|\^/| 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, 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 * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * 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)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > 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_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing 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_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float) 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_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) 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 for equation 1"); > 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, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*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)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; 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_sing := 0; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing 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 -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing 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 for equation 1") 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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 CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_m1[1] * array_const_2D0[1]; > #emit pre mult FULL LINEAR $eq_no = 1 i = 1 > #emit pre mult LINEAR - FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_x[1] * array_tmp1[1]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1]; > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp2[1] / (array_tmp4[1])); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp6[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1]; > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[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 CONST $eq_no = 1 i = 2 > array_tmp1[2] := array_m1[2] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp5[2] := ((array_tmp2[2] - ats(2,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp6[2]; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp9[2] := array_tmp8[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_tmp9[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 CONST $eq_no = 1 i = 3 > array_tmp1[3] := array_m1[3] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp5[3] := ((array_tmp2[3] - ats(3,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp6[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp6[3]; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp9[3] := array_tmp8[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_tmp9[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 CONST $eq_no = 1 i = 4 > array_tmp1[4] := array_m1[4] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp5[4] := ((array_tmp2[4] - ats(4,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp6[4]; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp9[4] := array_tmp8[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_tmp9[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 CONST $eq_no = 1 i = 5 > array_tmp1[5] := array_m1[5] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp5[5] := ((array_tmp2[5] - ats(5,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp6[5]; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp9[5] := array_tmp8[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_tmp9[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 CONST $eq_no = 1 i = 1 > array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1]; > #emit mult FULL LINEAR $eq_no = 1 i = 1 > array_tmp2[kkk] := array_tmp1[kkk-1] * array_x[2] + array_tmp1[kkk] * array_x[1]; > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit div FULL FULL $eq_no = 1 > array_tmp5[kkk] := ((array_tmp2[kkk] - ats(kkk,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp7[kkk] := array_tmp6[kkk]; > #emit div FULL FULL $eq_no = 1 > array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp9[kkk] := array_tmp8[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_tmp9[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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_m1[1]*array_const_2D0[1]; array_tmp2[1] := array_x[1]*array_tmp1[1]; array_tmp3[1] := array_x[1]*array_x[1]; array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1]; array_tmp5[1] := array_tmp2[1]/array_tmp4[1]; array_tmp6[1] := array_x[1]*array_x[1]; array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1]; array_tmp8[1] := array_tmp5[1]/array_tmp7[1]; array_tmp9[1] := array_const_0D0[1] + array_tmp8[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp9[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] := array_m1[2]*array_const_2D0[1]; array_tmp2[2] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp3[2] := 2*array_x[1]*array_x[2]; array_tmp4[2] := array_tmp3[2]; array_tmp5[2] := (array_tmp2[2] - ats(2, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp6[2] := 2*array_x[1]*array_x[2]; array_tmp7[2] := array_tmp6[2]; array_tmp8[2] := (array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[2] := array_tmp8[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp9[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] := array_m1[3]*array_const_2D0[1]; array_tmp2[3] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp3[3] := array_x[2]*array_x[2]; array_tmp4[3] := array_tmp3[3]; array_tmp5[3] := (array_tmp2[3] - ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp6[3] := array_x[2]*array_x[2]; array_tmp7[3] := array_tmp6[3]; array_tmp8[3] := (array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[3] := array_tmp8[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp9[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] := array_m1[4]*array_const_2D0[1]; array_tmp2[4] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[4] := array_tmp3[4]; array_tmp5[4] := (array_tmp2[4] - ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[4] := array_tmp6[4]; array_tmp8[4] := (array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[4] := array_tmp8[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp9[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] := array_m1[5]*array_const_2D0[1]; array_tmp2[5] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[5] := array_tmp3[5]; array_tmp5[5] := (array_tmp2[5] - ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[5] := array_tmp6[5]; array_tmp8[5] := (array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[5] := array_tmp8[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp9[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] := array_m1[kkk]*array_const_2D0[1]; array_tmp2[kkk] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[kkk] := array_tmp3[kkk]; array_tmp5[kkk] := ( array_tmp2[kkk] - ats(kkk, array_tmp4, array_tmp5, 2))/ array_tmp4[1]; array_tmp7[kkk] := array_tmp6[kkk]; array_tmp8[kkk] := ( array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/ array_tmp7[1]; array_tmp9[kkk] := array_tmp8[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_tmp9[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_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > 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 16 > # Begin Function number 17 > 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 17 > # Begin Function number 18 > 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 18 > # Begin Function number 19 > 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 19 > # Begin Function number 20 > 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 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > 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 22 > # Begin Function number 23 > 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 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > 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 26 > # Begin Function number 27 > 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 27 > # Begin Function number 28 > 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 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > 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 30 > # Begin Function number 31 > 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 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > 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 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(1.0 / (x * x + 0.000001)) ; > end; exact_soln_y := proc(x) return 1.0/(x*x + 0.1*10^(-5)) 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, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_0D000001, > #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_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_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_max_h := 0.1; > 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_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-200; > 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_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/sing1postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -2.0;"); > omniout_str(ALWAYS,"x_end := -1.5;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 500;"); > 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(1.0 / (x * x + 0.000001)) ;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #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_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= 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_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp9[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_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_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_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp9[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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_2D0[1] := 2.0; > array_const_0D000001 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D000001[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D000001[1] := 0.000001; > 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 := -2.0; > x_end := -1.5; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 500; > #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); > 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; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > 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_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 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);"); > 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,"2013-01-28T19:00:08-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing1") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);") > ; > 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," 165 ") > ; > logitem_str(html_log_file,"sing1 diffeq.mxt") > ; > logitem_str(html_log_file,"sing1 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > 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, 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_0D000001, 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_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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_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_max_h := 0.1; 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_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^(-200); 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_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/sing1postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.\ 000001) /( x * x + 0.000001);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -2.0;"); omniout_str(ALWAYS, "x_end := -1.5;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 500;"); 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(1.0 / (x * x + 0.000001)) ;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; 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_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := 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_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_0D000001 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D000001[term] := 0.; term := term + 1 end do; array_const_0D000001[1] := 0.1*10^(-5); 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 := -2.0; x_end := -1.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 500; 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); 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; if glob_max_h < glob_h then glob_h := glob_max_h 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_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 ) = m1 * 2.0 * x / (x * x + \ 0.000001) /( x * x + 0.000001);"); 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, "2013-01-28T19:00:08-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing1"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x\ / (x * x + 0.000001) /( x * x + 0.000001);"); 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, " 165 "); logitem_str(html_log_file, "sing1 diffeq.mxt"); logitem_str(html_log_file, "sing1 maple results") ; logitem_str(html_log_file, "All Tests - All Languages"); 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/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.0; x_end := -1.5; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 500; #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(1.0 / (x * x + 0.000001)) ; 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 = 0.5 estimated_steps = 500 step_error = 2.0000000000000000000000000000000e-13 est_needed_step_err = 2.0000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.0060551788397984124943226430006e-85 max_value3 = 1.0060551788397984124943226430006e-85 value3 = 1.0060551788397984124943226430006e-85 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.24999993750001562499609375097656 y[1] (numeric) = 0.24999993750001562499609375097656 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.999 y[1] (analytic) = 0.25025012499993743746875001564063 y[1] (numeric) = 0.25025012499993743746875001564063 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.999 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.998 y[1] (analytic) = 0.2505006882506409686360613275785 y[1] (numeric) = 0.25050068825064096863606132757849 absolute error = 1e-32 relative error = 3.9920050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.998 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.997 y[1] (analytic) = 0.2507516280049448221042575118919 y[1] (numeric) = 0.25075162800494482210425751189189 absolute error = 1e-32 relative error = 3.9880099999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.997 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.996 y[1] (analytic) = 0.25100294501755389095980263136427 y[1] (numeric) = 0.25100294501755389095980263136427 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.996 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.995 y[1] (analytic) = 0.25125464004506503223848286418229 y[1] (numeric) = 0.25125464004506503223848286418229 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.995 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.994 y[1] (analytic) = 0.251506713845972761319877053458 y[1] (numeric) = 0.251506713845972761319877053458 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.994 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.993 y[1] (analytic) = 0.25175916718067496632721138958472 y[1] (numeric) = 0.25175916718067496632721138958472 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.993 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.992 y[1] (analytic) = 0.25201200081147864261296122921374 y[1] (numeric) = 0.25201200081147864261296122921373 absolute error = 1e-32 relative error = 3.9680649999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.992 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.991 y[1] (analytic) = 0.25226521550260564741092641373211 y[1] (numeric) = 0.2522652155026056474109264137321 absolute error = 1e-32 relative error = 3.9640820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.991 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.25251881202019847473587163559717 y[1] (numeric) = 0.25251881202019847473587163559717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.99 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.989 y[1] (analytic) = 0.25277279113232605061219042284338 y[1] (numeric) = 0.25277279113232605061219042284338 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.989 Order of pole = 1 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.18 x[1] = -1.988 y[1] (analytic) = 0.25302715360898954871342018068669 y[1] (numeric) = 0.25302715360898954871342018068669 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.988 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.987 y[1] (analytic) = 0.25328190022212822649480645463595 y[1] (numeric) = 0.25328190022212822649480645463594 absolute error = 1e-32 relative error = 3.9481699999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.987 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.986 y[1] (analytic) = 0.25353703174562528190148717216711 y[1] (numeric) = 0.25353703174562528190148717216711 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.986 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.985 y[1] (analytic) = 0.25379254895531373073524209017452 y[1] (numeric) = 0.25379254895531373073524209017452 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.985 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.984 y[1] (analytic) = 0.25404845262898230476312903349553 y[1] (numeric) = 0.25404845262898230476312903349552 absolute error = 1e-32 relative error = 3.9362569999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.984 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.983 