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matrixsolving.c
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#include "ac.h"
complex add(complex a,complex b)
{
complex res;
res.real = a.real + b.real;
res.img = a.img + b.img;
return res;
}
complex sub(complex a,complex b)//a-b
{
complex res;
res.real = a.real-b.real;
res.img = a.img-b.img;
return res;
}
complex mult(complex a,complex b)
{
complex res;
res.real = a.real * b.real - a.img * b.img;
res.img = a.real*b.img + a.img * b.real;
return res;
}
complex div_(complex a,complex b)// a / b
{
double temp=b.real*b.real+b.img*b.img;
complex c;c.real=b.real;c.img=-1*b.img;
complex res=mult(a,c);
//----------------------TODO:check------------------------
if(temp==0)
{//fprintf(stderr,"division by zero\n");
res.real = 0;
res.img = 0;}
else
{res.real /= temp;
res.img /= temp;}
return res;
}
complex make_complex(double r,double i)
{
complex res;
res.real=r;res.img=i;
return res;
}
double abs_(complex a)
{
double res=a.real*a.real+a.img*a.img;
res = sqrt(res);
return res;
}
void init()//initialise for testing
{
n=2;
//scanf("%d",&n);
a = (complex**)calloc((n+10),sizeof(complex*));
for (int i = 0; i < n; ++i)
{a[i] = (complex*)calloc((n+10),sizeof(complex));}
a[0][0].real=2;a[0][0].img=0; a[0][1].real=3;a[0][1].img=0;
a[1][0].real=3;a[1][0].img=0; a[1][1].real=2;a[1][1].img=0;
for(i=0;i<n;++i)
{
for(j=0;j<n;++j)
{ao[i][j]=a[i][j];}
}
// for(int i=0;i<n;++i)
// {
// for(int j=0;j<n;++j)
// {scanf("%lf%lf",&a[i][j].real,&a[i][j].img);}
// }
values = (complex*)calloc((n+10),sizeof(complex));
values[0].real=4;values[0].img=-2;
values[1].real=5;values[1].img=-1;
// for(int i=0;i<n;++i)
// {
// scanf("%lf%lf",&values[i].real,&values[i].img);
// }
}
void print()
{
int i,j;
for(i=0;i<n;++i)
{
for(j=0;j<n;++j)
{printf("inverted_mat[%d][%d]=(%lf, %lf)\n",i,j,inverted_mat[i][j].real,inverted_mat[i][j].img);}
printf("\n");
}
for(i=0;i<n;++i)
{
printf("answer[%d]=(%lf, %lf)\n",i,answer[i].real,answer[i].img);
}
}
void test()
{
t = (complex*)calloc((n+10),sizeof(complex));
printf("n=%d\n",n);
int i,j;
/*for(i=0;i<n;++i)
{
for(j=0;j<n;++j)
{printf("a[%d][%d]=(%lf, %lf)\tmatrix[%d][%d]=(%lf, %lf)\n",i,j,ao[i][j].real,ao[i][j].img,i,j,matrix[i][j].real,matrix[i][j].img);}
printf("\n");
}*/
for(i=0;i<n;++i)
{
t[i].real=0;t[i].img=0;
// printf("t[%d]=(%lf, %lf)\n",i,t[i].real,t[i].img);
for(j=0;j<n;++j)
{
t[i] = add(t[i],mult(ao[i][j], answer[j]));
}
// printf("t[%d]=(%lf, %lf)\n",i,t[i].real,t[i].img);
}
int error=0;
for(i=0;i<n;++i)
{printf("t[%d]=(%lf, %lf)\n",i,t[i].real,t[i].img);
if(t[i].real!=values[i].real)
{++error;printf("t[%d].real=%lf, values[%d].real= %lf \n",i,t[i].real,i,values[i].real);}
if(t[i].img!=values[i].img)
{++error;printf("t[%d].img=%lf, values[%d].img= %lf \n",i,t[i].img,i,values[i].img);}
}
printf("Error count=%d\n",error);
print();
}
void solve_matrix()
{
int i,j;
inverted_mat = (complex**)calloc((n+10),sizeof(complex*));
for (i = 0; i < n; i++)
{inverted_mat[i] = (complex*)calloc((n+10),sizeof(complex));}
invert();
answer = (complex*)calloc((n+10),sizeof(complex));
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
answer[i] = add(answer[i], mult(inverted_mat[i][j], values[j]) );
}
}
}
/*
int main()
{
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{ao[i][j]=a[i][j];}
}
init();
solve_matrix();
// print();
test();
}*/
void invert()
{
complex** x;
complex** b;
x = (complex**)calloc((n+10),sizeof(complex*));
for (int i = 0; i < n; i++)
{x[i] = (complex*)calloc((n+10),sizeof(complex));}
b = (complex**)calloc((n+10),sizeof(complex*));
for (int i = 0; i < n; i++)
{b[i] = (complex*)calloc((n+10),sizeof(complex));}
int index[n];
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{b[i][j].real=0;b[i][j].img=0;}
}
for (int i=0; i<n; ++i)
{b[i][i].real=1;b[i][i].img=0;}
gaussian(index);
for (int i=0; i<n-1; ++i)
for (int j=i+1; j<n; ++j)
for (int k=0; k<n; ++k)
{b[index[j]][k] = sub(b[index[j]][k],mult(a[index[j]][i],b[index[i]][k]));}
for (int i=0; i<n; ++i)
{
x[n-1][i] = div_(b[index[n-1]][i],a[index[n-1]][n-1]);
for (int j=n-2; j>=0; --j)
{
x[j][i] = b[index[j]][i];
for (int k=j+1; k<n; ++k)
{
x[j][i] = sub(x[j][i],mult(a[index[j]][k], x[k][i]) );
}
x[j][i] = div_(x[j][i], a[index[j]][j]);
}
}
for (int i=0; i<n; ++i)
for (int j=0; j<n; ++j)
{inverted_mat[i][j].real=x[i][j].real;inverted_mat[i][j].img=x[i][j].img;}
}
void gaussian(int index[])
{
double c[n];
for (int i=0; i<n; ++i)
index[i] = i;
for (int i=0; i<n; ++i)
{
double c1 = 0;
for (int j=0; j<n; ++j)
{
double c0 = abs_(a[i][j]);
if (c0 > c1) c1 = c0;
}
c[i] = c1;
}
int k = 0;
for (int j=0; j<n-1; ++j)
{
double pi1 = 0;
for (int i=j; i<n; ++i)
{
double pi0 = abs_(a[index[i]][j]);
pi0 /= c[index[i]];
if (pi0 > pi1)
{
pi1 = pi0;
k = i;
}
}
int itmp = index[j];
index[j] = index[k];
index[k] = itmp;
for (int i=j+1; i<n; ++i)
{
complex pj = div_(a[index[i]][j], a[index[j]][j]);
a[index[i]][j] = pj;
for (int l=j+1; l<n; ++l)
a[index[i]][l] = sub(a[index[i]][l], mult(pj, a[index[j]][l]));
}
}
}