/* * Copyright(C) 1999-2020, 2023 National Technology & Engineering Solutions * of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with * NTESS, the U.S. Government retains certain rights in this software. * * See packages/seacas/LICENSE for details */ #include "defs.h" // for TRUE, FALSE, max, min #include "smalloc.h" // for sfree, smalloc #include "structs.h" #include // for printf, NULL /* Perform Rayleigh Quotient Iteration */ void rqi(struct vtx_data **A, /* matrix/graph being analyzed */ double **yvecs, /* eigenvectors to be refined */ int index, /* index of vector in yvecs to be refined */ int n, /* number of rows/columns in matrix */ double *r1, double *r2, double *v, double *w, double *x, double *y, double *work, /* work space for symmlq */ double tol, /* error tolerance in eigenpair */ double initshift, /* initial shift */ double *evalest, /* returned eigenvalue */ double *vwsqrt, /* square roots of vertex weights */ struct orthlink *orthlist, /* lower evecs to orthogonalize against */ int cube_or_mesh, /* 0 => hypercube, d => d-dimensional mesh */ int nsets, /* number of sets to divide into */ int *assignment, /* set number of each vtx (length n+1) */ int *active, /* space for nvtxs integers */ int mediantype, /* which partitioning strategy to use */ double *goal, /* desired set sizes */ int vwgt_max, /* largest vertex weight */ int ndims /* dimensionality of partition */ ) { extern int DEBUG_EVECS; /* debug flag for eigen computation */ extern int DEBUG_TRACE; /* trace main execution path */ extern int WARNING_EVECS; /* warning flag for eigen computation */ extern int RQI_CONVERGENCE_MODE; /* type of convergence monitoring to do */ int rqisteps; /* # rqi rqisteps */ double res; /* convergence quant for rqi */ double last_res; /* res on previous rqi step */ double macheps; /* machine precision calculated by symmlq */ double normxlim; /* a stopping criteria for symmlq */ double normx; /* norm of the solution vector */ int symmlqitns; /* # symmlq itns */ int inv_it_steps; /* initial steps of inverse iteration */ long itnmin; /* symmlq input */ double shift, rtol; /* symmlq input */ long precon, goodb, nout; /* symmlq input */ long checka, intlim; /* symmlq input */ double anorm, acond; /* symmlq output */ double rnorm, ynorm; /* symmlq output */ long istop, itn; /* symmlq output */ long long_n; /* copy of n for passing to symmlq */ int warning; /* warning on possible misconvergence */ double factor; /* ratio between previous res and new tol */ double minfactor; /* minimum acceptable value of factor */ int converged; /* has process converged yet? */ double *u; /* name of vector being refined */ int *old_assignment = NULL; /* previous assignment vector */ int *assgn_pntr; /* pntr to assignment vector */ int *old_assgn_pntr; /* pntr to previous assignment vector */ int assigndiff = 0; /* discrepancies between old and new assignment */ int assigntol = 0; /* tolerance on convergence of assignment vector */ int first; /* is this the first RQI step? */ int i; /* loop index */ if (DEBUG_TRACE > 0) { printf("\n"); } /* Initialize RQI loop */ u = yvecs[index]; splarax(y, A, n, u, vwsqrt, r1); shift = dot(u, 1, n, y); scadd(y, 1, n, -shift, u); res = ch_norm(y, 1, n); /* eigen-residual */ rqisteps = 0; /* a counter */ symmlqitns = 0; /* a counter */ /* Set invariant symmlq parameters */ precon = FALSE; /* FALSE until we figure out a good way */ goodb = TRUE; /* should be TRUE for this application */ nout = 0; /* set to 0 for no Symmlq output; 6 for lots */ checka = FALSE; /* if don't know by now, too bad */ intlim = n; /* set to enforce a maximum number of Symmlq itns */ itnmin = 0; /* set to enforce a minimum number of Symmlq itns */ long_n = n; /* type change for alint */ if (DEBUG_EVECS > 0) { printf("Using RQI/Symmlq refinement on graph with %d vertices.\n", n); } if (DEBUG_EVECS > 1) { printf(" step lambda est. Ares Symmlq its. istop factor delta\n"); printf(" 0"); doubleout(shift, 1); doubleout(res, 1); printf("\n"); } if (RQI_CONVERGENCE_MODE == 1) { assigntol = tol * n; old_assignment = smalloc((n + 1) * sizeof(int)); } /* Perform RQI */ inv_it_steps = 2; warning = FALSE; factor = 10; minfactor = factor / 2; first = TRUE; if (res < tol) { converged = TRUE; } else { converged = FALSE; } while (!converged) { if (res / tol < 1.2) { factor = max(factor / 2, minfactor); } rtol = res / factor; /* exit Symmlq if iterate is this large */ normxlim = 1.0 / rtol; if (rqisteps < inv_it_steps) { shift = initshift; } symmlq(&long_n, &u[1], &r1[1], &r2[1], &v[1], &w[1], &x[1], &y[1], work, &checka, &goodb, &precon, &shift, &nout, &intlim, &rtol, &istop, &itn, &anorm, &acond, &rnorm, &ynorm, (double *)A, vwsqrt, (double *)orthlist, &macheps, &normxlim, &itnmin); symmlqitns += itn; normx = ch_norm(x, 1, n); vecscale(u, 1, n, 1.0 / normx, x); splarax(y, A, n, u, vwsqrt, r1); shift = dot(u, 1, n, y); scadd(y, 1, n, -shift, u); last_res = res; res = ch_norm(y, 1, n); if (res > last_res) { warning = TRUE; } rqisteps++; if (res < tol) { converged = TRUE; } if (RQI_CONVERGENCE_MODE == 1 && !converged && ndims == 1) { if (first) { assign(A, yvecs, n, 1, cube_or_mesh, nsets, vwsqrt, assignment, active, mediantype, goal, vwgt_max); x2y(yvecs, ndims, n, vwsqrt); first = FALSE; assigndiff = n; /* dummy value for debug chart */ } else { /* copy assignment to old_assignment */ assgn_pntr = assignment; old_assgn_pntr = old_assignment; for (i = n + 1; i; i--) { *old_assgn_pntr++ = *assgn_pntr++; } assign(A, yvecs, n, ndims, cube_or_mesh, nsets, vwsqrt, assignment, active, mediantype, goal, vwgt_max); x2y(yvecs, ndims, n, vwsqrt); /* count differences in assignment */ assigndiff = 0; assgn_pntr = assignment; old_assgn_pntr = old_assignment; for (i = n + 1; i; i--) { if (*old_assgn_pntr++ != *assgn_pntr++) { assigndiff++; } } assigndiff = min(assigndiff, n - assigndiff); if (assigndiff <= assigntol) { converged = TRUE; } } } if (DEBUG_EVECS > 1) { printf(" %2d", rqisteps); doubleout(shift, 1); doubleout(res, 1); printf(" %3ld", itn); printf(" %ld", istop); printf(" %g", factor); if (RQI_CONVERGENCE_MODE == 1) { printf(" %d\n", assigndiff); } else { printf("\n"); } } } *evalest = shift; if (WARNING_EVECS > 0 && warning) { strout("WARNING: Residual convergence not monotonic; RQI may have misconverged.\n"); } if (DEBUG_EVECS > 0) { printf("Eval "); doubleout(*evalest, 1); printf(" RQI steps %d, Symmlq iterations %d.\n\n", rqisteps, symmlqitns); } if (RQI_CONVERGENCE_MODE == 1) { sfree(old_assignment); } }