数学建模-层次分析法Java实现

package cn.w.ahp; import cn.hutool.core.collection.CollUtil; import cn.hutool.core.map.MapUtil; import com.alibaba.fastjson.JSONArray; import com.alibaba.fastjson.JSONObject; import org.ujmp.core.DenseMatrix; import org.ujmp.core.Matrix; import org.ujmp.core.calculation.Calculation; import java.math.BigDecimal; import java.util.Arrays; import java.util.List; import java.util.Map; import java.util.concurrent.atomic.AtomicInteger; /** * 层次分析法工具 */ public class AHPUtil { private static final double[] RI_STANDARD = {0, 0, 0.58, 0.90, 1.12, 1.24, 1.32, 1.41, 1.45, 1.49, 1.51}; public static final String CR = "CR"; public static final String OPTIMAL_SOLUTION = "最优解"; public static final double CR_CRITICAL_VALUE = 0.1; private AHPUtil() { } /** * 矩阵列向量归一化 * * @param matrix 矩阵 * @return org.ujmp.core.Matrix */ public static Matrix normalizedColumn(Matrix matrix) { DenseMatrix normalize = Matrix.Factory.zeros(matrix.getRowCount(), matrix.getColumnCount()); long columnCount = matrix.getColumnCount(); long rowCount = matrix.getRowCount(); for (long i = 0; i < columnCount; i++) { Matrix columns = matrix.selectColumns(Calculation.Ret.LINK, i); double valueSum = columns.getAbsoluteValueSum(); for (long j = 0; j < rowCount; j++) { Matrix rows = columns.selectRows(Calculation.Ret.LINK, j); normalize.setAsObject(rows.getMaxValue() / valueSum, j, i); } } return normalize; } public static AHPAnalysisResult calculateMatrix(double[][] matrixArray) { return calculateMatrix(DenseMatrix.Factory.importFromArray(matrixArray)); } public static AHPAnalysisResult calculateMatrix(Matrix matrix) { AHPAnalysisResult result = new AHPAnalysisResult(); // 矩阵的特征向量与特征值 0为特征向量，1为特征值 Matrix[] eig = matrix.eig(); // 矩阵的最大特征值 Matrix eigenvalue = eig[1]; Double eigMax = eigenvalue.abs(Calculation.Ret.NEW).getMaxValue(); result.setMaxEigenvalue(eigMax); long maxIndex; long columnCount = eigenvalue.getColumnCount(); for (maxIndex = 0; maxIndex < columnCount; maxIndex++) { Matrix colMatrix = eigenvalue.selectColumns(Calculation.Ret.LINK, maxIndex); if (colMatrix.containsDouble(eigMax)) { break; } } // 矩阵的特征向量 Matrix eigenvector = eig[0]; // 最大特征值的特征向量归一化 Matrix colMatrix = eigenvector.selectColumns(Calculation.Ret.NEW, maxIndex); result.setEigenvector(colMatrix.toColumnVector(Calculation.Ret.LINK).toDoubleArray()[0]); Matrix normalizedColumn = AHPUtil.normalizedColumn(colMatrix); result.setWeight(normalizedColumn.toColumnVector(Calculation.Ret.LINK).abs(Calculation.Ret.NEW).toDoubleArray()[0]); // CI double ci = (eigMax - columnCount) / (columnCount - 1); ci = ci <= 0 ? 0 : ci; result.setCi(new BigDecimal(ci + "").doubleValue()); // RI double ri = RI_STANDARD[(int) (columnCount - 1)]; result.setRi(ri); // CR double cr = ri != 0 ? ci / ri : 0; result.setCr(new BigDecimal(cr + "").doubleValue()); if (cr > CR_CRITICAL_VALUE) { throw new RuntimeException("层次单排序一致性检验未通过"); } return result; } public static Map<String, Object> calcLevelOrdering(AHPAnalysisResult parent, List<AHPAnalysisResult> childList) { Map<String, Object> map = MapUtil.newHashMap(); String[] title = childList.get(0).getTitle(); double[] parentWeight = parent.getWeight(); double[][] childWeight = new double[title.length][parentWeight.length]; AtomicInteger index = new AtomicInteger(0); childList.stream().map(AHPAnalysisResult::getWeight).forEach(w -> { for (int i = 0; i < title.length; i++) { childWeight[i][index.get()] = i < w.length ? w[i] : 0; } index.incrementAndGet(); }); double max = 0; String maxTitle = ""; for (int i = 0; i < title.length; i++) { String t = title[i]; double w = 0; for (int j = 0; j < childWeight[i].length; j++) { w += parentWeight[j] * childWeight[i][j]; } max = Math.max(max, w); maxTitle = w == max ? t : maxTitle; map.put(t, w); } map.put(OPTIMAL_SOLUTION, maxTitle); double ci = 0; double ri = 0; for (int i = 0; i < parentWeight.length; i++) { ci += parentWeight[i] * childList.get(i).getCi(); ri += parentWeight[i] * childList.get(i).getRi(); } double cr = (ri != 0 ? ci / ri : 0) + parent.getCr(); map.put(CR, cr); if (cr > CR_CRITICAL_VALUE) { throw new RuntimeException("层次总排序一致性检验未通过"); } return map; } public static LevelCalcResult calcCriterionWeight(LevelCalcResult calcResult, MatrixMetaData metaData) { LevelCalcResult newCalcResult = new LevelCalcResult(); double[] calcWeight = calcResult.getWeight(); double[] criterionCi = metaData.getCi(); double[] criterionRi = metaData.getRi(); double[][] criterionWeight = transpositionWeight(metaData.getWeight()); double[] newCalcWeight = new double[criterionWeight.length]; double ci = 0; double ri = 0; for (int i = 0; i < criterionWeight.length; i++) { double[] colWeight = criterionWeight[i]; for (int j = 0; j < colWeight.length; j++) { newCalcWeight[i] += colWeight[j] * calcWeight[j]; } } for (int i = 0; i < criterionCi.length; i++) { ci += calcResult.getCi() * criterionCi[i]; ri += calcResult.getRi() * criterionRi[i]; } newCalcResult.setCi(ci); newCalcResult.setRi(ri); newCalcResult.setCr((ri != 0 ? ci / ri : 0) + calcResult.getCr()); newCalcResult.setWeight(newCalcWeight); return newCalcResult; } public static Map<String, Object> calcTotalOrdering(String[] measure, LevelCalcResult calcResult, MatrixMetaData metaData) { Map<String, Object> map = MapUtil.newHashMap(); double[][] measureWeight = transpositionWeight(metaData.getWeight()); double[] calcWeight = calcResult.getWeight(); double max = 0; String maxTitle = ""; for (int i = 0; i < measureWeight.length; i++) { double[] colWeight = measureWeight[i]; double calcMeasureWeight = 0; for (int j = 0; j < colWeight.length; j++) { calcMeasureWeight += colWeight[j] * calcWeight[j]; } max = Math.max(max, calcMeasureWeight); maxTitle = calcMeasureWeight == max ? measure[i] : maxTitle; map.put(measure[i], calcMeasureWeight); } map.put(OPTIMAL_SOLUTION, maxTitle); double ci = 0; double ri = 0; double[] measureCi = metaData.getCi(); double[] measureRi = metaData.getRi(); for (int i = 0; i < measureCi.length; i++) { ci += calcResult.getCi() * measureCi[i]; ri += calcResult.getRi() * measureRi[i]; } double cr = (ri != 0 ? ci / ri : 0) + calcResult.getCr(); if (cr > CR_CRITICAL_VALUE) { throw new RuntimeException("层次总排序一致性检验未通过"); } map.put(CR, cr);