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【模板】高斯消元

时间:2018-11-16 17:39:30      阅读:143      评论:0      收藏:0      [点我收藏+]

标签:sel   over   roc   process   ini   position   swap   ++i   ati   

出处:http://www.cnblogs.com/autsky-jadek/

求逆矩阵

 1 #include<cstdio>
 2 #include<cmath>
 3 #include<algorithm>
 4 #include<cstring>
 5 using namespace std;
 6 const double EPS=0.00000001;
 7 #define N 105
 8 int n;
 9 double B[N][N*2],A[N][N*2],C[N][N];
10 bool guass_jordan()
11 {
12     memcpy(B,A,sizeof(A));
13     for(int i=1;i<=n;++i){
14         for(int j=n+1;j<=n*2;++j){
15             if(i==j-n){
16                 B[i][j]=1.0;
17             }
18             else{
19                 B[i][j]=0.0;
20             }
21         }
22     }
23     for(int i=1;i<=n;++i){
24         int pivot=i;
25         for(int j=i+1;j<=n;++j){
26             if(fabs(B[j][i])>fabs(B[pivot][i])){
27                 pivot=j;
28             }
29         }
30         swap(B[i],B[pivot]);
31         if(fabs(B[i][i])<EPS){
32             return 0;
33         }
34         for(int j=i+1;j<=n*2;++j){
35             B[i][j]/=B[i][i];
36         }
37         for(int j=1;j<=n;++j){
38             if(i!=j){
39                 for(int k=i+1;k<=n*2;++k){
40                     B[j][k]-=B[j][i]*B[i][k];
41                 }
42             }
43         }
44     }
45     for(int i=1;i<=n;++i){
46         for(int j=n+1;j<=n*2;++j){
47             C[i][j-n]=B[i][j];
48         }
49     }
50 }
51 int T;
52 int main()
53 {
54 //  freopen("nijuzhen2.in","r",stdin);
55 //  freopen("nijuzhen2.out","w",stdout);
56     char t[10];
57     while(scanf("%d",&n)!=EOF){
58         memset(A,0,sizeof(A));
59         for(int i=1;i<=n;++i){
60             for(int j=1;j<=n;++j){
61                 scanf("%lf",&A[i][j]);
62             }
63         }
64         if(guass_jordan()){
65             for(int i=1;i<=n;++i){
66                 for(int j=1;j<=n;++j){
67                     sprintf(t,"%.3f",C[i][j]);
68                     if(t[0]==- && t[1]==0 && t[2]==. && t[3]==0 && t[4]==0 && t[5]==0){
69                         printf("0.000%c",j==n ? \n :  );
70                     }
71                     else{
72                         printf("%.3f%c",C[i][j],j==n ? \n :  );
73                     }
74                 }
75             }
76         }
77         else{
78             puts("NO");
79         }
80     }
81     return 0;
82 }

求矩阵秩

 1 #include<cstdio>
 2 #include<cmath>
 3 #include<algorithm>
 4 #include<cstring>
 5 using namespace std;
 6 const double EPS=0.00000001;
 7 #define N 105
 8 int n,m;
 9 double B[N][N],A[N][N];
10 int guass_jordan()
11 {
12     memcpy(B,A,sizeof(A));
13     for(int i=1;i<=n;++i)
14       {
15         int pivot=i;
16         for(int j=i+1;j<=n;++j)
17           if(fabs(B[j][i])>fabs(B[pivot][i]))
18             pivot=j;
19         swap(B[i],B[pivot]);
20         if(fabs(B[i][i])<EPS){
21             return i-1;
22         }
23         for(int j=i+1;j<=m;++j)
24           B[i][j]/=B[i][i];
25         for(int j=1;j<=n;++j)
26           if(i!=j)
27             for(int k=i+1;k<=m;++k)
28               B[j][k]-=B[j][i]*B[i][k];
29       }
30     return n;
31 }
32 int main()
33 {
34     while(scanf("%d%d",&n,&m)!=EOF){
35         memset(A,0,sizeof(A));
36         for(int i=1;i<=n;++i){
37             for(int j=1;j<=m;++j){
38                 scanf("%lf",&A[i][j]);
39             }
40         }
41         printf("%d\n",guass_jordan());
42     }
43     return 0;
44 }

