|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_x[1] * (array_x[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre div $eq_no = 1 i = 1 > array_tmp3[1] := (array_const_1D0[1] / (array_tmp2[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_x,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2] + array_const_1D0[2]; > #emit pre div $eq_no = 1 i = 2 > array_tmp3[2] := ((array_const_1D0[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 2 > array_tmp4[2] := array_const_0D0[2] + array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_x,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3] + array_const_1D0[3]; > #emit pre div $eq_no = 1 i = 3 > array_tmp3[3] := ((array_const_1D0[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 3 > array_tmp4[3] := array_const_0D0[3] + array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_x,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4] + array_const_1D0[4]; > #emit pre div $eq_no = 1 i = 4 > array_tmp3[4] := ((array_const_1D0[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 4 > array_tmp4[4] := array_const_0D0[4] + array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_x,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5] + array_const_1D0[5]; > #emit pre div $eq_no = 1 i = 5 > array_tmp3[5] := ((array_const_1D0[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 5 > array_tmp4[5] := array_const_0D0[5] + array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_x,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk] + array_const_1D0[kkk]; > #emit div $eq_no = 1 > array_tmp3[kkk] := ((array_const_1D0[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit add $eq_no = 1 > array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp4[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; array_tmp1[1] := array_x[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := array_const_1D0[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_x, array_x, 1); array_tmp2[2] := array_tmp1[2] + array_const_1D0[2]; array_tmp3[2] := ( array_const_1D0[2] - ats(2, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[2] := array_const_0D0[2] + array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_x, array_x, 1); array_tmp2[3] := array_tmp1[3] + array_const_1D0[3]; array_tmp3[3] := ( array_const_1D0[3] - ats(3, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[3] := array_const_0D0[3] + array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_x, array_x, 1); array_tmp2[4] := array_tmp1[4] + array_const_1D0[4]; array_tmp3[4] := ( array_const_1D0[4] - ats(4, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[4] := array_const_0D0[4] + array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_x, array_x, 1); array_tmp2[5] := array_tmp1[5] + array_const_1D0[5]; array_tmp3[5] := ( array_const_1D0[5] - ats(5, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[5] := array_const_0D0[5] + array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_x, array_x, 1); array_tmp2[kkk] := array_tmp1[kkk] + array_const_1D0[kkk]; array_tmp3[kkk] := ( array_const_1D0[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > arctan(x); > end; exact_soln_y := proc(x) arctan(x) end proc > > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_smallish_float, > years_in_century, > glob_optimal_expect_sec, > glob_log10relerr, > glob_iter, > glob_small_float, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > glob_no_eqs, > glob_hmax, > glob_h, > glob_not_yet_finished, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_hmin, > glob_reached_optimal_h, > glob_not_yet_start_msg, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_relerr, > glob_dump_analytic, > glob_max_hours, > glob_log10_relerr, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_clock_sec, > glob_max_opt_iter, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > centuries_in_millinium, > glob_max_minutes, > glob_max_sec, > glob_warned, > glob_almost_1, > glob_current_iter, > glob_start, > glob_max_iter, > glob_look_poles, > glob_large_float, > min_in_hour, > sec_in_min, > glob_display_flag, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_normmax, > glob_max_trunc_err, > glob_disp_incr, > glob_initial_pass, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_1D0, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_y_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_type_pole, > array_last_rel_error, > array_y, > array_x, > array_y_higher_work, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > DEBUGL := 3; > INFO := 2; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_smallish_float := 0.1e-100; > years_in_century := 100.0; > glob_optimal_expect_sec := 0.1; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_last_good_h := 0.1; > days_in_year := 365.0; > glob_no_eqs := 0; > glob_hmax := 1.0; > glob_h := 0.1; > glob_not_yet_finished := true; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > glob_not_yet_start_msg := true; > hours_in_day := 24.0; > glob_dump := false; > glob_html_log := true; > glob_subiter_method := 3; > MAX_UNCHANGED := 10; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > djd_debug2 := true; > glob_log10abserr := 0.0; > glob_warned2 := false; > glob_clock_sec := 0.0; > glob_max_opt_iter := 10; > glob_hmin_init := 0.001; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > glob_max_minutes := 0.0; > glob_max_sec := 10000.0; > glob_warned := false; > glob_almost_1 := 0.9990; > glob_current_iter := 0; > glob_start := 0; > glob_max_iter := 1000; > glob_look_poles := false; > glob_large_float := 9.0e100; > min_in_hour := 60.0; > sec_in_min := 60.0; > glob_display_flag := true; > djd_debug := true; > glob_log10normmin := 0.1; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_disp_incr := 0.1; > glob_initial_pass := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -2.0;"); > omniout_str(ALWAYS,"x_end := 1.0;"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_adjust_h := false;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"arctan(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_pole:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -2.0; > x_end := 1.0; > glob_h := 0.00001; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_adjust_h := false; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T04:03:44-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"sing2 diffeq.mxt") > ; > logitem_str(html_log_file,"sing2 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `glob_adjust_h` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, glob_adjust_h; global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float, years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin, glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours, glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2, glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, centuries_in_millinium, glob_max_minutes, glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start, glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min, glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done, glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass, array_const_1, array_const_1D0, array_const_0D0, array_pole, array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole, array_last_rel_error, array_y, array_x, array_y_higher_work, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; ALWAYS := 1; DEBUGMASSIVE := 4; glob_max_terms := 30; DEBUGL := 3; INFO := 2; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_smallish_float := 0.1*10^(-100); years_in_century := 100.0; glob_optimal_expect_sec := 0.1; glob_log10relerr := 0.; glob_iter := 0; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_last_good_h := 0.1; days_in_year := 365.0; glob_no_eqs := 0; glob_hmax := 1.0; glob_h := 0.1; glob_not_yet_finished := true; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; glob_not_yet_start_msg := true; hours_in_day := 24.0; glob_dump := false; glob_html_log := true; glob_subiter_method := 3; MAX_UNCHANGED := 10; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); djd_debug2 := true; glob_log10abserr := 0.; glob_warned2 := false; glob_clock_sec := 0.; glob_max_opt_iter := 10; glob_hmin_init := 0.001; glob_optimal_done := false; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; glob_max_minutes := 0.; glob_max_sec := 10000.0; glob_warned := false; glob_almost_1 := 0.9990; glob_current_iter := 0; glob_start := 0; glob_max_iter := 1000; glob_look_poles := false; glob_large_float := 0.90*10^101; min_in_hour := 60.0; sec_in_min := 60.0; glob_display_flag := true; djd_debug := true; glob_log10normmin := 0.1; glob_percent_done := 0.; glob_normmax := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_disp_incr := 0.1; glob_initial_pass := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing2postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -2.0;"); omniout_str(ALWAYS, "x_end := 1.0;"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_adjust_h := false;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "arctan(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := -2.0; x_end := 1.0; glob_h := 0.00001; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_adjust_h := false; glob_max_iter := 100; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T04:03:44-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "sing2 diffeq.mxt"); logitem_str(html_log_file, "sing2 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.0; x_end := 1.0; glob_h := 0.00001; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_adjust_h := false; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) arctan(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -2 y[1] (analytic) = -1.1071487177940905030170654601785 y[1] (numeric) = -1.1071487177940905030170654601785 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.244 Order of pole = 2.182 x[1] = -1.9999 y[1] (analytic) = -1.1071287169940611687237058863759 y[1] (numeric) = -1.1071287169940611687237058699494 absolute error = 1.64265e-26 relative error = 