|\^/| 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, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no, good_digits; > > > > > > #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 := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > good_digits := -trunc(log10(relerr/100.0)); > else > good_digits := -1; > fi;# end if 3 > ; > else > relerr := -1.0 ; > good_digits := -1; > 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,"%"); > print("good digits = ",good_digits); > 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, good_digits; global glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, 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 := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0)) else good_digits := -1 end if else relerr := -1.0; good_digits := -1 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, "%"); print("good digits = ", good_digits); 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, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(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 (omniabs(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"); > 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 > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(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 < omniabs(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"); 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; return hnew end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > 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, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, 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, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > 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 ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(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 ((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(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 ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(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, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(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 < omniabs(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 < omniabs(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 <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(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 omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(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 < omniabs(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 < omniabs(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, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(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, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[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_tmp2[1] * expt(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 FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[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_tmp2[2] * expt(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 FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[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_tmp2[3] * expt(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 FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[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_tmp2[4] * expt(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 FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[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_tmp2[5] * expt(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 FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[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_tmp2[kkk] * expt(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 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, glob_last; array_tmp1[1] := array_y[1]*array_y[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*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_y, array_y, 1); array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*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_y, array_y, 1); array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*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_y, array_y, 1); array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*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_y, array_y, 1); array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*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_y, array_y, 1); array_tmp2[kkk] := array_tmp1[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_tmp2[kkk]*expt(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_minute, 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_minute * 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_minute; > 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_minute, years_in_century; secs := secs_in; if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*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_minute; 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_minute, 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_minute * 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_minute; > 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_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*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_minute; 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_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > > > > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (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_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < 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 (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 < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 17 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 18 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > > > > if (nnn <= glob_max_terms) then # if number 13 > if (array_fact_1[nnn] = 0) then # if number 14 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 18 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # Begin Function number 19 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > > > > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13 > if (array_fact_2[mmm,nnn] = 0) then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 19 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # Begin Function number 20 > convfp := proc(mmm) > (mmm); > > # End Function number 20 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 21 > convfloat := proc(mmm) > (mmm); > > # End Function number 21 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0/(1.0 - 2.0*x)); > end; exact_soln_y := proc(x) return 2.0/(1.0 - 2.0*x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_warned2, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_abserr, > glob_dump_analytic, > glob_hmax, > glob_almost_1, > years_in_century, > glob_optimal_expect_sec, > glob_start, > glob_max_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_disp_incr, > glob_log10normmin, > glob_subiter_method, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_clock_sec, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_max_hours, > glob_large_float, > glob_optimal_done, > glob_not_yet_start_msg, > sec_in_minute, > glob_normmax, > MAX_UNCHANGED, > glob_current_iter, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > hours_in_day, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_percent_done, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_iter, > glob_hmin, > glob_h, > glob_initial_pass, > days_in_year, > djd_debug2, > glob_display_flag, > glob_html_log, > glob_warned, > glob_optimal_start, > glob_dump, > glob_log10abserr, > glob_reached_optimal_h, > glob_max_minutes, > glob_small_float, > djd_debug, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_pole, > array_last_rel_error, > array_norms, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y, > array_x, > array_fact_1, > array_real_pole, > array_y_higher, > array_y_higher_work, > array_poles, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_y_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > ALWAYS := 1; > DEBUGMASSIVE := 4; > INFO := 2; > glob_max_terms := 30; > DEBUGL := 3; > glob_warned2 := false; > min_in_hour := 60; > glob_max_sec := 10000.0; > glob_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_almost_1 := 0.9990; > years_in_century := 100; > glob_optimal_expect_sec := 0.1; > glob_start := 0; > glob_max_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_disp_incr := 0.1; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_unchanged_h_cnt := 0; > glob_last_good_h := 0.1; > glob_clock_sec := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_no_eqs := 0; > glob_max_hours := 0.0; > glob_large_float := 9.0e100; > glob_optimal_done := false; > glob_not_yet_start_msg := true; > sec_in_minute := 60; > glob_normmax := 0.0; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_look_poles := false; > glob_hmin_init := 0.001; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10; > hours_in_day := 24; > glob_curr_iter_when_opt := 0; > glob_smallish_float := 0.1e-100; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_iter := 1000; > glob_hmin := 0.00000000001; > glob_h := 0.1; > glob_initial_pass := true; > days_in_year := 365; > djd_debug2 := true; > glob_display_flag := true; > glob_html_log := true; > glob_warned := false; > glob_optimal_start := 0.0; > glob_dump := false; > glob_log10abserr := 0.0; > glob_reached_optimal_h := false; > glob_max_minutes := 0.0; > glob_small_float := 0.1e-50; > djd_debug := true; > glob_max_opt_iter := 10; > #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/nonlinear2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); > 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 := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.2 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 1;"); > 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,"return(2.0/(1.0 - 2.0*x));"); > omniout_str(ALWAYS,"end;"); > 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_m1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > 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_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_norms[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_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_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_type_pole[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 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 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_higher[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_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_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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[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 <=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_set_initial[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_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_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 > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.2 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.01; > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 1; > #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 := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(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] * expt(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]* expt(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(); > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(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] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(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] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(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] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(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 ) = y * y;"); > 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,"2012-08-12T23:50:02-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") > ; > 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," 119 ") > ; > logitem_str(html_log_file,"nonlinear2 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear2 maple results") > ; > logitem_str(html_log_file,"1st test with c++") > ; > 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; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, glob_warned2, min_in_hour, glob_max_sec, glob_relerr, glob_abserr, glob_dump_analytic, glob_hmax, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_start, glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_disp_incr, glob_log10normmin, glob_subiter_method, glob_unchanged_h_cnt, glob_last_good_h, glob_clock_sec, glob_optimal_clock_start_sec, glob_no_eqs, glob_max_hours, glob_large_float, glob_optimal_done, glob_not_yet_start_msg, sec_in_minute, glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, hours_in_day, glob_curr_iter_when_opt, glob_smallish_float, glob_percent_done, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_iter, glob_hmin, glob_h, glob_initial_pass, days_in_year, djd_debug2, glob_display_flag, glob_html_log, glob_warned, glob_optimal_start, glob_dump, glob_log10abserr, glob_reached_optimal_h, glob_max_minutes, glob_small_float, djd_debug, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_pole, array_last_rel_error, array_norms, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y, array_x, array_fact_1, array_real_pole, array_y_higher, array_y_higher_work, array_poles, array_fact_2, array_complex_pole, array_y_higher_work2, array_y_set_initial, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; ALWAYS := 1; DEBUGMASSIVE := 4; INFO := 2; glob_max_terms := 30; DEBUGL := 3; glob_warned2 := false; min_in_hour := 60; glob_max_sec := 10000.0; glob_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_dump_analytic := false; glob_hmax := 1.0; glob_almost_1 := 0.9990; years_in_century := 100; glob_optimal_expect_sec := 0.1; glob_start := 0; glob_max_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_unchanged_h_cnt := 0; glob_last_good_h := 0.1; glob_clock_sec := 0.; glob_optimal_clock_start_sec := 0.; glob_no_eqs := 0; glob_max_hours := 0.; glob_large_float := 0.90*10^101; glob_optimal_done := false; glob_not_yet_start_msg := true; sec_in_minute := 60; glob_normmax := 0.; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_look_poles := false; glob_hmin_init := 0.001; glob_not_yet_finished := true; glob_clock_start_sec := 0.; centuries_in_millinium := 10; hours_in_day := 24; glob_curr_iter_when_opt := 0; glob_smallish_float := 0.1*10^(-100); glob_percent_done := 0.; glob_log10relerr := 0.; glob_iter := 0; glob_orig_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_iter := 1000; glob_hmin := 0.1*10^(-10); glob_h := 0.1; glob_initial_pass := true; days_in_year := 365; djd_debug2 := true; glob_display_flag := true; glob_html_log := true; glob_warned := false; glob_optimal_start := 0.; glob_dump := false; glob_log10abserr := 0.; glob_reached_optimal_h := false; glob_max_minutes := 0.; glob_small_float := 0.1*10^(-50); djd_debug := true; glob_max_opt_iter := 10; 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/nonlinear2postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"); 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 := 0.0;"); omniout_str(ALWAYS, "x_end := 0.2 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 1;"); 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, "return(2.0/(1.0 - 2.0*x));"); omniout_str(ALWAYS, "end;"); 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_m1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_norms[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_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_1st_rel_error[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_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 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_higher[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_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_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[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 <= 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_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_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; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.2; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; 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 := expt(10.0, glob_log10_abserr); glob_relerr := expt(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]*expt(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]* expt(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(); if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(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]/( expt(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*expt(glob_h, calc_term - 1)/factorial_1(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]/( expt(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*expt(glob_h, calc_term - 1)/factorial_1(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]/( expt(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*expt(glob_h, calc_term - 1)/factorial_1(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 ) = y * y;"); 