|\^/| 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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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_1D0, 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_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_1D0, > #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_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 LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre div CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_1D0[1] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * 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 LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre div CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := -ats(2,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * 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 LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp1[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre div CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := -ats(3,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * 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 add FULL CONST $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre div CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := -ats(4,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * 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 add FULL CONST $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre div CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := -ats(5,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * 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 LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit div CONST FULL $eq_no = 1 i = 1 > array_tmp3[kkk] := -ats(kkk,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * 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_1D0, 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_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_x[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := array_const_1D0[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*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] := 2*array_x[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := -ats(2, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[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_x[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := -ats(3, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[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_tmp2[4] := array_tmp1[4]; array_tmp3[4] := -ats(4, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[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_tmp2[5] := array_tmp1[5]; array_tmp3[5] := -ats(5, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[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_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := -ats(kkk, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*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(arctan(x)); > end; exact_soln_y := proc(x) return arctan(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, 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_1D0, > #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_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/sing2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -2.0;"); > omniout_str(ALWAYS,"x_end := -1.5;"); > 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 := 100;"); > 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(arctan(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #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_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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1D0[1] := 1.0; > array_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 := 100; > #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 ) = 1.0/ (x * x + 1.0) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T19:03:30-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_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,"sing2 diffeq.mxt") > ; > logitem_str(html_log_file,"sing2 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_1D0, 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_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/sing2postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -2.0;"); omniout_str(ALWAYS, "x_end := -1.5;"); 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 := 100;"); 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(arctan(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; 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_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_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_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 := 100; 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 ) = 1.0/ (x * x + 1.0) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T19:03:30-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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, "sing2 diffeq.mxt"); logitem_str(html_log_file, "sing2 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/sing2postode.ode################# diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.0; x_end := -1.5; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; #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(arctan(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.5 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 = 1.5423793205590851374391492714693e-89 max_value3 = 1.5423793205590851374391492714693e-89 value3 = 1.5423793205590851374391492714693e-89 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = -1.1071487177940905030170654601785 y[1] (numeric) = -1.1071487177940905030170654601785 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.236 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -1.999 y[1] (analytic) = -1.106948637764747567059262846648 y[1] (numeric) = -1.106948637764747567059262846648 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.998 y[1] (analytic) = -1.1067483975592701523523682753958 y[1] (numeric) = -1.1067483975592701523523682753957 absolute error = 1e-31 relative error = 9.0354772792562059120416505345611e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.234 Order of pole = 1.81e-28 TOP MAIN SOLVE Loop x[1] = -1.997 y[1] (analytic) = -1.1065479970013122650430381404474 y[1] (numeric) = -1.1065479970013122650430381404474 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.996 y[1] (analytic) = -1.1063474359142968807862186779712 y[1] (numeric) = -1.1063474359142968807862186779711 absolute error = 1e-31 relative error = 9.0387519104574028519967794944694e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.995 y[1] (analytic) = -1.1061467141214156290212504508558 y[1] (numeric) = -1.1061467141214156290212504508557 absolute error = 1e-31 relative error = 9.0403920857304604426210877964644e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.994 y[1] (analytic) = -1.1059458314456284769108753479934 y[1] (numeric) = -1.1059458314456284769108753479933 absolute error = 1e-31 relative error = 9.0420341717175948049497190083926e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.231 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -1.993 y[1] (analytic) = -1.105744787709663412943428695263 y[1] (numeric) = -1.1057447877096634129434286952629 absolute error = 1e-31 relative error = 9.0436781716268063971992603060437e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.23 Order of pole = 2.18e-28 TOP MAIN SOLVE Loop x[1] = -1.992 y[1] (analytic) = -1.1055435827360161301985035103973 y[1] (numeric) = -1.1055435827360161301985035103972 absolute error = 1e-31 relative error = 9.0453240886730556478989646583430e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.991 y[1] (analytic) = -1.1053422163469497092763783943778 y[1] (numeric) = -1.1053422163469497092763783943777 absolute error = 1e-31 relative error = 9.0469719260782813712921493917677e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.228 Order of pole = 8.0e-29 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = -1.1051406883644943008915050378617 y[1] (numeric) = -1.1051406883644943008915050378616 absolute error = 1e-31 relative error = 9.0486216870714192400987702792324e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.989 y[1] (analytic) = -1.1049389986104468081303558325205 y[1] (numeric) = -1.1049389986104468081303558325204 absolute error = 1e-31 relative error = 9.0502733748884203158446404492898e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.226 Order of pole = 1.89e-28 TOP MAIN SOLVE Loop x[1] = -1.988 y[1] (analytic) = -1.1047371469063705683739366141761 y[1] (numeric) = -1.104737146906370568373936614176 absolute error = 1e-31 relative error = 9.0519269927722696369635959928604e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.225 Order of pole = 8.9e-29 TOP MAIN SOLVE Loop x[1] = -1.987 y[1] (analytic) = -1.1045351330735950348852741273846 y[1] (numeric) = -1.1045351330735950348852741273845 absolute error = 1e-31 relative error = 9.0535825439730048648797464965443e-30 % Correct digits = 31 h = 0.001 memory used=3.8MB, alloc=2.9MB, time=0.39 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.986 y[1] (analytic) = -1.1043329569332154580621923897538 y[1] (numeric) = -1.1043329569332154580621923897537 absolute error = 1e-31 relative error = 9.0552400317477349882777888728361e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.985 y[1] (analytic) = -1.1041306183060925663556967489111 y[1] (numeric) = -1.104130618306092566355696748911 absolute error = 1e-31 relative error = 9.0568994593606590857702068072494e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.984 y[1] (analytic) = -1.103928117012852246854289065787 y[1] (numeric) = -1.1039281170128522468542890657869 absolute error = 1e-31 relative error = 9.0585608300830851471710259195647e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.983 y[1] (analytic) = -1.1037254528738852255345421248616 y[1] (numeric) = -1.1037254528738852255345421248615 absolute error = 1e-31 relative error = 9.0602241471934489535866463604083e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.221 Order of pole = 2.46e-28 TOP MAIN SOLVE Loop x[1] = -1.982 y[1] (analytic) = -1.1035226257093467471782660653698 y[1] (numeric) = -1.1035226257093467471782660653697 absolute error = 1e-31 relative error = 