1.4837028204452323502640984565306e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.244 Order of pole = 2.182 x[1] = -1.9998 y[1] (analytic) = -1.1071087145938558209895590834752 y[1] (numeric) = -1.1071087145938558209895590506236 absolute error = 3.28516e-26 relative error = 2.9673327982113887913711516968491e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.244 Order of pole = 2.182 x[1] = -1.9997 y[1] (analytic) = -1.1070887105932984252506887980461 y[1] (numeric) = -1.1070887105932984252506887487707 absolute error = 4.92754e-26 relative error = 4.4508989684840058129113467346939e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.244 Order of pole = 2.182 x[1] = -1.9996 y[1] (analytic) = -1.1070687049922129238968604445428 y[1] (numeric) = -1.1070687049922129238968603788449 absolute error = 6.56979e-26 relative error = 5.9344013342389726704597722305454e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9995 y[1] (analytic) = -1.1070486977904232362683914605932 y[1] (numeric) = -1.1070486977904232362683913784741 absolute error = 8.21191e-26 relative error = 7.4178398984527841247657004325086e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9994 y[1] (analytic) = -1.1070286889877532586530013244488 y[1] (numeric) = -1.1070286889877532586530012259098 absolute error = 9.85390e-26 relative error = 8.9012146641025405924826718843224e-24 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9993 y[1] (analytic) = -1.1070086785840268642826612346212 y[1] (numeric) = -1.1070086785840268642826611196636 absolute error = 1.149576e-25 relative error = 1.0384525634165948296942932477934e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9992 y[1] (analytic) = -1.1069886665790679033304434517335 y[1] (numeric) = -1.1069886665790679033304433203586 absolute error = 1.313749e-25 relative error = 1.1867772811621319418976237938916e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9991 y[1] (analytic) = -1.1069686529727002029073703026122 y[1] (numeric) = -1.1069686529727002029073701548214 absolute error = 1.477908e-25 relative error = 1.3350947165768097092284950724347e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.999 y[1] (analytic) = -1.106948637764747567059262846648 y[1] (numeric) = -1.1069486377647475670592626824426 absolute error = 1.642054e-25 relative error = 1.4834057732938597438390958839044e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9989 y[1] (analytic) = -1.1069286209550337767635892044509 y[1] (numeric) = -1.1069286209550337767635890238321 absolute error = 1.806188e-25 relative error = 1.6317113550119072194871468295259e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9988 y[1] (analytic) = -1.1069086025433825899263125488282 y[1] (numeric) = -1.1069086025433825899263123517974 absolute error = 1.970308e-25 relative error = 1.7800096552441226248954617305999e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9987 y[1] (analytic) = -1.1068885825296177413787387581121 y[1] (numeric) = -1.1068885825296177413787385446707 absolute error = 2.134414e-25 relative error = 1.9283006742396207608636376351260e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9986 y[1] (analytic) = -1.1068685609135629428743637318635 y[1] (numeric) = -1.1068685609135629428743635020127 absolute error = 2.298508e-25 relative error = 2.0765862191468405087807932485533e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.243 Order of pole = 2.182 x[1] = -1.9985 y[1] (analytic) = -1.1068485376950418830857203689796 y[1] (numeric) = -1.1068485376950418830857201227209 absolute error = 2.462587e-25 relative error = 2.2248635799151141018375506851299e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 memory used=3.8MB, alloc=2.9MB, time=0.46 x[1] = -1.9984 y[1] (analytic) = -1.1068285128738782276012252082334 y[1] (numeric) = -1.106828512873878227601224945568 absolute error = 2.626654e-25 relative error = 2.3731354671916588502853345625555e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9983 y[1] (analytic) = -1.1068084864498956189220247312703 y[1] (numeric) = -1.1068084864498956189220244521996 absolute error = 2.790707e-25 relative error = 2.5214000743265291092200995526670e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9982 y[1] (analytic) = -1.1067884584229176764588413280921 y[1] (numeric) = -1.1067884584229176764588410326174 absolute error = 2.954747e-25 relative error = 2.6696583050841268464644329778032e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9981 y[1] (analytic) = -1.1067684287927679965288189250528 y[1] (numeric) = -1.1067684287927679965288186131754 absolute error = 3.118774e-25 relative error = 2.8179101597629337220726493080723e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.998 y[1] (analytic) = -1.1067483975592701523523682753958 y[1] (numeric) = -1.1067483975592701523523679471171 absolute error = 3.282787e-25 relative error = 2.9661547351137642437373473833400e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9979 y[1] (analytic) = -1.1067283647222476940500119123591 y[1] (numeric) = -1.1067283647222476940500115676805 absolute error = 3.446786e-25 relative