实现SOR算法解线性方程组代码,Java代码库,德仔网

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【Java】实现SOR算法解线性方程组
作者:郑岸以 / 发布于2014/10/8/ 528

	package linear_equation;
	
	import java.util.Scanner;
	
	/*使用SOR迭代法解线性方程组*/
	public class SOR_iterate {
	 /* 浮点数乘以二维矩阵 */
	 private static float[][] multiply3(float w, float[][] data) {
	 int m = data.length;
	 int n = data[0].length;
	 float temp[][] = new float[m][n];
	 for (int i = 0; i < m; i++) {
	 for (int j = 0; j < n; j++) {
	 temp[i][j] = w * data[i][j];
	 }
	 }
	 return temp;
	 }
	
	 /* 矩阵相减 */
	 private static float[][] subtract_matrix(float data1[][], float data2[][]) {
	 int m = data1.length;
	 int n = data1[0].length;
	 float temp[][] = new float[m][n];
	 for (int i = 0; i < m; i++) {
	 for (int j = 0; j < n; j++) {
	 temp[i][j] = data1[i][j] - data2[i][j];
	 }
	 }
	 return temp;
	 }
	
	 /* 求下三角矩阵，其中输入参数k代表求第k条对角线以下的元素 */
	 private static float[][] find_lower(float data[][], int k) {
	 int length = data.length;
	 float data2[][] = new float[length][length];
	 if (k >= 0) {
	 for (int i = 0; i <= length - k - 1; i++) {
	 for (int j = 0; j <= i + k; j++) {
	 data2[i][j] = data[i][j];
	 }
	 }
	 for (int i = length - k; i < length; i++) {
	 for (int j = 0; j < length; j++) {
	 data2[i][j] = data[i][j];
	 }
	 }
	 } else {
	 for (int i = -k; i < length; i++) {
	 for (int j = 0; j <= i + k; j++) {
	 data2[i][j] = data[i][j];
	 }
	 }
	 }
	 return data2;
	 }
	
	 /* 输入参数为原矩阵和一个整数,该整数代表从对角线往上或往下平移的元素个数 */
	 private static float[][] find_upper(float[][] data, int k) {
	 int length = data.length;
	 int M = length - k;
	 float[][] data2 = new float[length][length];
	 if (k >= 0) {
	 for (int i = 0; i < M; i++) {
	 for (int j = k; j < length; j++) {
	 data2[i][j] = data[i][j];
	 }
	 k += 1;
	 }
	 } else {
	 for (int i = 0; i < -k; i++) {
	 for (int j = 0; j < length; j++) {
	 data2[i][j] = data[i][j];
	 }
	 }
	 for (int i = -k; i < length; i++) {
	 for (int j = i + k; j < length; j++) {
	 data2[i][j] = data[i][j];
	 }
	 }
	 }
	 return data2;
	 }
	
	 /* 求矩阵的对角矩阵 */
	 private static float[][] find_diagnal(float A[][]) {
	 int m = A.length;
	 int n = A[0].length;
	 float B[][] = new float[m][n];
	 for (int i = 0; i < m; i++) {
	 for (int j = 0; j < n; j++) {
	 if (i == j) {
	 B[i][j] = A[i][j];
	 }
	 }
	 }
	 return B;
	
	 }
	
	 /* 原矩阵去掉第i+1行第j+1列后的剩余矩阵 */
	 private static float[][] get_complement(float[][] data, int i, int j) {
	
	 /* x和y为矩阵data的行数和列数 */
	 int x = data.length;
	 int y = data[0].length;
	
	 /* data2为所求剩余矩阵 */
	 float data2[][] = new float[x - 1][y - 1];
	 for (int k = 0; k < x - 1; k++) {
	 if (k < i) {
	 for (int kk = 0; kk < y - 1; kk++) {
	 if (kk < j) {
	 data2[k][kk] = data[k][kk];
	 } else {
	 data2[k][kk] = data[k][kk + 1];
	 }
	 }
	
