|\^/| 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 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > 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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then 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 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_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, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > 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; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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 > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > 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)); > glob_total_exp_sec := glob_optimal_expect_sec + total_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)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_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; 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_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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)); glob_total_exp_sec := glob_optimal_expect_sec + total_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)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_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 > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; > #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 > rad_c := glob_large_float; > ord_no := 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))) or ((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)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := 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 > rad_c := glob_large_float; > ord_no := 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) * omniabs(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 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > 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 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > 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 (reached_interval()) 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 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > 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 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > 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 (reached_interval()) 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 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > 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, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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 rad_c := glob_large_float; ord_no := 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]) or 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 or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := 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 rad_c := glob_large_float; ord_no := 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)*omniabs(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 if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if 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 if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if 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 reached_interval() 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 if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if 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 if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if 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 reached_interval() 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; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > 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; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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 > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , 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 * (1.0); > 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 * (3.0); > 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 * (4.0); > 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 * (5.0); > 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 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 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; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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*1.0/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*3.0/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*4.0/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*5.0/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 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > 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 > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_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, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > 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 if 0; > 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 > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > 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 2 > 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 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 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, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > 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 5 > 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 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 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 > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > 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 + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_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 + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_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 6 > 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 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_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 + arr_aa[iii_att]*arr_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 > # End Function number 14 > # Begin Function number 15 > 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 6 > 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 6 > 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 > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > 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 > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 24 > # Begin Function number 25 > 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 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > 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 > # End Function number 25 > # Begin Function number 26 > 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 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > 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 > # End Function number 26 > # Begin Function number 27 > 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 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > 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 > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > 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 > # End Function number 29 > # Begin Function number 30 > 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 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > 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 > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #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, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_log10normmin := 0.1; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-50; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_log10abserr := 0.0; > glob_log10relerr := 0.0; > glob_max_minutes := 0.0; > #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_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > 