156 lines
5.7 KiB
C++
156 lines
5.7 KiB
C++
/****************************************************************
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This software is part of J.-S. Caux's C++ library.
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Copyright (c) J.-S. Caux.
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-----------------------------------------------------------
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Integration_par.cc
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Defines all functions to perform integration of functions, parallel (MPI).
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******************************************************************/
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#include "ABACUS.h"
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#include "mpi.h"
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using namespace std;
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namespace ABACUS {
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void Improve_estimate_par (MPI_Comm comm, Integral_data& integdat, DP (*function) (Vect_DP, I_table),
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Vect_DP& args, int arg_to_integ, I_table Itable, int max_nr_pts)
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{
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// This function is only ever called by process rank 0.
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// We generate a max of 3* n_vals points
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data_pt* new_data = new data_pt[3* integdat.integ_res.n_vals];
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DP* new_abs_d2f_dx = new DP[integdat.integ_res.n_vals];
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// Check points in batches of 3; if needed, improve
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int threei = 0;
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int index_new = 0;
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int i, j;
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integdat.integ_res.abs_prec = 0.0;
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integdat.integ_res.integ_est = 0.0;
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DP new_max_abs_d2f_dx = 0.0;
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for (i = 0; i < integdat.integ_res.n_vals/3; ++i) {
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threei = 3 * i;
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if (integdat.abs_d2f_dx[i] <= 0.1 * integdat.max_abs_d2f_dx
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|| index_new + integdat.integ_res.n_vals - threei > max_nr_pts) {
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// simply transfer the data points into new_data
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new_abs_d2f_dx[index_new/3] = integdat.abs_d2f_dx[i];
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new_max_abs_d2f_dx = ABACUS::max(new_max_abs_d2f_dx, new_abs_d2f_dx[index_new/3]);
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for (j = 0; j < 3; ++j) {
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new_data[index_new].x = integdat.data[threei + j].x;
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new_data[index_new].f = integdat.data[threei + j].f;
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new_data[index_new].dx = integdat.data[threei + j].dx;
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integdat.integ_res.integ_est += new_data[index_new].dx * new_data[index_new].f;
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index_new++;
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}
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integdat.integ_res.abs_prec += abs_d2f_dx[i];
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}
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else { // create six new entries and transfer the three existing ones
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new_data[index_new].dx = integdat.data[threei].dx/3.0;
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for (j = 1; j < 9; ++j) new_data[index_new + j].dx = new_data[index_new].dx;
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new_data[index_new].x = integdat.data[threei].x - new_data[index_new].dx;
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new_data[index_new + 1].x = integdat.data[threei].x;
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new_data[index_new + 2].x = integdat.data[threei].x + new_data[index_new].dx;
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new_data[index_new + 3].x = integdat.data[threei + 1].x - new_data[index_new].dx;
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new_data[index_new + 4].x = integdat.data[threei + 1].x;
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new_data[index_new + 5].x = integdat.data[threei + 1].x + new_data[index_new].dx;
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new_data[index_new + 6].x = integdat.data[threei + 2].x - new_data[index_new].dx;
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new_data[index_new + 7].x = integdat.data[threei + 2].x;
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new_data[index_new + 8].x = integdat.data[threei + 2].x + new_data[index_new].dx;
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args[arg_to_integ] = new_data[index_new].x;
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new_data[index_new].f = function(args, Itable);
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new_data[index_new + 1].f = integdat.data[threei].f;
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args[arg_to_integ] = new_data[index_new + 2].x;
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new_data[index_new + 2].f = function(args, Itable);
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args[arg_to_integ] = new_data[index_new + 3].x;
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new_data[index_new + 3].f = function(args, Itable);
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new_data[index_new + 4].f = integdat.data[threei + 1].f;
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args[arg_to_integ] = new_data[index_new + 5].x;
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new_data[index_new + 5].f = function(args, Itable);
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args[arg_to_integ] = new_data[index_new + 6].x;
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new_data[index_new + 6].f = function(args, Itable);
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new_data[index_new + 7].f = integdat.data[threei + 2].f;
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args[arg_to_integ] = new_data[index_new + 8].x;
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new_data[index_new + 8].f = function(args, Itable);
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new_abs_d2f_dx[index_new/3] = fabs(new_data[index_new].dx * (new_data[index_new].f - 2.0 * new_data[index_new + 1].f + new_data[index_new + 2].f));
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new_abs_d2f_dx[index_new/3 + 1] = fabs(new_data[index_new].dx * (new_data[index_new + 3].f - 2.0 * new_data[index_new + 4].f + new_data[index_new + 5].f));
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new_abs_d2f_dx[index_new/3 + 2] = fabs(new_data[index_new].dx * (new_data[index_new + 6].f - 2.0 * new_data[index_new + 7].f + new_data[index_new + 8].f));
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new_max_abs_d2f_dx = ABACUS::max(new_max_abs_d2f_dx, new_abs_d2f_dx[index_new/3]);
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new_max_abs_d2f_dx = ABACUS::max(new_max_abs_d2f_dx, new_abs_d2f_dx[index_new/3 + 1]);
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new_max_abs_d2f_dx = ABACUS::max(new_max_abs_d2f_dx, new_abs_d2f_dx[index_new/3 + 2]);
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integdat.integ_res.integ_est += new_data[index_new].dx * (new_data[index_new].f + new_data[index_new + 1].f + new_data[index_new + 2].f
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+ new_data[index_new + 3].f + new_data[index_new + 4].f + new_data[index_new + 5].f
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+ new_data[index_new + 6].f + new_data[index_new + 7].f + new_data[index_new + 8].f);
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integdat.integ_res.abs_prec += new_abs_d2f_dx[index_new/3] + new_abs_d2f_dx[index_new/3 + 1] + new_abs_d2f_dx[index_new/3 + 2];
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index_new += 9;
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} // else
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} // for (i < nvals/3)
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integdat.integ_res.rel_prec = integdat.integ_res.abs_prec/integdat.integ_res.integ_est;
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integdat.integ_res.n_vals = index_new;
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delete[] integdat.data;
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integdat.data = new_data;
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integdat.max_abs_d2f_dx = new_max_abs_d2f_dx;
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delete[] integdat.abs_d2f_dx;
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integdat.abs_d2f_dx = new_abs_d2f_dx;
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return;
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}
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Integral_result Integrate_optimal_par_using_table (MPI_Comm comm, DP (*function) (Vect_DP, I_table),
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Vect_DP& args, int arg_to_integ,
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I_table Itable, DP xmin, DP xmax,
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DP req_rel_prec, DP req_abs_prec, int max_nr_pts, ofstream& outfile)
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{
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if (xmax < xmin) ABACUSerror("Use xmax > xmin in Integrate.");
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Integral_data integ_dat (function, args, arg_to_integ, Itable, xmin, xmax);
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while ((integ_dat.integ_res.rel_prec > req_rel_prec || integ_dat.integ_res.abs_prec > req_abs_prec)
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&& integ_dat.integ_res.n_vals < max_nr_pts) {
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Improve_estimate_par (comm, integ_dat, function, args, arg_to_integ, Itable, max_nr_pts);
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integ_dat.Save (outfile);
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}
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return(integ_dat.integ_res);
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}
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} // namespace ABACUS
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