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, "2012-08-12T23:50:02-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"); 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, " 119 "); logitem_str(html_log_file, "nonlinear2 diffeq.mxt"); logitem_str(html_log_file, "nonlinear2 maple results"); logitem_str(html_log_file, "1st test with c++"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.2 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0/(1.0 - 2.0*x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 1e-05 y[1] (analytic) = 2.000040000800016000320006400128 y[1] (numeric) = 2.0000400008000160003200064046094 absolute error = 4.4814e-27 relative error = 2.2406551860000000000000000000000e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 2e-05 y[1] (analytic) = 2.0000800032001280051202048081923 y[1] (numeric) = 2.0000800032001280051202048171559 absolute error = 8.9636e-27 relative error = 4.4816207280000000000000000000001e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 3e-05 y[1] (analytic) = 2.0001200072004320259215552933176 y[1] (numeric) = 2.0001200072004320259215553067642 absolute error = 1.34466e-26 relative error = 6.7228966020000000000000000000000e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 4e-05 y[1] (analytic) = 2.0001600128010240819265541243299 y[1] (numeric) = 2.0001600128010240819265541422603 absolute error = 1.79304e-26 relative error = 8.9644827840000000000000000000002e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 5e-05 y[1] (analytic) = 2.0002000200020002000200020002 y[1] (numeric) = 2.000200020002000200020002022615 absolute error = 2.24150e-26 relative error = 1.1206379250000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 6e-05 y[1] (analytic) = 2.0002400288034564147697723726847 y[1] (numeric) = 2.0002400288034564147697723995851 absolute error = 2.69004e-26 relative error = 1.3448585976000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 7e-05 y[1] (analytic) = 2.0002800392054887684275798611806 y[1] (numeric) = 2.0002800392054887684275798925672 absolute error = 3.13866e-26 relative error = 1.5691102938000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 8e-05 y[1] (analytic) = 2.0003200512081933109297487598016 y[1] (numeric) = 2.0003200512081933109297487956752 absolute error = 3.58736e-26 relative error = 1.7933930112000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.36 NO POLE x[1] = 9e-05 y[1] (analytic) = 2.0003600648116660998979816366946 y[1] (numeric) = 2.0003600648116660998979816770561 absolute error = 4.03615e-26 relative error = 2.0177117465000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0001 y[1] (analytic) = 2.0004000800160032006401280256051 y[1] (numeric) = 2.0004000800160032006401280704553 absolute error = 4.48502e-26 relative error = 2.2420614980000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00011 y[1] (analytic) = 2.0004400968213006861509532097061 y[1] (numeric) = 2.0004400968213006861509532590458 absolute error = 4.93397e-26 relative error = 2.4664422633000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00012 y[1] (analytic) = 2.0004801152276546371129070977034 y[1] (numeric) = 2.0004801152276546371129071515334 absolute error = 5.38300e-26 relative error = 2.6908540400000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00013 y[1] (analytic) = 2.00052013523516114189689319223 y[1] (numeric) = 2.000520135235161141896893250551 absolute error = 5.83210e-26 relative error = 2.9152918270000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00014 y[1] (analytic) = 2.0005601568439162965630376505422 y[1] (numeric) = 2.000560156843916296563037713355 absolute error = 6.28128e-26 relative error = 3.1397606207999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00015 y[1] (analytic) = 2.0006001800540162048614584375313 y[1] (numeric) = 2.0006001800540162048614585048368 absolute error = 6.73055e-26 relative error = 3.3642654174999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00016 y[1] (analytic) = 2.0006402048655569782330345710627 y[1] (numeric) = 2.0006402048655569782330346428618 absolute error = 7.17991e-26 relative error = 3.5888062144000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00017 y[1] (analytic) = 2.0006802312786347358101754596563 y[1] (numeric) = 2.0006802312786347358101755359496 absolute error = 7.62933e-26 relative error = 3.8133680139000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00018 y[1] (analytic) = 2.0007202592933456044175903325197 y[1] (numeric) = 2.0007202592933456044175904133081 absolute error = 8.07884e-26 relative error = 4.0379658088000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00019 y[1] (analytic) = 2.0007602889097857185730577619495 y[1] (numeric) = 2.0007602889097857185730578472339 absolute error = 8.52844e-26 relative error = 4.2625995964000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 2.0008003201280512204881952781112 y[1] (numeric) = 2.0008003201280512204881953678923 absolute error = 8.97811e-26 relative error = 4.4872593780000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00021 y[1] (analytic) = 2.000840352948238260069229076212 y[1] (numeric) = 2.0008403529482382600692291704906 absolute error = 9.42786e-26 relative error = 4.7119501494000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00022 y[1] (analytic) = 2.0008803873704429949177638160791 y[1] (numeric) = 2.000880387370442994917763914856 absolute error = 9.87769e-26 relative error = 4.9366719081999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00023 y[1] (analytic) = 2.0009204233947615903315525141565 y[1] (numeric) = 2.0009204233947615903315526174326 absolute error = 1.032761e-25 relative error = 5.1614296497000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.76 NO POLE x[1] = 0.00024 y[1] (analytic) = 2.0009604610212902193052665279334 y[1] (numeric) = 2.0009604610212902193052666357095 absolute error = 1.077761e-25 