java实现高斯赛德尔算法解线性方程组
【摘要】
package
linear_equation;
import
java.util.Scanner;
/*使用高斯赛德尔迭代法求解线性方程组*/
public
class
Gauss_Seidel_Iterate {
/...
package linear_equation;
import java.util.Scanner;
/*使用高斯赛德尔迭代法求解线性方程组*/
public class Gauss_Seidel_Iterate {
/*求下三角*/
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;
}
/*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;
}
/*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;
}
/*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;
}
/*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;
}
/*m*n矩阵与n维向量的乘法*/
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;
}
/*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;
}
/*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;
}
/*高斯赛德尔迭代法*/
private static float [] Gauss_Seidel_method( float [][] A, float [] B, float [] X){
float D[][]=find_diagnal(A);
float L[][]=find_lower(A, - 1 );
float U[][]=find_upper(A, 1 );
float temp1[][]=inv(matrix_add(D, L));
float temp2[][]=opposite_matrix(temp1);
float B0[][]=multiply(temp2, U);
float F[]=multiply2(temp1, B);
return matrix_add2(multiply2(B0, X), F);
}
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( "输入误差限：" );
float er=scan.nextFloat();
float temp[]= new float [M];
while (cal_error((temp=Gauss_Seidel_method(A, B, X)), X)>=er){
X=temp;
}
// while(cal_error((temp=Gauss_Seidel_method(A, B, X)), X)>=er){
// X=temp;
//
// }
X=temp;
System.out.println( "高斯赛德尔计算得到的解向量为：" );
for ( int i= 0 ;i<M;i++){
System.out.println(X[i]+ " " );
}
System.out.println();
}
}
原文：http://www.oschina.net/code/snippet_574827_39084
文章来源: blog.csdn.net，作者：网奇，版权归原作者所有，如需转载，请联系作者。
原文链接：blog.csdn.net/jacke121/article/details/55657524
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