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_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_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_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 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_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > 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_norms[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; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_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_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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[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 <=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; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=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 <=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; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_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_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[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_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #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)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > 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; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > 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 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > 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 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > 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(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3; > 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 ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #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 > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > 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 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-13T01:25:55-06:00") > ; > 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_good_digits(html_log_file,array_last_rel_error[1]) > ; > 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 4 > 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 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 156 ") > ; > logitem_str(html_log_file,"nonlinear2 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear2 maple results") > ; > logitem_str(html_log_file,"Languages compared - single equations") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > 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, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_log10normmin := 0.1; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-50); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_log10abserr := 0.; glob_log10relerr := 0.; glob_max_minutes := 0.; 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_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); 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_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_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_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); 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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[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_1st_rel_error[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_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_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_m1[term] := 0.; term := term + 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 <= 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; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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 <= 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; 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_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[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_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; 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); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; 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; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; 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; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; 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(); glob_log10normmin := -glob_large_float; 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 glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; 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 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, "2013-01-13T01:25:55-06:00"); 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_good_digits(html_log_file, array_last_rel_error[1]); 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_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 156 "); logitem_str(html_log_file, "nonlinear2 diffeq.mxt"); logitem_str(html_log_file, "nonlinear2 maple results"); logitem_str(html_log_file, "Languages compared - single equations"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > 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_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #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 Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.2 estimated_steps = 200 step_error = 5.0000000000000000000000000000000e-13 est_needed_step_err = 5.0000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.3435207994572800000000000000000e-70 max_value3 = 1.3435207994572800000000000000000e-70 value3 = 1.3435207994572800000000000000000e-70 best_h = 0.001 START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.5 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.001 y[1] (analytic) = 2.0040080160320641282565130260521 y[1] (numeric) = 2.0040080160320641282565130260521 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.499 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.002 y[1] (analytic) = 2.0080321285140562248995983935743 y[1] (numeric) = 2.0080321285140562248995983935743 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.498 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.003 y[1] (analytic) = 2.012072434607645875251509054326 y[1] (numeric) = 2.012072434607645875251509054326 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.497 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.004 y[1] (analytic) = 2.0161290322580645161290322580645 y[1] (numeric) = 2.0161290322580645161290322580646 absolute error = 1e-31 relative error = 4.9600000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.496 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.005 y[1] (analytic) = 2.020202020202020202020202020202 y[1] (numeric) = 2.0202020202020202020202020202021 absolute error = 1e-31 relative error = 4.9500000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.495 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.006 y[1] (analytic) = 2.0242914979757085020242914979757 y[1] (numeric) = 2.0242914979757085020242914979758 absolute error = 1e-31 relative error = 4.9400000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.494 Order of pole = 1 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.14 x[1] = 0.007 y[1] (analytic) = 2.0283975659229208924949290060852 y[1] (numeric) = 2.0283975659229208924949290060853 absolute error = 1e-31 relative error = 4.9300000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.493 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.008 y[1] (analytic) = 2.032520325203252032520325203252 y[1] (numeric) = 2.0325203252032520325203252032521 absolute error = 1e-31 relative error = 4.9200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.492 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.009 y[1] (analytic) = 2.0366598778004073319755600814664 y[1] (numeric) = 2.0366598778004073319755600814665 absolute error = 1e-31 relative error = 4.9100000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.491 