init

app.py

@@ -0,0 +1,416 @@
+import gradio as gr
+import numpy as np
+import plotly.graph_objects as go
+from plotly.subplots import make_subplots
+import time
+
+class MeanAnalyzer:
+    def __init__(self):
+        self.reset()
+    
+    def reset(self):
+        """重置所有數據"""
+        self.sequence = [100.0]  # 初始值
+        self.multipliers = []
+        self.arithmetic_means = [100.0]
+        self.geometric_means = [100.0]
+        self.current_step = 0
+    
+    def add_step(self, min_mult=0.1, max_mult=2.1, seed=None):
+        """添加一個新的步驟"""
+        if seed is not None:
+            np.random.seed(seed + self.current_step)
+        
+        # 生成隨機乘數
+        multiplier = np.random.uniform(min_mult, max_mult)
+        self.multipliers.append(multiplier)
+        
+        # 計算新值
+        new_value = self.sequence[-1] * multiplier
+        self.sequence.append(new_value)
+        
+        # 計算算術平均
+        arithmetic_mean = np.mean(self.sequence)
+        self.arithmetic_means.append(arithmetic_mean)
+        
+        # 計算幾何平均
+        geometric_mean = np.exp(np.mean(np.log(self.sequence)))
+        self.geometric_means.append(geometric_mean)
+        
+        self.current_step += 1
+        
+        return self.create_plot(), self.get_stats()
+    
+    def create_plot(self):
+        """創建四象限圖表"""
+        fig = make_subplots(
+            rows=2, cols=2,
+            subplot_titles=('Sequence Values & Means', 'Mean Difference (Arithmetic - Geometric)',
+                          'Mean Ratio (Arithmetic / Geometric)', 'Statistics Summary'),
+            specs=[[{'type': 'scatter'}, {'type': 'scatter'}],
+                   [{'type': 'scatter'}, {'type': 'table'}]],
+            vertical_spacing=0.12,
+            horizontal_spacing=0.15
+        )
+        
+        steps = list(range(len(self.sequence)))
+        
+        # 左上：數列值與平均數
+        fig.add_trace(
+            go.Scatter(x=steps, y=self.sequence, 
+                      mode='lines+markers', name='Sequence',
+                      line=dict(color='blue', width=2),
+                      marker=dict(size=6)),
+            row=1, col=1
+        )
+        fig.add_trace(
+            go.Scatter(x=steps, y=self.arithmetic_means,
+                      mode='lines', name='Arithmetic Mean',
+                      line=dict(color='red', dash='dash', width=2)),
+            row=1, col=1
+        )
+        fig.add_trace(
+            go.Scatter(x=steps, y=self.geometric_means,
+                      mode='lines', name='Geometric Mean',
+                      line=dict(color='green', dash='dot', width=2)),
+            row=1, col=1
+        )
+        
+        # 右上：差異
+        differences = [a - g for a, g in zip(self.arithmetic_means, self.geometric_means)]
+        fig.add_trace(
+            go.Scatter(x=steps, y=differences,
+                      mode='lines+markers', name='Difference',
+                      line=dict(color='purple', width=2),
+                      marker=dict(size=6)),
+            row=1, col=2
+        )
+        fig.add_trace(
+            go.Scatter(x=steps, y=[0]*len(steps),
+                      mode='lines', name='Zero Line',
+                      line=dict(color='gray', dash='dash', width=1),
+                      showlegend=False),
+            row=1, col=2
+        )
+        
+        # 左下：比值
+        ratios = [a/g if g != 0 else 1 for a, g in zip(self.arithmetic_means, self.geometric_means)]
+        fig.add_trace(
+            go.Scatter(x=steps, y=ratios,
+                      mode='lines+markers', name='Ratio',
+                      line=dict(color='orange', width=2),
+                      marker=dict(size=6)),
+            row=2, col=1
+        )
+        fig.add_trace(
+            go.Scatter(x=steps, y=[1]*len(steps),
+                      mode='lines', name='Ratio=1',
+                      line=dict(color='gray', dash='dash', width=1),
+                      showlegend=False),
+            row=2, col=1
