/* nag_real_sparse_eigensystem_init (f12aac) Example Program. * * Copyright 2005 Numerical Algorithms Group. * * Mark 8, 2005. */ #include #include #include #include #include #include static void tv(Integer, double *, double *); static void av(Integer, double *, double *); int main(void) { /* Constants */ Integer imon = 0; /* Scalars */ double sigmai = 0, sigmar = 0, estnrm; Integer exit_status, irevcm, j, lcomm, licomm, n, nconv, ncv, nev; Integer niter, nshift, nx; /* Arrays */ double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0; double *resid = 0, *v = 0; Integer *icomm = 0; /* Pointers */ double *mx = 0, *x = 0, *y = 0; /* Nag types */ NagError fail; exit_status = 0; INIT_FAIL(fail); printf("nag_real_sparse_eigensystem_init (f12aac) Example Program " "Results\n"); /* Skip heading in data file. */ scanf("%*[^\n] "); /* Read values for nx, nev and cnv from data file. */ scanf("%ld%ld%ld%*[^\n] ", &nx, &nev, &ncv); /* Allocate memory */ n = nx * nx; if (!(eigvr = NAG_ALLOC(ncv, double)) || !(eigvi = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) || !(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Initialise communication arrays for problem using nag_real_sparse_eigensystem_init (f12aac). The first call sets lcomm = licomm = -1 to perform a workspace query. */ lcomm = licomm = -1; if (!(comm = NAG_ALLOC(1, double)) || !(icomm = NAG_ALLOC(1, Integer))) { printf("Allocation failure\n"); exit_status = -1; goto END; } nag_real_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_real_sparse_eigensystem_init (f12aac).\n%s\n", fail.message); exit_status = 1; goto END; } lcomm = (Integer)comm[0]; licomm = icomm[0]; if (comm) NAG_FREE(comm); if (icomm) NAG_FREE(icomm); if (!(comm = NAG_ALLOC(lcomm, double)) || !(icomm = NAG_ALLOC(licomm, Integer))) { printf("Allocation failure\n"); exit_status = -1; goto END; } nag_real_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_real_sparse_eigensystem_init (f12aac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Select the required spectrum using nag_real_sparse_eigensystem_option (f12adc). */ nag_real_sparse_eigensystem_option("SMALLEST MAG", icomm, comm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_real_sparse_eigensystem_option (f12adc).\n%s\n", fail.message); exit_status = 1; goto END; } irevcm = 0; REVCOMLOOP: /* Repeated calls to reverse communication routine nag_real_sparse_eigensystem_iter (f12abc). */ nag_real_sparse_eigensystem_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm, icomm, &fail); if (irevcm != 5) { if (irevcm == -1 || irevcm == 1) { /* Perform matrix vector multiplication y <--- Op*x */ av(nx, x, y); } else if (irevcm == 4 && imon == 1) { /* If imon=1, get monitoring information using nag_real_sparse_eigensystem_monit (f12aec). */ nag_real_sparse_eigensystem_monit(&niter, &nconv, eigvr, eigvi, eigest, icomm, comm); /* Compute 2-norm of Ritz estimates using nag_dge_norm (f16rac).*/ nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, nev, 1, eigest, nev, &estnrm, &fail); printf("Iteration %3ld, ", niter); printf(" No. converged = %3ld,", nconv); printf(" norm of estimates = %17.8e\n", estnrm); } goto REVCOMLOOP; } if (fail.code == NE_NOERROR) { /* Post-Process using nag_real_sparse_eigensystem_sol (f12acc) to compute eigenvalues/vectors. */ nag_real_sparse_eigensystem_sol(&nconv, eigvr, eigvi, v, sigmar, sigmai, resid, v, comm, icomm, &fail); printf("\n\n The %4ld Ritz values", nconv); printf(" of smallest magnitude are:\n\n"); for (j = 0; j <= nconv-1; ++j) { printf("%8ld%5s( %12.4f , %12.4f )\n", j+1, "", eigvr[j], eigvi[j]); } } else { printf("Error from nag_real_sparse_eigensystem_iter (f12abc).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (comm) NAG_FREE(comm); if (eigvr) NAG_FREE(eigvr); if (eigvi) NAG_FREE(eigvi); if (eigest) NAG_FREE(eigest); if (resid) NAG_FREE(resid); if (v) NAG_FREE(v); if (icomm) NAG_FREE(icomm); return exit_status; } static void av(Integer nx, double *v, double *w) { /* Constants*/ const double beta = 1.0; /* Scalars */ double nx2; Integer j, lo; /* Nag types */ NagError fail; /* Function Body */ INIT_FAIL(fail); nx2 = -((double)((nx + 1) * (nx + 1))); tv(nx, v, w); nag_daxpby(nx, nx2, &v[nx], 1, beta, w, 1, &fail); for (j = 2; j <= nx - 1; ++j) { lo = (j - 1) * nx; tv(nx, &v[lo], &w[lo]); nag_daxpby(nx, nx2, &v[lo-nx], 1, beta, &w[lo], 1, &fail); nag_daxpby(nx, nx2, &v[lo+nx], 1, beta, &w[lo], 1, &fail); } lo = (nx - 1) * nx; tv(nx, &v[lo], &w[lo]); nag_daxpby(nx, nx2, &v[lo-nx], 1, beta, &w[lo], 1, &fail); return; } /* av */ static void tv(Integer nx, double *x, double *y) { /* Compute the matrix vector multiplication y<---T*x where T is a nx */ /* by nx tridiagonal matrix with constant diagonals (dd, dl and du). */ /* Scalars */ double dd, dl, du, nx1, nx2; Integer j; /* Function Body */ nx1 = (double)(nx + 1); nx2 = nx1 * nx1; dd = nx2 * 4.; dl = -nx2 - nx1 * 50.; du = -nx2 + nx1 * 50.; y[0] = dd * x[0] + du * x[1]; for (j = 1; j <= nx - 2; ++j) { y[j] = dl * x[j-1] + dd * x[j] + du * x[j+1]; } y[nx-1] = dl * x[nx-2] + dd * x[nx-1]; return; } /* tv */