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 2.0408163265306122448979591836735 y[1] (numeric) = 2.0408163265306122448979591836736 absolute error = 1e-31 relative error = 4.8999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.49 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.011 y[1] (analytic) = 2.0449897750511247443762781186094 y[1] (numeric) = 2.0449897750511247443762781186095 absolute error = 1e-31 relative error = 4.8900000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.489 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.012 y[1] (analytic) = 2.049180327868852459016393442623 y[1] (numeric) = 2.049180327868852459016393442623 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.488 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.013 y[1] (analytic) = 2.0533880903490759753593429158111 y[1] (numeric) = 2.0533880903490759753593429158111 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.487 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.014 y[1] (analytic) = 2.0576131687242798353909465020576 y[1] (numeric) = 2.0576131687242798353909465020576 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.486 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.015 y[1] (analytic) = 2.0618556701030927835051546391753 y[1] (numeric) = 2.0618556701030927835051546391752 absolute error = 1e-31 relative error = 4.8499999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.485 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.016 y[1] (analytic) = 2.0661157024793388429752066115702 y[1] (numeric) = 2.0661157024793388429752066115702 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.484 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.017 y[1] (analytic) = 2.0703933747412008281573498964803 y[1] (numeric) = 2.0703933747412008281573498964803 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.483 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.018 y[1] (analytic) = 2.0746887966804979253112033195021 y[1] (numeric) = 2.074688796680497925311203319502 absolute error = 1e-31 relative error = 4.8199999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.482 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.019 y[1] (analytic) = 2.0790020790020790020790020790021 y[1] (numeric) = 2.079002079002079002079002079002 absolute error = 1e-31 relative error = 4.8100000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.481 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 2.0833333333333333333333333333333 y[1] (numeric) = 2.0833333333333333333333333333333 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.48 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.021 y[1] (analytic) = 2.0876826722338204592901878914405 y[1] (numeric) = 2.0876826722338204592901878914405 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.479 Order of pole = 1 memory used=7.6MB, alloc=3.8MB, time=0.29 TOP MAIN SOLVE Loop x[1] = 0.022 y[1] (analytic) = 2.0920502092050209205020920502092 y[1] (numeric) = 2.0920502092050209205020920502092 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.478 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.023 y[1] (analytic) = 2.0964360587002096436058700209644 y[1] (numeric) = 2.0964360587002096436058700209644 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.477 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.024 y[1] (analytic) = 2.1008403361344537815126050420168 y[1] (numeric) = 2.1008403361344537815126050420168 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.476 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.025 y[1] (analytic) = 2.1052631578947368421052631578947 y[1] (numeric) = 2.1052631578947368421052631578947 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.475 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.026 y[1] (analytic) = 2.109704641350210970464135021097 y[1] (numeric) = 2.109704641350210970464135021097 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.474 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.027 y[1] (analytic) = 2.114164904862579281183932346723 y[1] (numeric) = 2.114164904862579281183932346723 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.473 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.028 y[1] (analytic) = 2.1186440677966101694915254237288 y[1] (numeric) = 2.1186440677966101694915254237288 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.472 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.029 y[1] (analytic) = 2.1231422505307855626326963906582 y[1] (numeric) = 2.1231422505307855626326963906582 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.471 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 2.1276595744680851063829787234043 y[1] (numeric) = 2.1276595744680851063829787234043 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.47 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.031 y[1] (analytic) = 2.1321961620469083155650319829424 y[1] (numeric) = 2.1321961620469083155650319829425 absolute error = 1e-31 relative error = 4.6900000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.469 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.032 y[1] (analytic) = 2.1367521367521367521367521367521 y[1] (numeric) = 2.1367521367521367521367521367522 absolute error = 1e-31 relative error = 4.6800000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.468 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.033 y[1] (analytic) = 2.1413276231263383297644539614561 y[1] (numeric) = 2.1413276231263383297644539614562 absolute error = 1e-31 relative error = 4.6700000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.467 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.034 y[1] (analytic) = 2.1459227467811158798283261802575 y[1] (numeric) = 2.1459227467811158798283261802576 absolute error = 1e-31 relative error = 4.6600000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.466 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.035 y[1] (analytic) = 2.1505376344086021505376344086022 y[1] (numeric) = 2.1505376344086021505376344086022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.465 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.036 y[1] (analytic) = 2.1551724137931034482758620689655 y[1] (numeric) = 2.1551724137931034482758620689656 absolute error = 1e-31 relative error = 4.6400000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.464 Order of pole = 1 memory used=11.4MB, alloc=3.9MB, time=0.45 TOP MAIN SOLVE Loop x[1] = 0.037 y[1] (analytic) = 2.1598272138228941684665226781857 y[1] (numeric) = 2.1598272138228941684665226781858 absolute error = 1e-31 relative error = 4.6300000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.463 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.038 y[1] (analytic) = 2.1645021645021645021645021645022 y[1] (numeric) = 2.1645021645021645021645021645022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.462 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.039 y[1] (analytic) = 2.1691973969631236442516268980477 y[1] (numeric) = 2.1691973969631236442516268980478 absolute error = 1e-31 relative error = 4.6100000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.461 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 2.1739130434782608695652173913043 y[1] (numeric) = 2.1739130434782608695652173913044 absolute error = 1e-31 relative error = 4.6000000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.46 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.041 y[1] (analytic) = 2.1786492374727668845315904139434 y[1] (numeric) = 2.1786492374727668845315904139434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.459 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.042 y[1] (analytic) = 2.1834061135371179039301310043668 y[1] (numeric) = 2.1834061135371179039301310043669 absolute error = 1e-31 relative error = 4.5800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.458 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.043 y[1] (analytic) = 2.1881838074398249452954048140044 y[1] (numeric) = 2.1881838074398249452954048140045 absolute error = 1e-31 relative