error = 3.1143920313861564109724183479283e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9978 y[1] (analytic) = -1.1067083302815241486392287648764 y[1] (numeric) = -1.1067083302815241486392284037991 absolute error = 3.610773e-25 relative error = 3.2626238559905775685380582038885e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9977 y[1] (analytic) = -1.1066882942369230200312984359004 y[1] (numeric) = -1.1066882942369230200312980584258 absolute error = 3.774746e-25 relative error = 3.4108484020812200763280042737610e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9976 y[1] (analytic) = -1.1066682565882677890281451433787 y[1] (numeric) = -1.1066682565882677890281447495081 absolute error = 3.938706e-25 relative error = 3.5590665735209411986520913968132e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9975 y[1] (analytic) = -1.1066482173353819133191813239063 y[1] (numeric) = -1.1066482173353819133191809136411 absolute error = 4.102652e-25 relative error = 3.7072774669790537329528602115067e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.242 Order of pole = 2.182 x[1] = -1.9974 y[1] (analytic) = -1.1066281764780888274781508990862 y[1] (numeric) = -1.1066281764780888274781504724277 absolute error = 4.266585e-25 relative error = 3.8554819863512467965411719562702e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9973 y[1] (analytic) = -1.1066081340162119429599722046223 y[1] (numeric) = -1.1066081340162119429599717615719 absolute error = 4.430504e-25 relative error = 4.0036792282742181440726630697132e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9972 y[1] (analytic) = -1.1065880899495746480975805821754 y[1] (numeric) = -1.1065880899495746480975801227345 absolute error = 4.594409e-25 relative error = 4.1518691929978746338303098406688e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9971 y[1] (analytic) = -1.1065680442780003080987706340082 y[1] (numeric) = -1.106568044278000308098770158178 absolute error = 4.758302e-25 relative error = 4.3000536881621567501633595344104e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.997 y[1] (analytic) = -1.1065479970013122650430381404474 y[1] (numeric) = -1.1065479970013122650430376482294 absolute error = 4.922180e-25 relative error = 4.4482300029812107131433308390986e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9969 y[1] (analytic) = -1.1065279481193338378784216401926 y[1] (numeric) = -1.1065279481193338378784211315881 absolute error = 5.086045e-25 relative error = 4.5963999451114577307772466471466e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9968 y[1] (analytic) = -1.106507897631888322418343673497 y[1] (numeric) = -1.1065078976318883224183431485074 absolute error = 5.249896e-25 relative error = 4.7445626111080220253124462335571e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9967 y[1] (analytic) = -1.1064878455387989913384516882505 y[1] (numeric) = -1.1064878455387989913384511468771 absolute error = 5.413734e-25 relative error = 4.8927189049815617171044122040887e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9966 y[1] (analytic) = -1.106467791839889094173458608992 y[1] (numeric) = -1.1064677918398890941734580512363 absolute error = 5.577557e-25 relative error = 5.0408670194776874125584221226905e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9965 y[1] (analytic) = -1.1064477365349818573139830688798 y[1] (numeric) = -1.106447736534981857313982494743 absolute error = 5.741368e-25 relative error = 5.1890096661772860920457107029806e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9964 y[1] (analytic) = -1.1064276796239004840033893046463 y[1] (numeric) = -1.1064276796239004840033887141299 absolute error = 5.905164e-25 relative error = 5.3371441340000616448800097998255e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.241 Order of pole = 2.182 x[1] = -1.9963 y[1] (analytic) = -1.1064076211064681543346267145685 y[1] (numeric) = -1.1064076211064681543346261076739 absolute error = 6.068946e-25 relative error = 5.4852713269732559857272609162264e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9962 y[1] (analytic) = -1.1063875609825080252470690794795 y[1] (numeric) = -1.1063875609825080252470684562079 absolute error = 6.232716e-25 relative error = 5.6333930530321093957571835858601e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9961 y[1] (analytic) = -1.1063674992518432305233534468502 y[1] (numeric) = -1.1063674992518432305233528072032 absolute error = 6.396470e-25 relative error = 5.7815056970902278176517769258969e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.996 y[1] (analytic) = -1.1063474359142968807862186779712 y[1] (numeric) = -1.10634743591429688078621802195 absolute error = 6.560212e-25 relative error = 5.9296128748005579678503496800972e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=1.02 Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9959 y[1] (analytic) = -1.10632737096969206349534365826 y[1] (numeric) = -1.1063273709696920634953429858661 absolute error = 6.723939e-25 relative error = 