+        )
+        
+        # 右下：統計表
+        stats_data = [
+            ['Current Step', str(self.current_step)],
+            ['Latest Value', f'{self.sequence[-1]:.2f}'],
+            ['Arithmetic Mean', f'{self.arithmetic_means[-1]:.2f}'],
+            ['Geometric Mean', f'{self.geometric_means[-1]:.2f}'],
+            ['Current Difference', f'{differences[-1]:.2f}'],
+            ['Current Ratio', f'{ratios[-1]:.3f}'],
+            ['Max Difference', f'{max(differences):.2f}'],
+            ['Avg Difference', f'{np.mean(differences):.2f}']
+        ]
+        
+        fig.add_trace(
+            go.Table(
+                header=dict(values=['Statistic', 'Value'],
+                           fill_color='lightgray',
+                           align='left',
+                           font=dict(size=14, color='black', family='Arial Black')),
+                cells=dict(values=[[row[0] for row in stats_data],
+                                  [row[1] for row in stats_data]],
+                          fill_color='white',
+                          align='left',
+                          font=dict(size=13, color='black', family='Arial'),
+                          height=30)
+            ),
+            row=2, col=2
+        )
+        
+        # 更新佈局
+        fig.update_xaxes(title_text="Steps", row=1, col=1)
+        fig.update_xaxes(title_text="Steps", row=1, col=2)
+        fig.update_xaxes(title_text="Steps", row=2, col=1)
+        fig.update_yaxes(title_text="Value", row=1, col=1)
+        fig.update_yaxes(title_text="Difference", row=1, col=2)
+        fig.update_yaxes(title_text="Ratio", row=2, col=1)
+        
+        fig.update_layout(
+            height=700,
+            showlegend=True,
+            title_text="Geometric Mean vs Arithmetic Mean - Real-time Analysis",
+            title_font_size=20,
+            hovermode='x unified'
+        )
+        
+        return fig
+    
+    def get_stats(self):
+        """獲取當前統計信息"""
+        if len(self.sequence) == 0:
+            return "尚無數據"
+        
+        diff = self.arithmetic_means[-1] - self.geometric_means[-1]
+        ratio = self.arithmetic_means[-1] / self.geometric_means[-1] if self.geometric_means[-1] != 0 else 1
+        
+        stats_text = f"""
+        ### 📊 當前狀態
+        - **步驟數**: {self.current_step}
+        - **序列最新值**: {self.sequence[-1]:.2f}
+        - **算術平均**: {self.arithmetic_means[-1]:.2f}
+        - **幾何平均**: {self.geometric_means[-1]:.2f}
+        - **差異 (算術-幾何)**: {diff:.2f}
+        - **比值 (算術/幾何)**: {ratio:.3f}
+        
+        ### 💡 觀察重點
+        - 算術平均 {'>' if diff > 0 else '='} 幾何平均 {'✓ (符合數學定理)' if diff >= 0 else ''}
+        - 差異程度: {'小' if diff < 5 else '中等' if diff < 20 else '大'}
+        """
+        
+        if len(self.multipliers) > 0:
+            stats_text += f"\n- 最後使用的乘數: {self.multipliers[-1]:.3f}"
+        
+        return stats_text
+    
+    def animate_sequence(self, seed, length, min_mult, max_mult, speed):
+        """生成動畫序列"""
+        self.reset()
+        frames = []
+        
+        for i in range(length):
+            self.add_step(min_mult, max_mult, seed)
+            frames.append((self.create_plot(), self.get_stats(), i+1))
+        
+        return frames
+
+# 創建全局分析器實例
+analyzer = MeanAnalyzer()
+
+def reset_sequence(initial_value):
+    """重置序列"""
+    analyzer.reset()
+    analyzer.sequence[0] = initial_value
+    analyzer.arithmetic_means[0] = initial_value
+    analyzer.geometric_means[0] = initial_value
+    return analyzer.create_plot(), analyzer.get_stats(), "✅ 已重置序列"
+
+def add_single_step(seed, min_mult, max_mult):
+    """添加單步"""
+    if seed == -1:
+        seed = None
+    plot, stats = analyzer.add_step(min_mult, max_mult, seed)
+    return plot, stats, f"✅ 已添加步驟 {analyzer.current_step}"
+
+def run_animation(seed, length, min_mult, max_mult, speed):
+    """運行動畫"""
+    if seed == -1:
+        seed = None
+    
+    analyzer.reset()
+    message = f"🎬 開始動畫 (共 {length} 步)..."