error = 4.5700000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.457 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.044 y[1] (analytic) = 2.1929824561403508771929824561404 y[1] (numeric) = 2.1929824561403508771929824561405 absolute error = 1e-31 relative error = 4.5599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.456 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.045 y[1] (analytic) = 2.1978021978021978021978021978022 y[1] (numeric) = 2.1978021978021978021978021978023 absolute error = 1e-31 relative error = 4.5500000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.455 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.046 y[1] (analytic) = 2.2026431718061674008810572687225 y[1] (numeric) = 2.2026431718061674008810572687226 absolute error = 1e-31 relative error = 4.5399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.454 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.047 y[1] (analytic) = 2.2075055187637969094922737306843 y[1] (numeric) = 2.2075055187637969094922737306845 absolute error = 2e-31 relative error = 9.0600000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.453 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.048 y[1] (analytic) = 2.2123893805309734513274336283186 y[1] (numeric) = 2.2123893805309734513274336283188 absolute error = 2e-31 relative error = 9.0399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.452 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.049 y[1] (analytic) = 2.2172949002217294900221729490022 y[1] (numeric) = 2.2172949002217294900221729490024 absolute error = 2e-31 relative error = 9.0200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.451 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 2.2222222222222222222222222222222 y[1] (numeric) = 2.2222222222222222222222222222224 absolute error = 2e-31 relative error = 9.0000000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.45 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.051 y[1] (analytic) = 2.22717149220489977728285077951 y[1] (numeric) = 2.2271714922048997772828507795102 absolute error = 2e-31 relative error = 8.9800000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.449 Order of pole = 1 memory used=15.2MB, alloc=4.0MB, time=0.61 TOP MAIN SOLVE Loop x[1] = 0.052 y[1] (analytic) = 2.2321428571428571428571428571429 y[1] (numeric) = 2.232142857142857142857142857143 absolute error = 1e-31 relative error = 4.4799999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.448 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.053 y[1] (analytic) = 2.2371364653243847874720357941834 y[1] (numeric) = 2.2371364653243847874720357941836 absolute error = 2e-31 relative error = 8.9400000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.447 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.054 y[1] (analytic) = 2.2421524663677130044843049327354 y[1] (numeric) = 2.2421524663677130044843049327356 absolute error = 2e-31 relative error = 8.9200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.446 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.055 y[1] (analytic) = 2.2471910112359550561797752808989 y[1] (numeric) = 2.2471910112359550561797752808991 absolute error = 2e-31 relative error = 8.8999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.445 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.056 y[1] (analytic) = 2.2522522522522522522522522522523 y[1] (numeric) = 2.2522522522522522522522522522525 absolute error = 2e-31 relative error = 8.8799999999999999999999999999998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.444 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.057 y[1] (analytic) = 2.2573363431151241534988713318284 y[1] (numeric) = 2.2573363431151241534988713318287 absolute error = 3e-31 relative error = 1.3290000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.443 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.058 y[1] (analytic) = 2.2624434389140271493212669683258 y[1] (numeric) = 2.2624434389140271493212669683261 absolute error = 3e-31 relative error = 1.3260000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.442 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.059 y[1] (analytic) = 2.2675736961451247165532879818594 y[1] (numeric) = 2.2675736961451247165532879818597 absolute error = 3e-31 relative error = 1.3230000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.441 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 2.2727272727272727272727272727273 y[1] (numeric) = 2.2727272727272727272727272727276 absolute error = 3e-31 relative error = 1.3200000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.44 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.061 y[1] (analytic) = 2.277904328018223234624145785877 y[1] (numeric) = 2.2779043280182232346241457858773 absolute error = 3e-31 relative error = 1.3170000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.439 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.062 y[1] (analytic) = 2.283105022831050228310502283105 y[1] (numeric) = 2.2831050228310502283105022831053 absolute error = 3e-31 relative error = 1.3140000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.438 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.063 y[1] (analytic) = 2.2883295194508009153318077803204 y[1] (numeric) = 2.2883295194508009153318077803206 absolute error = 2e-31 relative error = 8.7399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.437 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.064 y[1] (analytic) = 2.2935779816513761467889908256881 y[1] (numeric) = 2.2935779816513761467889908256883 absolute error = 2e-31 relative error = 8.7199999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.436 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.065 y[1] (analytic) = 2.2988505747126436781609195402299 y[1] (numeric) = 2.2988505747126436781609195402301 absolute error = 2e-31 relative error = 8.6999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.435 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.066 y[1] (analytic) = 2.3041474654377880184331797235023 y[1] (numeric) = 2.3041474654377880184331797235025 absolute error = 2e-31 relative error = 8.6800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 memory used=19.0MB, alloc=4.0MB, time=0.77 Real estimate of pole used Radius of convergence = 0.434 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.067 y[1] (analytic) = 2.3094688221709006928406466512702 y[1] (numeric) = 2.3094688221709006928406466512704 absolute error = 2e-31 relative error = 8.6600000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.433 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.068 y[1] (analytic) = 2.3148148148148148148148148148148 y[1] (numeric) = 2.314814814814814814814814814815 absolute error = 2e-31 relative error = 8.6400000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.432 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.069 y[1] (analytic) = 2.3201856148491879350348027842227 y[1] (numeric) = 2.3201856148491879350348027842229 absolute error = 2e-31 relative error = 8.6200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.431 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 2.3255813953488372093023255813953 y[1] (numeric) = 2.3255813953488372093023255813955 absolute error = 2e-31 relative error = 8.6000000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.43 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.071 y[1] (analytic) = 2.3310023310023310023310023310023 y[1] (numeric) = 2.3310023310023310023310023310025 absolute error = 2e-31 relative error = 8.5800000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.429 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.072 y[1] (analytic) = 2.3364485981308411214953271028037 y[1] (numeric) = 2.3364485981308411214953271028039 absolute error = 2e-31 relative error = 8.5600000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.428 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.073 y[1] (analytic) = 2.3419203747072599531615925058548 y[1] (numeric) = 2.341920374707259953161592505855 absolute error = 2e-31 