LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）

1）2）LU分解（是/否部分主元法）+

3）施密特（Schmidt）QR分解 +

4）吉文斯（Givens）QR分解 +

5）Household QR分解代码详解

可直接运行版本复测试用例（java8版）

更改测试用例：更改主方法内数组数据，或直接重写I/O流

import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.List;public class Fractorization {public static void main(String args[]){run(LUFractorization(new double[][]{{2.0, 2.0, 2.0},{4.0, 7.0, 7.0},{6.0, 18.0, 22.0},}, 0));run(LUFractorization(new double[][]{{1.0, 2.0, -3.0, 4.0},{4.0, 8.0, 12.0, -8.0},{2.0, 3.0, 2.0, 1.0},{-3.0, -1.0, 1.0, -4.0}}, 1));run(SchmidtQR(new double[][]{{1, 0, -1},{1, 2, 1},{1, 1, -3},{0, 1, 1}}));run(GivensQR(new double[][]{{0, -20, -14},{3, 27, -4},{4, 11, -2}}));run(HouseholdQR(new double[][]{{1, 19, -34},{-2, -5, 20},{2, 8, 37}}));}public static void run(List<double[][]> list){if(list.size() == 3){System.out.println("The matrix L of A is");print(list.get(0));System.out.println("The matrix U of A is");print(list.get(1));System.out.println("The matrix P of A is");print(list.get(2));System.out.println();}else{System.out.println("The matrix Q of A is");print(list.get(0));System.out.println("The matrix R of A is");print(list.get(1));System.out.println();}}public static List<double[][]> LUFractorization(double[][] matrix, int model){List<double[][]> list = new ArrayList<>();int length = matrix.length;double[][] L = new double[length][length];double[][] U = new double[length][length];double[][] P = new double[length][length];int[] indexP = new int[length];for(int i = 0; i < length; i++)indexP[i] = i;for(int i = 0; i < length; i++){if(model == 1)exchange(matrix, L, indexP, i, findExchange(matrix, i));for(int j = i+1; j < length; j++)L[j][i] = eliminate(matrix, i, j);}for(int i = 0; i < length; i++) {for(int j = length-1; j >= i; j--)U[i][j] = matrix[i][j];if(model == 1)P[i][indexP[i]] = 1;elseP[i][i] = 1;L[i][i] = 1;}list.add(L);list.add(U);list.add(P);return list;}public static List<double[][]> SchmidtQR(double[][] matrix){int m = matrix.length;int n = matrix[0].length;double[][] R = new double[n][n];List<double[][]> outList = new LinkedList<>();for(int i = 0; i < n; i++){double[][] u = new double[m][1];for(int j = 0; j < m; j++)u[j][0] = matrix[j][i];for(int j = 0; j < i; j++) {double[][] q = new double[m][1];for(int k = 0; k < m; k++)q[k][0] = matrix[k][j];double r = matrixProduct(T(q), u)[0][0];u = matrixPlus(u, matrixNumProduct(r, q), false);R[j][i] = r;}double mode = 0;for(int j = 0; j < m; j++)mode += u[j][0]*u[j][0];double r = Math.pow(mode, 0.5);R[i][i] = r;u = matrixNumProduct(1/r, u);for(int j = 0; j < m; j++)matrix[j][i] = u[j][0];}outList.add(matrix);outList.add(R);return outList;}public static List<double[][]> GivensQR(double[][] matrix){int maxRow = matrix.length;int maxCol = matrix[0].length;int m = matrix.length;int n = matrix[0].length;List<double[][]> QList = new LinkedList<>();List<double[][]> RList = new LinkedList<>();List<double[][]> outList = new LinkedList<>();while(maxRow > 1 && maxCol > 1){int row = matrix.length;double[][] u = new double[row][1];for(int i = 0; i < row; i++)u[i][0] = matrix[i][0];List<double[][]> TList = new LinkedList<>();for(int i = 1; i < row; i++){if(Double.doubleToLongBits(u[i][0]) == Double.doubleToLongBits(0.00))continue;double c = u[0][0] / Math.pow((u[0][0]*u[0][0])+(u[i][0]*u[i][0]), 0.5);double s = u[i][0] / Math.pow((u[0][0]*u[0][0])+(u[i][0]*u[i][0]), 0.5);double[][] T = eye(row);T[0][0] = T[i][i] = c;T[0][i] = s;T[i][0] = -s;u = matrixProduct(T, u);TList.add(T);}double[][] T = ((LinkedList<double[][]>)TList).poll();while(!TList.isEmpty()){double[][] temp = ((LinkedList<double[][]>)TList).poll();T = matrixProduct(temp, T);}QList.add(T);RList.add(matrixProduct(T, matrix));matrix = nextStep(matrixProduct(T, matrix));maxCol --;maxRow --;}outList.add(T(repairQList(QList, m, n)));outList.add(repairRList(RList, m, n));return outList;}public static List<double[][]> HouseholdQR(double[][] matrix){int maxRow = matrix.length;int maxCol = matrix[0].length;int m = matrix.length;int n = matrix[0].length;List<double[][]> QList = new LinkedList<>();List<double[][]> RList = new LinkedList<>();List<double[][]> outList = new LinkedList<>();while(maxRow > 1 && maxCol > 1){int row = matrix.length;double[][] u = new double[row][1];for(int i = 0; i < row; i++)u[i][0] = matrix[i][0];double mode = 0;for(int i = 0; i < row; i++)mode += u[i][0]*u[i][0];mode = Math.pow(mode, 0.5);u[0][0] -= mode;double coff = 2 / matrixProduct(T(u),u)[0][0];double[][] R = matrixPlus(eye(row), matrixNumProduct(coff, matrixProduct(u, T(u))), false);double[][] mid = matrixProduct(R, matrix);QList.add(R);RList.add(mid);matrix = nextStep(mid);maxCol --;maxRow --;}outList.add(T(repairQList(QList, m, n)));outList.add(repairRList(RList, m, n));return outList;}private static double[][] matrixProduct(double[][] A, double[][] B){int y = A.length;int x = B[0].length;double C[][] = new double[y][x];for (int i = 0; i < y; i++)for (int j = 0; j < x; j++)for (int k = 0; k < B.length; k++)C[i][j] += A[i][k] * B[k][j];return C;}private static double[][] matrixPlus(double[][] A, double[][] B, boolean positive){int row = A.length;int col = A[0].length;double[][] C = new double[row][col];for(int i = 0; i < row; i++){for(int j = 0; j < col; j++){if(positive)C[i][j] = A[i][j] + B[i][j];elseC[i][j] = A[i][j] - B[i][j];}}return C;}private static double[][] matrixNumProduct(double b, double[][] A){int row = A.length;int col = A[0].length;double[][] C = new double[row][col];for(int i = 0; i < row; i++) {for (int j = 0; j < col; j++) {C[i][j] = b * A[i][j];}}return C;}private static double[][] repairQList(List<double[][]> QList, int m, int n){double[][] Q = ((LinkedList<double[][]>)QList).poll();while(!QList.isEmpty()){double[][] temp = ((LinkedList<double[][]>)QList).poll();int row = temp.length;int col = temp[0].length;double[][] productor = new double[m][n];for(int i = 0; i < row; i++)for (int j = 0; j < col; j++)productor[m-row+i][n-col+j] = temp[i][j];for(int i = 0; i < m-row; i++)productor[i][i] = 1;Q = matrixProduct(productor, Q);}return Q;}private static double[][] repairRList(List<double[][]> RList, int m, int n){double[][] R = ((LinkedList<double[][]>)RList).poll();while(!RList.isEmpty()){double[][] temp = ((LinkedList<double[][]>)RList).poll();int row = temp.length;int col = temp[0].length;for(int i = 0; i < row; i++)for (int j = 0; j < col; j++)R[m-row+i][n-col+j] = temp[i][j];}return R;}private static double[][] T(double[][] A){int row = A.length;int col = A[0].length;double[][] C = new double[col][row];for(int i = 0; i < col; i++) {for (int j = 0; j < row; j++) {C[i][j] = A[j][i];}}return C;}private static double[][] eye(int x){double[][] I = new double[x][x];for(int i = 0; i < x; i++)I[i][i] = 1;return I;}private static double[][] nextStep(double[][] A){int row = A.length;int col = A[0].length;double[][] C = new double[row-1][col-1];for(int i = 0; i < col-1; i++)for (int j = 0; j < row-1; j++)C[i][j] = A[i+1][j+1];return C;}private static int findExchange(double[][] matrix, int pivot){int length = matrix.length;double max = matrix[pivot][pivot];int out = pivot;for(int i = pivot; i < length; i++){if(absoluteValue(matrix[i][pivot]) > absoluteValue(max)){max = matrix[i][pivot];out = i;}}return out;}private static void exchange(double[][] matrix, double[][] L, int[]indexP, int i, int exchange){double[] temp = matrix[i];matrix[i] = matrix[exchange];matrix[exchange] = temp;double[] LTemp = L[i];L[i] = L[exchange];L[exchange] = LTemp;int tempIndex = indexP[i];indexP[i] = indexP[exchange];indexP[exchange] = tempIndex;}private static double eliminate(double[][] matrix, int i, int j){int length = matrix.length;double coefficient = matrix[j][i]/matrix[i][i];matrix[j][i] = 0;for(int k = i+1; k < length; k++)matrix[j][k] -= coefficient*matrix[i][k];return coefficient;}private static double absoluteValue(double x){return x >= 0 ? x : -x;}private static double[][] copy(double[][] matrix){int length = matrix.length;double[][] out = new double[length][length];for(int i = 0; i < length; i++)for(int j = 0; j < length; j++)out[i][j] = matrix[i][j];return out;}private static void print(double[][] matrix){int row = matrix.length;int col = matrix[0].length;for(int i = 0; i < row; i++) {for (int j = 0; j < col; j++) {BigDecimal bigDecimal = new BigDecimal(matrix[i][j]);String out = String.valueOf(bigDecimal.setScale(3, BigDecimal.ROUND_HALF_UP).doubleValue());int add = 8 - out.length();for(int k = 0; k < add; k++)out += " ";System.out.print(out);}System.out.println();}}
}

LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）相关推荐

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LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）

LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）相关推荐

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LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解 代码详解，可直接运行版本复测试用例（java8版）

LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解 代码详解，可直接运行版本复测试用例（java8版）相关推荐

最新文章

热门文章

LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）

LU分解（是/否部分主元法）+ 施密特（Schmidt）QR分解 + 吉文斯（Givens）QR分解 + Household QR分解代码详解，可直接运行版本复测试用例（java8版）相关推荐