y[1] (analytic) = 0.25430474354638137065170676628631 y[1] (numeric) = 0.25430474354638137065170676628631 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.983 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.982 y[1] (analytic) = 0.25456142248922886981092450344613 y[1] (numeric) = 0.25456142248922886981092450344612 absolute error = 1e-32 relative error = 3.9283249999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.982 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.981 y[1] (analytic) = 0.25481849024121627923214015424673 y[1] (numeric) = 0.25481849024121627923214015424672 absolute error = 1e-32 relative error = 3.9243620000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.981 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.25507594758801459340511340549092 y[1] (numeric) = 0.25507594758801459340511340549091 absolute error = 1e-32 relative error = 3.9204010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.98 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.979 y[1] (analytic) = 0.25533379531728032739920570762953 y[1] (numeric) = 0.25533379531728032739920570762952 absolute error = 1e-32 relative error = 3.9164420000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.979 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.978 y[1] (analytic) = 0.25559203421866154119440713510723 y[1] (numeric) = 0.25559203421866154119440713510722 absolute error = 1e-32 relative error = 3.9124850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.978 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.977 y[1] (analytic) = 0.2558506650838038853481999626458 y[1] (numeric) = 0.2558506650838038853481999626458 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.977 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.976 y[1] (analytic) = 0.25610968870635666808466064313753 y[1] (numeric) = 0.25610968870635666808466064313753 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.976 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.975 y[1] (analytic) = 0.25636910588197894389259570130538 y[1] (numeric) = 0.25636910588197894389259570130538 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.975 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.974 y[1] (analytic) = 0.2566289174083456237199028813525 y[1] (numeric) = 0.2566289174083456237199028813525 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.974 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.973 y[1] (analytic) = 0.25688912408515360685174671759922 y[1] (numeric) = 0.25688912408515360685174671759922 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.973 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.972 y[1] (analytic) = 0.25714972671412793456053754578872 y[1] (numeric) = 0.25714972671412793456053754578873 absolute error = 1e-32 relative error = 3.8887850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.972 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.971 y[1] (analytic) = 0.25741072609902796561610485059624 y[1] (numeric) = 0.25741072609902796561610485059625 absolute error = 1e-32 relative error = 3.8848420000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.971 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.25767212304565357374485976323539 y[1] (numeric) = 0.2576721230456535737448597632354 absolute error = 1e-32 relative error = 3.8809010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.97 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.969 y[1] (analytic) = 0.2579339183618513671271474933208 y[1] (numeric) = 0.25793391836185136712714749332081 absolute error = 1e-32 relative error = 3.8769620000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.969 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.968 y[1] (analytic) = 0.25819611285752093002239851279039 y[1] (numeric) = 0.2581961128575209300223985127904 absolute error = 1e-32 relative error = 3.8730250000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.968 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.967 y[1] (analytic) = 0.25845870734462108661209741825597 y[1] (numeric) = 0.25845870734462108661209741825598 absolute error = 1e-32 relative error = 3.8690900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.967 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.966 y[1] (analytic) = 0.25872170263717618715100059324886 y[1] (numeric) = 0.25872170263717618715100059324887 memory used=7.6MB, alloc=4.2MB, time=0.39 absolute error = 1e-32 relative error = 3.8651570000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.966 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.965 y[1] (analytic) = 0.25898509955128241651744808514187 y[1] (numeric) = 0.25898509955128241651744808514188 absolute error = 1e-32 relative error = 3.8612260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.965 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.964 y[1] (analytic) = 0.25924889890511412525403151481465 y[1] (numeric) = 0.25924889890511412525403151481466 absolute error = 1e-32 relative error = 3.8572970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.964 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.963 y[1] (analytic) = 0.25951310151893018319029836221282 y[1] (numeric) = 0.25951310151893018319029836221283 absolute error = 1e-32 relative error = 3.8533699999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.963 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.962 y[1] (analytic) = 0.25977770821508035573959362973104 y[1] (numeric) = 0.25977770821508035573959362973105 absolute error = 1e-32 relative error = 3.8494450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.962 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.961 y[1] (analytic) = 0.26004271981801170296256268979868 y[1] (numeric) = 0.26004271981801170296256268979869 absolute error = 1e-32 relative error = 3.8455220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.961 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.26030813715427500149026408520822 y[1] (numeric) = 0.26030813715427500149026408520823 absolute error = 1e-32 relative error = 3.8416010000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.96 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.959 y[1] (analytic) = 0.26057396105253118940026818272072 y[1] (numeric) = 0.26057396105253118940026818272072 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.959 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.958 y[1] (analytic) = 0.26084019234355783413954689450188 y[1] (numeric) = 0.26084019234355783413954689450188 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.958 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.957 y[1] (analytic) = 0.26110683186025562358839119025549 y[1] (numeric) = 0.26110683186025562358839119025549 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.957 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.956 y[1] (analytic) = 0.26137388043765488036002683787004 y[1] (numeric) = 0.26137388043765488036002683787004 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.956 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.955 y[1] (analytic) = 0.26164133891292209943103474439996 y[1] (numeric) = 0.26164133891292209943103474439996 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.955 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.954 y[1] (analytic) = 0.26190920812536650919812043475881 y[1] (numeric) = 0.26190920812536650919812043475881 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.954 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.953 y[1] (analytic) = 0.26217748891644665605721761518113 y[1] (numeric) = 0.26217748891644665605721761518113 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.953 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.952 y[1] (analytic) = 0.26244618212977701260135343496124 y[1] (numeric) = 0.26244618212977701260135343496125 absolute error = 1e-32 relative error = 3.8103050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.952 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.951 y[1] (analytic) = 0.26271528861113460953414799592896 y[1] (numeric) = 0.26271528861113460953414799592897 absolute error = 1e-32 relative error = 3.8064020000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.951 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.2629848092084656913962678773786 y[1] (numeric) = 0.26298480920846569139626787737861 absolute error = 1e-32 relative error = 3.8025010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.95 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.949 y[1] (analytic) = 0.26325474477189239620260295761441 y[1] (numeric) = 0.26325474477189239620260295761442 absolute error = 1e-32 relative error = 3.7986020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.949 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.948 y[1] (analytic) = 0.26352509615371945908838763487544 y[1] (numeric) = 0.26352509615371945908838763487545 absolute error = 1e-32 relative error = 3.7947050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.948 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.947 y[1] (analytic) = 0.26379586420844094006294169320013 y[1] (numeric) = 0.26379586420844094006294169320015 absolute error = 2e-32 relative error = 7.5816200000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.947 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.946 y[1] (analytic) = 0.26406704979274697597016253590982 y[1] (numeric) = 0.26406704979274697597016253590983 absolute error = 1e-32 relative error = 3.7869170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.946 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.945 y[1] (analytic) = 0.26433865376553055675535933403577 y[1] (numeric) = 0.26433865376553055675535933403578 absolute error = 1e-32 relative error = 3.7830260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.945 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.944 y[1] (analytic) = 0.26461067698789432613848082247349 y[1] (numeric) = 0.2646106769878943261384808224735 absolute error = 1e-32 relative error = 3.7791370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.944 Order of pole = 1 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.61 x[1] = -1.943 y[1] (analytic) = 0.26488312032315740679425203628899 y[1] (numeric) = 0.264883120323157406794252036289 absolute error = 1e-32 relative error = 3.7752500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.943 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.942 y[1] (analytic) = 0.26515598463686225014020122687674 y[1] (numeric) = 0.26515598463686225014020122687675 absolute error = 1e-32 relative error = 3.7713650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.942 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.941 y[1] (analytic) = 0.26542927079678151083402654611223 y[1] (numeric) = 0.26542927079678151083402654611224 absolute error = 1e-32 relative error = 3.7674820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.941 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.26570297967292494608222284987171 y[1] (numeric) = 0.26570297967292494608222284987171 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.94 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.939 y[1] (analytic) = 0.26597711213754633986236216401106 y[1] (numeric) = 0.26597711213754633986236216401107 absolute error = 1e-32 relative error = 3.7597220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.939 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.938 y[1] (analytic) = 0.26625166906515045216189698989176 y[1] (numeric) = 0.26625166906515045216189698989176 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.938 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.937 y[1] (analytic) = 0.2665266513324999933368337166875 y[1] (numeric) = 0.2665266513324999933368337166875 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.937 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.936 y[1] (analytic) = 0.26680205981862262369410396796027 y[1] (numeric) = 0.26680205981862262369410396796027 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.936 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.935 y[1] (analytic) = 0.26707789540481797840194475440318 y[1] (numeric) = 0.26707789540481797840194475440318 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.935 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.934 y[1] (analytic) = 0.26735415897466471783308384734398 y[1] (numeric) = 0.26735415897466471783308384734398 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.934 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.933 y[1] (analytic) = 0.26763085141402760344601484280702 y[1] (numeric) = 0.26763085141402760344601484280702 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.933 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.932 y[1] (analytic) = 0.26790797361106459931013696795151 y[1] (numeric) = 0.26790797361106459931013696795151 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.932 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.931 y[1] (analytic) = 0.26818552645623399938102780493901 y[1] (numeric) = 0.26818552645623399938102780493901 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.931 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.26846351084230158063261278621902 y[1] (numeric) = 0.26846351084230158063261278621901 absolute error = 1e-32 relative error = 3.7249009999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.93 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.929 y[1] (analytic) = 0.26874192766434778215349356443706 y[1] (numeric) = 0.26874192766434778215349356443705 absolute error = 1e-32 relative error = 3.7210420000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.929 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.928 y[1] (analytic) = 0.26902077781977491031519819433254 y[1] (numeric) = 0.26902077781977491031519819433253 absolute error = 1e-32 relative error = 3.7171850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.928 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.927 y[1] (analytic) = 0.2693000622083143701206194978631 y[1] (numeric) = 0.26930006220831437012061949786309 absolute error = 1e-32 relative error = 3.7133300000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.927 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.926 y[1] (analytic) = 0.26957978173203392284141403222071 y[1] (numeric) = 0.2695797817320339228414140322207 absolute error = 1e-32 relative error = 3.7094770000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.926 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.925 y[1] (analytic) = 0.26985993729534497005364275833557 y[1] (numeric) = 0.26985993729534497005364275833555 absolute error = 2e-32 relative error = 7.4112520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.925 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.924 y[1] (analytic) = 0.27014052980500986418144582993519 y[1] (numeric) = 0.27014052980500986418144582993517 absolute error = 2e-32 relative error = 7.4035540000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.924 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.923 y[1] (analytic) = 0.27042156017014924565905790536868 y[1] (numeric) = 0.27042156017014924565905790536866 absolute error = 2e-32 relative error = 7.3958600000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.923 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.922 y[1] (analytic) = 0.27070302930224940682198704144599 y[1] (numeric) = 0.27070302930224940682198704144597 absolute error = 2e-32 relative error = 7.3881699999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.922 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.921 y[1] (analytic) = 0.27098493811516968263869957580018 y[1] (numeric) = 0.27098493811516968263869957580016 absolute error = 2e-32 relative error = 7.3804839999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.921 Order of pole = 1 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.84 x[1] = -1.92 y[1] (analytic) = 0.27126728752514986839467545717354 y[1] (numeric) = 0.27126728752514986839467545717352 absolute error = 2e-32 relative error = 7.3728020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.92 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.919 y[1] (analytic) = 0.2715500784508176644412232570694 y[1] (numeric) = 0.27155007845081766444122325706938 absolute error = 2e-32 relative error = 7.3651240000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.919 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.918 y[1] (analytic) = 0.27183331181319614812197160701058 y[1] (numeric) = 0.27183331181319614812197160701056 absolute error = 2e-32 relative error = 7.3574500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.918 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.917 y[1] (analytic) = 0.27211698853571127299048406891091 y[1] (numeric) = 0.27211698853571127299048406891089 absolute error = 2e-32 relative error = 7.3497799999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.917 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.916 y[1] (analytic) = 0.27240110954419939543297747760386 y[1] (numeric) = 0.27240110954419939543297747760385 absolute error = 1e-32 relative error = 3.6710570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.916 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.915 y[1] (analytic) = 0.27268567576691482881065961028854 y[1] (numeric) = 0.27268567576691482881065961028853 absolute error = 1e-32 relative error = 3.6672260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.915 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.914 y[1] (analytic) = 0.27297068813453742523674065355188 y[1] (numeric) = 0.27297068813453742523674065355187 absolute error = 1e-32 relative error = 3.6633970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.914 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.913 y[1] (analytic) = 0.27325614758018018510371437081406 y[1] (numeric) = 