void build_graph(void){ Point p1, p2; int i, j, n1, n2; minx = miny = 10001; maxx = maxy = 0; for (i = 0; i < num_edges; i++) { scanf("%d %d %d %d\n", &p1.x, &p1.y, &p2.x, &p2.y); minx = min(minx, min(p1.x, p2.x)); maxx = max(maxx, max(p1.x, p2.x)); miny = min(miny, min(p1.y, p2.y)); maxy = max(maxy, max(p1.y, p2.y)); n1 = node_index(p1); n2 = node_index(p2); graph[n1][n2] = graph[n2][n1] = 1; degree[n1]++; degree[n2]++; } /* find boundary */ for (i = 0; i < num_nodes; i++) for (j = i+1; j < num_nodes; j++) if (graph[i][j] == 1 && on_boundary(node[i], node[j])) graph[i][j] = graph[j][i] = -1; }
IGL_INLINE void igl::ears( const Eigen::MatrixBase<DerivedF> & F, Eigen::PlainObjectBase<Derivedear> & ear, Eigen::PlainObjectBase<Derivedear_opp> & ear_opp) { assert(F.cols() == 3 && "F should contain triangles"); Eigen::Array<bool,Eigen::Dynamic,3> B; { Eigen::Array<bool,Eigen::Dynamic,1> I; on_boundary(F,I,B); } find(B.rowwise().count() == 2,ear); Eigen::Array<bool,Eigen::Dynamic,3> Bear; slice(B,ear,1,Bear); Eigen::Array<bool,Eigen::Dynamic,1> M; mat_min(Bear,2,M,ear_opp); }
int main( int argc, char **argv ) { /* Basic variables */ int i,j,k,p,m; int dim = 2; int deg = 3; int pdim = binomial( dim + deg, dim ); int plm = 0; int radn = 10; int nnz; int ret,ns; double zrt = 1e-6; double sum; double xx,res; double tol = zrt; double sft = 0.0; int neig = 100; double *ev = (double*) malloc( 2 * neig * sizeof(double) ); double *alpha = (double*) malloc( ( neig + 3 ) * sizeof(double) ); double *beta = (double*) malloc( ( neig + 3 ) * sizeof(double) ); double *gamma = (double*) malloc( ( neig + 3 ) * sizeof(double) ); /* Switches */ int b_sft = 0; /* Use argument as shift */ int b_prj = 0; /* Build projected system matrices */ int b_pc = 0; /* Build a preconditioner */ int b_grd = 0; /* Load points from grid file */ int b_ext = 0; /* Load external potential */ /* Other stuff */ char gfn[1024]; FILE *fp; rkp_t rk; nuclei_t ext; symtab_t sym; symbol_t ss; /* Take in the options */ int optc; while( ( optc = getopt( argc, argv, "C:g:d:s:t:S:r:x:pPc" ) ) != -1 ) { switch( optc ) { case 'C': symtab_init( &sym, 1024 ); cfgread_load_symbols_f( optarg, &sym ); symtab_print( &sym ); break; case 'r': radn = atoi( optarg ); break; case 'c': b_pc = 1; break; case 'd': deg = atoi( optarg ); break; case 't': tol = atof( optarg ); break; case 'S': sft = atof( optarg ); b_sft = 1; break; case 'p': plm = 1; break; case 'P': b_prj = 1; break; case 'g': b_grd = 1; strcpy( gfn, optarg ); break; case 'x': b_ext = 1; load_nuclei( optarg, &ext, 0 ); nuclei_print( &ext ); break; case '?': default: fprintf( stderr, "I don't understand the jibberish you are spouting. Goodbye.\n" ); return 0; break; } } if( !b_ext ) { fprintf( stderr, "Please specify an external potential. Exiting.\n" ); return 0; } /* Allocate and generate grid points */ int nb; int npts; double *pts,*dlt,*val,*gqw; /* Load points from file if switch is set */ if( b_grd ) { fprintf( stderr, "Loading points from file... " ); load_points( gfn, &dim, &npts, &pts, 0 ); fprintf( stderr, "dim = %d npts = %d. Done.\n", dim, npts ); fflush( stderr ); } /* Set up the plot points */ int pgx = 70; int pgy = 70; double x = 5.0; double y = 5.0; double pdx = x / (double) ( pgx - 1 ); double pdy = y / (double) ( pgy - 1 ); int nppts = pgx * pgy; double *ppts = (double*) malloc( nppts * dim * sizeof(double) ); for(i=0;i<pgx;i++) for(j=0;j<pgy;j++) ppts[i*pgy*dim+j*dim+0] = (double) i * pdx, ppts[i*pgy*dim+j*dim+1] = (double) j * pdy; /* Generate supports */ dlt = (double*) malloc( npts * sizeof(double) ); val = (double*) malloc( npts * sizeof(double) ); gqw = (double*) malloc( npts * sizeof(double) ); generate_cloud_supports_min( 2, npts, pts, radn, 1.05, dlt, 0.001 ); for(i=0;i<npts;i++) gqw[i] = 1.0; /* Build variables */ double f,g,r,s,rr,a,b; double *vv,*ww,*pc,*xv,*xvh,*rv,*rvh,*rrv,*rrvh,*pv,*pvh; /* Variables for CG iteration */ double *amat,*bmat,*cmat,*cmatt,*smat,*tmat,*temp,*dv,*rhs; long *iamat,*jamat,*ibmat,*jbmat,*icmat,*jcmat,*icmatt,*jcmatt,*ismat,*jsmat,*itmat,*jtmat,*list; /* Calculate the number of non-zeros */ for(nnz=0,i=0;i<npts;i++) { for(j=0;j<npts;j++) { xx = 0.0; for(k=0;k<dim;k++) xx += pow( pts[i*dim+k] - pts[j*dim+k], 2.0 ); if( xx < pow( dlt[j], 2.0 ) ) ++nnz; } } fprintf( stderr, "nnz = %5d\n", nnz ); nnz = nnz + 1; /* Allocate this stuff static for now, but make dynamic ASAP */ iamat = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jamat = (long*) malloc( nnz * sizeof(long) ); ibmat = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jbmat = (long*) malloc( nnz * sizeof(long) ); icmat = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jcmat = (long*) malloc( nnz * sizeof(long) ); icmatt = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jcmatt = (long*) malloc( nnz * sizeof(long) ); ismat = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jsmat = (long*) malloc( npts * npts * sizeof(long) ); itmat = (long*) malloc( ( npts + 1 ) * sizeof(long) ); jtmat = (long*) malloc( npts * npts * sizeof(long) ); list = (long*) malloc( ( npts + 1 ) * sizeof(long) ); temp = (double*) malloc( ( npts + 1 ) * sizeof(double) ); /* Allocate stuff; can't use stack for this garbage!!! */ vv = (double*) malloc( npts * npts * sizeof(double) ); ww = (double*) malloc( npts * npts * sizeof(double) ); pc = (double*) malloc( npts * sizeof(double) ); xv = (double*) malloc( npts * sizeof(double) ); xvh = (double*) malloc( npts * sizeof(double) ); rv = (double*) malloc( npts * sizeof(double) ); rvh = (double*) malloc( npts * sizeof(double) ); rrv = (double*) malloc( npts * sizeof(double) ); rrvh = (double*) malloc( npts * sizeof(double) ); pv = (double*) malloc( npts * sizeof(double) ); pvh = (double*) malloc( npts * sizeof(double) ); /* Allocate matrix storage */ amat = (double*) malloc( nnz * sizeof(double) ); bmat = (double*) malloc( nnz * sizeof(double) ); cmat = (double*) malloc( nnz * sizeof(double) ); cmatt = (double*) malloc( nnz * sizeof(double) ); smat = (double*) malloc( npts * npts * sizeof(double) ); tmat = (double*) malloc( npts * npts * sizeof(double) ); rhs = (double*) malloc( npts * sizeof(double) ); dv = (double*) malloc( npts * sizeof(double) ); /* Initialize the RKP basis */ rkp_init( &rk, npts, dim, deg, pts, dlt, gqw, val, cubic, 1.0 ); rkp_basis_generate_scaled_const( &rk ); rkp_wavelet_basis_generate_scaled_const( &rk ); /* Form the Laplace operator correctly with wavelets */ int ord[2] = { 2, 4 }; /* Indexes which contain the xx and yy second derivatives */ /* Build the matrices here to simplify things as much as possible */ for(i=0;i<nnz;i++) /* Don't need this many entries anymore */ amat[i] = 0.0, bmat[i] = 0.0; for(i=0;i<npts;i++) iamat[i] = -1, ibmat[i] = -1; for(p=0,i=0;i<npts;i++) { for(j=0;j<npts;j++) { /* Check to see if window function at j is large enough to be nonzero */ xx = 0.0; for(k=0;k<dim;k++) xx += pow( pts[i*dim+k] - pts[j*dim+k], 2.0 ); if( xx > pow( dlt[j] * rk.wrad, 2.0 ) ) continue; if( iamat[i] == -1 ) iamat[i] = p; /* The beginning of row i entries in amat */ if( ibmat[i] == -1 ) ibmat[i] = p; jamat[p] = j; jbmat[p] = j; for(k=0;k<dim;k++) amat[p] -= 2.0 * 0.5 * gqw[j] * rkp_wavelet_term_evaluate_node_scaled_const( &rk, j, ord[k], i ) / dlt[i] / dlt[i]; amat[p] += gqw[j] * rkp_term_evaluate_node_scaled_const( &rk, j, i ) * coulomb_potential( dim, pts + i * dim, ext.np, ext.pts ); bmat[p] = gqw[j] * rkp_term_evaluate_node_scaled_const( &rk, j, i ); ++p; } } iamat[npts] = p; ibmat[npts] = p; /* Save some garbage in case dumb shit happens */ smsave( "amat.oct", npts, npts, iamat, jamat, amat, 1 ); smsave( "bmat.oct", npts, npts, ibmat, jbmat, bmat, 1 ); fprintf( stderr, "nnz = %d\n", p ); fflush( stderr ); /* Generate a random initial state vector */ srand((unsigned)time(0)); /* Count the number of boundary nodes */ nb = 0; for(i=0;i<npts;i++) if( on_boundary( pts + i * dim ) == 1 ) ++nb; /* QR factorization first */ fprintf( stderr, "Running QR factorization... " ); fflush( stderr ); eigenvalue_qrfactorize( dim, npts, pts, ibmat, jbmat, bmat, rhs, vv ); fprintf( stderr, "Done.