9.0618894139773330165351300543921e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.981 y[1] (analytic) = -1.1033196353391562549566043472836 y[1] (numeric) = -1.1033196353391562549566043472834 absolute error = 2e-31 relative error = 1.8127113267454971152612358353300e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.219 Order of pole = 1.20e-28 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = -1.103116481582997069681401512326 y[1] (numeric) = -1.1031164815829970696814015123258 absolute error = 2e-31 relative error = 1.8130451619487679319549811460408e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.979 y[1] (analytic) = -1.1029131642603160687241897734317 y[1] (numeric) = -1.1029131642603160687241897734315 absolute error = 2e-31 relative error = 1.8133793890667064395766718593860e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.978 y[1] (analytic) = -1.1027096831903233646031462660842 y[1] (numeric) = -1.102709683190323364603146266084 absolute error = 2e-31 relative error = 1.8137140087621846406009302369409e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.216 Order of pole = 1.36e-28 TOP MAIN SOLVE Loop x[1] = -1.977 y[1] (analytic) = -1.1025060381919919832383776219549 y[1] (numeric) = -1.1025060381919919832383776219547 absolute error = 2e-31 relative error = 1.8140490216995230012810776614791e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.976 y[1] (analytic) = -1.1023022290840575418758933793661 y[1] (numeric) = -1.1023022290840575418758933793659 absolute error = 2e-31 relative error = 1.8143844285444943112046018465636e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.215 Order of pole = 1.32e-28 TOP MAIN SOLVE Loop x[1] = -1.975 y[1] (analytic) = -1.1020982556850179266806346264257 y[1] (numeric) = -1.1020982556850179266806346264256 absolute error = 1e-31 relative error = 9.0736011498216377747754979365750e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.974 y[1] (analytic) = -1.1018941178131329699989291813655 y[1] (numeric) = -1.1018941178131329699989291813653 absolute error = 2e-31 relative error = 1.8150564266277117959243675854204e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.213 Order of pole = 1.49e-28 TOP MAIN SOLVE Loop x[1] = -1.973 y[1] (analytic) = -1.1016898152864241272907495507763 y[1] (numeric) = -1.1016898152864241272907495507761 absolute error = 2e-31 relative error = 1.8153930192048000723184921159141e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.212 Order of pole = 2.8e-29 TOP MAIN SOLVE Loop x[1] = -1.972 y[1] (analytic) = -1.1014853479226741537321548702117 y[1] (numeric) = -1.1014853479226741537321548702116 absolute error = 1e-31 relative error = 9.0786500418360665270098367538807e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.971 y[1] (analytic) = -1.1012807155394267804883030231387 y[1] (numeric) = -1.1012807155394267804883030231386 absolute error = 1e-31 relative error = 9.0803369739402211001202600955206e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.21 Order of pole = 6.1e-29 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = -1.1010759179539863906574241535935 y[1] (numeric) = -1.1010759179539863906574241535935 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.969 y[1] (analytic) = -1.1008709549834176948861518352737 y[1] (numeric) = -1.1008709549834176948861518352737 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.968 y[1] (analytic) = -1.1006658264445454066566132352894 y[1] (numeric) = -1.1006658264445454066566132352894 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.207 Order of pole = 2.22e-28 TOP MAIN SOLVE Loop x[1] = -1.967 y[1] (analytic) = -1.1004605321539539172456847145512 y[1] (numeric) = -1.1004605321539539172456847145512 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.966 y[1] (analytic) = -1.1002550719279869703568244389027 y[1] (numeric) = -1.1002550719279869703568244389027 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.965 y[1] (analytic) = -1.1000494455827473364248987357562 y[1] (numeric) = -1.1000494455827473364248987357562 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.205 Order of pole = 1.30e-28 TOP MAIN SOLVE Loop x[1] = -1.964 y[1] (analytic) = -1.0998436529340964865944241202885 y[1] (numeric) = -1.0998436529340964865944241202884 absolute error = 1e-31 relative error = 9.0922013991012302698553316089919e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.963 y[1] (analytic) = -1.0996376937976542663716521333248 y[1] (numeric) = -1.0996376937976542663716521333247 absolute error = 1e-31 relative error = 9.0939043435883826168198000358170e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.87 x[1] = -1.962 y[1] (analytic) = -1.0994315679887985689509293800305 y[1] (numeric) = -1.0994315679887985689509293800304 absolute error = 1e-31 relative error = 9.0956093049912169162666286652321e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.961 y[1] (analytic) = -1.0992252753226650082157704345585 y[1] (numeric) = -1.0992252753226650082157704345583 absolute error = 2e-31 relative error = 1.8194632573499757573522657907884e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = -1.0990188156141465914150865810103 y[1] (numeric) = -1.0990188156141465914150865810101 absolute error = 2e-31 relative error = 