relative error = 5.3862183736000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00025 y[1] (analytic) = 2.0010005002501250625312656328164 y[1] (numeric) = 2.0010005002501250625312657450933 absolute error = 1.122769e-25 relative error = 5.6110380775000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00026 y[1] (analytic) = 2.0010405410813623084003681914596 y[1] (numeric) = 2.001040541081362308400368308238 absolute error = 1.167784e-25 relative error = 5.8358837615999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00027 y[1] (analytic) = 2.0010805835150981530026214155644 y[1] (numeric) = 2.0010805835150981530026215368452 absolute error = 1.212808e-25 relative error = 6.0607654184000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00028 y[1] (analytic) = 2.0011206275514288001280717201633 y[1] (numeric) = 2.0011206275514288001280718459473 absolute error = 1.257840e-25 relative error = 6.2856780480000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00029 y[1] (analytic) = 2.0011606731904504612675351703988 y[1] (numeric) = 2.0011606731904504612675353006869 absolute error = 1.302881e-25 relative error = 6.5106266451000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 2.0012007204322593556133680208125 y[1] (numeric) = 2.0012007204322593556133681556054 absolute error = 1.347929e-25 relative error = 6.7356012130000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00031 y[1] (analytic) = 2.0012407692769517100602373471552 y[1] (numeric) = 2.0012407692769517100602374864538 absolute error = 1.392986e-25 relative error = 6.9606117434000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00032 y[1] (analytic) = 2.0012808197246237592058917707333 y[1] (numeric) = 2.0012808197246237592058919145383 absolute error = 1.438050e-25 relative error = 7.1856482399999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00033 y[1] (analytic) = 2.0013208717753717453519322753017 y[1] (numeric) = 2.001320871775371745351932423614 absolute error = 1.483123e-25 relative error = 7.4107206941000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00034 y[1] (analytic) = 2.0013609254292919185045831165192 y[1] (numeric) = 2.0013609254292919185045832693396 absolute error = 1.528204e-25 relative error = 7.6358241064000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00035 y[1] (analytic) = 2.0014009806864805363754628239768 y[1] (numeric) = 2.001400980686480536375462981306 absolute error = 1.573292e-25 relative error = 7.8609534779999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00036 y[1] (analytic) = 2.001441037547033864382355295813 y[1] (numeric) = 2.0014410375470338643823554576519 absolute error = 1.618389e-25 relative error = 8.0861187995999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00037 y[1] (analytic) = 2.0014810960110481756499809859296 y[1] (numeric) = 2.001481096011048175649981152279 absolute error = 1.663494e-25 relative error = 8.3113150721999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00038 y[1] (analytic) = 2.0015211560786197510107681838197 y[1] (numeric) = 2.0015211560786197510107683546804 absolute error = 1.708607e-25 relative error = 8.5365422934000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.17 NO POLE x[1] = 0.00039 y[1] (analytic) = 2.0015612177498448790056243870219 y[1] (numeric) = 2.0015612177498448790056245623947 absolute error = 1.753728e-25 relative error = 8.7618004607999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 2.001601281024819855884707766213 y[1] (numeric) = 2.0016012810248198558847079460987 absolute error = 1.798857e-25 relative error = 8.9870895719999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00041 y[1] (analytic) = 2.0016413459036409856081987229528 y[1] (numeric) = 2.0016413459036409856081989073523 absolute error = 1.843995e-25 relative error = 9.2124146205000000000000000000001e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00042 y[1] (analytic) = 2.0016814123864045798470715400937 y[1] (numeric) = 2.0016814123864045798470717290077 absolute error = 1.889140e-25 relative error = 9.4377656119999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00043 y[1] (analytic) = 2.0017214804732069579838661248674 y[1] (numeric) = 2.0017214804732069579838663182968 absolute error = 1.934294e-25 relative error = 9.6631525357999999999999999999999e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00044 y[1] (analytic) = 2.0017615501641444471134598446633 y[1] (numeric) = 2.0017615501641444471134600426089 absolute error = 1.979456e-25 relative error = 9.8885703936000000000000000000000e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00045 y[1] (analytic) = 2.00180162145931338204383945551 y[1] (numeric) = 2.0018016214593133820438396579726 absolute error = 2.024626e-25 relative error = 1.0114019183000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00046 y[1] (analytic) = 2.0018416943588101052968731232734 y[1] (numeric) = 2.0018416943588101052968733302539 absolute error = 2.069805e-25 relative error = 1.0339503897000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00047 y[1] (analytic) = 2.0018817688627309671090825375853 y[1] (numeric) = 2.0018817688627309671090827490845 absolute error = 2.114992e-25 relative error = 1.0565019537600000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00048 y[1] (analytic) = 2.0019218449711723254324151185138 y[1] (numeric) = 2.0019218449711723254324153345324 absolute error = 2.160186e-25 relative error = 1.0790561107200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00049 y[1] (analytic) = 2.0019619226842305459350163159897 y[1] (numeric) = 2.0019619226842305459350165365286 absolute error = 2.205389e-25 relative error = 1.1016138593900000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 2.002002002002002002002002002002 y[1] (numeric) = 2.002002002002002002002002227062 absolute error = 2.250600e-25 relative error = 