/* nag_real_sparse_eigensystem_iter (f12abc) Example Program. * * Copyright 2005 Numerical Algorithms Group. * * Mark 8, 2005. */ #include #include #include #include #include #include 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 h, rho, s, s1, s2, s3, estnrm, sigmai, sigmar; Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv; Integer nev, niter, nshift, nx; /* Nag types */ NagError fail; /* Arrays */ double *comm = 0, *dd = 0, *dl = 0, *du = 0, *du2 = 0, *eigvr = 0; double *eigvi = 0, *eigest = 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_sparse_eigensystem_iter (f12abc) Example Program " "Results\n"); /* Skip heading in data file */ scanf("%*[^\n] "); /* Read problem parameter values from data file. */ scanf("%ld%ld%ld%lf%lf%lf%*[^\n] ", &nx, &nev, &ncv, &rho, &sigmar, &sigmai); n = nx * nx; lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60; /* Allocate memory */ if (!(comm = NAG_ALLOC(lcomm, double)) || !(eigvr = NAG_ALLOC(ncv, double)) || !(eigvi = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) || !(dd = NAG_ALLOC(n, double)) || !(dl = NAG_ALLOC(n, double)) || !(du = NAG_ALLOC(n, double)) || !(du2 = NAG_ALLOC(n, 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_sparse_eigensystem_init (f12aac). */ 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 mode using nag_real_sparse_eigensystem_option (f12adc). */ nag_real_sparse_eigensystem_option("SHIFTED INVERSE REAL", icomm, comm, &fail); /* Construct C = A - sigma*I, and factorize using my_dgttrf. */ h = 1.0 / (double)(n + 1); s = rho * h / 2.0; s1 = -1.0 - s; s2 = 2.0 - sigmar; s3 = s - 1.0; for (j = 0; j <= n - 2; ++j) { dl[j] = s1; dd[j] = s2; du[j] = s3; } dd[n - 1] = s2; my_dgttrf(n, dl, dd, du, du2, ipiv, &info); 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 y <--- OP*x = inv[A-SIGMA*I]*x. */ /* Use my_dgttrs, a cut down C version of Lapack's dgttrs. */ my_dgttrs(n, dl, dd, du, du2, ipiv, 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); /* Print computed eigenvalues. */ printf("\n"); printf(" The %4ld Ritz values of closest", nconv); printf(" to unity 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 (dd) NAG_FREE(dd); if (dl) NAG_FREE(dl); if (du) NAG_FREE(du); if (du2) NAG_FREE(du2); if (resid) NAG_FREE(resid); if (v) NAG_FREE(v); if (icomm) NAG_FREE(icomm); if (ipiv) NAG_FREE(ipiv); return exit_status; } 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; }