/* nag_real_symm_sparse_eigensystem_iter (f12fbc) 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 *); static void av(Integer, Integer, double *, double *); static void atv(Integer, Integer, double *, double *); extern int ex1(void), ex2(void); int main(void) { Vprintf("nag_real_symm_sparse_eigensystem_iter (f12fbc) Example Program " "Results\n"); ex1(); ex2(); return 0; } int ex1(void) { /* Constants */ Integer licomm=140, imon=0; /* Scalars */ double estnrm, h2, sigma; 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); Vprintf("\nExample 1\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%*[^\n] "); /* Read values for nx, nev and cnv from data file. */ Vscanf("%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)) ) { Vprintf("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); /* Select the required spectrum using nag_real_symm_sparse_eigensystem_option (f12fdc). */ nag_real_symm_sparse_eigensystem_option("largest magnitude", icomm, comm, &fail); /* Select the required mode */ nag_real_symm_sparse_eigensystem_option("shifted inverse", icomm, comm, &fail); h2 = 1.0 / (double) ((n + 1) * (n + 1)); sigma = 0.0; for (j = 0; j <= n-1; ++j) { dd[j] = 2.0 / h2 - sigma; dl[j] = -1.0 / h2; du[j] = dl[j]; } 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 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_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); Vprintf("Iteration %3ld, ", niter); Vprintf(" No. converged = %3ld,", nconv); Vprintf(" norm of estimates = %16.8e\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); Vprintf("\n"); Vprintf(" The %4ld Ritz values", nconv); Vprintf(" closest to %8.4f are:\n\n", sigma); for (j = 0; j <= nconv-1; ++j) { Vprintf("%8ld%5s%12.4f\n", j+1, "", eigv[j]); } } else { Vprintf(" Error from nag_real_symm_sparse_eigensystem_iter (f12fbc)." "\n%s\n", fail.message); exit_status = 1; goto END; } END: if (dd) NAG_FREE(dd); if (dl) NAG_FREE(dl); if (du) NAG_FREE(du); if (du2) NAG_FREE(du2); if (comm) NAG_FREE(comm); if (eigv) NAG_FREE(eigv); if (eigest) NAG_FREE(eigest); 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; } int ex2(void) { /* Constants */ Integer licomm=140; /* Scalars */ double sigma=0, axnorm; Integer exit_status=0, irevcm, j, lcomm, m, n, nconv, ncv; Integer nev, nshift; NagError fail; /* Arrays */ double *comm=0, *eigv=0, *eigest=0; double *resid=0, *v=0, *ax=0; Integer *icomm=0; /* Ponters */ double *mx=0, *x=0, *y=0; INIT_FAIL(fail); Vprintf("\nExample 2\n"); /* Skip heading in data file. */ Vscanf("%*[^\n] "); /* Read values for m, n, nev and cnv from data file. */ Vscanf("%ld%ld%ld%ld*[^\n] ", &m, &n, &nev, &ncv); /* Allocate memory */ lcomm = 3*n + ncv*ncv + 8*ncv + 60; if ( !(comm = NAG_ALLOC(lcomm, double)) || !(eigv = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) || !(resid = NAG_ALLOC(n, double)) || !(ax = NAG_ALLOC(m, double)) || !(v = NAG_ALLOC(n * ncv, double)) || !(icomm = NAG_ALLOC(licomm, Integer)) ) { Vprintf("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); 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 matrix vector multiplication y <--- Op*x */ av(m, n, x, ax); atv(m, n, ax, y); } goto REVCOMLOOP; } if (fail.code == NE_NOERROR) { /* Post-Process using nag_real_symm_sparse_eigensystem_sol (f12fcc) to compute singular values/vectors. */ nag_real_symm_sparse_eigensystem_sol(&nconv, eigv, v, sigma, resid, v, comm, icomm, &fail); /* Singular values (squared) are returned in eigv and the corresponding right singular vectors are returned in the first nev n-length vectors in v. */ Vprintf("\n The %4ld leading Singular values and",nconv); Vprintf(" direct residuals are:\n\n"); for (j = 0; j <= nconv-1; ++j) { eigv[j] = sqrt(eigv[j]); /* Compute the left singular vectors from the formula u = Av/sigma u should have norm 1 so divide by norm(Av). */ av(m,n,&v[j*n],ax); /* Compute 2-norm of Av using nag_dge_norm (f16rac).*/ nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, m, 1, ax, m, &axnorm, &fail); resid[j] = axnorm*fabs(1.0-eigv[j]/axnorm); Vprintf("%8ld%5s%12.4f%5s%12.7f\n", j+1, "", eigv[j], "", resid[j]); } } else { Vprintf(" Error from nag_real_symm_sparse_eigensystem_iter (f12fbc)." "\n%s\n", fail.message); exit_status = 1; goto END; } END: if (comm) NAG_FREE(comm); if (eigv) NAG_FREE(eigv); if (eigest) NAG_FREE(eigest); if (resid) NAG_FREE(resid); if (v) NAG_FREE(v); if (ax) NAG_FREE(ax); if (icomm) NAG_FREE(icomm); return exit_status; } static void av(Integer m, Integer n, double *x, double *w) { /* Computes w <- A*x. */ /* Local Scalars */ double h, k, s, t; Integer i, j; /* Executable Statements */ h = 1.0/(double)(m+1); k = 1.0/(double)(n+1); for (i=0; i