1.1241747000000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00051 y[1] (analytic) = 2.0020420829245830747362309555747 y[1] (numeric) = 2.0020420829245830747362311851566 absolute error = 2.295819e-25 relative error = 1.1467386323100000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00052 y[1] (analytic) = 2.0020821654520701529590774405382 y[1] (numeric) = 2.0020821654520701529590776746428 absolute error = 2.341046e-25 relative error = 1.1693056560800000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00053 y[1] (analytic) = 2.0021222495845596332112038761087 y[1] (numeric) = 2.0021222495845596332112041147368 absolute error = 2.386281e-25 relative error = 1.1918757710700000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=1.56 NO POLE x[1] = 0.00054 y[1] (analytic) = 2.0021623353221479197533336002883 y[1] (numeric) = 2.0021623353221479197533338434408 absolute error = 2.431525e-25 relative error = 1.2144494765000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00055 y[1] (analytic) = 2.0022024226649314245670237260987 y[1] (numeric) = 2.0022024226649314245670239737763 absolute error = 2.476776e-25 relative error = 1.2370257732000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00056 y[1] (analytic) = 2.0022425116130065673554380906615 y[1] (numeric) = 2.0022425116130065673554383428651 absolute error = 2.522036e-25 relative error = 1.2596056598400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00057 y[1] (analytic) = 2.0022826021664697755441202971387 y[1] (numeric) = 2.0022826021664697755441205538691 absolute error = 2.567304e-25 relative error = 1.2821886367200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00058 y[1] (analytic) = 2.0023226943254174842817668495455 y[1] (numeric) = 2.0023226943254174842817671108034 absolute error = 2.612579e-25 relative error = 1.3047742041800000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00059 y[1] (analytic) = 2.0023627880899461364410003804489 y[1] (numeric) = 2.0023627880899461364410006462353 absolute error = 2.657864e-25 relative error = 1.3273638602400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 2.0024028834601521826191429715659 y[1] (numeric) = 2.0024028834601521826191432418815 absolute error = 2.703156e-25 relative error = 1.3499561064000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00061 y[1] (analytic) = 2.0024429804361320811389895672721 y[1] (numeric) = 2.0024429804361320811389898421177 absolute error = 2.748456e-25 relative error = 1.3725514418400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00062 y[1] (analytic) = 2.0024830790179822980495814810365 y[1] (numeric) = 2.002483079017982298049581760413 absolute error = 2.793765e-25 relative error = 1.3951503657000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00063 y[1] (analytic) = 2.0025231792057993071269799947934 y[1] (numeric) = 2.0025231792057993071269802787016 absolute error = 2.839082e-25 relative error = 1.4177523783400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00064 y[1] (analytic) = 2.0025632809996795898750400512656 y[1] (numeric) = 2.0025632809996795898750403397063 absolute error = 2.884407e-25 relative error = 1.4403574795200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00065 y[1] (analytic) = 2.002603384399719635526184039251 y[1] (numeric) = 2.002603384399719635526184332225 absolute error = 2.929740e-25 relative error = 1.4629656690000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00066 y[1] (analytic) = 2.0026434894060159410421756718869 y[1] (numeric) = 2.002643489406015941042175969395 absolute error = 2.975081e-25 relative error = 1.4855769465400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00067 y[1] (analytic) = 2.0026835960186650111148939579036 y[1] (numeric) = 2.0026835960186650111148942599466 absolute error = 3.020430e-25 relative error = 1.5081913119000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00068 y[1] (analytic) = 2.0027237042377633581671072658816 y[1] (numeric) = 2.0027237042377633581671075724603 absolute error = 3.065787e-25 relative error = 1.5308087648400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE memory used=19.0MB, alloc=4.0MB, time=1.98 x[1] = 0.00069 y[1] (analytic) = 2.0027638140634075023532474815245 y[1] (numeric) = 2.0027638140634075023532477926398 absolute error = 3.111153e-25 relative error = 1.5534298044300000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 2.0028039254956939715601842579611 y[1] (numeric) = 2.0028039254956939715601845736138 absolute error = 3.156527e-25 relative error = 1.5760539311000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00071 y[1] (analytic) = 2.0028440385347193014079993590899 y[1] (numeric) = 2.0028440385347193014079996792808 absolute error = 3.201909e-25 relative error = 1.5986811446100000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00072 y[1] (analytic) = 2.0028841531805800352507610959782 y[1] (numeric) = 2.0028841531805800352507614207081 absolute error = 3.247299e-25 relative error = 1.6213114447200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00073 y[1] (analytic) = 2.0029242694333727241772988563302 y[1] (numeric) = 2.0029242694333727241772991856 absolute error = 3.292698e-25 relative error = 1.6439453304600000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00074 y[1] (analytic) = 2.002964387293193927011977727036 y[1] (numeric) = 2.0029643872931939270119780608464 absolute error = 3.338104e-25 relative error = 1.6665818030400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00075 y[1] (analytic) = 2.0030045067601402103154732098147 y[1] (numeric) = 2.0030045067601402103154735481666 absolute error = 3.383519e-25 relative error = 1.6892218607500000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00076 y[1] (analytic) = 2.0030446278343081483855460299655 y[1] (numeric) = 2.0030446278343081483855463728597 absolute error = 3.428942e-25 relative error = 