MatrixCSR<T>::MatrixCSR(const MatrixNxN<T> &matrix)
{
int entries = matrix.m_iN * matrix.m_iN;
entries = entries - matrix.NumZeros();
m_dValues = new T[entries];
m_iColInd = new int[entries];
m_iRowPtr = new int[matrix.m_iN+1];
m_iN = matrix.m_iN;
m_iNumVal = entries;
int index = 0;
m_iRowPtr[0] = 0;
//for every row
for(int i=0;i<matrix.m_iN;i++)
{
int EntriesInRow = 0;
//iterate through the columns of the row
for(int j=0;j<matrix.m_iN;j++)
{
if(matrix(i,j)!=0.0)
{
m_dValues[index] = matrix(i,j);
m_iColInd[index] = j;
index++;
EntriesInRow++;
}
}
m_iRowPtr[i+1]=m_iRowPtr[i]+EntriesInRow;
}
}
void CLinearSolverLU<T>::SolveForwardBackward(MatrixNxN<T>& A, VectorN<T>& b, VectorN<T>& x, int iperm[])
{
int i,j,k,n;
n=A.rows();
for(i=0;i<n;i++)
{
j = iperm[i];
x(i)=b(j);
}
for(i=1;i<n;i++)
{
T sum=0.0;
for(k=0;k<i;k++)
sum+=A(i,k)*x(k);
x(i)=(x(i)-sum);
}
//x(n-1) is already done, because of:
x(n-1)=x(n-1)/A(n-1,n-1);
for(i=n-2;i>=0;i--)
{
T sum = 0.0;
for(k=i+1;k<n;k++)
sum += A(i,k)*x(k);
x(i)=(x(i)-sum)/A(i,i);
}
x.OutputVector();
}
void CLinearSolverLU<T>::Linsolve(MatrixNxN<T> &A, VectorN<T> &b, VectorN<T> &x)
{
T sum=0;
int i,j,k,n,p;
n=A.rows();
int *iperm = new int[n];
for(i=0;i<n;i++)iperm[i]=i;
for(j=0;j<=n-1;j++)
{
//partial pivoting
p=j;
//check for largest |a_ij| as pivot
for(i=j+1;i<n;i++)
{
if(fabs(A(i,j)) > fabs(A(j,j)))
{
//swap rows if we find a bigger element
A.SwapRows(j,i);
T temp = b(j);
b(j)=b(i);
b(i)=temp;
}
}
//check if there are only zero pivots
while((A(p,j)==0.0) && (p<n))
{
p++;
}
if(p==n)
{
std::cout<<"No solution exists..."<<std::endl;
return;
}
else
{
if(p !=j )
{
A.SwapRows(j,p);
T temp = b(j);
b(j)=b(p);
b(p)=temp;
}
}
//compute the betas : colums of U
for(i=0;i<=j;i++)
{
sum=0.0;
for(k=0;k<=i-1;k++)
sum+=A(i,k)*A(k,j);
//set the beta_ij
A(i,j) = A(i,j) - sum;
}//end i
//compute the alphas colums of L
for(i=j+1;i<=n-1;i++)
{
sum=0.0;
for(k=0;k<=j-1;k++)
{
//sum up the alphas before the diagonal and the
//betas above the diagonal
sum+=A(i,k)*A(k,j);
}//end k
//set alpha(i,j)
A(i,j) = (1.0/A(j,j))*(A(i,j) - sum);
}//end for i
}//end for j
SolveForwardBackward(A,b,x,iperm);
}
void CLinearSolverGauss<T>::Linsolve(MatrixNxN<T> &A, VectorN<T> &b, VectorN<T> &x)
{
int n = A.m_iN;
int k=0;
int p;
for(;k<n-1;k++)
{
p=k;
//check for largest |a_ij| as pivot
for(int i=k+1;i<n;i++)
{
if(fabs(A(i,k)) > fabs(A(k,k)))
{
//swap rows if we find a bigger element
A.SwapRows(k,i);
T temp = b(k);
b(k)=b(i);
b(i)=temp;
}
}
//check if there are only zero pivots
while((A(p,k)==0.0) && (p<n))
{
p++;
}
if(p==n)
{
std::cout<<"No solution exists..."<<std::endl;
return;
}
else
{
if(p !=k )
{
A.SwapRows(k,p);
T temp = b(k);
b(k)=b(p);
b(p)=temp;
}
}
for(int i=k+1;i<n;i++)
{
T p = A(i,k);
T pivot = A(i,k)/A(k,k);
//reduce the k+1-row
for(int j=0;j<n;j++)
A(i,j)=A(i,j) - pivot * A(k,j);
//reduce the rhs
b(i) = b(i) - pivot * b(k);
}//end for i
}//end for k
if(A(n-1,n-1) == 0)
{
std::cout<<"No solution exists..."<<std::endl;
return;
}
//backwards substitution
for(int i=n-1;i>=0;i--)
{
T Sum = 0;
x(i)=0;
for(int j=i; j<=n-1;j++)
{
Sum += A(i,j) * x(j);
}
x(i)=(b(i)-Sum)/A(i,i);
}
}