int gaussSeidel(MAT &A,VEC b,VEC &x,int maxIter,double tol)
{
int k = 0;
double theta=0.0;
VEC newx(A.dim()),ans(A.dim()),temp(A.dim());
MAT LU(A.dim()),a = A;
LU = luFact(a); //LU in-place decomposition
temp=fwdSubs(LU,b); //forward substitution
ans= bckSubs(LU,temp);//backward substitution
while( k < maxIter)
{
x = newx;
for(int i=0; i< A.dim(); i++)
{
theta = 0.0;
for(int j=0; j < A.dim();j++){
if(i!=j){
theta += (A[i][j]*newx[j]);
}
}
newx[i]= (b[i]-theta)/A[i][i];
}
k++;
if (linfnorm(newx - x) < tol)
break;
}
printf("Diffrence w.r.t. hw4: %E\n",linfnorm(newx-ans));
return k;
}
void dj(double val[],int col[],int rowp[],double f[],double ui[], double us[], double u[])
{
int n = N; // Size of matrix
// Jacobi Parameter
double omega = 2.0/3.0;
// Stoping Parameters
double rm[n],rnorm=0.0,rnorm_min=1e-6; // Residual
double em[n],enorm=0.0,enorm_min=0.0; // Error
// double e1m[n],e1norm=0.0,e1norm_min=0.0; // um+1 - um = wD^-1(rm);
int itr=0, itr_max = 10000; // No. of iterations performed
int i=0;
//char s2;
multi(val,col,rowp,ui,rm); // rm = au - multiply A and ui
for (i=0;i<n;i++){
rm[i]=f[i]-rm[i];
em[i]=us[i]-u[i];
// e1m[i]=(omega/val[0])*(rm[i]);
u[i]=ui[i]; // Initilizing u, just in case for redundant u
}
rnorm = linfnorm(rm);
enorm = linfnorm(em);
// e1norm = linfnorm(e1m);
// Computations involved in iterations
while (itr<=itr_max && rnorm>=rnorm_min && enorm>=enorm_min){ // e1norm>=e1norm_min
for(i=1;i<n-1;i++){
u[i] = u[i] + (omega/val[2])*rm[i]; // val[0] for aii
}
u[0] = u[0] + (omega)*rm[0];
u[n-1] = u[n-1] + (omega)*rm[n-1];
multi(val,col,rowp,u,rm); // rm = au - multiply a and u-new
for (i=0;i<n;i++)
{
em[i]=us[i]-u[i];
rm[i]=f[i]-rm[i];
// e1m[i]=(omega/val[0])*(rm[i]);
}
rnorm = linfnorm(rm);
enorm = linfnorm(em);
// e1norm = linfnorm(e1m);
itr++;
}
// printf("No. of Iteration: %d\n",itr-1);
// printf("Residual rm: %lf\n",rnorm);
// printf("Error em: %lf\n",enorm);
// printf("Improvement in last iteration: %lf\n",e1norm);
}
double linfnorm(int mpi_rank, std::vector<double>& v1, std::vector<double>& v2) {
if (v1.size() != v2.size()) {
std::cout << "Error! in linfnorm(...): vectors are not same length. assuming 0's for missing elements" << std::endl;
//exit(EXIT_FAILURE);
}
return linfnorm(mpi_rank, v1, v2, 0, v1.size());
}
double linfnorm(int mpi_rank, std::vector<double>& v1, std::vector<double>& v2, int n1, int n2) {
double global_val = 0;
// reuse the local norms from norms.h
double local_val = linfnorm(v1, v2, n1, n2);
// Get max of max (will bcast norm to all ranks)
NORM_REDUCE(&local_val, &global_val, 1, MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD);
return global_val;
}
double linfnorm(int mpi_rank, std::vector<double>& v1, int n1, int n2) {
double global_val = 0;
double local_val = linfnorm(v1, n1, n2);
NORM_REDUCE(&local_val, &global_val, 1, MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD);
return global_val;
}
double linfnorm(int mpi_rank, std::vector<double>& v1)
{
return linfnorm(mpi_rank, v1, 0, v1.size());
}
