zoneMap, $tailMap, $headMap
+    )
+    {
+        $zone = $zoneMap[$num];
+        $tail = $tailMap[$num];
+        $head = $headMap[$num];
+
+        $score = 0;
+
+        // 区域二阶转移得分（权重40%）
+        $zoneStateKey = $prev1Zone . '-' . $prev2Zone;
+        if (isset($zoneTrans2nd['prob_matrix'][$zoneStateKey][$zone])) {
+            $prob = $zoneTrans2nd['prob_matrix'][$zoneStateKey][$zone];
+            $score += $prob * 40;
+        }
+
+        // 尾号二阶转移得分（权重35%）
+        $tailStateKey = $prev1Tail . '-' . $prev2Tail;
+        if (isset($tailTrans2nd['prob_matrix'][$tailStateKey][$tail])) {
+            $prob = $tailTrans2nd['prob_matrix'][$tailStateKey][$tail];
+            $score += $prob * 35;
+        }
+
+        // 首号二阶转移得分（权重25%）
+        $headStateKey = $prev1Head . '-' . $prev2Head;
+        if (isset($headTrans2nd['prob_matrix'][$headStateKey][$head])) {
+            $prob = $headTrans2nd['prob_matrix'][$headStateKey][$head];
+            $score += $prob * 25;
+        }
+
+        return round($score, 2);
+    }
+
     /**
      * 计算单双平衡得分
      * @param int $num 待评分号码