多项式回归

1：修改了返回值类型
2：修改了多项式计算公式

src/main/java/com/gunshi/project/hsz/controller/ProjectSafeAnalyseController.java

@@ -6,6 +6,7 @@ import com.gunshi.project.hsz.entity.dto.ProjectSafeCalculateDto;
 import com.gunshi.project.hsz.entity.dto.ProjectSaveReportDto;
 import com.gunshi.project.hsz.entity.dto.SyRegressionDataDto;
 import com.gunshi.project.hsz.entity.vo.ForecastResultVo;
+import com.gunshi.project.hsz.entity.vo.ProjectSafeCalculateVo;
 import com.gunshi.project.hsz.model.ForecastTask;
 import com.gunshi.project.hsz.model.RegressionEquation;
 import com.gunshi.project.hsz.model.SyRegressionData;
@@ -40,8 +41,8 @@ public class ProjectSafeAnalyseController {
 
     @Operation(summary = "多项式回归")
     @PostMapping("/caculate")
-    public R<Map<String, RegressionEquation>> calculate(@RequestBody ProjectSafeCalculateDto dto){
+    public R<ProjectSafeCalculateVo> calculate(@RequestBody ProjectSafeCalculateDto dto){
-        Map<String, RegressionEquation> ans = jcskSyRService.calculate(dto);
+        ProjectSafeCalculateVo ans = jcskSyRService.calculate(dto);
         return R.ok(ans);
     }
 

src/main/java/com/gunshi/project/hsz/entity/vo/ProjectSafeCalculateVo.java

@@ -0,0 +1,21 @@
+package com.gunshi.project.hsz.entity.vo;
+
+
+import com.gunshi.project.hsz.common.model.vo.OsmoticPressDetailVo;
+import lombok.Data;
+
+import java.util.List;
+
+@Data
+public class ProjectSafeCalculateVo {
+
+    private String one;
+
+    private String two;
+
+    private String three;
+
+    private String four;
+
+    private List<OsmoticPressDetailVo> datas;
+}

src/main/java/com/gunshi/project/hsz/service/JcskSyRService.java

@@ -26,6 +26,7 @@ import com.gunshi.project.hsz.util.*;
 import com.ruoyi.common.utils.StringUtils;
 import jakarta.servlet.http.HttpServletResponse;
 import lombok.extern.slf4j.Slf4j;
+import org.jetbrains.annotations.NotNull;
 import org.springframework.beans.BeanUtils;
 import org.springframework.beans.factory.annotation.Autowired;
 import org.springframework.stereotype.Service;
@@ -790,9 +791,9 @@ public class JcskSyRService extends ServiceImpl<JcskSyRMapper, JcskSyR> {
      * @param dto
      * @return
      */
-    public Map<String, RegressionEquation> calculate(ProjectSafeCalculateDto dto) {
+    public ProjectSafeCalculateVo calculate(@NotNull ProjectSafeCalculateDto dto) {
         LambdaQueryWrapper<JcskSyB> queryWrapper = new LambdaQueryWrapper<>();
-        Map<String, RegressionEquation> res = new HashMap<>();
+        ProjectSafeCalculateVo res = new ProjectSafeCalculateVo();
         //根据dvcd查询stcd和mpcd
         queryWrapper.eq(JcskSyB::getDvcd, dto.getDvcd());
         JcskSyB jcskSyB = jcskSyBService.getBaseMapper().selectOne(queryWrapper);
@@ -835,13 +836,22 @@ public class JcskSyRService extends ServiceImpl<JcskSyRMapper, JcskSyR> {
             return res;
         }
         RegressionEquation first = RegressionAnalysis.calculateLinear(data);
+        if(first != null){
+            res.setOne(first.toString());
+        }
         RegressionEquation second = RegressionAnalysis.calculateQuadratic(data);
+        if(second != null){
+            res.setTwo(second.toString());
+        }
         RegressionEquation three = RegressionAnalysis.calculateCubic(data);
+        if(three != null){
+            res.setThree(three.toString());
+        }
         RegressionEquation four = RegressionAnalysis.calculateQuartic(data);
-        res.put("first", first);
+        if(four != null){
-        res.put("second", second);
+            res.setFour(four.toString());
-        res.put("three", three);
+        }
-        res.put("four", four);
+        res.setDatas(data);
         return res;
     }
 

src/main/java/com/gunshi/project/hsz/util/RegressionAnalysis.java

@@ -163,179 +163,166 @@ public class RegressionAnalysis {
         return new RegressionEquation(2, coefficients, rSquared, n);
     }
 
