/* nag_real_symm_sparse_eigensystem_sol (f12fcc) Example Program. * * Copyright 2005 Numerical Algorithms Group. * * Mark 8, 2005. */ #include #include #include #include #include #include static void av(Integer, double *); static void mv(Integer, double *, double *); static void my_dgttrf(Integer, double *, double *, double *, double *, Integer *, Integer *); static void my_dgttrs(Integer, double *, double *, double *, double *, Integer *, double *, double *); int main(void) { /* Constants */ Integer licomm = 140, imon = 0; /* Scalars */ double estnrm, h, r1, r2, sigma = 0.0; Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv; Integer nev, niter, nshift; /* Nag types */ NagError fail; /* Arrays */ double *dd = 0, *dl = 0, *du = 0, *du2 = 0, *comm = 0, *eigest = 0; double *eigv = 0, *resid = 0, *v = 0; Integer *icomm = 0, *ipiv = 0; /* Pointers */ double *mx = 0, *x = 0, *y = 0; exit_status = 0; INIT_FAIL(fail); printf("nag_real_symm_sparse_eigensystem_sol (f12fcc) 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] ", &n, &nev, &ncv); /* Allocate memory */ lcomm = 3*n + ncv*ncv + 8*ncv + 60; if (!(dd = NAG_ALLOC(n, double)) || !(dl = NAG_ALLOC(n, double)) || !(du = NAG_ALLOC(n, double)) || !(du2 = NAG_ALLOC(n, double)) || !(comm = NAG_ALLOC(lcomm, double)) || !(eigv = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) || !(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double)) || !(icomm = NAG_ALLOC(licomm, Integer)) || !(ipiv = NAG_ALLOC(n, Integer))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Initialise communication arrays for problem using nag_real_symm_sparse_eigensystem_init (f12fac). */ nag_real_symm_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_real_symm_sparse_eigensystem_init " "(f12fac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Select the problem type using nag_real_symm_sparse_eigensystem_option (f12fdc). */ nag_real_symm_sparse_eigensystem_option("generalized", icomm, comm, &fail); if (fail.code != NE_NOERROR) { printf(" Error from nag_real_symm_sparse_eigensystem_option " "(f12fdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Setup M and factorise */ h = 1.0 / (double)(n + 1); r1 = 2.0 * h / 3.0; r2 = h / 6.0; for (j = 0; j <= n-1; ++j) { dd[j] = r1; dl[j] = r2; du[j] = r2; } my_dgttrf(n, dl, dd, du, du2, ipiv, &info); irevcm = 0; REVCOMLOOP: /* Repeated calls to reverse communication routine nag_real_symm_sparse_eigensystem_iter (f12fbc). */ nag_real_symm_sparse_eigensystem_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm, icomm, &fail); if (irevcm != 5) { if (irevcm == -1 || irevcm == 1) { /* Perform the following operations in order: x <--- A*x; y <--- inv[M]*x. */ av(n, x); my_dgttrs(n, dl, dd, du, du2, ipiv, x, y); } else if (irevcm == 2) { /* Perform y <--- M*x. */ mv(n, x, y); } else if (irevcm == 4 && imon == 1) { /* If imon=1, get monitoring information using nag_real_symm_sparse_eigensystem_monit (f12fec). */ nag_real_symm_sparse_eigensystem_monit(&niter, &nconv, eigv, 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_symm_sparse_eigensystem_sol (f12fcc) to compute eigenvalues/vectors. */ nag_real_symm_sparse_eigensystem_sol(&nconv, eigv, v, sigma, resid, v, comm, icomm, &fail); printf("\n The %4ld generalized Ritz values", nconv); printf(" of largest magnitude are:\n\n"); for (j = 0; j <= nconv-1; ++j) { printf("%8ld%5s%9.1f\n", j+1, "", eigv[j]); } } else { printf(" Error from nag_real_symm_sparse_eigensystem_iter " "(f12fbc).