0.27325614758018018510371437081405 absolute error = 1e-32 relative error = 3.6595700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.913 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.912 y[1] (analytic) = 0.27354205503939689447704913772706 y[1] (numeric) = 0.27354205503939689447704913772705 absolute error = 1e-32 relative error = 3.6557450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.912 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.911 y[1] (analytic) = 0.27382841145018979047197612654378 y[1] (numeric) = 0.27382841145018979047197612654377 absolute error = 1e-32 relative error = 3.6519219999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.911 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.27411521775301725473061189917713 y[1] (numeric) = 0.27411521775301725473061189917713 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.91 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.909 y[1] (analytic) = 0.27440247489080153511720552910011 y[1] (numeric) = 0.2744024748908015351172055291001 absolute error = 1e-32 relative error = 3.6442820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.909 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.908 y[1] (analytic) = 0.27469018380893649574985613101623 y[1] (numeric) = 0.27469018380893649574985613101622 absolute error = 1e-32 relative error = 3.6404650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.908 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.907 y[1] (analytic) = 0.2749783454552953954876053510786 y[1] (numeric) = 0.27497834545529539548760535107859 absolute error = 1e-32 relative error = 3.6366500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.907 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.906 y[1] (analytic) = 0.27526696078023869499237097618198 y[1] (numeric) = 0.27526696078023869499237097618196 absolute error = 2e-32 relative error = 7.2656739999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.906 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.905 y[1] (analytic) = 0.27555603073662189248575237543076 y[1] (numeric) = 0.27555603073662189248575237543075 absolute error = 1e-32 relative error = 3.6290260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.905 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.904 y[1] (analytic) = 0.27584555627980338832130600733694 y[1] (numeric) = 0.27584555627980338832130600733693 absolute error = 1e-32 relative error = 3.6252170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.904 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.903 y[1] (analytic) = 0.27613553836765237849345972977376 y[1] (numeric) = 0.27613553836765237849345972977375 absolute error = 1e-32 relative error = 3.6214100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.903 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.902 y[1] (analytic) = 0.27642597796055677720480815346065 y[1] (numeric) = 0.27642597796055677720480815346063 absolute error = 2e-32 relative error = 7.2352099999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.902 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.901 y[1] (analytic) = 0.27671687602143116861410780114683 y[1] (numeric) = 0.27671687602143116861410780114681 absolute error = 2e-32 relative error = 7.2276039999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.901 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.27700823351572478788787039117164 y[1] (numeric) = 0.27700823351572478788787039117162 absolute error = 2e-32 relative error = 7.2200019999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.9 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.899 y[1] (analytic) = 0.27730005141142953167903517329312 y[1] (numeric) = 0.2773000514114295316790351732931 absolute error = 2e-32 relative error = 7.2124040000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.899 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.898 y[1] (analytic) = 0.27759233067908799815678692429086 y[1] (numeric) = 0.27759233067908799815678692429083 absolute error = 3e-32 relative error = 1.0807215000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.898 Order of pole = 1 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.06 x[1] = -1.897 y[1] (analytic) = 0.27788507229180155671217497867232 y[1] (numeric) = 0.2778850722918015567121749786723 absolute error = 2e-32 relative error = 7.1972200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.897 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.896 y[1] (analytic) = 0.27817827722523844746478054376621 y[1] (numeric) = 0.27817827722523844746478054376618 absolute error = 3e-32 relative error = 1.0784451000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.896 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.895 y[1] (analytic) = 0.2784719464576419106962745466059 y[1] (numeric) = 0.27847194645764191069627454660587 absolute error = 3e-32 relative error = 1.0773078000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.895 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.894 y[1] (analytic) = 0.27876608096983834633730640044134 y[1] (numeric) = 0.27876608096983834633730640044131 absolute error = 3e-32 relative error = 1.0761711000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.894 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.893 y[1] (analytic) = 0.27906068174524550363476537973182 y[1] (numeric) = 0.27906068174524550363476537973179 absolute error = 3e-32 relative error = 1.0750350000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.893 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.892 y[1] (analytic) = 0.27935574976988070112706077244658 y[1] (numeric) = 0.27935574976988070112706077244655 absolute error = 3e-32 relative error = 1.0738995000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.892 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.891 y[1] (analytic) = 0.27965128603236907705567465593104 y[1] (numeric) = 0.27965128603236907705567465593101 absolute error = 3e-32 relative error = 1.0727646000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.891 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.27994729152395187034185203609864 y[1] (numeric) = 0.27994729152395187034185203609861 absolute error = 3e-32 relative error = 1.0716303000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.89 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.889 y[1] (analytic) = 0.28024376723849473225790721801452 y[1] (numeric) = 0.28024376723849473225790721801448 absolute error = 4e-32 relative error = 1.4273288000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.889 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.888 y[1] (analytic) = 0.28054071417249606892324265789883 y[1] (numeric) = 0.2805407141724960689232426578988 absolute error = 3e-32 relative error = 1.0693635000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.888 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.887 y[1] (analytic) = 0.28083813332509541475579720116716 y[1] (numeric) = 0.28083813332509541475579720116713 absolute error = 3e-32 relative error = 1.0682310000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.887 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.886 y[1] (analytic) = 0.28113602569808183701026455743426 y[1] (numeric) = 0.28113602569808183701026455743423 absolute error = 3e-32 relative error = 1.0670991000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.886 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.885 y[1] (analytic) = 0.28143439229590237153505012065092 y[1] (numeric) = 0.28143439229590237153505012065089 absolute error = 3e-32 relative error = 1.0659678000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.885 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.884 y[1] (analytic) = 0.2817332341256704898805648300571 y[1] (numeric) = 0.28173323412567048988056483005707 absolute error = 3e-32 relative error = 1.0648371000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.884 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.883 y[1] (analytic) = 0.28203255219717459789208870487832 y[1] (numeric) = 0.28203255219717459789208870487828 absolute error = 4e-32 relative error = 1.4182760000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.883 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.882 y[1] (analytic) = 0.28233234752288656592107399224998 y[1] (numeric) = 0.28233234752288656592107399224994 absolute error = 4e-32 relative error = 1.4167700000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.882 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.881 y[1] (analytic) = 0.28263262111797029078939856343491 y[1] (numeric) = 0.28263262111797029078939856343488 absolute error = 3e-32 relative error = 1.0614486000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.881 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.28293337400029028964172429783717 y[1] (numeric) = 0.28293337400029028964172429783714 absolute error = 3e-32 relative error = 1.0603203000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.88 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.879 y[1] (analytic) = 0.28323460719042032582176272757193 y[1] (numeric) = 0.28323460719042032582176272757189 absolute error = 4e-32 relative error = 1.4122568000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.879 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.878 y[1] (analytic) = 0.28353632171165206690890119751565 y[1] (numeric) = 0.28353632171165206690890119751562 absolute error = 3e-32 relative error = 1.0580655000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.878 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.877 y[1] (analytic) = 0.28383851859000377505229724705021 y[1] (numeric) = 0.28383851859000377505229724705017 absolute error = 4e-32 relative error = 1.4092520000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.877 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.876 y[1] (analytic) = 0.28414119885422902974020686047559 y[1] (numeric) = 0.28414119885422902974020686047555 absolute error = 4e-32 relative error = 1.4077508000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.876 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.875 y[1] (analytic) = 0.28444436353582548314297368377637 y[1] (numeric) = 0.28444436353582548314297368377633 absolute error = 4e-32 relative error = 1.4062504000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.875 Order of pole = 1 memory used=22.8MB, alloc=4.3MB, time=1.29 TOP MAIN SOLVE Loop x[1] = -1.874 y[1] (analytic) = 0.2847480136690436481687712866937 y[1] (numeric) = 0.28474801366904364816877128669365 absolute error = 5e-32 relative error = 1.7559385000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.874 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.873 y[1] (analytic) = 0.28505215029089571937185908161898 y[1] (numeric) = 0.28505215029089571937185908161894 absolute error = 4e-32 relative error = 1.4032520000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.873 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.872 y[1] (analytic) = 0.28535677444116442685378461556022 y[1] (numeric) = 0.28535677444116442685378461556018 absolute error = 4e-32 relative error = 1.4017540000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.872 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.871 y[1] (analytic) = 0.28566188716241192329864064934375 y[1] (numeric) = 0.28566188716241192329864064934371 absolute error = 4e-32 relative error = 1.4002568000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.871 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.28596748949998870428416475044618 y[1] (numeric) = 0.28596748949998870428416475044614 absolute error = 4e-32 relative error = 1.3987604000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.87 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.869 y[1] (analytic) = 0.28627358250204256201115207367995 y[1] (numeric) = 0.28627358250204256201115207367991 absolute error = 4e-32 relative error = 1.3972648000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.869 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.868 y[1] (analytic) = 0.28658016721952757259433860879658 y[1] (numeric) = 0.28658016721952757259433860879654 absolute error = 4e-32 relative error = 1.3957700000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.868 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.867 y[1] (analytic) = 0.28688724470621311705860245747614 y[1] (numeric) = 0.2868872447062131170586024574761 absolute error = 4e-32 relative error = 1.3942760000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.867 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.866 y[1] (analytic) = 0.28719481601869293618502468583041 y[1] (numeric) = 0.28719481601869293618502468583037 absolute error = 4e-32 relative error = 1.3927828000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.866 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.865 y[1] (analytic) = 0.28750288221639421935204900429127 y[1] (numeric) = 0.28750288221639421935204900429123 absolute error = 4e-32 relative error = 1.3912904000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.865 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.864 y[1] (analytic) = 0.28781144436158672751768097655574 y[1] (numeric) = 0.28781144436158672751768097655571 absolute error = 3e-32 relative error = 1.0423491000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.864 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.863 y[1] (analytic) = 0.28812050351939195048937267522769 y[1] (numeric) = 0.28812050351939195048937267522765 absolute error = 4e-32 relative error = 1.3883080000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.863 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.862 y[1] (analytic) = 0.28843006075779229862894770618783 y[1] (numeric) = 0.2884300607577922986289477061878 absolute error = 3e-32 relative error = 1.0401135000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.862 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.861 y[1] (analytic) = 0.28874011714764032914063433893816 y[1] (numeric) = 0.28874011714764032914063433893813 absolute error = 3e-32 relative error = 1.0389966000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.861 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.28905067376266800709099112874577 y[1] (numeric) = 0.28905067376266800709099112874574 absolute error = 3e-32 relative error = 1.0378803000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.86 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.859 y[1] (analytic) = 0.28936173167949600131022992104476 y[1] (numeric) = 0.28936173167949600131022992104473 absolute error = 3e-32 relative error = 1.0367646000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.859 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.858 y[1] (analytic) = 0.2896732919776430153251655120772 y[1] (numeric) = 0.28967329197764301532516551207718 absolute error = 2e-32 relative error = 6.9043300000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.858 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.857 y[1] (analytic) = 0.28998535573953515347474952514898 y[1] (numeric) = 0.28998535573953515347474952514896 absolute error = 2e-32 relative error = 6.8969000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.857 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.856 y[1] (analytic) = 0.29029792405051532235987827227449 y[1] (numeric) = 0.29029792405051532235987827227447 absolute error = 2e-32 relative error = 6.8894739999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.856 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.855 y[1] (analytic) = 0.2906109979988526677799005296676 y[1] (numeric) = 0.29061099799885266777990052966759 absolute error = 1e-32 relative error = 3.4410260000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.855 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.854 y[1] (analytic) = 0.29092457867575204730899128593609 y[1] (numeric) = 0.29092457867575204730899128593608 absolute error = 1e-32 relative error = 3.4373170000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.854 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.853 y[1] (analytic) = 0.29123866717536353866630164753714 y[1] (numeric) = 0.29123866717536353866630164753713 absolute error = 1e-32 relative error = 3.4336100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.853 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.852 y[1] (analytic) = 0.29155326459479198403454323078919 y[1] (numeric) = 0.29155326459479198403454323078918 absolute error = 1e-32 relative error = 3.4299050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 memory used=26.7MB, alloc=4.4MB, time=1.51 Complex estimate of poles used for equation 1 Radius of convergence = 1.852 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.851 y[1] (analytic) = 0.29186837203410657048241755740029 y[1] (numeric) = 0.29186837203410657048241755740028 absolute error = 1e-32 relative error = 3.4262020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.851 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.29218399059635044664705722511111 y[1] (numeric) = 0.2921839905963504466470572251111 absolute error = 1e-32 relative error = 3.4225010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.85 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.849 y[1] (analytic) = 0.29250012138755037583340597086348 y[1] (numeric) = 0.29250012138755037583340597086347 absolute error = 1e-32 relative error = 3.4188020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.849 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.848 y[1] (analytic) = 0.29281676551672642568822920525138 y[1] (numeric) = 0.29281676551672642568822920525137 absolute error = 1e-32 relative error = 3.4151050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.848 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.847 y[1] (analytic) = 0.2931339240959016946072151984077 