relative error = 8.5400000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.427 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.074 y[1] (analytic) = 2.3474178403755868544600938967136 y[1] (numeric) = 2.3474178403755868544600938967138 absolute error = 2e-31 relative error = 8.5200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.426 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.075 y[1] (analytic) = 2.3529411764705882352941176470588 y[1] (numeric) = 2.352941176470588235294117647059 absolute error = 2e-31 relative error = 8.5000000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.425 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.076 y[1] (analytic) = 2.3584905660377358490566037735849 y[1] (numeric) = 2.3584905660377358490566037735851 absolute error = 2e-31 relative error = 8.4800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.424 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.077 y[1] (analytic) = 2.3640661938534278959810874704492 y[1] (numeric) = 2.3640661938534278959810874704494 absolute error = 2e-31 relative error = 8.4599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.423 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.078 y[1] (analytic) = 2.3696682464454976303317535545024 y[1] (numeric) = 2.3696682464454976303317535545026 absolute error = 2e-31 relative error = 8.4399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.422 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.079 y[1] (analytic) = 2.3752969121140142517814726840855 y[1] (numeric) = 2.3752969121140142517814726840857 absolute error = 2e-31 relative error = 8.4200000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.421 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 2.3809523809523809523809523809524 y[1] (numeric) = 2.3809523809523809523809523809526 absolute error = 2e-31 relative error = 8.3999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.42 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.081 y[1] (analytic) = 2.3866348448687350835322195704057 y[1] (numeric) = 2.3866348448687350835322195704059 absolute error = 2e-31 relative error = 8.3800000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 memory used=22.8MB, alloc=4.1MB, time=0.93 Real estimate of pole used Radius of convergence = 0.419 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.082 y[1] (analytic) = 2.3923444976076555023923444976077 y[1] (numeric) = 2.3923444976076555023923444976078 absolute error = 1e-31 relative error = 4.1799999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.418 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.083 y[1] (analytic) = 2.3980815347721822541966426858513 y[1] (numeric) = 2.3980815347721822541966426858515 absolute error = 2e-31 relative error = 8.3400000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.417 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.084 y[1] (analytic) = 2.4038461538461538461538461538462 y[1] (numeric) = 2.4038461538461538461538461538463 absolute error = 1e-31 relative error = 4.1599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.416 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.085 y[1] (analytic) = 2.4096385542168674698795180722892 y[1] (numeric) = 2.4096385542168674698795180722893 absolute error = 1e-31 relative error = 4.1499999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.415 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.086 y[1] (analytic) = 2.4154589371980676328502415458937 y[1] (numeric) = 2.4154589371980676328502415458939 absolute error = 2e-31 relative error = 8.2800000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.414 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.087 y[1] (analytic) = 2.4213075060532687651331719128329 y[1] (numeric) = 2.4213075060532687651331719128331 absolute error = 2e-31 relative error = 8.2600000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.413 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.088 y[1] (analytic) = 2.4271844660194174757281553398058 y[1] (numeric) = 2.427184466019417475728155339806 absolute error = 2e-31 relative error = 8.2400000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.412 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.089 y[1] (analytic) = 2.43309002433090024330900243309 y[1] (numeric) = 2.4330900243309002433090024330902 absolute error = 2e-31 relative error = 8.2200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.411 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 2.4390243902439024390243902439024 y[1] (numeric) = 2.4390243902439024390243902439026 absolute error = 2e-31 relative error = 8.2000000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.41 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.091 y[1] (analytic) = 2.4449877750611246943765281173594 y[1] (numeric) = 2.4449877750611246943765281173596 absolute error = 2e-31 relative error = 8.1800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.409 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.092 y[1] (analytic) = 2.4509803921568627450980392156863 y[1] (numeric) = 2.4509803921568627450980392156865 absolute error = 2e-31 relative error = 8.1599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.408 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.093 y[1] (analytic) = 2.4570024570024570024570024570025 y[1] (numeric) = 2.4570024570024570024570024570027 absolute error = 2e-31 relative error = 8.1399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.407 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.094 y[1] (analytic) = 2.4630541871921182266009852216749 y[1] (numeric) = 2.4630541871921182266009852216751 absolute error = 2e-31 relative error = 8.1199999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.406 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.095 y[1] (analytic) = 2.4691358024691358024691358024691 y[1] (numeric) = 2.4691358024691358024691358024694 absolute error = 3e-31 relative error = 1.2150000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.405 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.096 y[1] (analytic) = 2.4752475247524752475247524752475 y[1] (numeric) = 2.4752475247524752475247524752478 absolute error = 3e-31 relative error = 1.2120000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 memory used=26.7MB, alloc=4.1MB, time=1.09 Real estimate of pole used Radius of convergence = 0.404 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.097 y[1] (analytic) = 2.4813895781637717121588089330025 y[1] (numeric) = 2.4813895781637717121588089330028 absolute error = 3e-31 relative error = 1.2090000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.403 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.098 y[1] (analytic) = 2.4875621890547263681592039800995 y[1] (numeric) = 2.4875621890547263681592039800998 absolute error = 3e-31 relative error = 1.2060000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.402 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.099 y[1] (analytic) = 2.4937655860349127182044887780549 y[1] (numeric) = 2.4937655860349127182044887780552 absolute error = 3e-31 relative error = 1.2030000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.401 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 2.5 y[1] (numeric) = 2.5000000000000000000000000000003 absolute error = 3e-31 relative error = 1.2000000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.4 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 2.5062656641604010025062656641604 y[1] (numeric) = 2.5062656641604010025062656641607 absolute error = 3e-31 relative error = 1.1970000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.399 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 2.5125628140703517587939698492462 y[1] (numeric) = 2.5125628140703517587939698492465 absolute error = 3e-31 relative error = 1.1940000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.398 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 2.5188916876574307304785894206549 y[1] (numeric) = 2.5188916876574307304785894206552 absolute error = 3e-31 relative error = 