java实现SOR算法解线性方程组
http://www.thinksaas.cn/group/topic/344715/
package juzhen;
import java.util.Scanner;
public class SOR_iterate {
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;
}
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;
}
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;
}
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;
}
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;
}
private static float[][] get_complement(float[][] data,int i, int j) {
int x = data.length;
int y = data[0].length;
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;
}
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) {
ans = ans + data[0][i] * cal_det(data_temp);
} else {
ans = ans - data[0][i] * cal_det(data_temp);
}
}
}
return ans;
}
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);
}
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];
}
}
return data2;
}
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;
}
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;
}
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;
}
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;
}
private static float[] matrix_add2(float[] data1,float[] data2){
int M=data1.length;
float data[]=new float[M];
for(int i=0;i data[i]=data1[i]+data2[i]; } return data; } 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 for(int j=0;j data_temp[i][j]=-data[i][j]; } } return data_temp; } 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); } private static double cal_error(float[] X1,float[] X2){ int M=X1.length; double temp=0; for(int i=0;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 for(int j=0;j A[i][j]=scan.nextFloat(); } } System.out.println("输入值向量"); float[] B=new float[M]; for(int i=0;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 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 System.out.println(X[i]+""); } System.out.println(); } }