	 } else {
	 for (int kk = 0; kk < y - 1; kk++) {
	 if (kk < j) {
	 data2[k][kk] = data[k + 1][kk];
	 } else {
	 data2[k][kk] = data[k + 1][kk + 1];
	 }
	 }
	 }
	 }
	 return data2;
	
	 }
	
	 /* 计算矩阵行列式 */
	 private static float cal_det(float[][] data) {
	 float ans = 0;
	 /* 若为2*2的矩阵可直接求值并返回 */
	 if (data[0].length == 2) {
	 ans = data[0][0] * data[1][1] - data[0][1] * data[1][0];
	 } else {
	 for (int i = 0; i < data[0].length; i++) {
	 /* 若矩阵不为2*2那么需求出矩阵第一行代数余子式的和 */
	 float[][] data_temp = get_complement(data, 0, i);
	 if (i % 2 == 0) {
	 /* 递归 */
	 ans = ans + data[0][i] * cal_det(data_temp);
	 } else {
	 ans = ans - data[0][i] * cal_det(data_temp);
	 }
	 }
	 }
	 return ans;
	
	 }
	
	 /* 计算矩阵的伴随矩阵 */
	 private static float[][] ajoint(float[][] data) {
	 int M = data.length;
	 int N = data[0].length;
	 float data2[][] = new float[M][N];
	 for (int i = 0; i < M; i++) {
	 for (int j = 0; j < N; j++) {
	 if ((i + j) % 2 == 0) {
	 data2[i][j] = cal_det(get_complement(data, i, j));
	 } else {
	 data2[i][j] = -cal_det(get_complement(data, i, j));
	 }
	 }
	 }
	
	 return trans(data2);
	
	 }
	
	 /* 转置矩阵 */
	 private static float[][] trans(float[][] data) {
	 int i = data.length;
	 int j = data[0].length;
	 float[][] data2 = new float[j][i];
	 for (int k2 = 0; k2 < j; k2++) {
	 for (int k1 = 0; k1 < i; k1++) {
	 data2[k2][k1] = data[k1][k2];
	 }
	 }
	
	 /* 将矩阵转置便可得到伴随矩阵 */
	 return data2;
	
	 }
	
	 /* 求矩阵的逆，输入参数为原矩阵 */
	 private static float[][] inv(float[][] data) {
	 int M = data.length;
	 int N = data[0].length;
	 float data2[][] = new float[M][N];
	 float det_val = cal_det(data);
	 data2 = ajoint(data);
	 for (int i = 0; i < M; i++) {
	 for (int j = 0; j < N; j++) {
	 data2[i][j] = data2[i][j] / det_val;
	 }
	 }
	
	 return data2;
	 }
	
	 /* 矩阵相乘 */
	 private static float[][] multiply(float[][] data1, float[][] data2) {
	 int M = data1.length;
	 int N = data1[0].length;
	 int K = data2[0].length;
	 float[][] data3 = new float[M][K];
	 for (int i = 0; i < M; i++) {
	 for (int j = 0; j < K; j++) {
	 for (int k = 0; k < N; k++) {
	 data3[i][j] += data1[i][k] * data2[k][j];
	 }
	 }
	 }
	 return data3;
	 }
	
	 /* 二维矩阵与一维向量相乘 */
	 private static float[] multiply2(float[][] data1, float[] data2) {
	 int M = data1.length;
	 int N = data1[0].length;
	 float[] data3 = new float[M];
	 for (int k = 0; k < M; k++) {
	 for (int j = 0; j < N; j++) {
	 data3[k] += data1[k][j] * data2[j];
	 }
	 }
	 return data3;
	 }
	