y[1] (numeric) = 0.29313392409590169460721519840769 absolute error = 1e-32 relative error = 3.4114100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.847 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.846 y[1] (analytic) = 0.2934515982401120750343998636037 y[1] (numeric) = 0.29345159824011207503439986360369 absolute error = 1e-32 relative error = 3.4077170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.846 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.845 y[1] (analytic) = 0.29376978906741605381392504052554 y[1] (numeric) = 0.29376978906741605381392504052554 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.845 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.844 y[1] (analytic) = 0.29408849769890454975492135044262 y[1] (numeric) = 0.29408849769890454975492135044262 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.844 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.843 y[1] (analytic) = 0.29440772525871078857109210545685 y[1] (numeric) = 0.29440772525871078857109210545685 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.843 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.842 y[1] (analytic) = 0.29472747287402021535736442904657 y[1] (numeric) = 0.29472747287402021535736442904657 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.842 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.841 y[1] (analytic) = 0.29504774167508044476676771068327 y[1] (numeric) = 0.29504774167508044476676771068326 absolute error = 1e-32 relative error = 3.3892820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.841 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.29536853279521124905149779906138 y[1] (numeric) = 0.29536853279521124905149779906137 absolute error = 1e-32 relative error = 3.3856010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.84 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.839 y[1] (analytic) = 0.29568984737081458413292796226524 y[1] (numeric) = 0.29568984737081458413292796226524 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.839 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.838 y[1] (analytic) = 0.29601168654138465386613463499539 y[1] (numeric) = 0.29601168654138465386613463499539 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.838 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.837 y[1] (analytic) = 0.2963340514495180126653173589524 y[1] (numeric) = 0.2963340514495180126653173589524 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.837 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.836 y[1] (analytic) = 0.29665694324092370665730812896389 y[1] (numeric) = 0.29665694324092370665730812896389 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.836 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.835 y[1] (analytic) = 0.29698036306443345353118561094503 y[1] (numeric) = 0.29698036306443345353118561094503 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.835 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.834 y[1] (analytic) = 0.29730431207201186125283442498522 y[1] (numeric) = 0.29730431207201186125283442498521 absolute error = 1e-32 relative error = 3.3635570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.834 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.833 y[1] (analytic) = 0.29762879141876668581411891460732 y[1] (numeric) = 0.29762879141876668581411891460732 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.833 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.832 y[1] (analytic) = 0.29795380226295912818717457858159 y[1] (numeric) = 0.29795380226295912818717457858159 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.832 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.831 y[1] (analytic) = 0.29827934576601417065515865180122 y[1] (numeric) = 0.29827934576601417065515865180122 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.831 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.29860542309253095269164421402723 y[1] (numeric) = 0.29860542309253095269164421402723 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.83 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.829 y[1] (analytic) = 0.29893203541029318656168970735152 y[1] (numeric) = 0.29893203541029318656168970735152 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.829 Order of pole = 1 memory used=30.5MB, alloc=4.4MB, time=1.74 TOP MAIN SOLVE Loop x[1] = -1.828 y[1] (analytic) = 0.29925918389027961281846788275624 y[1] (numeric) = 0.29925918389027961281846788275624 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.828 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.827 y[1] (analytic) = 0.29958686970667449587019500109349 y[1] (numeric) = 0.2995868697066744958701950010935 absolute error = 1e-32 relative error = 3.3379300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.827 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.826 y[1] (analytic) = 0.29991509403687815979296261228446 y[1] (numeric) = 0.29991509403687815979296261228447 absolute error = 1e-32 relative error = 3.3342770000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.826 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.825 y[1] (analytic) = 0.30024385806151756456594045683904 y[1] (numeric) = 0.30024385806151756456594045683905 absolute error = 1e-32 relative error = 3.3306260000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.825 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.824 y[1] (analytic) = 0.30057316296445692290629000440941 y[1] (numeric) = 0.30057316296445692290629000440941 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.824 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.823 y[1] (analytic) = 0.30090300993280835788200389368495 y[1] (numeric) = 0.30090300993280835788200389368495 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.823 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.822 y[1] (analytic) = 0.301233400156942601481767095372 y[1] (numeric) = 0.301233400156942601481767095372 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.822 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.821 y[1] (analytic) = 0.30156433483049973432182101432973 y[1] (numeric) = 0.30156433483049973432182101432973 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.821 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.30189581515039996667070200739584 y[1] (numeric) = 0.30189581515039996667070200739584 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.82 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.819 y[1] (analytic) = 0.3022278423168544609736209494669 y[1] (numeric) = 0.3022278423168544609736209494669 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.819 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.818 y[1] (analytic) = 0.30256041753337619605915056162778 y[1] (numeric) = 0.30256041753337619605915056162777 absolute error = 1e-32 relative error = 3.3051249999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.818 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.817 y[1] (analytic) = 0.30289354200679087321179225137741 y[1] (numeric) = 0.3028935420067908732117922513774 absolute error = 1e-32 relative error = 3.3014900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.817 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.816 y[1] (analytic) = 0.30322721694724786429490423629648 y[1] (numeric) = 0.30322721694724786429490423629647 absolute error = 1e-32 relative error = 3.2978570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.816 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.815 y[1] (analytic) = 0.30356144356823120210938775906692 y[1] (numeric) = 0.30356144356823120210938775906692 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.815 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.814 y[1] (analytic) = 0.30389622308657061317444828400439 y[1] (numeric) = 0.30389622308657061317444828400439 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.814 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.813 y[1] (analytic) = 0.30423155672245259311767372382468 y[1] (numeric) = 0.30423155672245259311767372382468 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.813 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.812 y[1] (analytic) = 0.30456744569943152486260201105884 y[1] (numeric) = 0.30456744569943152486260201105885 absolute error = 1e-32 relative error = 3.2833450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.812 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.811 y[1] (analytic) = 0.30490389124444083980288573238829 y[1] (numeric) = 0.3049038912444408398028857323883 absolute error = 1e-32 relative error = 3.2797220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.811 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.30524089458780422215310211742556 y[1] (numeric) = 0.30524089458780422215310211742557 absolute error = 1e-32 relative error = 3.2761010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.81 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.809 y[1] (analytic) = 0.30557845696324685666720244756121 y[1] (numeric) = 0.30557845696324685666720244756122 absolute error = 1e-32 relative error = 3.2724820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.809 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.808 y[1] (analytic) = 0.30591657960790671991654595708296 y[1] (numeric) = 0.30591657960790671991654595708297 absolute error = 1e-32 relative error = 3.2688650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.808 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.807 y[1] (analytic) = 0.30625526376234591532041956971135 y[1] (numeric) = 0.30625526376234591532041956971136 absolute error = 1e-32 relative error = 3.2652500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.807 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.806 y[1] (analytic) = 0.30659451067056205212290638105957 y[1] (numeric) = 0.30659451067056205212290638105958 absolute error = 1e-32 relative error = 3.2616370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.806 Order of pole = 1 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=1.96 x[1] = -1.805 y[1] (analytic) = 0.30693432157999966851093269360036 y[1] (numeric) = 0.30693432157999966851093269360037 absolute error = 1e-32 relative error = 3.2580260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.805 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.804 y[1] (analytic) = 0.30727469774156169906929566801058 y[1] (numeric) = 0.3072746977415616990692956680106 absolute error = 2e-32 relative error = 6.5088340000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.804 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.803 y[1] (analytic) = 0.3076156404096209867694513059822 y[1] (numeric) = 0.30761564040962098676945130598222 absolute error = 2e-32 relative error = 6.5016200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.803 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.802 y[1] (analytic) = 0.30795715084203183968982555767191 y[1] (numeric) = 0.30795715084203183968982555767192 absolute error = 1e-32 relative error = 3.2472050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.802 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.801 y[1] (analytic) = 0.30829923030014163266639988506605 y[1] (numeric) = 0.30829923030014163266639988506606 absolute error = 1e-32 relative error = 3.2436020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.801 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.30864188004880245407331664403807 y[1] (numeric) = 0.30864188004880245407331664403809 absolute error = 2e-32 relative error = 6.4800020000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.8 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.799 y[1] (analytic) = 0.30898510135638279793424920637177 y[1] (numeric) = 0.30898510135638279793424920637178 absolute error = 1e-32 relative error = 3.2364020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.799 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.798 y[1] (analytic) = 0.30932889549477930156628686233781 y[1] (numeric) = 0.30932889549477930156628686233783 absolute error = 2e-32 relative error = 6.4656100000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.798 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.797 y[1] (analytic) = 0.30967326373942852895909525859266 y[1] (numeric) = 0.30967326373942852895909525859267 absolute error = 1e-32 relative error = 3.2292100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.797 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.796 y[1] (analytic) = 0.31001820736931880009312946949374 y[1] (numeric) = 0.31001820736931880009312946949375 absolute error = 1e-32 relative error = 3.2256170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.796 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.795 y[1] (analytic) = 0.31036372766700206640169880689976 y[1] (numeric) = 0.31036372766700206640169880689976 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.795 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.794 y[1] (analytic) = 0.31070982591860583258271017888497 y[1] (numeric) = 0.31070982591860583258271017888497 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.794 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.793 y[1] (analytic) = 0.31105650341384512496695024651228 y[1] (numeric) = 0.31105650341384512496695024651228 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.793 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.792 y[1] (analytic) = 0.31140376144603450665080583508368 y[1] (numeric) = 0.31140376144603450665080583508368 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.792 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.791 y[1] (analytic) = 0.31175160131210013960236706755844 y[1] (numeric) = 0.31175160131210013960236706755844 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.791 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.31210002431259189395090853877578 y[1] (numeric) = 0.31210002431259189395090853877577 absolute error = 1e-32 relative error = 3.2041010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.79 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.789 y[1] (analytic) = 0.3124490317516955046708005756561 y[1] (numeric) = 0.31244903175169550467080057565609 absolute error = 1e-32 relative error = 3.2005220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.789 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.788 y[1] (analytic) = 0.31279862493724477587196526684069 y[1] (numeric) = 0.31279862493724477587196526684068 absolute error = 1e-32 relative error = 3.1969450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.788 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.787 y[1] (analytic) = 0.31314880518073383291006053166404 y[1] (numeric) = 0.31314880518073383291006053166403 absolute error = 1e-32 relative error = 3.1933700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.787 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.786 y[1] (analytic) = 0.31349957379732942253065006958123 y[1] (numeric) = 0.31349957379732942253065006958122 absolute error = 1e-32 relative error = 3.1897970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.786 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.785 y[1] (analytic) = 0.31385093210588326126269762408567 y[1] (numeric) = 0.31385093210588326126269762408566 absolute error = 1e-32 relative error = 3.1862260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.785 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.784 y[1] (analytic) = 0.31420288142894443227781064689032 y[1] (numeric) = 0.3142028814289444322778106468903 absolute error = 2e-32 relative error = 6.3653140000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.784 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.783 y[1] (analytic) = 0.314555423092771830932751196097 y[1] (numeric) = 0.31455542309277183093275119609698 absolute error = 2e-32 relative error = 6.3581799999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.783 Order of pole = 1 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.19 x[1] = -1.782 y[1] (analytic) = 0.31490855842734665921383078388613 y[1] (numeric) = 0.31490855842734665921383078388611 absolute error = 2e-32 relative error = 6.3510500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.782 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.781 y[1] (analytic) = 0.3152622887663849693029109428171 y[1] (numeric) = 0.31526228876638496930291094281708 absolute error = 2e-32 relative error = 6.3439239999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.781 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.31561661544735025648584254328919 y[1] (numeric) = 0.31561661544735025648584254328917 absolute error = 2e-32 relative error = 6.3368019999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.78 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.779 y[1] (analytic) = 0.31597153981146610162529440648222 y[1] (numeric) = 0.3159715398114661016252944064822 absolute error = 2e-32 relative error = 6.3296840000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.779 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.778 y[1] (analytic) = 0.31632706320372886342104555584201 y[1] (numeric) = 0.31632706320372886342104555584199 absolute error = 2e-32 relative error = 6.3225699999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.778 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.777 y[1] (analytic) = 0.31668318697292042068194557482749 y[1] (numeric) = 0.31668318697292042068194557482747 absolute error = 2e-32 relative error = 6.3154599999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.777 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.776 y[1] (analytic) = 0.31703991247162096483488402838522 y[1] (numeric) = 0.3170399124716209648348840283852 absolute error = 2e-32 relative error = 6.3083539999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.776 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.775 