1.8198050584624185222028007802136e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.2 Order of pole = 3.1e-29 TOP MAIN SOLVE Loop x[1] = -1.959 y[1] (analytic) = -1.0988121886778933915150186955938 y[1] (numeric) = -1.0988121886778933915150186955936 absolute error = 2e-31 relative error = 1.8201472650266363786040457441318e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.958 y[1] (analytic) = -1.0986053943283122192268279388266 y[1] (numeric) = -1.0986053943283122192268279388265 absolute error = 1e-31 relative error = 9.1024493886760896795704879744568e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.199 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -1.957 y[1] (analytic) = -1.0983984323795662947113033201895 y[1] (numeric) = -1.0983984323795662947113033201894 absolute error = 1e-31 relative error = 9.1041644864113990463622488837287e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.198 Order of pole = 6.0e-29 TOP MAIN SOLVE Loop x[1] = -1.956 y[1] (analytic) = -1.0981913026455749189601506209025 y[1] (numeric) = -1.0981913026455749189601506209023 absolute error = 2e-31 relative error = 1.8211763243634707297899427387834e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.197 Order of pole = 3.9e-29 TOP MAIN SOLVE Loop x[1] = -1.955 y[1] (analytic) = -1.0979840049400131448548326136238 y[1] (numeric) = -1.0979840049400131448548326136236 absolute error = 2e-31 relative error = 1.8215201596759756677534523102427e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.196 Order of pole = 1.4e-29 TOP MAIN SOLVE Loop x[1] = -1.954 y[1] (analytic) = -1.0977765390763114479033360009882 y[1] (numeric) = -1.0977765390763114479033360009881 absolute error = 1e-31 relative error = 9.1093220195925998444635623885240e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.195 Order of pole = 7.6e-29 TOP MAIN SOLVE Loop x[1] = -1.953 y[1] (analytic) = -1.0975689048676553966553460081481 y[1] (numeric) = -1.097568904867655396655346008148 absolute error = 1e-31 relative error = 9.1110452889568675187843218323314e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.952 y[1] (analytic) = -1.0973611021269853227963151079938 y[1] (numeric) = -1.0973611021269853227963151079937 absolute error = 1e-31 relative error = 9.1127706099817741512425971545534e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.951 y[1] (analytic) = -1.0971531306669959909209179316523 y[1] (numeric) = -1.0971531306669959909209179316522 absolute error = 1e-31 relative error = 9.1144979861841768468166098275057e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = -1.0969449903001362679863900213251 y[1] (numeric) = -1.096944990300136267986390021325 absolute error = 1e-31 relative error = 9.1162274210887179709159703187133e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.949 y[1] (analytic) = -1.0967366808386087924462537176792 y[1] (numeric) = -1.0967366808386087924462537176791 absolute error = 1e-31 relative error = 9.1179589182278461608582254086509e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.948 y[1] (analytic) = -1.0965282020943696430649401399777 y[1] (numeric) = -1.0965282020943696430649401399776 absolute error = 1e-31 relative error = 9.1196924811418374040986375519891e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.19 Order of pole = 1.60e-28 TOP MAIN SOLVE Loop x[1] = -1.947 y[1] (analytic) = -1.0963195538791280074138219140809 y[1] (numeric) = -1.0963195538791280074138219140807 absolute error = 2e-31 relative error = 1.8242856226757632366914219309903e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.189 Order of pole = 2.66e-28 TOP MAIN SOLVE Loop x[1] = -1.946 y[1] (analytic) = -1.0961107360043458500491770314935 y[1] (numeric) = -1.0961107360043458500491770314934 absolute error = 1e-31 relative error = 9.1231658184947766895871771316607e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.188 Order of pole = 1.61e-28 TOP MAIN SOLVE Loop x[1] = -1.945 y[1] (analytic) = -1.095901748281237580372609981937 y[1] (numeric) = -1.0959017482812375803726099819368 absolute error = 2e-31 relative error = 1.8249811200107208201866004508942e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.187 Order of pole = 2.48e-28 TOP MAIN SOLVE Loop x[1] = -1.944 y[1] (analytic) = -1.0956925905207697201744620926103 y[1] (numeric) = -1.0956925905207697201744620926102 absolute error = 1e-31 relative error = 9.1266474616270959314213236512886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.943 y[1] (analytic) = -1.0954832625336605708607488295345 y[1] (numeric) = -1.0954832625336605708607488295344 absolute error = 1e-31 relative error = 9.1283914067949834461363363505802e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.185 Order of pole = 1.42e-28 TOP MAIN SOLVE Loop x[1] = -1.942 y[1] (analytic) = -1.0952737641303798803641676702742 y[1] (numeric) = -1.0952737641303798803641676702741 absolute error = 1e-31 relative error = 9.1301374391449531452265050565231e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.184 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.941 y[1] (analytic) = -1.0950640951211485097397260430628 y[1] (numeric) = -1.0950640951211485097397260430627 absolute error = 1e-31 relative error = 