	 /* 矩阵加法 */
	 private static float[][] matrix_add(float[][] data1, float[][] data2) {
	 int M = data1.length;
	 int N = data1[0].length;
	 float data[][] = new float[M][N];
	 for (int i = 0; i < M; i++) {
	 for (int j = 0; j < N; j++) {
	 data[i][j] = data1[i][j] + data2[i][j];
	 }
	 }
	 return data;
	 }
	 /*向量加法*/
	 private static float[] matrix_add2(float[] data1,float[] data2){
	 int M=data1.length;
	 float data[]=new float[M];
	 for(int i=0;i<M;i++){
	 data[i]=data1[i]+data2[i];
	 }
	 return data;
	 }
	 /*求原矩阵的负*/
	 private static float[][] opposite_matrix(float[][] data){
	 int M=data.length;
	 int N=data[0].length;
	 float data_temp[][]=new float[M][N];
	 for(int i=0;i<M;i++){
	 for(int j=0;j<N;j++){
	 data_temp[i][j]=-data[i][j];
	 }
	 }
	 return data_temp;
	 }
	 /* SOR迭代法,A为系数矩阵,Y为值向量,X为初始迭代向量,w为松弛因子 */
	 private static float[] SOR_method(float A[][], float Y[], float X[], float w) {
	 float D[][] = find_diagnal(A);
	 float L[][] = opposite_matrix(find_lower(A, -1));
	 float U[][] = opposite_matrix(find_upper(A, 1));
	 float wL[][] = multiply3(w, L);
	 float wU[][] = multiply3(w, U);
	 float D_sub_wL[][] = subtract_matrix(D, wL);
	 float inv_D_sub_wL[][] = inv(D_sub_wL);
	 float sub_w=1-w;
	 float one_sub_w_D[][] = multiply3(sub_w, D);
	 float temp1[][]=matrix_add(one_sub_w_D, wU);
	 float B0[][]=multiply(inv_D_sub_wL, temp1);
	 float temp2[][]=multiply3(w, inv_D_sub_wL);
	 float F[]=multiply2(temp2, Y);
	
	 return matrix_add2(multiply2(B0, X),F);
	
	 }
	 /*求两向量之差的二范数（用于检验误差）*/
	 private static double cal_error(float[] X1,float[] X2){
	 int M=X1.length;
	 double temp=0;
	 for(int i=0;i<M;i++){
	 temp+=Math.pow((X1[i]-X2[i]),2);
	 }
	 temp=Math.sqrt(temp);
	 return temp;
	 }
	 public static void main(String[] args) {
	 System.out.println("输入系数矩阵的行和列数：");
	 Scanner scan=new Scanner(System.in);
	 int M=scan.nextInt();
	 System.out.println("输入方程组右侧方程值的维度：");
	 int K=scan.nextInt();
	 if(M!=K){
	 System.out.println("方程组个数和未知数个数不等！");
	 System.exit(0);
	 }
	
	 System.out.println("输入系数矩阵：");
	 float[][] A=new float[M][M];
	 for(int i=0;i<M;i++){
	 for(int j=0;j<M;j++){
	 A[i][j]=scan.nextFloat();
	 }
	 }
	
	 System.out.println("输入值向量");
	 float[] B=new float[M];
	 for(int i=0;i<M;i++){
	 B[i]=scan.nextFloat();
	 }
	
	 System.out.println("输入初始迭代向量：");
	 float[] X=new float[M];
	 for(int i=0;i<M;i++){
	 X[i]=scan.nextFloat();
	 }
	 System.out.println("输入松弛因子：");
	 float w=scan.nextFloat();
	
	 System.out.println("输入误差限：");
	 float er=scan.nextFloat();
	 float temp[]=new float[M];
	
	 while(cal_error((temp=SOR_method(A, B, X, w)), X)>=er){
	 X=temp;
	 }
	 X=temp;
	 System.out.println("SOR法计算得到的解向量为：");
	 for(int i=0;i<M;i++){
	 System.out.println(X[i]+" ");
	 }
	 System.out.println();
	 }
	
	}
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　SOR　　线性方程组　　 SOR算法　
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