y[1] (analytic) = 0.31739724105622184289725279991976 y[1] (numeric) = 0.31739724105622184289725279991974 absolute error = 2e-32 relative error = 6.3012520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.775 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.774 y[1] (analytic) = 0.31775517408693845114053453410895 y[1] (numeric) = 0.31775517408693845114053453410893 absolute error = 2e-32 relative error = 6.2941540000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.774 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.773 y[1] (analytic) = 0.31811371292782317967380619876381 y[1] (numeric) = 0.31811371292782317967380619876379 absolute error = 2e-32 relative error = 6.2870600000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.773 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.772 y[1] (analytic) = 0.31847285894677840817710912631748 y[1] (numeric) = 0.31847285894677840817710912631746 absolute error = 2e-32 relative error = 6.2799700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.772 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.771 y[1] (analytic) = 0.31883261351556955301580580798242 y[1] (numeric) = 0.3188326135155695530158058079824 absolute error = 2e-32 relative error = 6.2728840000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.771 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.31919297800983816596821923195147 y[1] (numeric) = 0.31919297800983816596821923195145 absolute error = 2e-32 relative error = 6.2658020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.77 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.769 y[1] (analytic) = 0.31955395380911508480003272232487 y[1] (numeric) = 0.31955395380911508480003272232485 absolute error = 2e-32 relative error = 6.2587240000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.769 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.768 y[1] (analytic) = 0.31991554229683363592011708908848 y[1] (numeric) = 0.31991554229683363592011708908846 absolute error = 2e-32 relative error = 6.2516500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.768 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.767 y[1] (analytic) = 0.32027774486034288935364748309734 y[1] (numeric) = 0.32027774486034288935364748309732 absolute error = 2e-32 relative error = 6.2445800000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.767 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.766 y[1] (analytic) = 0.32064056289092096626957470556379 y[1] (numeric) = 0.32064056289092096626957470556377 absolute error = 2e-32 relative error = 6.2375139999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.766 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.765 y[1] (analytic) = 0.3210039977837883993007248912278 y[1] (numeric) = 0.32100399778378839930072489122778 absolute error = 2e-32 relative error = 6.2304519999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.765 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.764 y[1] (analytic) = 0.32136805093812154589601751070236 y[1] (numeric) = 0.32136805093812154589601751070234 absolute error = 2e-32 relative error = 6.2233940000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.764 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.763 y[1] (analytic) = 0.32173272375706605494551456323174 y[1] (numeric) = 0.32173272375706605494551456323172 absolute error = 2e-32 relative error = 6.2163400000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.763 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.762 y[1] (analytic) = 0.32209801764775038692024369936015 y[1] (numeric) = 0.32209801764775038692024369936013 absolute error = 2e-32 relative error = 6.2092900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.762 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.761 y[1] (analytic) = 0.32246393402129938776997486716098 y[1] (numeric) = 0.32246393402129938776997486716096 absolute error = 2e-32 relative error = 6.2022440000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.761 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.32283047429284791682337395939632 y[1] (numeric) = 0.3228304742928479168233739593963 absolute error = 2e-32 relative error = 6.1952020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.76 Order of pole = 1 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.41 x[1] = -1.759 y[1] (analytic) = 0.32319763988155452893620789623546 y[1] (numeric) = 0.32319763988155452893620789623544 absolute error = 2e-32 relative error = 6.1881640000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.759 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.758 y[1] (analytic) = 0.32356543221061521113453365323169 y[1] (numeric) = 0.32356543221061521113453365323167 absolute error = 2e-32 relative error = 6.1811300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.758 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.757 y[1] (analytic) = 0.32393385270727717400106898171393 y[1] (numeric) = 0.32393385270727717400106898171391 absolute error = 2e-32 relative error = 6.1741000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.757 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.756 y[1] (analytic) = 0.32430290280285269805421501347316 y[1] (numeric) = 0.32430290280285269805421501347314 absolute error = 2e-32 relative error = 6.1670740000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.756 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.755 y[1] (analytic) = 0.3246725839327330353704806387998 y[1] (numeric) = 0.32467258393273303537048063879978 absolute error = 2e-32 relative error = 6.1600520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.755 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.754 y[1] (analytic) = 0.32504289753640236670234554205291 y[1] (numeric) = 0.32504289753640236670234554205289 absolute error = 2e-32 relative error = 6.1530340000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.754 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.753 y[1] (analytic) = 0.32541384505745181434489311782259 y[1] (numeric) = 0.32541384505745181434489311782257 absolute error = 2e-32 relative error = 6.1460200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.753 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.752 y[1] (analytic) = 0.32578542794359351100584621950445 y[1] (numeric) = 0.32578542794359351100584621950443 absolute error = 2e-32 relative error = 6.1390100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.752 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.751 y[1] (analytic) = 0.32615764764667472493494785717687 y[1] (numeric) = 0.32615764764667472493494785717685 absolute error = 2e-32 relative error = 6.1320040000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.751 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.32653050562269204156994560981368 y[1] (numeric) = 0.32653050562269204156994560981366 absolute error = 2e-32 relative error = 6.1250020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.75 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.749 y[1] (analytic) = 0.32690400333180560195776269515352 y[1] (numeric) = 0.3269040033318056019577626951535 absolute error = 2e-32 relative error = 6.1180040000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.749 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.748 y[1] (analytic) = 0.32727814223835339821077039638292 y[1] (numeric) = 0.3272781422383533982107703963829 absolute error = 2e-32 relative error = 6.1110100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.748 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.747 y[1] (analytic) = 0.32765292381086562625941592589801 y[1] (numeric) = 0.32765292381086562625941592589799 absolute error = 2e-32 relative error = 6.1040200000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.747 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.746 y[1] (analytic) = 0.32802834952207909616380686084414 y[1] (numeric) = 0.32802834952207909616380686084412 absolute error = 2e-32 relative error = 6.0970340000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.746 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.745 y[1] (analytic) = 0.32840442084895170024820806127764 y[1] (numeric) = 0.32840442084895170024820806127762 absolute error = 2e-32 relative error = 6.0900520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.745 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.744 y[1] (analytic) = 0.32878113927267693932376952836674 y[1] (numeric) = 0.32878113927267693932376952836673 absolute error = 1e-32 relative error = 3.0415370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.744 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.743 y[1] (analytic) = 0.32915850627869850726617402610227 y[1] (numeric) = 0.32915850627869850726617402610226 absolute error = 1e-32 relative error = 3.0380500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.743 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.742 y[1] (analytic) = 0.32953652335672493421627152491378 y[1] (numeric) = 0.32953652335672493421627152491378 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.742 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.741 y[1] (analytic) = 0.32991519200074428867315367911525 y[1] (numeric) = 0.32991519200074428867315367911524 absolute error = 1e-32 relative error = 3.0310820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.741 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.33029451370903893875051567230953 y[1] (numeric) = 0.33029451370903893875051567230952 absolute error = 1e-32 relative error = 3.0276010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.74 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.739 y[1] (analytic) = 0.33067448998420037286855490618434 y[1] (numeric) = 0.33067448998420037286855490618433 absolute error = 1e-32 relative error = 3.0241220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.739 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.738 y[1] (analytic) = 0.33105512233314408015506621930084 y[1] (numeric) = 0.33105512233314408015506621930083 absolute error = 1e-32 relative error = 3.0206450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.738 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.737 y[1] (analytic) = 0.33143641226712449083081165463 y[1] (numeric) = 0.33143641226712449083081165462999 absolute error = 1e-32 relative error = 3.0171700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.737 Order of pole = 1 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.64 x[1] = -1.736 y[1] (analytic) = 0.33181836130174997685566929920294 y[1] (numeric) = 0.33181836130174997685566929920293 absolute error = 1e-32 relative error = 3.0136970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.736 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.735 y[1] (analytic) = 0.33220097095699791311350044813911 y[1] (numeric) = 0.3322009709569979131135004481391 absolute error = 1e-32 relative error = 3.0102260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.735 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.734 y[1] (analytic) = 0.33258424275722979941511735068714 y[1] (numeric) = 0.33258424275722979941511735068713 absolute error = 1e-32 relative error = 3.0067570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.734 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.733 y[1] (analytic) = 0.3329681782312064436001851303071 y[1] (numeric) = 0.33296817823120644360018513030709 absolute error = 1e-32 relative error = 3.0032900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.733 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.732 y[1] (analytic) = 0.33335277891210320602035118715258 y[1] (numeric) = 0.33335277891210320602035118715258 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.732 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.731 y[1] (analytic) = 0.3337380463375253056873635428563 y[1] (numeric) = 0.3337380463375253056873635428563 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.731 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.33412398204952318837141622793403 y[1] (numeric) = 0.33412398204952318837141622793403 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.73 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.729 y[1] (analytic) = 0.33451058759460795693644499542055 y[1] (numeric) = 0.33451058759460795693644499542055 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.729 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.728 y[1] (analytic) = 0.33489786452376686420059042493516 y[1] (numeric) = 0.33489786452376686420059042493516 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.728 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.727 y[1] (analytic) = 0.33528581439247886861154791401931 y[1] (numeric) = 0.33528581439247886861154791401931 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.727 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.726 y[1] (analytic) = 0.33567443876073025302803519345086 y[1] (numeric) = 0.33567443876073025302803519345086 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.726 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.725 y[1] (analytic) = 0.33606373919303030690012790585914 y[1] (numeric) = 0.33606373919303030690012790585914 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.725 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.724 y[1] (analytic) = 0.33645371725842707214274250826919 y[1] (numeric) = 0.33645371725842707214274250826919 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.724 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.723 y[1] (analytic) = 0.33684437453052315299808335550892 y[1] (numeric) = 0.33684437453052315299808335550892 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.723 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.722 y[1] (analytic) = 0.33723571258749159018441734942847 y[1] (numeric) = 0.33723571258749159018441734942847 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.722 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.721 y[1] (analytic) = 0.33762773301209179963009505571195 y[1] (numeric) = 0.33762773301209179963009505571195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.721 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.3380204373916855760933017532106 y[1] (numeric) = 0.3380204373916855760933017532106 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.72 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.719 y[1] (analytic) = 0.33841382731825316196959554809842 y[1] (numeric) = 0.33841382731825316196959554809842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.719 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.718 y[1] (analytic) = 0.33880790438840938159087251505578 y[1] (numeric) = 0.33880790438840938159087251505578 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.718 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.717 y[1] (analytic) = 0.3392026702034198413209908788402 y[1] (numeric) = 0.3392026702034198413209908788402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.717 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.716 y[1] (analytic) = 0.33959812636921719575488758113424 y[1] (numeric) = 0.33959812636921719575488758113424 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.716 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.715 y[1] (analytic) = 0.33999427449641748032963124900977 y[1] (numeric) = 0.33999427449641748032963124900977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.715 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.714 y[1] (analytic) = 0.34039111620033651065747565267444 y[1] (numeric) = 0.34039111620033651065747565267444 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.714 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.713 y[1] (analytic) = 0.34078865310100634889260727174828 y[1] (numeric) = 0.34078865310100634889260727174828 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.713 Order of pole = 1 memory used=49.5MB, alloc=4.4MB, time=2.87 TOP MAIN SOLVE Loop x[1] = -1.712 y[1] (analytic) = 0.34118688682319183744491964195848 y[1] (numeric) = 0.34118688682319183744491964195848 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.712 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.711 y[1] (analytic) = 0.34158581899640720035579578906666 y[1] (numeric) = 0.34158581899640720035579578906666 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.711 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.34198545125493271265253833571412 y[1] (numeric) = 0.34198545125493271265253833571412 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.71 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.709 y[1] (analytic) = 0.34238578523783143799975485177777 y[1] (numeric) = 0.34238578523783143799975485177777 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.709 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.708 y[1] (analytic) = 0.34278682258896603496768377230043 y[1] (numeric) = 0.34278682258896603496768377230043 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.708 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.707 y[1] (analytic) = 0.34318856495701563223913379206205 y[1] (numeric) = 0.34318856495701563223913379206205 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.707 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.706 y[1] (analytic) = 0.34359101399549277307840712580276 y[1] (numeric) = 0.34359101399549277307840712580276 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.706 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.705 y[1] (analytic) = 0.34399417136276042938728446185208 y[1] (numeric) = 0.34399417136276042938728446185208 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.705 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.704 y[1] (analytic) = 0.34439803872204908567486689876798 y[1] (numeric) = 0.34439803872204908567486689876799 absolute error = 1e-32 relative error = 