1.1910000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.397 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 2.5252525252525252525252525252525 y[1] (numeric) = 2.5252525252525252525252525252528 absolute error = 3e-31 relative error = 1.1880000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.396 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = 2.5316455696202531645569620253165 y[1] (numeric) = 2.5316455696202531645569620253167 absolute error = 2e-31 relative error = 7.8999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.395 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 2.5380710659898477157360406091371 y[1] (numeric) = 2.5380710659898477157360406091373 absolute error = 2e-31 relative error = 7.8799999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.394 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 2.544529262086513994910941475827 y[1] (numeric) = 2.5445292620865139949109414758272 absolute error = 2e-31 relative error = 7.8599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.393 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 2.5510204081632653061224489795918 y[1] (numeric) = 2.5510204081632653061224489795921 absolute error = 3e-31 relative error = 1.1760000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.392 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 2.5575447570332480818414322250639 y[1] (numeric) = 2.5575447570332480818414322250642 absolute error = 3e-31 relative error = 1.1730000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.391 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 2.5641025641025641025641025641026 y[1] (numeric) = 2.5641025641025641025641025641028 absolute error = 2e-31 relative error = 7.7999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.39 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.111 y[1] (analytic) = 2.5706940874035989717223650385604 y[1] (numeric) = 2.5706940874035989717223650385606 absolute error = 2e-31 relative error = 7.7800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.389 Order of pole = 1 memory used=30.5MB, alloc=4.1MB, time=1.26 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 2.5773195876288659793814432989691 y[1] (numeric) = 2.5773195876288659793814432989693 absolute error = 2e-31 relative error = 7.7599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.388 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = 2.5839793281653746770025839793282 y[1] (numeric) = 2.5839793281653746770025839793284 absolute error = 2e-31 relative error = 7.7399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.387 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 2.5906735751295336787564766839378 y[1] (numeric) = 2.5906735751295336787564766839381 absolute error = 3e-31 relative error = 1.1580000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.386 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 2.5974025974025974025974025974026 y[1] (numeric) = 2.5974025974025974025974025974029 absolute error = 3e-31 relative error = 1.1550000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.385 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.116 y[1] (analytic) = 2.6041666666666666666666666666667 y[1] (numeric) = 2.604166666666666666666666666667 absolute error = 3e-31 relative error = 1.1520000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.384 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 2.6109660574412532637075718015666 y[1] (numeric) = 2.6109660574412532637075718015669 absolute error = 3e-31 relative error = 1.1490000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.383 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 2.6178010471204188481675392670157 y[1] (numeric) = 2.617801047120418848167539267016 absolute error = 3e-31 relative error = 1.1460000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.382 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 2.6246719160104986876640419947507 y[1] (numeric) = 2.624671916010498687664041994751 absolute error = 3e-31 relative error = 1.1430000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.381 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 2.6315789473684210526315789473684 y[1] (numeric) = 2.6315789473684210526315789473688 absolute error = 4e-31 relative error = 1.5200000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.38 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 2.6385224274406332453825857519789 y[1] (numeric) = 2.6385224274406332453825857519793 absolute error = 4e-31 relative error = 1.5160000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.379 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.122 y[1] (analytic) = 2.6455026455026455026455026455026 y[1] (numeric) = 2.6455026455026455026455026455031 absolute error = 5e-31 relative error = 1.8900000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.378 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 2.6525198938992042440318302387268 y[1] (numeric) = 2.6525198938992042440318302387272 absolute error = 4e-31 relative error = 1.5080000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.377 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 2.6595744680851063829787234042553 y[1] (numeric) = 2.6595744680851063829787234042557 absolute error = 4e-31 relative error = 1.5040000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.376 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 2.6666666666666666666666666666667 y[1] (numeric) = 2.666666666666666666666666666667 absolute error = 3e-31 relative error = 1.1250000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.375 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 2.673796791443850267379679144385 y[1] (numeric) = 2.6737967914438502673796791443854 absolute error = 4e-31 relative error = 1.4960000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.374 Order of pole = 1 memory used=34.3MB, alloc=4.1MB, time=1.42 TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 2.6809651474530831099195710455764 y[1] (numeric) = 2.6809651474530831099195710455768 absolute error = 4e-31 relative error = 1.4920000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.373 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 2.6881720430107526881720430107527 y[1] (numeric) = 2.6881720430107526881720430107531 absolute error = 4e-31 relative error = 1.4880000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.372 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 2.695417789757412398921832884097 y[1] (numeric) = 2.6954177897574123989218328840974 absolute error = 4e-31 relative error = 1.4840000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.371 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 2.7027027027027027027027027027027 y[1] (numeric) = 2.7027027027027027027027027027031 absolute error = 4e-31 relative error = 1.4800000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.37 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 2.7100271002710027100271002710027 y[1] (numeric) = 2.7100271002710027100271002710031 absolute error = 4e-31 relative error = 1.4760000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.369 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = 2.7173913043478260869565217391304 y[1] (numeric) = 2.7173913043478260869565217391308 absolute error = 4e-31 relative error = 1.4720000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.368 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = 2.7247956403269754768392370572207 y[1] (numeric) = 2.7247956403269754768392370572211 absolute error = 4e-31 relative error = 1.4680000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.367 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 2.7322404371584699453551912568306 y[1] (numeric) = 2.732240437158469945355191256831 absolute error = 4e-31 relative error = 1.4640000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.366 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 2.739726027397260273972602739726 y[1] (numeric) = 2.7397260273972602739726027397264 absolute error = 4e-31 relative error = 1.4600000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.365 