feat: normal distribution

src/main/java/me/hatter/math/NormalDistribution.java

@@ -0,0 +1,45 @@
+package me.hatter.math;
+
+import me.hatter.math.util.MathUtil;
+import me.hatter.tools.commons.string.StringUtil;
+
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+import java.util.ArrayList;
+import java.util.List;
+
+public class NormalDistribution {
+
+    public static void main(String[] args) {
+        BigDecimal mu = BigDecimal.valueOf(0);
+        BigDecimal sigma = MathUtil.sqrt(BigDecimal.valueOf(0.2), 100);
+
+        List<String> list = new ArrayList<>();
+        list.add("G = Graphics()");
+        for (int i = -200; i <= 200; i++) {
+            double x = ((double) i) / 100;
+            BigDecimal fx = nd(mu, sigma, BigDecimal.valueOf(x)).setScale(10, RoundingMode.HALF_UP);
+//            System.out.println(Arrays.asList(x, fx.toPlainString()));
+            list.add("G += point((" + x + ", " + fx.toPlainString() + "), color='blue', size=10)");
+        }
+        list.add("G += line([(-2, 0), (2, 0)], color='black')");
+        list.add("G += line([(0, -0.1), (0, 1.1)], color='black')");
+        list.add("show(G, xmin=-2, xmax=2, ymin=-0.1, ymax=1.1, aspect_ratio=1)");
+        System.out.println(StringUtil.join(list, "\n"));
+    }
+
+    public static BigDecimal nd(BigDecimal mu, BigDecimal sigma, BigDecimal x) {
+        // \frac{1}{\sigma \times \sqrt{2\times \pi}}
+        BigDecimal pa = BigDecimal.ONE.divide(
+                sigma.multiply(MathUtil.sqrt(BigDecimal.valueOf(2).multiply(MathUtil.PI), 100))
+                , 100, RoundingMode.HALF_UP
+        );
+        // \frac{(x-\mu)^2}{2\times \sigma^2}
+        BigDecimal pb = x.subtract(mu).pow(2).divide(
+                BigDecimal.valueOf(2).multiply(sigma.pow(2))
+                , 100, RoundingMode.HALF_UP
+        );
+        return pa.multiply(MathUtil.pow(MathUtil.E, BigDecimal.ZERO.subtract(pb)))
+                .setScale(100, RoundingMode.HALF_UP);
+    }
+}

src/main/java/me/hatter/math/util/MathUtil.java

@@ -87,4 +87,33 @@ public class MathUtil {
 
         return x;
     }
+
+    // 泰勒级数展开（Generated By Qwen3-Coder）
+    public static BigDecimal pow(BigDecimal base, BigDecimal exponent) {
+        if (exponent.compareTo(BigDecimal.ZERO) == 0) {
+            return BigDecimal.ONE;
+        }
+        if (base.compareTo(BigDecimal.ONE) == 0) {
+            return BigDecimal.ONE;
+        }
+        if (exponent.compareTo(BigDecimal.ONE) == 0) {
+            return base;
+        }
+        // 使用公式: a^b = e^(b * ln(a))
+        BigDecimal lnBase = ln(base);
+        BigDecimal exponentLnBase = exponent.multiply(lnBase);
+        return exp(exponentLnBase);
+    }
+
+    // 这里需要实现自然对数的计算，可以使用泰勒级数
+    // 简化处理：使用Math.log转换
+    public static BigDecimal ln(BigDecimal x) {
+        return BigDecimal.valueOf(Math.log(x.doubleValue()));
+    }
+
+    // 指数函数的近似计算（简化版）
+    // 简化处理：使用Math.exp转换
+    public static BigDecimal exp(BigDecimal x) {
+        return BigDecimal.valueOf(Math.exp(x.doubleValue()));
+    }
 }