1.7118650040800000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00077 y[1] (analytic) = 2.0030847505157943232578170382389 y[1] (numeric) = 2.0030847505157943232578173856761 absolute error = 3.474372e-25 relative error = 1.7345107335600000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00078 y[1] (analytic) = 2.0031248748046953247065422058411 y[1] (numeric) = 2.0031248748046953247065425578222 absolute error = 3.519811e-25 relative error = 1.7571600474200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00079 y[1] (analytic) = 2.0031650007011077502453877125859 y[1] (numeric) = 2.0031650007011077502453880691117 absolute error = 3.565258e-25 relative error = 1.7798124461800000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0008 y[1] (analytic) = 2.0032051282051282051282051282051 y[1] (numeric) = 2.0032051282051282051282054892765 absolute error = 3.610714e-25 relative error = 1.8024684288000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00081 y[1] (analytic) = 2.0032452573168533023498066868327 y[1] (numeric) = 2.0032452573168533023498070524504 absolute error = 3.656177e-25 relative error = 1.8251269966300000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00082 y[1] (analytic) = 2.0032853880363796626467406546737 y[1] (numeric) = 2.0032853880363796626467410248386 absolute error = 3.701649e-25 relative error = 1.8477891478200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00083 y[1] (analytic) = 2.0033255203638039144980667908728 y[1] (numeric) = 2.0033255203638039144980671655858 absolute error = 3.747130e-25 relative error = 1.8704548821000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00084 y[1] (analytic) = 2.0033656542992226941261319015947 y[1] (numeric) = 2.0033656542992226941261322808564 absolute error = 3.792617e-25 relative error = 1.8931227017200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.0MB, time=2.40 NO POLE x[1] = 0.00085 y[1] (analytic) = 2.0034057898427326454973454873285 y[1] (numeric) = 2.0034057898427326454973458711398 absolute error = 3.838113e-25 relative error = 1.9157941039500000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00086 y[1] (analytic) = 2.0034459269944304203229554834315 y[1] (numeric) = 2.0034459269944304203229558717933 absolute error = 3.883618e-25 relative error = 1.9384690885200000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00087 y[1] (analytic) = 2.0034860657544126780598240939234 y[1] (numeric) = 2.0034860657544126780598244868365 absolute error = 3.929131e-25 relative error = 1.9611471560300000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00088 y[1] (analytic) = 2.0035262061227760859112037185446 y[1] (numeric) = 2.0035262061227760859112041160098 absolute error = 3.974652e-25 relative error = 1.9838283062400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00089 y[1] (analytic) = 2.0035663480996173188275129730921 y[1] (numeric) = 2.0035663480996173188275133751102 absolute error = 4.020181e-25 relative error = 2.0065125389100000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 2.0036064916850330595071128030455 y[1] (numeric) = 2.0036064916850330595071132096173 absolute error = 4.065718e-25 relative error = 2.0291998538000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00091 y[1] (analytic) = 2.0036466368791199983970826904967 y[1] (numeric) = 2.0036466368791199983970831016231 absolute error = 4.111264e-25 relative error = 2.0518907497600000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00092 y[1] (analytic) = 2.0036867836819748336939969543961 y[1] (numeric) = 2.0036867836819748336939973700779 absolute error = 4.156818e-25 relative error = 2.0745847274400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00093 y[1] (analytic) = 2.0037269320936942713447011441281 y[1] (numeric) = 2.0037269320936942713447015643661 absolute error = 4.202380e-25 relative error = 2.0972817866000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00094 y[1] (analytic) = 2.0037670821143750250470885264297 y[1] (numeric) = 2.0037670821143750250470889512247 absolute error = 4.247950e-25 relative error = 2.1199819270000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00095 y[1] (analytic) = 2.0038072337441138162508766656648 y[1] (numeric) = 2.0038072337441138162508770950176 absolute error = 4.293528e-25 relative error = 2.1426851484000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00096 y[1] (analytic) = 2.0038473869830073741583840974671 y[1] (numeric) = 2.0038473869830073741583845313786 absolute error = 4.339115e-25 relative error = 2.1653919496000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00097 y[1] (analytic) = 2.0038875418311524357253070957658 y[1] (numeric) = 2.0038875418311524357253075342367 absolute error = 4.384709e-25 relative error = 2.1881013322700000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00098 y[1] (analytic) = 2.0039276982886457456614965332051 y[1] (numeric) = 2.0039276982886457456614969762363 absolute error = 4.430312e-25 relative error = 2.2108142942400000000000000000000e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00099 y[1] (analytic) = 2.0039678563555840564317348349732 y[1] (numeric) = 2.0039678563555840564317352825656 absolute error = 4.475924e-25 relative error = 2.2335308352400000000000000000001e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.0MB, time=2.82 NO POLE x[1] = 0.001 y[1] (analytic) = 2.0040080160320641282565130260521 y[1] (numeric) = 2.0040080160320641282565134782064 absolute error = 4.521543e-25 relative error = 2.2562499570000000000000000000000e-23 % "good digits = ", 24 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = y * y; Iterations = 100 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Expected Time Remaining = 8 Minutes 58 Seconds Optimized Time Remaining = 8 Minutes 53 Seconds Time to Timeout = 57 Seconds Percent Done = 0.505 % > quit memory used=26.8MB, alloc=4.0MB, time=2.84