+
     /**
-     * 计算三次回归方程（3阶）- 优化版本
+     * 计算三次回归方程（3阶）- 高精度版本
      */
     public static RegressionEquation calculateCubic(List<OsmoticPressDetailVo> data) {
-        int n = 0;
-        List<BigDecimal> coefficientsList = null;
-        BigDecimal rSquared = null;
         try {
             List<OsmoticPressDetailVo> validData = filterValidData(data);
             if (validData.size() < 4) {
                 throw new IllegalArgumentException("三次回归至少需要4个数据点");
             }
 
-            n = validData.size();
+            int n = validData.size();
 
-            // 使用中心化数据提高数值稳定性
+            // 使用高精度计算各项和
-            BigDecimal meanX = calculateMean(validData, OsmoticPressDetailVo::getRz);
+            MathContext mc = new MathContext(200, RoundingMode.HALF_UP); // 提高精度到200位
 
-            // 计算各项和（使用中心化数据）
             BigDecimal sumX = BigDecimal.ZERO, sumY = BigDecimal.ZERO;
             BigDecimal sumX2 = BigDecimal.ZERO, sumX3 = BigDecimal.ZERO, sumX4 = BigDecimal.ZERO;
             BigDecimal sumX5 = BigDecimal.ZERO, sumX6 = BigDecimal.ZERO;
             BigDecimal sumXY = BigDecimal.ZERO, sumX2Y = BigDecimal.ZERO, sumX3Y = BigDecimal.ZERO;
 
             for (OsmoticPressDetailVo vo : validData) {
-                BigDecimal x = vo.getRz().subtract(meanX); // 中心化
+                BigDecimal x = vo.getRz();
                 BigDecimal y = vo.getValue();
 
-                BigDecimal x2 = x.multiply(x);
+                BigDecimal x2 = x.multiply(x, mc);
-                BigDecimal x3 = x2.multiply(x);
+                BigDecimal x3 = x2.multiply(x, mc);
-                BigDecimal x4 = x3.multiply(x);
+                BigDecimal x4 = x3.multiply(x, mc);
-                BigDecimal x5 = x4.multiply(x);
+                BigDecimal x5 = x4.multiply(x, mc);
-                BigDecimal x6 = x5.multiply(x);
+                BigDecimal x6 = x5.multiply(x, mc);
 
-                sumX = sumX.add(x);
+                sumX = sumX.add(x, mc);
-                sumY = sumY.add(y);
+                sumY = sumY.add(y, mc);
-                sumX2 = sumX2.add(x2);
+                sumX2 = sumX2.add(x2, mc);
-                sumX3 = sumX3.add(x3);
+                sumX3 = sumX3.add(x3, mc);
-                sumX4 = sumX4.add(x4);
+                sumX4 = sumX4.add(x4, mc);
-                sumX5 = sumX5.add(x5);
+                sumX5 = sumX5.add(x5, mc);
-                sumX6 = sumX6.add(x6);
+                sumX6 = sumX6.add(x6, mc);
-                sumXY = sumXY.add(x.multiply(y));
+                sumXY = sumXY.add(x.multiply(y, mc), mc);
-                sumX2Y = sumX2Y.add(x2.multiply(y));
+                sumX2Y = sumX2Y.add(x2.multiply(y, mc), mc);
-                sumX3Y = sumX3Y.add(x3.multiply(y));
+                sumX3Y = sumX3Y.add(x3.multiply(y, mc), mc);
             }
 
             BigDecimal nBig = new BigDecimal(n);
 
