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Java로 프로그램을 작성했습니다. 그것은 선형 방정식의 시스템을 해결하기 위해 두 가지 방법을 사용하며 각 방법의 실행 시간을 계산하려고합니다.다른 메소드 호출 순서가 다른 실행 시간 결과
두 가지 방법의 실행 순서를 변경하면 실행 시간이 달라지는 것을 발견했습니다.
왜 그렇습니까?
/*using direct_method and Jacobi_method to resolve the linear equation,and compare each running time*/
public class Jacobi_iterat {
/*Jacobi part*/
/*find lower triangular matrix*/
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;
}
/*negative of the matrix*/
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;
}
/*inverse matrix of the diagnal matrix*/
private static float[][] inv_diagnal(float[][] data){
int M=data.length;
int N=data[0].length;
float[][] data2=new float[M][N];
float fenzi=1;
for(int i=0;i<M;i++){
for(int j=0;j<N;j++){
if(i==j){
data2[i][j]=fenzi/data[i][j];
}
}
}
return data2;
}
/*upper triangular matrix*/
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;
}
/*add two matrix*/
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<M;i++){
data[i]=data1[i]+data2[i];
}
return data;
}
/*multiply two matrix*/
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;
}
/*calculate the diagnal matrix */
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;
}
/*Jacobi_method*/
private static float[] Jacobi_method(float[][] A,float[] B,float[] X){
float[][] D=find_diagnal(A);
float[][] inv_D=inv_diagnal(D);
float[][] opposite_D=opposite_matrix(inv_D);
float[][] L=find_lower(A, -1);
float[][] U=find_upper(A, 1);
float[][] Bo=multiply(opposite_D,matrix_add(L, U));
float[] F=multiply2(inv_D, B);
return matrix_add2(multiply2(Bo, X),F);
}
/*calculate the two norm between two vector*/
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;
}
/*end of Jacobi part*/
/*direct method part*/
private static float[] cal_direct(float[][] A,float[] B){
int M=A[0].length;
float X[]=new float[M];
float[][] inv_A=inv(A);
X=multiply2(inv_A, B);
return X;
}
/*transpose of the matrix*/
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;
}
/*calculate the ajoint matrix of the matrix*/
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);
}
/*inverse of the matrix*/
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;
}
/* calculate the determinant of the matrix*/
private static float cal_det(float[][] data) {
float ans=0;
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++){
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[][] 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;
}
/*end of direct method part*/
public static void main(String args[]){
System.out.println("input the dimensions of the coefficient square：");
Scanner scan=new Scanner(System.in);
int M=scan.nextInt();
System.out.println("input the dimensions of the equation value vector：");
int K=scan.nextInt();
if(M!=K){
System.out.println("the number of equations and unknowns are not equal!");
System.exit(0);
}
System.out.println("input coefficient matrix：");
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("input the value vector");
float[] B=new float[M];
for(int i=0;i<M;i++){
B[i]=scan.nextFloat();
}
System.out.println("input the initial iteration vector：");
float[] X=new float[M];
for(int i=0;i<M;i++){
X[i]=scan.nextFloat();
}
System.out.println("input the bound of error：");
float er=scan.nextFloat();
float temp[]=new float[M];
/*calculate the running time of two method,but I get the different running time result when I exchange the running order of two method, why?*/
/*calculate the running time of Jacobi_method*/
long startTime=System.nanoTime();
while(cal_error((temp=Jacobi_method(A, B, X)), X)>=er){
X=temp;
}
X=temp;
long endTime=System.nanoTime();
System.out.println("the solution vector of Jacobi_method is：");
for(int i=0;i<M;i++){
System.out.println(X[i]);
}
System.out.println("the running time of Jacobi_method is：");
System.out.println(endTime-startTime+"ns");
/*calculate the running time of direct_method*/
long startTime2=System.nanoTime();
X=cal_direct(A, B);
long endTime2=System.nanoTime();
System.out.println("the solution vector of direct_method is：");
for(int i=0;i<M;i++){
System.out.println(X[i]);
}
System.out.println("the running time of direct_method is：");
System.out.println(endTime2-startTime2+"ns");
}
}
'나는 다른 실행 시간의 결과를 얻을 것을 발견했다? 각 주문의 실행 시간은? 가장 관련성있는 정보를 빠뜨린 것입니다. – Eran
BTW,'Math.pow (x, 2)'는'Math.exp (Math.log (x) * 2)'와 같은 작업을합니다. 예상대로 이것은 매우 비쌉니다. 대신'x * x'를하는 것이 좋습니다. –
큰 matricies의 경우 행렬 곱셈을 수행하기 전에 두 번째 행렬을 조 변경해야합니다. –