double PDECond::Passo(){
for(int i=1; i<X-1;i++){
for(int j=1; j<Y-1;j++){
if(M == mSOR)
succ[i][j] = SOR(i,j);
else if(M == mGaussSeidel)
succ[i][j] = GaussSeidel(i,j);
else
succ[i][j] = Jacobi(i,j);
}
}
return getErr();//ritorna l'errore la precisione e` decisa dall'utente
}
int main(int argc, char** argv)
{
int i, j, N, flag;
Matrix A=NULL, Q=NULL;
Vector b, grid, e, lambda=NULL;
double time, sum, h, tol=1e-4;
if (argc < 3) {
printf("need two parameters, N and flag [and tolerance]\n");
printf(" - N is the problem size (in each direction\n");
printf(" - flag = 1 -> Dense LU\n");
printf(" - flag = 2 -> Dense Cholesky\n");
printf(" - flag = 3 -> Full Gauss-Jacobi iterations\n");
printf(" - flag = 4 -> Full Gauss-Jacobi iterations using BLAS\n");
printf(" - flag = 5 -> Full Gauss-Seidel iterations\n");
printf(" - flag = 6 -> Full Gauss-Seidel iterations using BLAS\n");
printf(" - flag = 7 -> Full CG iterations\n");
printf(" - flag = 8 -> Matrix-less Gauss-Jacobi iterations\n");
printf(" - flag = 9 -> Matrix-less Gauss-Seidel iterations\n");
printf(" - flag = 10 -> Matrix-less Red-Black Gauss-Seidel iterations\n");
printf(" - flag = 11 -> Diagonalization\n");
printf(" - flag = 12 -> Diagonalization - FST\n");
printf(" - flag = 13 -> Matrix-less CG iterations\n");
return 1;
}
N=atoi(argv[1]);
flag=atoi(argv[2]);
if (argc > 3)
tol = atof(argv[3]);
if (N < 0) {
printf("invalid problem size given\n");
return 2;
}
if (flag < 0 || flag > 13) {
printf("invalid flag given\n");
return 3;
}
if (flag == 10 && (N-1)%2 != 0) {
printf("need an even size for red-black iterations\n");
return 4;
}
if (flag == 12 && (N & (N-1)) != 0) {
printf("need a power-of-two for fst-based diagonalization\n");
return 5;
}
h = 1.0/N;
grid = equidistantMesh(0.0, 1.0, N);
b = createVector(N-1);
e = createVector(N-1);
evalMeshInternal(b, grid, source);
evalMeshInternal(e, grid, exact);
scaleVector(b, pow(h, 2));
axpy(b, e, alpha);
if (flag < 8) {
A = createMatrix(N-1,N-1);
diag(A, -1, -1.0);
diag(A, 0, 2.0+alpha);
diag(A, 1, -1.0);
}
if (flag >= 11 && flag < 13)
lambda = generateEigenValuesP1D(N-1);
if (flag == 11)
Q = generateEigenMatrixP1D(N-1);
time = WallTime();
if (flag == 1) {
int* ipiv=NULL;
lusolve(A, b, &ipiv);
free(ipiv);
} else if (flag == 2)
llsolve(A,b,0);
else if (flag == 3)
printf("Gauss-Jacobi used %i iterations\n",
GaussJacobi(A, b, tol, 10000000));
else if (flag == 4)
printf("Gauss-Jacobi used %i iterations\n",
GaussJacobiBlas(A, b, tol, 10000000));
else if (flag == 5)
printf("Gauss-Seidel used %i iterations\n",
GaussSeidel(A, b, tol, 10000000));
else if (flag == 6)
printf("Gauss-Seidel used %i iterations\n",
GaussSeidelBlas(A, b, tol, 10000000));
else if (flag == 7)
printf("CG used %i iterations\n", cg(A, b, 1e-8));
else if (flag == 8)
printf("Gauss-Jacobi used %i iterations\n",
GaussJacobiPoisson1D(b, tol, 10000000));
else if (flag == 9)
printf("Gauss-Jacobi used %i iterations\n",
GaussSeidelPoisson1D(b, tol, 10000000));
else if (flag == 10)
printf("Gauss-Jacobi used %i iterations\n",
GaussSeidelPoisson1Drb(b, tol, 10000000));
else if (flag == 11)
DiagonalizationPoisson1D(b,lambda,Q);
else if (flag == 12)
DiagonalizationPoisson1Dfst(b,lambda);
else if (flag == 13)
printf("CG used %i iterations\n", cgMatrixFree(Poisson1D, b, tol));
printf("elapsed: %f\n", WallTime()-time);
evalMeshInternal(e, grid, exact);
axpy(b,e,-1.0);
printf("max error: %e\n", maxNorm(b));
if (A)
freeMatrix(A);
if (Q)
freeMatrix(Q);
freeVector(grid);
freeVector(b);
freeVector(e);
if (lambda)
freeVector(lambda);
return 0;
}
int main(int argc, char* argv[])
{
if (argc != 4) {
std::cout << "Missing parameters. Please run as: \n"
<< " ./project-01-solution <npoints> <tol> <maxiter> <storage> with:\n"
<< "\n<npoints> the number of grid points on the side of the"
<< "regular square grid\n"
<< "\n<tol> the desired accuracy for the CG solver\n"
<< "\n<maxiter> the maximum number of iterations\n"
<< std::endl;
return 1;
}
// Number of points along one side of the square regular grid
unsigned long nx = atoi(argv[1]);
// Tolerance for the CG solver
Scalar tol = static_cast<Scalar>(atof(argv[2]));
// Maximum number of CG iterations to perform
int maxIter = atoi(argv[3]);
// Timer object
WallClock timer;
timer.start();
/*
* Number of DOF (N) is equal to just the interior grid points, because of
* the Dirichlet boundary conditions.
*/
unsigned long N = (nx - 2) * (nx - 2);
// Right hand side vector
Vector<Scalar> b(N);
// Dirichlet boundary conditions on the lower side of the square:
// u(x,0) = 1;
// The static casts are needed to prevent some warnings (-Wconversion)
Scalar h = static_cast<Scalar>(1.0 / static_cast<Scalar>(nx - 1));
Scalar h2 = h * h;
for (unsigned long i = 0; i < nx - 2; ++i) {
b[i] = static_cast<Scalar>(1.0 / h2);
}
// Solution vector
Vector<Scalar> u(N);
// Fill the system matrix A
// The Laplacian matrix generator needs a pointer to the base class
AbstractMatrix<Scalar>* A;
Laplacian2DMatrixGenerator(A, nx, "dense");
// Solve the system Ax = b;
int numIter = GaussSeidel(*A, b, u, tol, maxIter);
timer.stop();
std::cout << "Solution reached after " << numIter << " iterations:\n";
u.Print();
std::cout << "Total execution time is: "
<< timer.elapsedTime() << std::endl;
delete A;
return 0;
}