6.0777118748372744595109217140018e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9958 y[1] (analytic) = -1.1063073044178518429441851707255 y[1] (numeric) = -1.1063073044178518429441844819603 absolute error = 6.887652e-25 relative error = 6.2258036013098007092106794269138e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9957 y[1] (analytic) = -1.1062872362585992602568154326151 y[1] (numeric) = -1.1062872362585992602568147274799 absolute error = 7.051352e-25 relative error = 6.3738889583931862614389218113146e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9956 y[1] (analytic) = -1.106267166491757333384759295275 y[1] (numeric) = -1.1062671664917573333847585737712 absolute error = 7.215038e-25 relative error = 6.5219670424465755849642442992804e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9955 y[1] (analytic) = -1.1062470951171490571038311072518 y[1] (numeric) = -1.1062470951171490571038303693808 absolute error = 7.378710e-25 relative error = 6.6700378537207470403253380991948e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9954 y[1] (analytic) = -1.1062270221345974030109712406631 y[1] (numeric) = -1.1062270221345974030109704864263 absolute error = 7.542368e-25 relative error = 6.8181013924665286824900200672097e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9953 y[1] (analytic) = -1.1062069475439253195210822808668 y[1] (numeric) = -1.1062069475439253195210815102657 absolute error = 7.706011e-25 relative error = 6.9661567549448150059689471645851e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.24 Order of pole = 2.182 x[1] = -1.9952 y[1] (analytic) = -1.1061868713449557318638648794575 y[1] (numeric) = -1.1061868713449557318638640924934 absolute error = 7.869641e-25 relative error = 7.1142057493700934994155468649160e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9951 y[1] (analytic) = -1.1061667935375115420806532706179 y[1] (numeric) = -1.1061667935375115420806524672923 absolute error = 8.033256e-25 relative error = 7.2622465679969644941836721956898e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.995 y[1] (analytic) = -1.1061467141214156290212504508558 y[1] (numeric) = -1.10614671412141562902124963117 absolute error = 8.196858e-25 relative error = 7.4102810191056410522782204473151e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9949 y[1] (analytic) = -1.1061266330964908483407630221531 y[1] (numeric) = -1.1061266330964908483407621861085 absolute error = 8.360446e-25 relative error = 7.5583081989408100888420219319365e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9948 y[1] (analytic) = -1.106106550462560032496435698558 y[1] (numeric) = -1.106106550462560032496434846156 absolute error = 8.524020e-25 relative error = 7.7063281077535980779150976435992e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9947 y[1] (analytic) = -1.1060864662194459907444854762476 y[1] (numeric) = -1.1060864662194459907444846074897 absolute error = 8.687579e-25 relative error = 7.8543398417067301967989014021957e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9946 y[1] (analytic) = -1.1060663803669715091369354670908 y[1] (numeric) = -1.1060663803669715091369345819783 absolute error = 8.851125e-25 relative error = 8.0023452092119166500122509528926e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9945 y[1] (analytic) = -1.10604629290495935051844839574 y[1] (numeric) = -1.1060462929049593505184474942743 absolute error = 9.014657e-25 relative error = 8.1503433064483982871976160158024e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9944 y[1] (analytic) = -1.1060262038332322545231597602807 y[1] (numeric) = -1.1060262038332322545231588424634 absolute error = 9.178173e-25 relative error = 8.2983323253920792035079324982618e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9943 y[1] (analytic) = -1.1060061131516129375715106564691 y[1] (numeric) = -1.1060061131516129375715097223014 absolute error = 9.341677e-25 relative error = 8.4463158828123305656176922127015e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9942 y[1] (analytic) = -1.1059860208599240928670802655841 y[1] (numeric) = -1.1059860208599240928670793150676 absolute error = 9.505165e-25 relative error = 8.5942903623768794620901007382102e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.9941 y[1] (analytic) = -1.1059659269579883903934180059269 y[1] (numeric) = -1.105965926957988390393417039063 absolute error = 9.668639e-25 relative error = 8.7422575726126111588795684114886e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.239 Order of pole = 2.182 x[1] = -1.994 y[1] (analytic) = -1.1059458314456284769108753479934 y[1] (numeric) = -1.1059458314456284769108743647835 absolute error = 9.832099e-25 relative error = 8.8902175137710392164151327312698e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9939 y[1] (analytic) = -1.1059257343226669759534372933514 y[1] (numeric) = -1.1059257343226669759534362937969 absolute error = 9.995545e-25 relative error = 9.0381701861037270680757979645949e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9938 y[1] (analytic) = -1.1059056355889264878255535172509 