2.9036170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.704 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.703 y[1] (analytic) = 0.34480261774147389326979770430417 y[1] (numeric) = 0.34480261774147389326979770430418 absolute error = 1e-32 relative error = 2.9002100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.703 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.702 y[1] (analytic) = 0.34520791009405189510512443882139 y[1] (numeric) = 0.3452079100940518951051244388214 absolute error = 1e-32 relative error = 2.8968050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.702 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.701 y[1] (analytic) = 0.34561391745771932140780990681558 y[1] (numeric) = 0.34561391745771932140780990681558 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.701 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.34602064151534895662665860669252 y[1] (numeric) = 0.34602064151534895662665860669253 absolute error = 1e-32 relative error = 2.8900010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.7 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.699 y[1] (analytic) = 0.34642808395476757793419390688429 y[1] (numeric) = 0.34642808395476757793419390688429 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.699 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.698 y[1] (analytic) = 0.34683624646877346563980015295478 y[1] (numeric) = 0.34683624646877346563980015295479 absolute error = 1e-32 relative error = 2.8832050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.698 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.697 y[1] (analytic) = 0.34724513075515398585323337303503 y[1] (numeric) = 0.34724513075515398585323337303503 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.697 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.696 y[1] (analytic) = 0.34765473851670324573940426579317 y[1] (numeric) = 0.34765473851670324573940426579318 absolute error = 1e-32 relative error = 2.8764170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.696 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.695 y[1] (analytic) = 0.34806507146123982170714779469451 y[1] (numeric) = 0.34806507146123982170714779469452 absolute error = 1e-32 relative error = 2.8730260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.695 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.694 y[1] (analytic) = 0.34847613130162456087651504354035 y[1] (numeric) = 0.34847613130162456087651504354036 absolute error = 1e-32 relative error = 2.8696370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.694 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.693 y[1] (analytic) = 0.34888791975577845617095508068033 y[1] (numeric) = 0.34888791975577845617095508068034 absolute error = 1e-32 relative error = 2.8662500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.693 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.692 y[1] (analytic) = 0.34930043854670059538259750285116 y[1] (numeric) = 0.34930043854670059538259750285117 absolute error = 1e-32 relative error = 2.8628650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.692 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.691 y[1] (analytic) = 0.34971368940248618456070015478328 y[1] (numeric) = 0.34971368940248618456070015478328 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.691 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.3501276740563446460751913185143 y[1] (numeric) = 0.3501276740563446460751913185143 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.69 Order of pole = 1 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=3.10 x[1] = -1.689 y[1] (analytic) = 0.35054239424661779170911150823669 y[1] (numeric) = 0.3505423942466177917091115082367 absolute error = 1e-32 relative error = 2.8527220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.689 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.688 y[1] (analytic) = 0.3509578517167980711356469644778 y[1] (numeric) = 0.35095785171679807113564696447781 absolute error = 1e-32 relative error = 2.8493450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.688 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.687 y[1] (analytic) = 0.35137404821554689613734508796649 y[1] (numeric) = 0.3513740482155468961373450879665 absolute error = 1e-32 relative error = 2.8459700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.687 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.686 y[1] (analytic) = 0.3517909854967130409270114617021 y[1] (numeric) = 0.35179098549671304092701146170211 absolute error = 1e-32 relative error = 2.8425970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.686 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.685 y[1] (analytic) = 0.35220866531935111893170885304657 y[1] (numeric) = 0.35220866531935111893170885304658 absolute error = 1e-32 relative error = 2.8392260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.685 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.684 y[1] (analytic) = 0.35262708944774013640321074017484 y[1] (numeric) = 0.35262708944774013640321074017485 absolute error = 1e-32 relative error = 2.8358570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.684 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.683 y[1] (analytic) = 0.35304625965140212322020554353237 y[1] (numeric) = 0.35304625965140212322020554353238 absolute error = 1e-32 relative error = 2.8324900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.683 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.682 y[1] (analytic) = 0.3534661777051208412495029381876 y[1] (numeric) = 0.35346617770512084124950293818761 absolute error = 1e-32 relative error = 2.8291250000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.682 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.681 y[1] (analytic) = 0.35388684538896057063546045279114 y[1] (numeric) = 0.35388684538896057063546045279115 absolute error = 1e-32 relative error = 2.8257620000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.681 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.35430826448828497438882710146432 y[1] (numeric) = 0.35430826448828497438882710146433 absolute error = 1e-32 relative error = 2.8224010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.68 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.679 y[1] (analytic) = 0.35473043679377604164819112308366 y[1] (numeric) = 0.35473043679377604164819112308367 absolute error = 1e-32 relative error = 2.8190420000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.679 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.678 y[1] (analytic) = 0.35515336410145310998922109539952 y[1] (numeric) = 0.35515336410145310998922109539953 absolute error = 1e-32 relative error = 2.8156850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.678 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.677 y[1] (analytic) = 0.35557704821269196715890382707577 y[1] (numeric) = 0.35557704821269196715890382707578 absolute error = 1e-32 relative error = 2.8123300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.677 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.676 y[1] (analytic) = 0.35600149093424403261400858746796 y[1] (numeric) = 0.35600149093424403261400858746797 absolute error = 1e-32 relative error = 2.8089770000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.676 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.675 y[1] (analytic) = 0.35642669407825561924504549073897 y[1] (numeric) = 0.35642669407825561924504549073897 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.675 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.674 y[1] (analytic) = 0.35685265946228727566903628727638 y[1] (numeric) = 0.35685265946228727566903628727639 absolute error = 1e-32 relative error = 2.8022770000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.674 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.673 y[1] (analytic) = 0.35727938890933320947647851143115 y[1] (numeric) = 0.35727938890933320947647851143116 absolute error = 1e-32 relative error = 2.7989300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.673 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.672 y[1] (analytic) = 0.35770688424784079181995897102038 y[1] (numeric) = 0.35770688424784079181995897102038 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.672 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.671 y[1] (analytic) = 0.35813514731173014373396002208978 y[1] (numeric) = 0.35813514731173014373396002208978 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.671 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.35856417994041380457750203395531 y[1] (numeric) = 0.35856417994041380457750203395531 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.67 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.669 y[1] (analytic) = 0.35899398397881648299337799697153 y[1] (numeric) = 0.35899398397881648299337799697153 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.669 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.668 y[1] (analytic) = 0.35942456127739489077986144183163 y[1] (numeric) = 0.35942456127739489077986144183163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.668 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.667 y[1] (analytic) = 0.35985591369215766007290680811403 y[1] (numeric) = 0.35985591369215766007290680811403 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.667 Order of pole = 1 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.33 x[1] = -1.666 y[1] (analytic) = 0.36028804308468534423901220547804 y[1] (numeric) = 0.36028804308468534423901220547803 absolute error = 1e-32 relative error = 2.7755570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.666 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.665 y[1] (analytic) = 0.36072095132215050288107823821002 y[1] (numeric) = 0.36072095132215050288107823821001 absolute error = 1e-32 relative error = 2.7722260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.665 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.664 y[1] (analytic) = 0.36115464027733787136177329817613 y[1] (numeric) = 0.36115464027733787136177329817613 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.664 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.663 y[1] (analytic) = 0.36158911182866461525110555870942 y[1] (numeric) = 0.36158911182866461525110555870941 absolute error = 1e-32 relative error = 2.7655700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.663 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.662 y[1] (analytic) = 0.36202436786020067010710490923144 y[1] (numeric) = 0.36202436786020067010710490923143 absolute error = 1e-32 relative error = 2.7622450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.662 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.661 y[1] (analytic) = 0.36246041026168916700073434479119 y[1] (numeric) = 0.36246041026168916700073434479118 absolute error = 1e-32 relative error = 2.7589220000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.661 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.36289724092856694419837995413705 y[1] (numeric) = 0.36289724092856694419837995413704 absolute error = 1e-32 relative error = 2.7556010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.66 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.659 y[1] (analytic) = 0.36333486176198514541751172299931 y[1] (numeric) = 0.36333486176198514541751172299931 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.659 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.658 y[1] (analytic) = 0.36377327466882990507336397516884 y[1] (numeric) = 0.36377327466882990507336397516883 absolute error = 1e-32 relative error = 2.7489650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.658 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.657 y[1] (analytic) = 0.3642124815617431209367545025768 y[1] (numeric) = 0.3642124815617431209367545025768 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.657 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.656 y[1] (analytic) = 0.36465248435914331462544537742808 y[1] (numeric) = 0.36465248435914331462544537742808 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.656 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.655 y[1] (analytic) = 0.36509328498524658035374618568791 y[1] (numeric) = 0.3650932849852465803537461856879 absolute error = 1e-32 relative error = 2.7390260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.655 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.654 y[1] (analytic) = 0.36553488537008762236737206370396 y[1] (numeric) = 0.36553488537008762236737206370395 absolute error = 1e-32 relative error = 2.7357170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.654 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.653 y[1] (analytic) = 0.36597728744954088149289455096417 y[1] (numeric) = 0.36597728744954088149289455096416 absolute error = 1e-32 relative error = 2.7324100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.653 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.652 y[1] (analytic) = 0.36642049316534175123346298511783 y[1] (numeric) = 0.36642049316534175123346298511782 absolute error = 1e-32 relative error = 2.7291050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.652 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.651 y[1] (analytic) = 0.3668645044651078838448280542754 y[1] (numeric) = 0.36686450446510788384482805427539 absolute error = 1e-32 relative error = 2.7258020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.651 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 0.36730932330236058682806728078337 y[1] (numeric) = 0.36730932330236058682806728078336 absolute error = 1e-32 relative error = 2.7225010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.65 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.649 y[1] (analytic) = 0.36775495163654631027779473536721 y[1] (numeric) = 0.36775495163654631027779473536721 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.649 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.648 y[1] (analytic) = 0.36820139143305822552703426666249 y[1] (numeric) = 0.36820139143305822552703426666249 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.648 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.647 y[1] (analytic) = 0.36864864466325789553234707532598 y[1] (numeric) = 0.36864864466325789553234707532597 absolute error = 1e-32 relative error = 2.7126100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.647 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.646 y[1] (analytic) = 0.36909671330449703744523066145453 y[1] (numeric) = 0.36909671330449703744523066145452 absolute error = 1e-32 relative error = 2.7093170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.646 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.645 y[1] (analytic) = 0.36954559934013937781824712696774 y[1] (numeric) = 0.36954559934013937781824712696773 absolute error = 1e-32 relative error = 2.7060260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.645 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.644 y[1] (analytic) = 0.36999530475958260089679461967628 y[1] (numeric) = 0.36999530475958260089679461967627 absolute error = 1e-32 relative error = 2.7027370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.644 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.643 y[1] (analytic) = 0.37044583155828039044990646242753 y[1] (numeric) = 0.37044583155828039044990646242753 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 memory used=61.0MB, alloc=4.4MB, time=3.55 Complex estimate of poles used for equation 1 Radius of convergence = 1.643 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.642 y[1] (analytic) = 0.3708971817377645655959483191867 y[1] (numeric) = 0.3708971817377645655959483191867 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.642 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.641 y[1] (analytic) = 0.37134935730566731108158471110134 y[1] (numeric) = 0.37134935730566731108158471110134 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.641 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.37180236027574350247490241117549 y[1] (numeric) = 0.37180236027574350247490241117549 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.64 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.639 y[1] (analytic) = 0.37225619266789312673610981855489 y[1] (numeric) = 0.37225619266789312673610981855489 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.639 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.638 y[1] (analytic) = 0.37271085650818379863177844575846 y[1] (numeric) = 0.37271085650818379863177844575846 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.638 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.637 y[1] (analytic) = 0.37316635382887337346115524839818 y[1] (numeric) = 0.37316635382887337346115524839819 absolute error = 1e-32 relative error = 2.6797700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.637 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.636 y[1] (analytic) = 0.37362268666843265656565279169003 y[1] (numeric) = 0.37362268666843265656565279169004 absolute error = 1e-32 relative error = 2.6764970000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.636 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.635 y[1] (analytic) = 0.374079857071568210095218286819 y[1] (numeric) = 0.374079857071568210095218286819 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.635 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.634 y[1] (analytic) = 0.37453786708924525750789244920424 y[1] (numeric) = 0.37453786708924525750789244920424 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.634 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.633 y[1] (analytic) = 0.37499671877871068628149503691843 y[1] (numeric) = 0.37499671877871068628149503691843 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.633 