13. Matrices(Symmetric Mattrix, Tridiagonal Matrix, Band Matrix, Toeplitz Matrix, Sparse Matrix)
15 Jun 2020 | Algorithm
- Diagonal Matrix
- Lower Triangular Matrix
- Upper Triangular Matrix
- Symmetric Matrix
- Tridiagonal Matrix
- Band Matrix
- Toeplitz Matrix
- sparse matrix
4. Symmetrix Matrix
5. Tridiagonal Matrix
6. Square Band Matrix
7. Toeplitz Matrix
Sparse Matrix
Create a sparse matrix
struct Element
{
int i;
int j;
int x;
};
struct Sparse
{
int m;
int n;
int num;
struct Element * ele;
};
void create(Sparse* s)
{
int i;
printf("Eneter Dimensions");
scanf("%d%d",&s->m,&s->n);
printf("Number of non-zero");
scanf("%d",&s->num);
s->ele= new Element[s->num];
printf("Eneter non-zero Elements");
for(i=0;i<s->num;i++)
scanf("%d%d%d",&s->ele[i].i,&s->ele[i].j,&s->ele[i].x);
}
struct Sparse* add(struct Sparse* s1,struct Sparse* s2)
{
struct Sparse* sum;
int i,j,k;
i=j=k=0;
if(s1->n != s2->n && s1->m != s2->m)
return NULL;
sum= new Spares;
sum->ele= new Spares(s1->num+s2->num)
while(i<s1->num && j<s2->num)
{
if(s1->ele[i].i<s2->ele[j].i)
sum->ele[k++]=s1->ele[i++];
else if(s1->ele[i].i>s2->ele[j].i)
sum->ele[k++]=s2->ele[j++];
else
{
if(s1->ele[i].j<s2->ele[j].j)
sum->ele[k++]=s1->ele[i++];
else if(s1->ele[i].j>s2->ele[j].j)
sum->ele[k++]=s2->ele[j++];
else
{
sum->ele[k]=s1->ele[i];
sum->ele[k++].x=s1->ele[i++].x+s2->ele[j++].x;
}
}
}
for(;i<s1->num;i++)
sum->ele[k++]=s1->ele[i];
for(;j<s2->num;j++)
sum->ele[k++]=s2->ele[j];
sum->m=s1->m;
sum->n=s1->n;
sum->num=k;
return sum;
}
void display(struct Sparse s)
{
int i,j,k=0;
for(i=0;i<s.m;i++)
{
for(j=0;j<s.n;j++)
{
if(i==s.ele[k].i && j==s.ele[k].j)
{
printf("%d ",s.ele[k++].x);
}
else
{
printf("0 ");
}
}
printf("\n");
}
}
int main()
{
struct Sparse s1,s2,* s3;
create(&s1)
create(&s2)
s3=add(&s1,&s2);
printf("First Matrix\n");
display(s1);
printf("Second Matrix\n");
display(s2);
printf("Sum Matrix\n");
display(*s3);
return 0;
}
- Diagonal Matrix
- Lower Triangular Matrix
- Upper Triangular Matrix
- Symmetric Matrix
- Tridiagonal Matrix
- Band Matrix
- Toeplitz Matrix
- sparse matrix
4. Symmetrix Matrix
5. Tridiagonal Matrix
6. Square Band Matrix
7. Toeplitz Matrix
Sparse Matrix
Create a sparse matrix
struct Element
{
int i;
int j;
int x;
};
struct Sparse
{
int m;
int n;
int num;
struct Element * ele;
};
void create(Sparse* s)
{
int i;
printf("Eneter Dimensions");
scanf("%d%d",&s->m,&s->n);
printf("Number of non-zero");
scanf("%d",&s->num);
s->ele= new Element[s->num];
printf("Eneter non-zero Elements");
for(i=0;i<s->num;i++)
scanf("%d%d%d",&s->ele[i].i,&s->ele[i].j,&s->ele[i].x);
}
struct Sparse* add(struct Sparse* s1,struct Sparse* s2)
{
struct Sparse* sum;
int i,j,k;
i=j=k=0;
if(s1->n != s2->n && s1->m != s2->m)
return NULL;
sum= new Spares;
sum->ele= new Spares(s1->num+s2->num)
while(i<s1->num && j<s2->num)
{
if(s1->ele[i].i<s2->ele[j].i)
sum->ele[k++]=s1->ele[i++];
else if(s1->ele[i].i>s2->ele[j].i)
sum->ele[k++]=s2->ele[j++];
else
{
if(s1->ele[i].j<s2->ele[j].j)
sum->ele[k++]=s1->ele[i++];
else if(s1->ele[i].j>s2->ele[j].j)
sum->ele[k++]=s2->ele[j++];
else
{
sum->ele[k]=s1->ele[i];
sum->ele[k++].x=s1->ele[i++].x+s2->ele[j++].x;
}
}
}
for(;i<s1->num;i++)
sum->ele[k++]=s1->ele[i];
for(;j<s2->num;j++)
sum->ele[k++]=s2->ele[j];
sum->m=s1->m;
sum->n=s1->n;
sum->num=k;
return sum;
}
void display(struct Sparse s)
{
int i,j,k=0;
for(i=0;i<s.m;i++)
{
for(j=0;j<s.n;j++)
{
if(i==s.ele[k].i && j==s.ele[k].j)
{
printf("%d ",s.ele[k++].x);
}
else
{
printf("0 ");
}
}
printf("\n");
}
}
int main()
{
struct Sparse s1,s2,* s3;
create(&s1)
create(&s2)
s3=add(&s1,&s2);
printf("First Matrix\n");
display(s1);
printf("Second Matrix\n");
display(s2);
printf("Sum Matrix\n");
display(*s3);
return 0;
}
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