y[1] (numeric) = -1.1059056355889264878255525013532 absolute error = 1.0158977e-24 relative error = 9.1861155898622880322902413462040e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9937 y[1] (analytic) = -1.1058855352442295895989691749966 y[1] (numeric) = -1.1058855352442295895989681427572 absolute error = 1.0322394e-24 relative error = 9.3340528210456682664005691795853e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9936 y[1] (analytic) = -1.1058654332883988351095553721126 y[1] (numeric) = -1.1058654332883988351095543235329 absolute error = 1.0485797e-24 relative error = 9.4819827841254237038163839213318e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9935 y[1] (analytic) = -1.1058453297212567549541392983283 y[1] (numeric) = -1.1058453297212567549541382334097 absolute error = 1.0649186e-24 relative error = 9.6299054793533116451283985724972e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 memory used=11.4MB, alloc=4.1MB, time=1.60 x[1] = -1.9934 y[1] (analytic) = -1.1058252245426258564873340254153 y[1] (numeric) = -1.1058252245426258564873329441593 absolute error = 1.0812560e-24 relative error = 9.7778200026791051444376022806238e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9933 y[1] (analytic) = -1.1058051177523286238183679689045 y[1] (numeric) = -1.1058051177523286238183668713126 absolute error = 1.0975919e-24 relative error = 9.9257263543053327645867299447367e-23 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9932 y[1] (analytic) = -1.1057850093501875178079140137136 y[1] (numeric) = -1.1057850093501875178079128997871 absolute error = 1.1139265e-24 relative error = 1.0073626343104405203221428713195e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9931 y[1] (analytic) = -1.1057648993360249760649183037131 y[1] (numeric) = -1.1057648993360249760649171734535 absolute error = 1.1302596e-24 relative error = 1.0221518160674871091845083678313e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.993 y[1] (analytic) = -1.105744787709663412943428695263 y[1] (numeric) = -1.1057447877096634129434275486717 absolute error = 1.1465913e-24 relative error = 1.0369402711587203061813016233345e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.238 Order of pole = 2.182 x[1] = -1.9929 y[1] (analytic) = -1.1057246744709252195394228747471 y[1] (numeric) = -1.1057246744709252195394217118256 absolute error = 1.1629215e-24 relative error = 1.0517279091709178983899090308742e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9928 y[1] (analytic) = -1.1057045596196327636876361401371 y[1] (numeric) = -1.1057045596196327636876349608868 absolute error = 1.1792503e-24 relative error = 1.0665148205644257221696429087906e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9927 y[1] (analytic) = -1.1056844431556083899583888466142 y[1] (numeric) = -1.1056844431556083899583876510366 absolute error = 1.1955776e-24 relative error = 1.0813009149227403080757097931777e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9926 y[1] (analytic) = -1.1056643250786744196544135162799 y[1] (numeric) = -1.1056643250786744196544123043765 absolute error = 1.2119034e-24 relative error = 1.0960861922661437547351862216401e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9925 y[1] (analytic) = -1.1056442053886531508076816119845 y[1] (numeric) = -1.1056442053886531508076803837567 absolute error = 1.2282278e-24 relative error = 1.1108707430599309165371941130414e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9924 y[1] (analytic) = -1.105624084085366858176229975304 y[1] (numeric) = -1.1056240840853668581762287307533 absolute error = 1.2445507e-24 relative error = 1.1256544768826747210370268704884e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9923 y[1] (analytic) = -1.105603961168637793240986928695 y[1] (numeric) = -1.1056039611686377932409856678229 absolute error = 1.2608721e-24 relative error = 1.1404373937546694033485920764396e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9922 y[1] (analytic) = -1.105583836638288184202598041858 y[1] (numeric) = -1.1055838366382881842025967646659 absolute error = 1.2771921e-24 relative error = 1.1552195841461605714720911970702e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9921 y[1] (analytic) = -1.1055637104941402359782515623386 y[1] (numeric) = -1.1055637104941402359782502688279 absolute error = 1.2935107e-24 relative error = 1.1700010480823899384376194685645e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.992 y[1] (analytic) = -1.1055435827360161301985035103973 y[1] (numeric) = -1.1055435827360161301985022005696 absolute error = 1.3098277e-24 relative error = 1.1847816046821224531259510710819e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9919 y[1] (analytic) = -1.1055234533637380252041024381781 y[1] (numeric) = -1.1055234533637380252041011120348 absolute error = 1.3261433e-24 relative error = 1.1995614348705037310223426155766e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.237 Order of pole = 2.182 x[1] = -1.9918 y[1] (analytic) = -1.1055033223771280560428138532052 