+    
+    for i in range(length):
+        plot, stats = analyzer.add_step(min_mult, max_mult, seed)
+        progress = f"進度: {i+1}/{length} 步"
+        yield plot, stats, message, progress
+        time.sleep(1.0 / speed)  # 控制動畫速度
+    
+    # 最終統計
+    differences = [a - g for a, g in zip(analyzer.arithmetic_means, analyzer.geometric_means)]
+    final_message = f"""
+    ### 🎬 動畫完成！序列分析摘要：
+    - **總步驟數**: {length}
+    - **最終序列值**: {analyzer.sequence[-1]:.2f}
+    - **最終算術平均**: {analyzer.arithmetic_means[-1]:.2f}
+    - **最終幾何平均**: {analyzer.geometric_means[-1]:.2f}
+    - **最大差異**: {max(differences):.2f}
+    - **平均差異**: {np.mean(differences):.2f}
+    - **最終比值**: {analyzer.arithmetic_means[-1]/analyzer.geometric_means[-1]:.3f}
+    
+    ### 💡 關鍵洞察
+    - 算術平均始終 ≥ 幾何平均 ✓
+    - 差異隨著數列波動而變化
+    - 幾何平均更適合計算成長率
+    """
+    yield plot, stats, final_message, f"完成 {length}/{length} 步"
+
+def create_demo():
+    """創建 Gradio 界面"""
+    with gr.Blocks(title="幾何平均 vs 算術平均", theme=gr.themes.Soft()) as demo:
+        gr.Markdown("""
+        # 🔢 幾何平均數 vs 算術平均數 - 差異分析器
+        
+        此介面為-國立高雄科技大學 114學年-財管系-財管系二甲 統計學(一) 上課教材
+        
+        > 探索兩種平均數在隨機序列中的差異演變，理解為什麼投資報酬率要用幾何平均計算！
+        
+        ### 📚 數學概念
+        - **算術平均**: `(a₁ + a₂ + ... + aₙ) / n` - 一般的平均值
+        - **幾何平均**: `(a₁ × a₂ × ... × aₙ)^(1/n)` - 適合計算平均成長率
+        - **定理**: 算術平均 ≥ 幾何平均（AM-GM 不等式）
+        """)
+        
+        with gr.Tabs():
+            # 互動模式標籤
+            with gr.Tab("🎮 互動模式"):
+                with gr.Row():
+                    with gr.Column(scale=1):
+                        gr.Markdown("### 🎛️ 控制面板")
+                        
+                        seed_input = gr.Number(
+                            label="🎲 隨機種子 (-1 為真隨機)",
+                            value=42,
+                            precision=0
+                        )
+                        
+                        initial_value = gr.Number(
+                            label="🏁 初始值",
+                            value=100,
+                            minimum=1
+                        )
+                        
+                        with gr.Row():
+                            min_mult = gr.Slider(
+                                label="📉 最小乘數",
+                                minimum=0.1,
+                                maximum=1.0,
+                                value=0.5,
+                                step=0.1
+                            )
+                            max_mult = gr.Slider(
+                                label="📈 最大乘數",
+                                minimum=1.0,
+                                maximum=3.0,
+                                value=1.5,
+                                step=0.1
+                            )
+                        
+                        with gr.Row():
+                            reset_btn = gr.Button("🔄 重置", variant="secondary")
+                            add_btn = gr.Button("➕ 添加步驟", variant="primary")
+                        
+                        status_text = gr.Textbox(
+                            label="狀態訊息",
+                            value="✅ 就緒",
+                            interactive=False
+                        )
+                        
+                        stats_display = gr.Markdown(analyzer.get_stats())
+                    
+                    with gr.Column(scale=3):
+                        gr.Markdown("### 📈 實時比較圖表")
+                        plot_display = gr.Plot(value=analyzer.create_plot())
+            
+            # 動畫模式標籤
+            with gr.Tab("🎬 動畫模式"):
+                with gr.Row():