-            // 构建正规方程组（中心化后的矩阵条件数更好）
+            // 构建正规方程组 - 使用中心化数据提高数值稳定性
+            BigDecimal meanX = sumX.divide(nBig, mc);
+
+            // 重新计算中心化后的各阶矩
+            BigDecimal m2 = BigDecimal.ZERO, m3 = BigDecimal.ZERO, m4 = BigDecimal.ZERO, m5 = BigDecimal.ZERO, m6 = BigDecimal.ZERO;
+            BigDecimal m1y = BigDecimal.ZERO, m2y = BigDecimal.ZERO, m3y = BigDecimal.ZERO;
+
+            for (OsmoticPressDetailVo vo : validData) {
+                BigDecimal xCentered = vo.getRz().subtract(meanX, mc);
+                BigDecimal y = vo.getValue();
+
+                BigDecimal x2 = xCentered.multiply(xCentered, mc);
+                BigDecimal x3 = x2.multiply(xCentered, mc);
+                BigDecimal x4 = x3.multiply(xCentered, mc);
+                BigDecimal x5 = x4.multiply(xCentered, mc);
+                BigDecimal x6 = x5.multiply(xCentered, mc);
+
+                m2 = m2.add(x2, mc);
+                m3 = m3.add(x3, mc);
+                m4 = m4.add(x4, mc);
+                m5 = m5.add(x5, mc);
+                m6 = m6.add(x6, mc);
+                m1y = m1y.add(xCentered.multiply(y, mc), mc);
+                m2y = m2y.add(x2.multiply(y, mc), mc);
+                m3y = m3y.add(x3.multiply(y, mc), mc);
+            }
+
+            // 中心化后的正规方程组（常数项为0）
             BigDecimal[][] matrix = {
-                    {nBig, sumX, sumX2, sumX3},
+                    {nBig, BigDecimal.ZERO, m2, m3},
-                    {sumX, sumX2, sumX3, sumX4},
+                    {BigDecimal.ZERO, m2, m3, m4},
-                    {sumX2, sumX3, sumX4, sumX5},
+                    {m2, m3, m4, m5},
-                    {sumX3, sumX4, sumX5, sumX6}
+                    {m3, m4, m5, m6}
             };
 
-            BigDecimal[] vector = {sumY, sumXY, sumX2Y, sumX3Y};
+            // 注意：第一个方程对应常数项，右侧是sumY
-
+            BigDecimal[] vector = {
-            // 使用改进的高斯消元法
+                    sumY,    // 对应常数项
-            BigDecimal[] centeredCoefficients = solveLinearSystemImproved(matrix, vector);
+                    m1y,     // 对应一次项
+                    m2y,     // 对应二次项
+                    m3y      // 对应三次项
+            };
 
+            // 使用高精度求解
+            BigDecimal[] centeredCoefficients = solveLinearSystemHighPrecision(matrix, vector, mc);
             if (centeredCoefficients == null) {
                 throw new IllegalArgumentException("无法求解三次回归方程");
             }
 
             // 将中心化系数转换回原始坐标
-            BigDecimal[] originalCoefficients = convertToOriginalCoefficients(centeredCoefficients, meanX);
+            BigDecimal[] originalCoefficients = convertCenteredToOriginalCubic(centeredCoefficients, meanX, mc);
 
             // 计算R²
-            BigDecimal meanY = sumY.divide(nBig, MathContext.DECIMAL128);
+            BigDecimal meanY = sumY.divide(nBig, mc);
-            coefficientsList = Arrays.asList(originalCoefficients);
+            List<BigDecimal> coefficientsList = Arrays.asList(originalCoefficients);
-            rSquared = calculateRSquared(validData, coefficientsList, meanY);
+            BigDecimal rSquared = calculateRSquared(validData, coefficientsList, meanY);
+
+            return new RegressionEquation(3, coefficientsList, rSquared, n);
         } catch (IllegalArgumentException e) {
             e.printStackTrace();
             return null;
         }
-
-        return new RegressionEquation(3, coefficientsList, rSquared, n);
     }
 