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 2.7472527472527472527472527472527 y[1] (numeric) = 2.7472527472527472527472527472531 absolute error = 4e-31 relative error = 1.4560000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.364 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 2.7548209366391184573002754820937 y[1] (numeric) = 2.754820936639118457300275482094 absolute error = 3e-31 relative error = 1.0890000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.363 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 2.7624309392265193370165745856354 y[1] (numeric) = 2.7624309392265193370165745856357 absolute error = 3e-31 relative error = 1.0860000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.362 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = 2.7700831024930747922437673130194 y[1] (numeric) = 2.7700831024930747922437673130197 absolute error = 3e-31 relative error = 1.0830000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.361 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 2.7777777777777777777777777777778 y[1] (numeric) = 2.7777777777777777777777777777781 absolute error = 3e-31 relative error = 1.0800000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.36 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = 2.7855153203342618384401114206128 y[1] (numeric) = 2.7855153203342618384401114206131 absolute error = 3e-31 relative error = 1.0770000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.359 Order of pole = 1 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.59 x[1] = 0.142 y[1] (analytic) = 2.7932960893854748603351955307263 y[1] (numeric) = 2.7932960893854748603351955307265 absolute error = 2e-31 relative error = 7.1599999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.358 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = 2.8011204481792717086834733893557 y[1] (numeric) = 2.801120448179271708683473389356 absolute error = 3e-31 relative error = 1.0710000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.357 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 2.8089887640449438202247191011236 y[1] (numeric) = 2.8089887640449438202247191011239 absolute error = 3e-31 relative error = 1.0680000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.356 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 2.8169014084507042253521126760563 y[1] (numeric) = 2.8169014084507042253521126760566 absolute error = 3e-31 relative error = 1.0650000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.355 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 2.8248587570621468926553672316384 y[1] (numeric) = 2.8248587570621468926553672316387 absolute error = 3e-31 relative error = 1.0620000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.354 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 2.83286118980169971671388101983 y[1] (numeric) = 2.8328611898016997167138810198303 absolute error = 3e-31 relative error = 1.0590000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.353 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 2.8409090909090909090909090909091 y[1] (numeric) = 2.8409090909090909090909090909094 absolute error = 3e-31 relative error = 1.0560000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.352 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = 2.8490028490028490028490028490028 y[1] (numeric) = 2.8490028490028490028490028490032 absolute error = 4e-31 relative error = 1.4040000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.351 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 2.8571428571428571428571428571429 y[1] (numeric) = 2.8571428571428571428571428571432 absolute error = 3e-31 relative error = 1.0500000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.35 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 2.8653295128939828080229226361032 y[1] (numeric) = 2.8653295128939828080229226361035 absolute error = 3e-31 relative error = 1.0470000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.349 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 2.8735632183908045977011494252874 y[1] (numeric) = 2.8735632183908045977011494252877 absolute error = 3e-31 relative error = 1.0440000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.348 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 2.8818443804034582132564841498559 y[1] (numeric) = 2.8818443804034582132564841498563 absolute error = 4e-31 relative error = 1.3880000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.347 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 2.8901734104046242774566473988439 y[1] (numeric) = 2.8901734104046242774566473988443 absolute error = 4e-31 relative error = 1.3840000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.346 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 2.8985507246376811594202898550725 y[1] (numeric) = 2.8985507246376811594202898550728 absolute error = 3e-31 relative error = 1.0350000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.345 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 2.9069767441860465116279069767442 y[1] (numeric) = 2.9069767441860465116279069767445 absolute error = 3e-31 relative error = 1.0320000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.344 Order of pole = 1 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=1.76 x[1] = 0.157 y[1] (analytic) = 2.9154518950437317784256559766764 y[1] (numeric) = 2.9154518950437317784256559766767 absolute error = 3e-31 relative error = 1.0290000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.343 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 2.9239766081871345029239766081871 y[1] (numeric) = 2.9239766081871345029239766081875 absolute error = 4e-31 relative error = 1.3680000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.342 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 2.9325513196480938416422287390029 y[1] (numeric) = 2.9325513196480938416422287390033 absolute error = 4e-31 relative error = 1.3640000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.341 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 2.9411764705882352941176470588235 y[1] (numeric) = 2.9411764705882352941176470588239 absolute error = 4e-31 relative error = 1.3600000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.34 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 2.9498525073746312684365781710914 y[1] (numeric) = 2.9498525073746312684365781710918 absolute error = 4e-31 relative error = 1.3560000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.339 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 2.9585798816568047337278106508876 y[1] (numeric) = 2.9585798816568047337278106508879 absolute error = 3e-31 relative error = 1.0140000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.338 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 2.967359050445103857566765578635 y[1] (numeric) = 2.9673590504451038575667655786353 absolute error = 3e-31 relative error = 1.0110000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.337 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 2.9761904761904761904761904761905 y[1] (numeric) = 2.9761904761904761904761904761908 absolute error = 3e-31 relative error = 1.0080000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.336 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 2.9850746268656716417910447761194 y[1] (numeric) = 2.9850746268656716417910447761197 absolute error = 3e-31 relative error = 1.0050000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.335 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = 2.9940119760479041916167664670659 y[1] (numeric) = 2.9940119760479041916167664670662 absolute error = 3e-31 relative error = 1.0020000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.334 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 3.003003003003003003003003003003 y[1] (numeric) = 3.0030030030030030030030030030033 absolute error = 3e-31 relative error = 9.9900000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.333 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 3.0120481927710843373493975903614 y[1] (numeric) = 