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.632 y[1] (analytic) = 0.37545641420351614931901592873837 y[1] (numeric) = 0.37545641420351614931901592873838 absolute error = 1e-32 relative error = 2.6634250000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.632 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.631 y[1] (analytic) = 0.37591695543354126553194880612534 y[1] (numeric) = 0.37591695543354126553194880612535 absolute error = 1e-32 relative error = 2.6601620000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.631 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.37637834454501692008847902123564 y[1] (numeric) = 0.37637834454501692008847902123565 absolute error = 1e-32 relative error = 2.6569010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.63 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.629 y[1] (analytic) = 0.37684058362054866481612817403403 y[1] (numeric) = 0.37684058362054866481612817403403 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.629 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.628 y[1] (analytic) = 0.37730367474914021925116539672538 y[1] (numeric) = 0.37730367474914021925116539672539 absolute error = 1e-32 relative error = 2.6503850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.628 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.627 y[1] (analytic) = 0.37776762002621707282981946485439 y[1] (numeric) = 0.3777676200262170728298194648544 absolute error = 1e-32 relative error = 2.6471300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.627 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.626 y[1] (analytic) = 0.37823242155365018871906673419376 y[1] (numeric) = 0.37823242155365018871906673419377 absolute error = 1e-32 relative error = 2.6438770000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.626 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.625 y[1] (analytic) = 0.3786980814397798097875276544274 y[1] (numeric) = 0.37869808143977980978752765442741 absolute error = 1e-32 relative error = 2.6406260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.625 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.624 y[1] (analytic) = 0.37916460179943936721977934895163 y[1] (numeric) = 0.37916460179943936721977934895164 absolute error = 1e-32 relative error = 2.6373770000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.624 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.623 y[1] (analytic) = 0.37963198475397949228018359002783 y[1] (numeric) = 0.37963198475397949228018359002784 absolute error = 1e-32 relative error = 2.6341300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.623 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.622 y[1] (analytic) = 0.38010023243129213173513855603723 y[1] (numeric) = 0.38010023243129213173513855603724 absolute error = 1e-32 relative error = 2.6308850000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.622 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.621 y[1] (analytic) = 0.38056934696583476744548914958735 y[1] (numeric) = 0.38056934696583476744548914958736 absolute error = 1e-32 relative error = 2.6276420000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.621 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.38103933049865474064367449943816 y[1] (numeric) = 0.38103933049865474064367449943817 absolute error = 1e-32 relative error = 2.6244010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.62 Order of pole = 1 memory used=64.8MB, alloc=4.4MB, time=3.78 TOP MAIN SOLVE Loop x[1] = -1.619 y[1] (analytic) = 0.38151018517741368141305268426751 y[1] (numeric) = 0.38151018517741368141305268426752 absolute error = 1e-32 relative error = 2.6211620000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.619 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.618 y[1] (analytic) = 0.38198191315641204388972182167174 y[1] (numeric) = 0.38198191315641204388972182167175 absolute error = 1e-32 relative error = 2.6179250000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.618 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.617 y[1] (analytic) = 0.38245451659661374771005358187778 y[1] (numeric) = 0.38245451659661374771005358187778 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.617 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.616 y[1] (analytic) = 0.38292799766567092623007003370149 y[1] (numeric) = 0.3829279976656709262300700337015 absolute error = 1e-32 relative error = 2.6114570000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.616 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.615 y[1] (analytic) = 0.3834023585379487820457276324981 y[1] (numeric) = 0.38340235853794878204572763249811 absolute error = 1e-32 relative error = 2.6082260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.615 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.614 y[1] (analytic) = 0.3838776013945505503461232392974 y[1] (numeric) = 0.3838776013945505503461232392974 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.614 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.613 y[1] (analytic) = 0.38435372842334257063460644099978 y[1] (numeric) = 0.38435372842334257063460644099978 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.613 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.612 y[1] (analytic) = 0.38483074181897946735577024835052 y[1] (numeric) = 0.38483074181897946735577024835052 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.612 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.611 y[1] (analytic) = 0.38530864378292943996929860726338 y[1] (numeric) = 0.38530864378292943996929860726338 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.611 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.38578743652349966301467419672304 y[1] (numeric) = 0.38578743652349966301467419672305 absolute error = 1e-32 relative error = 2.5921010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.61 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.609 y[1] (analytic) = 0.38626712225586179671379383069603 y[1] (numeric) = 0.38626712225586179671379383069604 absolute error = 1e-32 relative error = 2.5888820000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.609 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.608 y[1] (analytic) = 0.38674770320207760866160156091373 y[1] (numeric) = 0.38674770320207760866160156091374 absolute error = 1e-32 relative error = 2.5856650000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.608 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.607 y[1] (analytic) = 0.38722918159112470715793142171194 y[1] (numeric) = 0.38722918159112470715793142171195 absolute error = 1e-32 relative error = 2.5824500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.607 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.606 y[1] (analytic) = 0.38771155965892238673685279793986 y[1] (numeric) = 0.38771155965892238673685279793987 absolute error = 1e-32 relative error = 2.5792370000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.606 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.605 y[1] (analytic) = 0.38819483964835758645293176388748 y[1] (numeric) = 0.38819483964835758645293176388749 absolute error = 1e-32 relative error = 2.5760260000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.605 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.604 y[1] (analytic) = 0.3886790238093109614869615678068 y[1] (numeric) = 0.38867902380931096148696156780682 absolute error = 2e-32 relative error = 5.1456340000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.604 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.603 y[1] (analytic) = 0.38916411439868306863687485649573 y[1] (numeric) = 0.38916411439868306863687485649575 absolute error = 2e-32 relative error = 5.1392200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.603 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.602 y[1] (analytic) = 0.3896501136804206662627293821513 y[1] (numeric) = 0.38965011368042066626272938215131 absolute error = 1e-32 relative error = 2.5664050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.602 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.601 y[1] (analytic) = 0.3901370239255431292578579448674 y[1] (numeric) = 0.39013702392554312925785794486741 absolute error = 1e-32 relative error = 2.5632020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.601 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.39062484741216897962149233535456 y[1] (numeric) = 0.39062484741216897962149233535457 absolute error = 1e-32 relative error = 2.5600010000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.6 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.599 y[1] (analytic) = 0.39111358642554253321141019132494 y[1] (numeric) = 0.39111358642554253321141019132496 absolute error = 2e-32 relative error = 5.1136040000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.599 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.598 y[1] (analytic) = 0.39160324325806066325841310617735 y[1] (numeric) = 0.39160324325806066325841310617736 absolute error = 1e-32 relative error = 2.5536050000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.598 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.597 y[1] (analytic) = 0.39209382020929968122772416983936 y[1] (numeric) = 0.39209382020929968122772416983937 absolute error = 1e-32 relative error = 2.5504100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.597 Order of pole = 1 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=4.00 x[1] = -1.596 y[1] (analytic) = 0.39258531958604233561569351963339 y[1] (numeric) = 0.3925853195860423356156935196334 absolute error = 1e-32 relative error = 2.5472170000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.596 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.595 y[1] (analytic) = 0.39307774370230492927352157564427 y[1] (numeric) = 0.39307774370230492927352157564429 absolute error = 2e-32 relative error = 5.0880520000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.595 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.594 y[1] (analytic) = 0.3935710948793645558530515731627 y[1] (numeric) = 0.39357109487936455585305157316272 absolute error = 2e-32 relative error = 5.0816740000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.594 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.593 y[1] (analytic) = 0.39406537544578645597304592831951 y[1] (numeric) = 0.39406537544578645597304592831953 absolute error = 2e-32 relative error = 5.0753000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.593 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.592 y[1] (analytic) = 0.39456058773745149370774502705699 y[1] (numeric) = 0.39456058773745149370774502705701 absolute error = 2e-32 relative error = 5.0689300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.592 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.591 y[1] (analytic) = 0.39505673409758375400291235824377 y[1] (numeric) = 0.39505673409758375400291235824379 absolute error = 2e-32 relative error = 5.0625640000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.591 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.39555381687677826162799666627243 y[1] (numeric) = 0.39555381687677826162799666627245 absolute error = 2e-32 relative error = 5.0562020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.59 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.589 y[1] (analytic) = 0.39605183843302882227649012523951 y[1] (numeric) = 0.39605183843302882227649012523953 absolute error = 2e-32 relative error = 5.0498440000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.589 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.588 y[1] (analytic) = 0.39655080113175598643003158527131 y[1] (numeric) = 0.39655080113175598643003158527133 absolute error = 2e-32 relative error = 5.0434900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.588 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.587 y[1] (analytic) = 0.39705070734583513660529586233458 y[1] (numeric) = 0.3970507073458351366052958623346 absolute error = 2e-32 relative error = 5.0371400000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.587 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.586 y[1] (analytic) = 0.39755155945562469860622398770453 y[1] (numeric) = 0.39755155945562469860622398770455 absolute error = 2e-32 relative error = 5.0307939999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.586 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.585 y[1] (analytic) = 0.39805335984899447740768545505062 y[1] (numeric) = 0.39805335984899447740768545505065 absolute error = 3e-32 relative error = 7.5366780000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.585 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.584 y[1] (analytic) = 0.39855611092135411830022195589817 y[1] (numeric) = 0.3985561109213541183002219558982 absolute error = 3e-32 relative error = 7.5271710000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.584 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.583 y[1] (analytic) = 0.39905981507568169392910303325365 y[1] (numeric) = 0.39905981507568169392910303325368 absolute error = 3e-32 relative error = 7.5176700000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.583 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.582 y[1] (analytic) = 0.39956447472255241786452766484532 y[1] (numeric) = 0.39956447472255241786452766484534 absolute error = 2e-32 relative error = 5.0054500000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.582 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.581 y[1] (analytic) = 0.40007009228016748534343216931606 y[1] (numeric) = 0.40007009228016748534343216931609 absolute error = 3e-32 relative error = 7.4986860000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.581 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.40057667017438304182701416959855 y[1] (numeric) = 0.40057667017438304182701416959858 absolute error = 3e-32 relative error = 7.4892030000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.58 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.579 y[1] (analytic) = 0.40108421083873928002175480759589 y[1] (numeric) = 0.40108421083873928002175480759592 absolute error = 3e-32 relative error = 7.4797260000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.579 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.578 y[1] (analytic) = 0.40159271671448966601541714439467 y[1] (numeric) = 0.4015927167144896660154171443947 absolute error = 3e-32 relative error = 7.4702550000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.578 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.577 y[1] (analytic) = 0.4021021902506302951832178629877 y[1] (numeric) = 0.40210219025063029518321786298773 absolute error = 3e-32 relative error = 7.4607900000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.577 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.576 y[1] (analytic) = 0.40261263390392937852311217955557 y[1] (numeric) = 0.4026126339039293785231121795556 absolute error = 3e-32 relative error = 7.4513310000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.576 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.575 y[1] (analytic) = 0.40312405013895686008289842967058 y[1] (numeric) = 0.4031240501389568600828984296706 absolute error = 2e-32 relative error = 4.9612519999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.575 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.574 y[1] (analytic) = 0.40363644142811416614563929352321 y[1] (numeric) = 0.40363644142811416614563929352323 absolute error = 2e-32 relative error = 4.9549540000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.574 Order of pole = 1 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=4.22 x[1] = -1.573 y[1] (analytic) = 0.40414981025166408684371122687758 y[1] (numeric) = 0.4041498102516640868437112268776 absolute error = 2e-32 relative error = 4.9486600000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.573 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.572 y[1] (analytic) = 0.40466415909776079087563254066369 y[1] (numeric) = 0.40466415909776079087563254066371 absolute error = 2e-32 relative error = 4.9423700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.572 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.571 y[1] (analytic) = 0.40517949046247997400368389192728 y[1] (numeric) = 0.40517949046247997400368389192731 absolute error = 3e-32 relative error = 7.4041260000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.571 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.40569580684984914201422288359654 y[1] (numeric) = 0.40569580684984914201422288359657 absolute error = 3e-32 relative error = 7.3947030000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.57 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.569 y[1] (analytic) = 0.40621311077187802882650719281555 y[1] (numeric) = 0.40621311077187802882650719281558 absolute error = 3e-32 relative error = 7.3852860000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.569 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.568 y[1] (analytic) = 0.40673140474858915043977833138441 y[1] (numeric) = 0.40673140474858915043977833138444 absolute error = 3e-32 relative error = 7.3758750000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.568 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.567 y[1] (analytic) = 0.40725069130804849541232096241483 y[1] (numeric) = 0.40725069130804849541232096241486 absolute error = 3e-32 relative error = 7.3664700000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.567 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.566 y[1] (analytic) = 0.40777097298639635257020083128191 y[1] (numeric) = 0.40777097298639635257020083128193 absolute error = 2e-32 relative error = 4.9047139999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.566 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.565 