     /**
-     * 将中心化系数转换回原始坐标
+     * 高精度线性方程组求解
      */
-    private static BigDecimal[] convertToOriginalCoefficients(BigDecimal[] centeredCoeffs, BigDecimal meanX) {
+    private static BigDecimal[] solveLinearSystemHighPrecision(BigDecimal[][] matrix, BigDecimal[] vector, MathContext mc) {
-        // 对于三次多项式：y = a + b(x - μ) + c(x - μ)² + d(x - μ)³
-        // 展开后：y = (a - bμ + cμ² - dμ³) + (b - 2cμ + 3dμ²)x + (c - 3dμ)x² + d x³
-
-        BigDecimal a = centeredCoeffs[0];
-        BigDecimal b = centeredCoeffs[1];
-        BigDecimal c = centeredCoeffs[2];
-        BigDecimal d = centeredCoeffs[3];
-
-        BigDecimal mu = meanX;
-        BigDecimal mu2 = mu.multiply(mu);
-        BigDecimal mu3 = mu2.multiply(mu);
-
-        BigDecimal newA = a.subtract(b.multiply(mu))
-                .add(c.multiply(mu2))
-                .subtract(d.multiply(mu3));
-
-        BigDecimal newB = b.subtract(BigDecimal.valueOf(2).multiply(c).multiply(mu))
-                .add(BigDecimal.valueOf(3).multiply(d).multiply(mu2));
-
-        BigDecimal newC = c.subtract(BigDecimal.valueOf(3).multiply(d).multiply(mu));
-        BigDecimal newD = d;
-
-        return new BigDecimal[]{newA, newB, newC, newD};
-    }
-
-    /**
-     * 带完全主元的高斯消元法，提高数值稳定性
-     */
-    private static BigDecimal[] solveLinearSystemWithPivot(BigDecimal[][] matrix, BigDecimal[] vector) {
         int n = vector.length;
 
+        // 复制矩阵和向量
         BigDecimal[][] a = new BigDecimal[n][n];
         BigDecimal[] b = new BigDecimal[n];
         for (int i = 0; i < n; i++) {
-            System.arraycopy(matrix[i], 0, a[i], 0, n);
+            a[i] = matrix[i].clone();
             b[i] = vector[i];
         }
 
-        int[] rowPerm = new int[n];
+        // 部分主元高斯消元
-        int[] colPerm = new int[n];
-        for (int i = 0; i < n; i++) {
-            rowPerm[i] = i;
-            colPerm[i] = i;
-        }
-
-        // 完全主元高斯消元
         for (int k = 0; k < n; k++) {
             // 寻找主元
-            int maxRow = k, maxCol = k;
+            int maxRow = k;
-            BigDecimal maxVal = a[rowPerm[k]][colPerm[k]].abs();
+            BigDecimal maxVal = a[k][k].abs();
-
+            for (int i = k + 1; i < n; i++) {
-            for (int i = k; i < n; i++) {
+                BigDecimal current = a[i][k].abs();
-                for (int j = k; j < n; j++) {
+                if (current.compareTo(maxVal) > 0) {
-                    BigDecimal current = a[rowPerm[i]][colPerm[j]].abs();
+                    maxVal = current;
-                    if (current.compareTo(maxVal) > 0) {
+                    maxRow = i;
-                        maxVal = current;
-                        maxRow = i;
-                        maxCol = j;
-                    }
                 }
             }
 
             // 交换行
             if (maxRow != k) {
-                int temp = rowPerm[k];
+                BigDecimal[] tempRow = a[k];
-                rowPerm[k] = rowPerm[maxRow];
+                a[k] = a[maxRow];
-                rowPerm[maxRow] = temp;
+                a[maxRow] = tempRow;
+
+                BigDecimal tempB = b[k];
+                b[k] = b[maxRow];
+                b[maxRow] = tempB;
             }
 
-            // 交换列
+            // 检查主元是否为0 - 增加容错
-            if (maxCol != k) {
+            if (a[k][k].abs().compareTo(new BigDecimal("1E-100")) < 0) {
-                int temp = colPerm[k];
+                // 尝试使用伪逆或特殊处理
-                colPerm[k] = colPerm[maxCol];
+                return solveSingularSystem(a, b, mc);
-                colPerm[maxCol] = temp;
-            }
-
-            // 主元为0，矩阵奇异
-            if (a[rowPerm[k]][colPerm[k]].compareTo(BigDecimal.ZERO) == 0) {
-                return null;
             }
 
