Vector gauss(Matrix a) {
Matrix ac(a);
Vector xs(a.size());
for (int i = 0; i < xs.size(); ++i) xs[i] = i;
for (int i = 0; i < ac.size(); ++i) {
double max = fabs(a[i][i]), maxI = i, maxJ = i;
for (int l = i; l < ac.size(); ++l) {
for (int m = i; m < ac.size(); ++m) {
if (fabs(ac[l][m]) > max) {
max = fabs(ac[l][m]);
maxI = l;
maxJ = m;
}
}
}
if (maxI != i) ac = swap_rows(ac, i, maxI);
if (maxJ != i) ac = swap_cols(ac, i, maxJ);
swap(xs[i], xs[maxJ]);
for (int k = i + 1; k < ac.size(); ++k) {
double c = - ac[k][i] / ac[i][i];
for (int j = i; j < ac[0].size(); ++j) {
ac[k][j] += c * ac[i][j];
}
}
for (int j = ac[0].size() - 1; j >= i; --j) {
ac[i][j] /= ac[i][i];
}
}
Vector v(ac.size());
for (int i = ac.size() - 1; i >= 0; --i) {
v[xs[i]] = ac[i][ac[0].size()-1];
for (int j = i + 1; j < ac.size(); ++j) {
v[xs[i]] -= v[xs[j]] * ac[i][j];
}
}
return v;
}
bool matrix::inverse()
{
if (n!=m) return false;
matrix temp(n,n);
temp=*this;
matrix E(n,n);
for(size_t i=0; i<n; i++)
{
for(size_t j=0; j<n; j++)
{
(i==j)?E.p[n*i+j]=1.0:E.p[n*i+j]=0.0;
}
}
for(size_t k=0; k<n; k++)
{
size_t left_col,upper_row;
bool has_nozero=false;
for(size_t i=k; i<n; i++)
{
for(size_t j=k; j<n; j++)
{
if (p[i+j*n]!=0.0)
{
has_nozero=true;
upper_row=j;
break;
}
}
if (has_nozero)
{
left_col=i;
break;
}
}
if (!has_nozero)
{
*this=temp;
return false;
}
swap_cols(k,left_col);
E.swap_cols(k,left_col);
swap_rows(k,upper_row);
E.swap_rows(k,upper_row);
long double coeff=p[k*(n+1)];
divide_row(k,coeff);
E.divide_row(k,coeff);
for(size_t i=k+1; i<n; i++)
{
coeff=p[i*n+k];
sub_multed_row(k,i,coeff);
E.sub_multed_row(k,i,coeff);
}
}
for(size_t k=n-1; k>0; k--)
{
for(size_t i=k; i>0;)
{
long double coeff=p[--i*n+k];
sub_multed_row(k,i,coeff);
E.sub_multed_row(k,i,coeff);
}
}
*this=E;
return true;
}