+                    with gr.Column(scale=1):
+                        gr.Markdown("### 🎥 動畫設置")
+                        
+                        anim_seed = gr.Number(
+                            label="🎲 隨機種子 (-1 為真隨機)",
+                            value=42,
+                            precision=0
+                        )
+                        
+                        anim_length = gr.Slider(
+                            label="📏 序列長度",
+                            minimum=10,
+                            maximum=100,
+                            value=30,
+                            step=5
+                        )
+                        
+                        with gr.Row():
+                            anim_min_mult = gr.Slider(
+                                label="📉 最小乘數",
+                                minimum=0.1,
+                                maximum=1.0,
+                                value=0.5,
+                                step=0.1
+                            )
+                            anim_max_mult = gr.Slider(
+                                label="📈 最大乘數",
+                                minimum=1.0,
+                                maximum=3.0,
+                                value=1.5,
+                                step=0.1
+                            )
+                        
+                        anim_speed = gr.Slider(
+                            label="⚡ 播放速度",
+                            minimum=1,
+                            maximum=10,
+                            value=3,
+                            step=1
+                        )
+                        
+                        play_btn = gr.Button("▶️ 播放完整動畫", variant="primary", size="lg")
+                        
+                        anim_progress = gr.Textbox(
+                            label="進度",
+                            value="等待開始...",
+                            interactive=False
+                        )
+                        
+                        anim_message = gr.Markdown("### 準備就緒")
+                    
+                    with gr.Column(scale=3):
+                        gr.Markdown("### 🎬 動畫圖表")
+                        anim_plot = gr.Plot(value=analyzer.create_plot())
+                        anim_stats = gr.Markdown("等待動畫開始...")
+        
+        gr.Markdown("""
+        ---
+        ### 🎓 學習指南
+        
+        1. **互動模式**：手動控制每一步，仔細觀察差異變化
+        2. **動畫模式**：自動播放完整序列，看整體趨勢
+        3. **實驗建議**：
+           - 嘗試不同的乘數範圍，看差異如何變化
+           - 使用相同種子，改變參數對比結果
+           - 觀察極端情況（很小或很大的乘數範圍）
+        
+        ### 💡 重要發現
+        - 當數列波動越大，兩種平均數的差異越明顯
+        - 幾何平均對極端值（特別是接近 0 的值）更敏感
+        - 這就是為什麼計算投資報酬率要用幾何平均！
+        """)
+        
+        # 事件綁定 - 互動模式
+        reset_btn.click(
+            fn=reset_sequence,
+            inputs=[initial_value],
+            outputs=[plot_display, stats_display, status_text]
+        )
+        
+        add_btn.click(
+            fn=add_single_step,
+            inputs=[seed_input, min_mult, max_mult],
+            outputs=[plot_display, stats_display, status_text]
+        )
+        
+        # 事件綁定 - 動畫模式
+        play_btn.click(
+            fn=run_animation,
+            inputs=[anim_seed, anim_length, anim_min_mult, anim_max_mult, anim_speed],
+            outputs=[anim_plot, anim_stats, anim_message, anim_progress]
+        )
+    
+    return demo
+
+# 啟動應用
+if __name__ == "__main__":
+    demo = create_demo()
+    demo.launch(share=True)

requirements.txt

@@ -0,0 +1,8 @@
+gradio
+numpy
+pandas
+matplotlib
+seaborn
+scipy
+websockets
+plotly