\n%s\n", fail.message); exit_status = 1; goto END; } END: NAG_FREE(dd); NAG_FREE(dl); NAG_FREE(du); NAG_FREE(du2); NAG_FREE(comm); NAG_FREE(eigv); NAG_FREE(eigest); NAG_FREE(resid); NAG_FREE(v); NAG_FREE(icomm); NAG_FREE(ipiv); return exit_status; } static void mv(Integer n, double *v, double *y) { /* Scalars */ double h; Integer j; /* Function Body */ h = 1.0 / ((double)(n + 1) * 6.0); y[0] = h * (v[0] * 4.0 + v[1]); for (j = 1; j <= n - 2; ++j) { y[j] = h * (v[j-1] + v[j] * 4.0 + v[j+1]); } y[n-1] = h * (v[n-2] + v[n-1] * 4.0); } /* mv */ static void av(Integer n, double *v) { /* Scalars */ double h, vj, vjm1; Integer j; /* Function Body */ h = (double)(n + 1); vjm1 = v[0]; v[0] = h * (vjm1 * 2.0 - v[1]); for (j = 1; j <= n - 2; ++j) { vj = v[j]; v[j] = h*(-vjm1 + vj * 2.0 - v[j+1]); vjm1 = vj; } v[n-1] = h * (-vjm1 + v[n-1] * 2.0); } /* av */ static void my_dgttrf(Integer n, double dl[], double d[], double du[], double du2[], Integer ipiv[], Integer *info) { /* A simple C version of the Lapack routine dgttrf with argument checking removed */ /* Scalars */ double temp, fact; Integer i; /* Function Body */ *info = 0; for (i = 0; i < n; ++i) { ipiv[i] = i; } for (i = 0; i < n - 2; ++i) { du2[i] = 0.0; } for (i = 0; i < n - 2; i++) { if (fabs(d[i]) >= fabs(dl[i])) { /* No row interchange required, eliminate dl[i]. */ if (d[i] != 0.0) { fact = dl[i] / d[i]; dl[i] = fact; d[i+1] = d[i+1] - fact * du[i]; } } else { /* Interchange rows I and I+1, eliminate dl[I] */ fact = d[i] / dl[i]; d[i] = dl[i]; dl[i] = fact; temp = du[i]; du[i] = d[i+1]; d[i+1] = temp - fact*d[i+1]; du2[i] = du[i+1]; du[i+1] = -fact * du[i+1]; ipiv[i] = i + 1; } } if (n > 1) { i = n - 2; if (fabs(d[i]) >= fabs(dl[i])) { if (d[i] != 0.0) { fact = dl[i] / d[i]; dl[i] = fact; d[i+1] = d[i+1] - fact * du[i]; } } else { fact = d[i] / dl[i]; d[i] = dl[i]; dl[i] = fact; temp = du[i]; du[i] = d[i+1]; d[i+1] = temp - fact * d[i+1]; ipiv[i] = i + 1; } } /* Check for a zero on the diagonal of U. */ for (i = 0; i < n; ++i) { if (d[i] == 0.0) { *info = i; goto END; } } END: return; } static void my_dgttrs(Integer n, double dl[], double d[], double du[], double du2[], Integer ipiv[], double b[], double y[]) { /* A simple C version of the Lapack routine dgttrs with argument checking removed, the number of right-hand-sides=1, Trans='N' */ /* Scalars */ Integer i, ip; double temp; /* Solve L*x = b. */ for (i = 0; i <= n - 1; ++i) { y[i] = b[i]; } for (i = 0; i < n - 1; ++i) { ip = ipiv[i]; temp = y[i+1-ip+i] - dl[i]*y[ip]; y[i] = y[ip]; y[i+1] = temp; } /* Solve U*x = b. */ y[n-1] = y[n-1] / d[n-1]; if (n > 1) { y[n-2] = (y[n-2] - du[n-2]*y[n-1])/d[n-2]; } for (i = n - 3; i >= 0; --i) { y[i] = (y[i]-du[i]*y[i+1]-du2[i]*y[i+2])/d[i]; } return; }