             // 消元
             for (int i = k + 1; i < n; i++) {
-                BigDecimal factor = a[rowPerm[i]][colPerm[k]].divide(a[rowPerm[k]][colPerm[k]], 100, RoundingMode.HALF_UP);
+                BigDecimal factor = a[i][k].divide(a[k][k], mc);
                 for (int j = k; j < n; j++) {
-                    a[rowPerm[i]][colPerm[j]] = a[rowPerm[i]][colPerm[j]].subtract(
+                    a[i][j] = a[i][j].subtract(factor.multiply(a[k][j], mc), mc);
-                            factor.multiply(a[rowPerm[k]][colPerm[j]]));
                 }
-                b[rowPerm[i]] = b[rowPerm[i]].subtract(factor.multiply(b[rowPerm[k]]));
+                b[i] = b[i].subtract(factor.multiply(b[k], mc), mc);
             }
         }
 
@@ -344,18 +331,75 @@ public class RegressionAnalysis {
         for (int i = n - 1; i >= 0; i--) {
             BigDecimal sum = BigDecimal.ZERO;
             for (int j = i + 1; j < n; j++) {
-                sum = sum.add(a[rowPerm[i]][colPerm[j]].multiply(x[colPerm[j]]));
+                sum = sum.add(a[i][j].multiply(x[j], mc), mc);
             }
-            x[colPerm[i]] = b[rowPerm[i]].subtract(sum).divide(a[rowPerm[i]][colPerm[i]], 100, RoundingMode.HALF_UP);
+            x[i] = b[i].subtract(sum, mc).divide(a[i][i], mc);
         }
 
-        // 恢复原始顺序
+        return x;
-        BigDecimal[] result = new BigDecimal[n];
+    }
-        for (int i = 0; i < n; i++) {
+
-            result[i] = x[i];
+    /**
+     * 处理奇异或接近奇异的系统
+     */
+    private static BigDecimal[] solveSingularSystem(BigDecimal[][] a, BigDecimal[] b, MathContext mc) {
+        int n = b.length;
+
+        // 简单处理：将接近0的主元设为一个小值
+        for (int k = 0; k < n; k++) {
+            if (a[k][k].abs().compareTo(new BigDecimal("1E-100")) < 0) {
+                a[k][k] = new BigDecimal("1E-50"); // 设置一个小值
+            }
+
+            for (int i = k + 1; i < n; i++) {
+                BigDecimal factor = a[i][k].divide(a[k][k], mc);
+                for (int j = k; j < n; j++) {
+                    a[i][j] = a[i][j].subtract(factor.multiply(a[k][j], mc), mc);
+                }
+                b[i] = b[i].subtract(factor.multiply(b[k], mc), mc);
+            }
         }
 
-        return result;
+        // 回代
+        BigDecimal[] x = new BigDecimal[n];
+        for (int i = n - 1; i >= 0; i--) {
+            BigDecimal sum = BigDecimal.ZERO;
+            for (int j = i + 1; j < n; j++) {
+                sum = sum.add(a[i][j].multiply(x[j], mc), mc);
+            }
+            x[i] = b[i].subtract(sum, mc).divide(a[i][i], mc);
+        }
+
+        return x;
+    }
+
+    /**
+     * 将中心化三次系数转换回原始坐标
+     */
+    private static BigDecimal[] convertCenteredToOriginalCubic(BigDecimal[] centeredCoeffs, BigDecimal mean, MathContext mc) {
+        // centered: y = a + b(x-μ) + c(x-μ)² + d(x-μ)³
+        // original: y = A + Bx + Cx² + Dx³
+
+        BigDecimal a = centeredCoeffs[0];
+        BigDecimal b = centeredCoeffs[1];
+        BigDecimal c = centeredCoeffs[2];
+        BigDecimal d = centeredCoeffs[3];
+
+        BigDecimal mu = mean;
+        BigDecimal mu2 = mu.multiply(mu, mc);
+        BigDecimal mu3 = mu2.multiply(mu, mc);
+
+        BigDecimal A = a.subtract(b.multiply(mu, mc), mc)
+                .add(c.multiply(mu2, mc), mc)
+                .subtract(d.multiply(mu3, mc), mc);
+
+        BigDecimal B = b.subtract(BigDecimal.valueOf(2).multiply(c, mc).multiply(mu, mc), mc)
+                .add(BigDecimal.valueOf(3).multiply(d, mc).multiply(mu2, mc), mc);
+
+        BigDecimal C = c.subtract(BigDecimal.valueOf(3).multiply(d, mc).multiply(mu, mc), mc);
+        BigDecimal D = d;
+
+        return new BigDecimal[]{A, B, C, D};
     }