求行列式

 1 #include<cstdio>
 2 #include<cmath>
 3 #include<algorithm>
 4 #include<cstring>
 5 using namespace std;
 6 const double EPS=0.00000001;
 7 #define N 105
 8 int n;
 9 double B[N][N],A[N][N];
10 double guass_jordan()
11 {
12     double res=1.0;
13     memcpy(B,A,sizeof(A));
14     for(int i=1;i<=n;++i)
15       {
16         int pivot=i;
17         for(int j=i+1;j<=n;++j)
18           if(fabs(B[j][i])>fabs(B[pivot][i]))
19             pivot=j;
20         swap(B[i],B[pivot]);
21         if(i!=pivot){
22             res*=(-1.0);
23         }
24         if(fabs(B[i][i])<EPS){
25             return 0.0;
26         }
27         for(int j=i+1;j<=n;++j)
28           B[i][j]/=B[i][i];
29         res*=B[i][i];
30         for(int j=1;j<=n;++j)
31           if(i!=j)
32             for(int k=i+1;k<=n;++k)
33               B[j][k]-=B[j][i]*B[i][k];
34       }
35     return res;
36 }
37 int main()
38 {
39 //  freopen("hanglieshi3.in","r",stdin);
40 //  freopen("hanglieshi3.out","w",stdout);
41     char t[1000];
42     while(scanf("%d",&n)!=EOF){
43         memset(A,0,sizeof(A));
44         for(int i=1;i<=n;++i){
45             for(int j=1;j<=n;++j){
46                 scanf("%lf",&A[i][j]);
47             }
48         }
49         double ans=guass_jordan();
50         sprintf(t,"%.3f",ans);
51         if(t[0]==- && t[1]==0 && t[2]==. && t[3]==0 && t[4]==0 && t[5]==0){
52             puts("0.000");
53         }
54         else{
55             printf("%.3f\n",ans);
56         }
57     }
58     return 0;
59 }

 

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
using namespace std;
const double EPS=0.00000001;
#define N 105
int n;
double B[N][N*2],A[N][N*2],C[N][N];
bool guass_jordan()
{
    memcpy(B,A,sizeof(A));
    for(int i=1;i<=n;++i){
        for(int j=n+1;j<=n*2;++j){
            if(i==j-n){
                B[i][j]=1.0;
            }
            else{
                B[i][j]=0.0;
            }
        }
    }
    for(int i=1;i<=n;++i){
        int pivot=i;
        for(int j=i+1;j<=n;++j){
            if(fabs(B[j][i])>fabs(B[pivot][i])){
                pivot=j;
            }
        }
        swap(B[i],B[pivot]);
        if(fabs(B[i][i])<EPS){
            return 0;
        }
        for(int j=i+1;j<=n*2;++j){
            B[i][j]/=B[i][i];
        }
        for(int j=1;j<=n;++j){
            if(i!=j){
                for(int k=i+1;k<=n*2;++k){
                    B[j][k]-=B[j][i]*B[i][k];
                }
            }
        }
    }
    for(int i=1;i<=n;++i){
        for(int j=n+1;j<=n*2;++j){
            C[i][j-n]=B[i][j];
        }
    }
}
int T;
int main()
{
//  freopen("nijuzhen2.in","r",stdin);
//  freopen("nijuzhen2.out","w",stdout);
    char t[10];
    while(scanf("%d",&n)!=EOF){
        memset(A,0,sizeof(A));
        for(int i=1;i<=n;++i){
            for(int j=1;j<=n;++j){
                scanf("%lf",&A[i][j]);
            }
        }
        if(guass_jordan()){
            for(int i=1;i<=n;++i){
                for(int j=1;j<=n;++j){
                    sprintf(t,"%.3f",C[i][j]);
                    if(t[0]==‘-‘ && t[1]==‘0‘ && t[2]==‘.‘ && t[3]==‘0‘ && t[4]==‘0‘ && t[5]==‘0‘){
                        printf("0.000%c",j==n ? ‘\n‘ ‘ ‘);
                    }
                    else{
                        printf("%.3f%c",C[i][j],j==n ? ‘\n‘ ‘ ‘);
                    }
                }
            }
        }
        else{
            puts("NO");
        }
    }
    return 0;
}

【模板】高斯消元

标签:sel   over   roc   process   ini   position   swap   ++i   ati   

原文地址:https://www.cnblogs.com/greenty1208/p/9969860.html

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