\n" ); fflush( stderr ); /* Now build the subspace projection matrix */ fprintf( stderr, "Building subspace projection matrix... " ); fflush( stderr ); eigenvalue_subprojmat( npts, nb, vv, ww ); fprintf( stderr, "Done.\n" ); fflush( stderr ); /* Save the projection matrix */ msave( "wmat.oct", npts - nb, npts, ww, 1 ); /* Build smat and tmat */ fprintf( stderr, "Building smat and tmat... " ); fflush( stderr ); sparse_symbmm( (long) npts, (long) npts, (long) npts, ibmat, jbmat, iamat, jamat, ismat, jsmat, list ); sparse_dgemm( (long) npts, (long) npts, (long) npts, ibmat, jbmat, bmat, iamat, jamat, amat, ismat, jsmat, smat, temp ); sparse_symbmm( (long) npts, (long) npts, (long) npts, ibmat, jbmat, ibmat, jbmat, itmat, jtmat, list ); sparse_dgemm( (long) npts, (long) npts, (long) npts, ibmat, jbmat, bmat, ibmat, jbmat, bmat, itmat, jtmat, tmat, temp ); fprintf( stderr, "Done.\n" ); fflush( stderr ); /* Initialize to a normalized random vector */ eigenvalue_initialize( npts, rhs ); /* Now subtract out all vectors in vv from rhs */ eigenvalue_project( npts, nb, vv, rhs ); /* Normalize first using tmat */ eigenvalue_normalize( npts, itmat, jtmat, tmat, rhs, temp ); /* Initialize the preconditioner to the identity */ for(i=0;i<npts;i++) pc[i] = 1.0; /* Solve the eigenvalue problem actually */ fprintf( stderr, "\n" ); fprintf( stderr, "Solving Jacobi-Davidson method:\n" ); eigenvalue_solver( npts, iamat, jamat, amat, ibmat, jbmat, bmat, icmat, jcmat, cmat, icmatt, jcmatt, cmatt, ismat, jsmat, smat, itmat, jtmat, tmat, rv, rvh, rrv, rrvh, pv, pvh, xv, xvh, dv, pc, rhs, temp, r, tol, nb, b_pc, -0.145, vv ); /* Attempt constrained sparse generalized unsymmetric Lanczos biorthogonalization to solve for bottom few eigenvalues */ fprintf( stderr, "\n" ); fprintf( stderr, "Solving with constrained Lanczos method:\n" ); csgulanczoslp( npts, neig, iamat, jamat, amat, ibmat, jbmat, bmat, alpha, beta, gamma, NULL, NULL, nb, vv, 1e-10, 200, 0, &ret ); //csgulanczoslp( npts, neig, ibmat, jbmat, bmat, iamat, jamat, amat, alpha, beta, gamma, NULL, NULL, nb, vv, 1e-10, 1000, 0, &ret ); //sgulanczos( npts, neig, iamat, jamat, amat, ibmat, jbmat, bmat, alpha, beta, gamma, NULL, NULL, 1e-10, 200, 0, &ret ); fprintf( stderr, "lanczos ret = %d\n", ret ); treigtridqds( neig, alpha + 1, beta + 1, gamma + 1, 100000, ev, &ret, &ns ); complex_bubble_sort( neig, ev ); fprintf( stderr, "Reduction = %d Steps = %d\n", ret, ns ); for(i=0;i<neig;i++) fprintf( stderr, "%15.7f+%15.7fi\n", ev[2*i+0], ev[2*i+1] ); /* Calculate actual eigenvalue */ eigenvalue_calculate( npts, iamat, jamat, amat, ibmat, jbmat, bmat, rhs, temp, &f ); fprintf( stderr, "RQ = %15.7f\n", f ); /* Copy the solution into the rk structure */ for(i=0;i<npts;i++) rk.vals[i] = rhs[i]; /* Output the function */ if( plm ) { fp = fopen( "plot", "w" ); for(i=0;i<pgx*pgy;i++) { fprintf( fp, "%15.7f%15.7f%15.7f\n", ppts[i*dim+0], ppts[i*dim+1], rkp_evaluate_scaled_const( &rk, ppts + i * dim, 0.2 ), 0.1 ); if( ( i + 1 ) % pgy == 0 ) fprintf( fp, "\n" ); } fclose( fp ); } else { fp = fopen( "plot", "w" ); for(i=0;i<npts;i++) fprintf( fp, "%15.7f%15.7f%15.7f\n", pts[i*dim+0], pts[i*dim+1], rkp_evaluate_node_scaled_const( &rk, i ) ); } free( pts ); free( dlt ); free( val ); free( gqw ); free( ppts ); return 0; }