y[1] (analytic) = 0.40829225232787827664739799430514 y[1] (numeric) = 0.40829225232787827664739799430516 absolute error = 2e-32 relative error = 4.8984520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.565 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.564 y[1] (analytic) = 0.40881453188487619256309132466946 y[1] (numeric) = 0.40881453188487619256309132466948 absolute error = 2e-32 relative error = 4.8921940000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.564 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.563 y[1] (analytic) = 0.40933781421793963904591542262083 y[1] (numeric) = 0.40933781421793963904591542262084 absolute error = 1e-32 relative error = 2.4429700000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.563 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.562 y[1] (analytic) = 0.40986210189581715231910223805201 y[1] (numeric) = 0.40986210189581715231910223805202 absolute error = 1e-32 relative error = 2.4398450000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.562 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.561 y[1] (analytic) = 0.41038739749548779056453711174274 y[1] (numeric) = 0.41038739749548779056453711174276 absolute error = 2e-32 relative error = 4.8734440000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.561 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.41091370360219279988790274165732 y[1] (numeric) = 0.41091370360219279988790274165734 absolute error = 2e-32 relative error = 4.8672020000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.56 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.559 y[1] (analytic) = 0.41144102280946742251125496917895 y[1] (numeric) = 0.41144102280946742251125496917897 absolute error = 2e-32 relative error = 4.8609640000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.559 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.558 y[1] (analytic) = 0.41196935771917284792357144475594 y[1] (numeric) = 0.41196935771917284792357144475596 absolute error = 2e-32 relative error = 4.8547300000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.558 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.557 y[1] (analytic) = 0.41249871094152830772403836238012 y[1] (numeric) = 0.41249871094152830772403836238014 absolute error = 2e-32 relative error = 4.8485000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.557 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.556 y[1] (analytic) = 0.41302908509514331489709173830312 y[1] (numeric) = 0.41302908509514331489709173830314 absolute error = 2e-32 relative error = 4.8422740000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.556 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.555 y[1] (analytic) = 0.41356048280705004826250834358274 y[1] (numeric) = 0.41356048280705004826250834358276 absolute error = 2e-32 relative error = 4.8360520000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.555 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.554 y[1] (analytic) = 0.41409290671273588284814757608647 y[1] (numeric) = 0.41409290671273588284814757608649 absolute error = 2e-32 relative error = 4.8298340000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.554 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.553 y[1] (analytic) = 0.41462635945617606693727947060506 y[1] (numeric) = 0.41462635945617606693727947060509 absolute error = 3e-32 relative error = 7.2354300000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.553 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.552 y[1] (analytic) = 0.41516084368986654654679589239861 y[1] (numeric) = 0.41516084368986654654679589239864 absolute error = 3e-32 relative error = 7.2261150000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.552 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.551 y[1] (analytic) = 0.41569636207485693809699193798475 y[1] (numeric) = 0.41569636207485693809699193798478 absolute error = 3e-32 relative error = 7.2168060000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.551 Order of pole = 1 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=4.45 x[1] = -1.55 y[1] (analytic) = 0.4162329172807836500380228769936 y[1] (numeric) = 0.41623291728078365003802287699363 absolute error = 3e-32 relative error = 7.2075030000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.55 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.549 y[1] (analytic) = 0.41677051198590315420258881171225 y[1] (numeric) = 0.41677051198590315420258881171228 absolute error = 3e-32 relative error = 7.1982060000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.549 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.548 y[1] (analytic) = 0.41730914887712540765887480934188 y[1] (numeric) = 0.41730914887712540765887480934191 absolute error = 3e-32 relative error = 7.1889150000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.548 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.547 y[1] (analytic) = 0.41784883065004742584227878038283 y[1] (numeric) = 0.41784883065004742584227878038286 absolute error = 3e-32 relative error = 7.1796300000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.547 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.546 y[1] (analytic) = 0.41838956000898700774899304092645 y[1] (numeric) = 0.41838956000898700774899304092648 absolute error = 3e-32 relative error = 7.1703510000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.546 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.545 y[1] (analytic) = 0.41893133966701661397906851454488 y[1] (numeric) = 0.41893133966701661397906851454491 absolute error = 3e-32 relative error = 7.1610780000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.545 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.544 y[1] (analytic) = 0.41947417234599739842118311012413 y[1] (numeric) = 0.41947417234599739842118311012417 absolute error = 4e-32 relative error = 9.5357480000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.544 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.543 y[1] (analytic) = 0.42001806077661339437595816620115 y[1] (numeric) = 0.42001806077661339437595816620118 absolute error = 3e-32 relative error = 7.1425499999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.543 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.542 y[1] (analytic) = 0.42056300769840585591931919260314 y[1] (numeric) = 0.42056300769840585591931919260317 absolute error = 3e-32 relative error = 7.1332950000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.542 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.541 y[1] (analytic) = 0.42110901585980775531207968056354 y[1] (numeric) = 0.42110901585980775531207968056358 absolute error = 4e-32 relative error = 9.4987280000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.541 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.42165608801817843726663970878744 y[1] (numeric) = 0.42165608801817843726663970878747 absolute error = 3e-32 relative error = 7.1148030000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.54 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.539 y[1] (analytic) = 0.42220422693983843088643466262927 y[1] (numeric) = 0.4222042269398384308864346626293 absolute error = 3e-32 relative error = 7.1055660000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.539 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.538 y[1] (analytic) = 0.42275343540010442009854382579176 y[1] (numeric) = 0.4227534354001044200985438257918 absolute error = 4e-32 relative error = 9.4617800000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.538 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.537 y[1] (analytic) = 0.4233037161833243734046741196341 y[1] (numeric) = 0.42330371618332437340467411963413 absolute error = 3e-32 relative error = 7.0871099999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.537 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.536 y[1] (analytic) = 0.42385507208291283378057107689282 y[1] (numeric) = 0.42385507208291283378057107689285 absolute error = 3e-32 relative error = 7.0778910000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.536 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.535 y[1] (analytic) = 0.4244075059013863695587774687148 y[1] (numeric) = 0.42440750590138636955877746871483 absolute error = 3e-32 relative error = 7.0686780000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.535 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.534 y[1] (analytic) = 0.42496102045039918713456008247643 y[1] (numeric) = 0.42496102045039918713456008247646 absolute error = 3e-32 relative error = 7.0594710000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.534 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.533 y[1] (analytic) = 0.42551561855077890633975720078805 y[1] (numeric) = 0.42551561855077890633975720078808 absolute error = 3e-32 relative error = 7.0502700000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.533 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.532 y[1] (analytic) = 0.42607130303256249933426358901162 y[1] (numeric) = 0.42607130303256249933426358901165 absolute error = 3e-32 relative error = 7.0410750000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.532 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.531 y[1] (analytic) = 0.42662807673503239386986649100967 y[1] (numeric) = 0.4266280767350323938698664910097 absolute error = 3e-32 relative error = 7.0318859999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.531 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.42718594250675274178617549396578 y[1] (numeric) = 0.42718594250675274178617549396582 absolute error = 4e-32 relative error = 9.3636040000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.53 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.529 y[1] (analytic) = 0.42774490320560585360345138807499 y[1] (numeric) = 0.42774490320560585360345138807502 absolute error = 3e-32 relative error = 7.0135259999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.529 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.528 y[1] (analytic) = 0.42830496169882880008223455264618 y[1] (numeric) = 0.42830496169882880008223455264621 absolute error = 3e-32 relative error = 7.0043549999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.528 Order of pole = 1 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=4.68 x[1] = -1.527 y[1] (analytic) = 0.42886612086305018162480218550175 y[1] (numeric) = 0.42886612086305018162480218550179 absolute error = 4e-32 relative error = 9.3269200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.527 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.526 y[1] (analytic) = 0.42942838358432706639864609819224 y[1] (numeric) = 0.42942838358432706639864609819227 absolute error = 3e-32 relative error = 6.9860309999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.526 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.525 y[1] (analytic) = 0.42999175275818209806735906805307 y[1] (numeric) = 0.42999175275818209806735906805311 absolute error = 4e-32 relative error = 9.3025040000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.525 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.524 y[1] (analytic) = 0.43055623128964077401954811401301 y[1] (numeric) = 0.43055623128964077401954811401305 absolute error = 4e-32 relative error = 9.2903080000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.524 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.523 y[1] (analytic) = 0.4311218220932688949916577927425 y[1] (numeric) = 0.43112182209326889499165779274253 absolute error = 3e-32 relative error = 6.9585899999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.523 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.522 y[1] (analytic) = 0.43168852809321018698588594357399 y[1] (numeric) = 0.43168852809321018698588594357403 absolute error = 4e-32 relative error = 9.2659400000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.522 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.521 y[1] (analytic) = 0.43225635222322409638970849496119 y[1] (numeric) = 0.43225635222322409638970849496123 absolute error = 4e-32 relative error = 9.2537680000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.521 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.43282529742672375920889923437533 y[1] (numeric) = 0.43282529742672375920889923437537 absolute error = 4e-32 relative error = 9.2416040000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.52 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.519 y[1] (analytic) = 0.4333953666568141453313350917628 y[1] (numeric) = 0.43339536665681414533133509176284 absolute error = 4e-32 relative error = 9.2294480000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.519 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.518 y[1] (analytic) = 0.43396656287633037874431775031734 y[1] (numeric) = 0.43396656287633037874431775031738 absolute error = 4e-32 relative error = 9.2173000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.518 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.517 y[1] (analytic) = 0.43453888905787623463361853569085 y[1] (numeric) = 0.43453888905787623463361853569089 absolute error = 4e-32 relative error = 9.2051600000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.517 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.516 y[1] (analytic) = 0.43511234818386281429796580626101 y[1] (numeric) = 0.43511234818386281429796580626104 absolute error = 3e-32 relative error = 6.8947709999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.516 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.515 y[1] (analytic) = 0.43568694324654739881824273513806 y[1] (numeric) = 0.4356869432465473988182427351381 absolute error = 4e-32 relative error = 9.1809040000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.515 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.514 y[1] (analytic) = 0.43626267724807248242624870375452 y[1] (numeric) = 0.43626267724807248242624870375456 absolute error = 4e-32 relative error = 9.1687880000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.514 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.513 y[1] (analytic) = 0.43683955320050498652349978376442 y[1] (numeric) = 0.43683955320050498652349978376446 absolute error = 4e-32 relative error = 9.1566800000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.513 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.512 y[1] (analytic) = 0.43741757412587565530620323732747 y[1] (numeric) = 0.4374175741258756553062032373275 absolute error = 3e-32 relative error = 6.8584349999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.512 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.511 y[1] (analytic) = 0.43799674305621863395823788654308 y[1] (numeric) = 0.43799674305621863395823788654311 absolute error = 3e-32 relative error = 6.8493659999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.511 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.43857706303361123037970686386261 y[1] (numeric) = 0.43857706303361123037970686386264 absolute error = 3e-32 relative error = 6.8403030000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.51 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.509 y[1] (analytic) = 0.43915853711021386142440193194624 y[1] (numeric) = 0.43915853711021386142440193194627 absolute error = 3e-32 relative error = 6.8312459999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.509 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.508 y[1] (analytic) = 0.43974116834831018462532953103803 y[1] (numeric) = 0.43974116834831018462532953103806 absolute error = 3e-32 relative error = 6.8221950000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.508 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.507 y[1] (analytic) = 0.44032495982034741639329825411153 y[1] (numeric) = 0.44032495982034741639329825411156 absolute error = 3e-32 relative error = 6.8131500000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.507 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.506 y[1] (analytic) = 0.44090991460897683767945584661979 y[1] (numeric) = 0.44090991460897683767945584661981 absolute error = 2e-32 relative error = 4.5360740000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.506 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.505 y[1] (analytic) = 0.44149603580709448809859136274815 y[1] (numeric) = 0.44149603580709448809859136274818 absolute error = 3e-32 relative error = 6.7950780000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.505 Order of pole = 1 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=4.90 x[1] = -1.504 y[1] (analytic) = 0.4420833265178820495159850699619 y[1] (numeric) = 0.44208332651788204951598506996192 absolute error = 2e-32 relative error = 4.5240340000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.504 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.503 y[1] (analytic) = 0.44267178985484792010659536699705 y[1] (numeric) = 0.44267178985484792010659536699707 absolute error = 2e-32 relative error = 4.5180200000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.503 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.502 y[1] (analytic) = 0.44326142894186847990141865820333 y[1] (numeric) = 0.44326142894186847990141865820335 absolute error = 2e-32 relative error = 4.5120100000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.502 Order of pole = 1 TOP MAIN SOLVE Loop x[1] = -1.501 y[1] (analytic) = 0.44385224691322954884194510257869 y[1] (numeric) = 0.44385224691322954884194510257871 absolute error = 2e-32 relative error = 4.5060040000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.501 Order of pole = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); Iterations = 500 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Time to Timeout = 2 Minutes 55 Seconds Percent Done = 100.2 % > quit memory used=84.5MB, alloc=4.4MB, time=4.95