package gaodai.matrix; import gaodai.determinant.DeterminantCalculation; import java.util.ArrayList; import java.util.List; import java.util.Scanner; /** * Matrix inversion (elementary row transformation) * @author Qiu Wanchi * */ public class InverseOfMatrix { private List<List<Double>> matrix; private int lineNum; private int columnNum; public InverseOfMatrix(List<List<Double>> data){ matrix = data; lineNum = data.size(); columnNum = data.get(0).size(); } public void caculate() throws Exception{ //1. Non-square cannot be reversed //2. Founder's determinant value is zero and cannot be inverted if( lineNum != columnNum){ throw new Exception("This matrix cannot be inverse>>>>>>>>>>>>>>>>>>"); } List<List<Double>> tempList = new ArrayList<List<Double>>(); for(List<Double> l : matrix){ List<Double> newList = new ArrayList<Double>(); newList.addAll(l); tempList.add(newList); } DeterminantCalculation d = new DeterminantCalculation(tempList); d.chang2UpperTriangle(); double result = d.getValue(); if(result == 0){ throw new Exception("This matrix cannot be inverse>>>>>>>>>>>>>>>>>>"); } //Increase the identity matrix for(int i = 0; i < lineNum; i++){ List<Double> list = matrix.get(i); for(int j = 0; j < columnNum; j++){ if(i == j){ list.add(1.0); }else{ list.add(0.0); } } } print(); chang2UpperTriangle();//Turn into upper triangle changeReducedMatrix();//Reduced matrix print(); } public void getValue(){ boolean flag = true; for(int i = 0; i < lineNum; i++){ if(matrix.get(i).get(i) == 0){ flag = false; } if(!flag){ break; } } if(!flag){ System.out.println("This matrix is irreversible>>>>>>>>>>>>>>"); }else{ for(int i = 0; i < lineNum; i++){ List<Double> list = matrix.get(i); for(int j = 0; j < columnNum; j++){ list.remove(0); } } System.out.println("逆矩阵为>>>>>>>>>>>>>>>>>"); print(); } } /** * Print */ public void print() { int i = 0, j = 0; for (List<Double> line : matrix) { for (double element : line) { System.out.print(element); System.out.print("(" + i + "," + j + ") "); System.out.print(" "); j++; } System.out.println(); i++; j = 0; } System.out.println(); } /** * Check whether it is an upper triangle, if not, continue to calculate * * @return */ public boolean isCaculate() { boolean hasCaculate = false; for (int i = 0; i < matrix.size(); i++) { for (int j = 0; j < i; j++) { if (matrix.get(i).get(j) != 0.0) { System.out.println("(" + (i + 1) + "," + (j + 1) + ") element value is not zero"); hasCaculate = true; break; } } if (hasCaculate) { break; } } return hasCaculate; } private int caculateTimes; /** * into an upper triangle * @throws Exception */ public void chang2UpperTriangle() throws Exception { if (!isCaculate()) { return; } int min = lineNum; caculateTimes++; System.out.println("-------------th" + caculateTimes + "time calculation-------------"); for (int i = 0; i < min; i++) { for (int j = i + 1; j < min; j++) { double multiplyNum = -1 * matrix.get(j).get(i) / matrix.get(i).get(i); if (multiplyNum == 0) { continue; } this.lineMultiplyNumAdd2OtherLine(multiplyNum, (i + 1), (j + 1)); print(); } } print(); chang2UpperTriangle(); } /** * becomes a reduced matrix */ public void changeReducedMatrix() throws Exception{ for(int i = 0; i < lineNum; i++){//行 if(i == 0){ //continue; } List<Double> temp = matrix.get(i); for(Double d : temp){ if(d == 0){ continue; } double multiplyNum = 1.0 / d; for(int a = 0; a < temp.size(); a++){ temp.set(a, temp.get(a) * multiplyNum); } break; } print(); for(int j = 0; j <= columnNum; j++){//列 if(temp.get(j) != 0){//This number is not zero, this number is the i-th row and the j-th column for(int t = 0; t < lineNum; t++){//行 if(t == i || matrix.get(t).get(j) == 0){//Other lines in this column continue; } double multiplyNum = -1 * matrix.get(t).get(j) / temp.get(j); this.lineMultiplyNumAdd2OtherLine(multiplyNum, (i + 1), (t + 1)); print(); } break; } } } } /** * Line a times number and add to line b * @param number The number to multiply by * @param a line number * @param b line number * @throws Exception */ public void lineMultiplyNumAdd2OtherLine(double number, int a, int b) throws Exception { if (a < 1 || a > matrix.size() || b < 1 || b > matrix.size()) { throw new Exception("The input line number is invalid"); } List<Double> aLine = matrix.get(a - 1); List<Double> bLine = matrix.get(b - 1); for (int i = 0; i < bLine.size(); i++) { double temp = bLine.get(i) + aLine.get(i) * number; bLine.set (i, temp); } System.out.println("Line " + a + " multiplied by " + number + " and added to line " + b + " Line: "); } public static void main(String[] args) { Scanner scanner = new Scanner(System.in); System.out.println("Please enter the number of rows and columns of the matrix, separated by commas:"); String sn = scanner.next(); String[] snArr = sn.split(","); int lineNum = Integer.valueOf(snArr[0]); int columnNum = Integer.valueOf(snArr[1]); List<List<Double>> matrix = new ArrayList<List<Double>>(); for(int i = 0; i < lineNum; i++){ System.out.println("Please enter the number of lines " + (i + 1) + ", separated by commas: "); String lineData = scanner.next(); String[] lineDataArr = lineData.split(","); List<Double> line = new ArrayList<Double>(); matrix.add(line); for(int j = 0; j < columnNum; j++){ line.add(Double.valueOf(lineDataArr[j])); } } InverseOfMatrix m = new InverseOfMatrix(matrix); m.print(); try { m.caculate(); m.getValue(); } catch (Exception e) { e.printStackTrace (); } } }