y[1] (numeric) = -1.1055033223771280560428125107477 absolute error = 1.3424575e-24 relative error = 1.2143405386727893643329527049289e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9917 y[1] (analytic) = -1.1054831897760083344662443062389 y[1] (numeric) = -1.1054831897760083344662429474688 absolute error = 1.3587701e-24 relative error = 1.2291187351978751957645916739646e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9916 y[1] (analytic) = -1.1054630555602009489266651435213 y[1] (numeric) = -1.10546305556020094892666376844 absolute error = 1.3750813e-24 relative error = 1.2438962053808014103007694755253e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9915 y[1] (analytic) = -1.1054429197295279645738359234408 y[1] (numeric) = -1.1054429197295279645738345320498 absolute error = 1.3913910e-24 relative error = 1.2586728587853598176297922778645e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9914 y[1] (analytic) = -1.1054227822838114232518274976473 y[1] (numeric) = -1.1054227822838114232518260899481 absolute error = 1.4076992e-24 relative error = 1.2734486954318811147057532082921e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9913 y[1] (analytic) = -1.1054026432228733434958447566473 y[1] (numeric) = -1.1054026432228733434958433326414 absolute error = 1.4240059e-24 relative error = 1.2882237153406998624223290038415e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9912 y[1] (analytic) = -1.1053825025465357205290490399104 y[1] (numeric) = -1.1053825025465357205290475995993 absolute error = 1.4403111e-24 relative error = 1.3029979185321544865083976214056e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9911 y[1] (analytic) = -1.105362360254620526259380210517 y[1] (numeric) = -1.1053623602546205262593787539021 absolute error = 1.4566149e-24 relative error = 1.3177713954946578367202519628474e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.991 y[1] (analytic) = -1.1053422163469497092763783943778 y[1] (numeric) = -1.1053422163469497092763769214606 absolute error = 1.4729172e-24 relative error = 1.3325440557837829178215793064104e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9909 y[1] (analytic) = -1.1053220708233451948480053840565 y[1] (numeric) = -1.1053220708233451948480038948385 absolute error = 1.4892180e-24 relative error = 1.3473158994198803324992171769887e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=2.16 Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9908 y[1] (analytic) = -1.1053019236836288849174657072253 y[1] (numeric) = -1.1053019236836288849174642017081 absolute error = 1.5055172e-24 relative error = 1.3620868359502873091251701777198e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.236 Order of pole = 2.182 x[1] = -1.9907 y[1] (analytic) = -1.1052817749276226581000273597847 y[1] (numeric) = -1.1052817749276226581000258379697 absolute error = 1.5218150e-24 relative error = 1.3768570463397473944509022327953e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9906 y[1] (analytic) = -1.1052616245551483696798422036778 y[1] (numeric) = -1.1052616245551483696798406655665 absolute error = 1.5381113e-24 relative error = 1.3916264401372546438420814677396e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9905 y[1] (analytic) = -1.1052414725660278516067660294304 y[1] (numeric) = -1.1052414725660278516067644750243 absolute error = 1.5544061e-24 relative error = 1.4063950173631751395331839020399e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9904 y[1] (analytic) = -1.1052213189600829124931782834471 y[1] (numeric) = -1.1052213189600829124931767127478 absolute error = 1.5706993e-24 relative error = 1.4211626875582633195303873135873e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9903 y[1] (analytic) = -1.1052011637371353376108014600956 y[1] (numeric) = -1.1052011637371353376107998731045 absolute error = 1.5869911e-24 relative error = 1.4359296317004739942995493423265e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9902 y[1] (analytic) = -1.1051810068970068888875201586078 y[1] (numeric) = -1.1051810068970068888875185553265 absolute error = 1.6032813e-24 relative error = 1.4506956688493033976037099648081e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.9901 y[1] (analytic) = -1.1051608484395193049041998048316 y[1] (numeric) = -1.1051608484395193049041981852615 absolute error = 1.6195701e-24 relative error = 1.4654609799893142873179933034563e-22 % h = 0.0001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.235 Order of pole = 2.182 x[1] = -1.99 y[1] (analytic) = -1.1051406883644943008915050378617 y[1] (numeric) = -1.1051406883644943008915034020044 absolute error = 1.6358573e-24 relative error = 1.4802253841734096785276026082305e-22 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; Iterations = 100 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Expected Time Remaining = 11 Minutes 9 Seconds Optimized Time Remaining = 11 Minutes 3 Seconds Time to Timeout = 14 Minutes 57 Seconds Percent Done = 0.3367 % > quit memory used=16.6MB, alloc=4.1MB, time=2.36