3.0120481927710843373493975903617 absolute error = 3e-31 relative error = 9.9600000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.332 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 3.0211480362537764350453172205438 y[1] (numeric) = 3.0211480362537764350453172205441 absolute error = 3e-31 relative error = 9.9300000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.331 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 3.030303030303030303030303030303 y[1] (numeric) = 3.0303030303030303030303030303033 absolute error = 3e-31 relative error = 9.9000000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.33 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 3.0395136778115501519756838905775 y[1] (numeric) = 3.0395136778115501519756838905778 absolute error = 3e-31 relative error = 9.8700000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.329 Order of pole = 1 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=1.92 x[1] = 0.172 y[1] (analytic) = 3.048780487804878048780487804878 y[1] (numeric) = 3.0487804878048780487804878048783 absolute error = 3e-31 relative error = 9.8400000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.328 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 3.0581039755351681957186544342508 y[1] (numeric) = 3.058103975535168195718654434251 absolute error = 2e-31 relative error = 6.5399999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.327 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 3.0674846625766871165644171779141 y[1] (numeric) = 3.0674846625766871165644171779143 absolute error = 2e-31 relative error = 6.5200000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.326 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 3.0769230769230769230769230769231 y[1] (numeric) = 3.0769230769230769230769230769233 absolute error = 2e-31 relative error = 6.5000000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.325 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = 3.0864197530864197530864197530864 y[1] (numeric) = 3.0864197530864197530864197530866 absolute error = 2e-31 relative error = 6.4800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.324 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 3.0959752321981424148606811145511 y[1] (numeric) = 3.0959752321981424148606811145513 absolute error = 2e-31 relative error = 6.4600000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.323 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 3.1055900621118012422360248447205 y[1] (numeric) = 3.1055900621118012422360248447207 absolute error = 2e-31 relative error = 6.4400000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.322 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = 3.115264797507788161993769470405 y[1] (numeric) = 3.1152647975077881619937694704052 absolute error = 2e-31 relative error = 6.4200000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.321 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 3.125 y[1] (numeric) = 3.1250000000000000000000000000002 absolute error = 2e-31 relative error = 6.4000000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.32 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 3.1347962382445141065830721003135 y[1] (numeric) = 3.1347962382445141065830721003137 absolute error = 2e-31 relative error = 6.3800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.319 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 3.1446540880503144654088050314465 y[1] (numeric) = 3.1446540880503144654088050314468 absolute error = 3e-31 relative error = 9.5400000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.318 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = 3.1545741324921135646687697160883 y[1] (numeric) = 3.1545741324921135646687697160886 absolute error = 3e-31 relative error = 9.5100000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.317 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 3.1645569620253164556962025316456 y[1] (numeric) = 3.1645569620253164556962025316458 absolute error = 2e-31 relative error = 6.3199999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.316 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 3.1746031746031746031746031746032 y[1] (numeric) = 3.1746031746031746031746031746034 absolute error = 2e-31 relative error = 6.2999999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.315 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 3.1847133757961783439490445859873 y[1] (numeric) = 3.1847133757961783439490445859875 absolute error = 2e-31 relative error = 6.2799999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.314 Order of pole = 1 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.08 x[1] = 0.187 y[1] (analytic) = 3.1948881789137380191693290734824 y[1] (numeric) = 3.1948881789137380191693290734827 absolute error = 3e-31 relative error = 9.3900000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.313 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 3.2051282051282051282051282051282 y[1] (numeric) = 3.2051282051282051282051282051285 absolute error = 3e-31 relative error = 9.3600000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.312 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = 3.2154340836012861736334405144695 y[1] (numeric) = 3.2154340836012861736334405144698 absolute error = 3e-31 relative error = 9.3299999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.311 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 3.2258064516129032258064516129032 y[1] (numeric) = 3.2258064516129032258064516129036 absolute error = 4e-31 relative error = 1.2400000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.31 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 3.2362459546925566343042071197411 y[1] (numeric) = 3.2362459546925566343042071197415 absolute error = 4e-31 relative error = 1.2360000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.309 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 3.2467532467532467532467532467532 y[1] (numeric) = 3.2467532467532467532467532467536 absolute error = 4e-31 relative error = 1.2320000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.308 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.193 y[1] (analytic) = 3.2573289902280130293159609120521 y[1] (numeric) = 3.2573289902280130293159609120525 absolute error = 4e-31 relative error = 1.2280000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.307 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 3.267973856209150326797385620915 y[1] (numeric) = 3.2679738562091503267973856209154 absolute error = 4e-31 relative error = 1.2240000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.306 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 3.2786885245901639344262295081967 y[1] (numeric) = 3.2786885245901639344262295081971 absolute error = 4e-31 relative error = 1.2200000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.305 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 3.2894736842105263157894736842105 y[1] (numeric) = 3.2894736842105263157894736842109 absolute error = 4e-31 relative error = 1.2160000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.304 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 3.30033003300330033003300330033 y[1] (numeric) = 3.3003300330033003300330033003304 absolute error = 4e-31 relative error = 1.2120000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.303 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = 3.3112582781456953642384105960265 y[1] (numeric) = 3.3112582781456953642384105960269 absolute error = 4e-31 relative error = 1.2080000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.302 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 3.3222591362126245847176079734219 y[1] (numeric) = 3.3222591362126245847176079734223 absolute error = 4e-31 relative error = 1.2040000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.301 Order of pole = 1 Finished! diff ( y , x , 1 ) = y * y; Iterations = 200 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Time to Timeout = 2 Minutes 57 Seconds Percent Done = 100.5 % > quit memory used=52.8MB, alloc=4.1MB, time=2.21