9.1318855622726683162933453765985e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.183 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = -1.094854255315938099445544745049 y[1] (numeric) = -1.0948542553159380994455447450489 absolute error = 1e-31 relative error = 9.1336357797817906555132445465154e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.183 Order of pole = 5.3e-29 TOP MAIN SOLVE Loop x[1] = -1.939 y[1] (analytic) = -1.0946442445244707353093982021949 y[1] (numeric) = -1.0946442445244707353093982021948 absolute error = 1e-31 relative error = 9.1353880952840019577444348270348e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.182 Order of pole = 2.67e-28 TOP MAIN SOLVE Loop x[1] = -1.938 y[1] (analytic) = -1.0944340625562186141815589154218 y[1] (numeric) = -1.0944340625562186141815589154217 absolute error = 1e-31 relative error = 9.1371425123990258758722792088744e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.181 Order of pole = 1.02e-28 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=1.33 x[1] = -1.937 y[1] (analytic) = -1.0942237092204037092745194520772 y[1] (numeric) = -1.0942237092204037092745194520771 absolute error = 1e-31 relative error = 9.1388990347546497496470803801347e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.936 y[1] (analytic) = -1.0940131843259974351901713888221 y[1] (numeric) = -1.094013184325997435190171388822 absolute error = 1e-31 relative error = 9.1406576659867465042696801106602e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.935 y[1] (analytic) = -1.0938024876817203126350266917691 y[1] (numeric) = -1.093802487681720312635026691769 absolute error = 1e-31 relative error = 9.1424184097392966189811773144578e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.934 y[1] (analytic) = -1.0935916190960416328240731322788 y[1] (numeric) = -1.0935916190960416328240731322787 absolute error = 1e-31 relative error = 9.1441812696644101659141590900677e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.177 Order of pole = 1.68e-28 TOP MAIN SOLVE Loop x[1] = -1.933 y[1] (analytic) = -1.0933805783771791215738614824 y[1] (numeric) = -1.0933805783771791215738614823999 absolute error = 1e-31 relative error = 9.1459462494223489194639100349531e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.932 y[1] (analytic) = -1.093169365333098603085428412664 y[1] (numeric) = -1.093169365333098603085428412664 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.175 Order of pole = 7.5e-29 TOP MAIN SOLVE Loop x[1] = -1.931 y[1] (analytic) = -1.0929579797715136634176652269667 y[1] (numeric) = -1.0929579797715136634176652269666 absolute error = 1e-31 relative error = 9.1494825831186408072528603110266e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = -1.0927464214998853136517488147424 y[1] (numeric) = -1.0927464214998853136517488147423 absolute error = 1e-31 relative error = 9.1512539444184759784150934509128e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.174 Order of pole = 3.5e-29 TOP MAIN SOLVE Loop x[1] = -1.929 y[1] (analytic) = -1.0925346903254216527472574797095 y[1] (numeric) = -1.0925346903254216527472574797094 absolute error = 1e-31 relative error = 9.1530274402741451465902543897967e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.928 y[1] (analytic) = -1.0923227860550775300906006172872 y[1] (numeric) = -1.0923227860550775300906006172871 absolute error = 1e-31 relative error = 9.1548030743870027244830602811850e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.172 Order of pole = 8.8e-29 TOP MAIN SOLVE Loop x[1] = -1.927 y[1] (analytic) = -1.0921107084955542077363975595155 y[1] (numeric) = -1.0921107084955542077363975595155 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.171 Order of pole = 8.8e-29 TOP MAIN SOLVE Loop x[1] = -1.926 y[1] (analytic) = -1.0918984574532990223424472870959 y[1] (numeric) = -1.0918984574532990223424472870958 absolute error = 1e-31 relative error = 9.1583607722311526406783794450876e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.925 y[1] (analytic) = -1.0916860327345050467989371231669 y[1] (numeric) = -1.0916860327345050467989371231669 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.169 Order of pole = 1.34e-28 TOP MAIN SOLVE Loop x[1] = -1.924 y[1] (analytic) = -1.0914734341451107515525449727968 y[1] (numeric) = -1.0914734341451107515525449727968 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.923 y[1] (analytic) = -1.0912606614907996656260961560552 y[1] (numeric) = -1.0912606614907996656260961560551 absolute error = 1e-31 relative error = 9.1637134489377992004496602860778e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.167 Order of pole = 1.18e-28 TOP MAIN SOLVE Loop x[1] = -1.922 y[1] (analytic) = -1.0910477145770000373344424010914 y[1] (numeric) = -1.0910477145770000373344424010914 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.921 y[1] (analytic) = -1.0908345932088844946972371170395 y[1] (numeric) = -1.0908345932088844946972371170395 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = -1.0906212971913697055492876549513 y[1] (numeric) = -1.0906212971913697055492876549513 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.165 Order of pole = 6.8e-29 TOP MAIN SOLVE Loop x[1] = -1.919 y[1] (analytic) = -1.0904078263291160373491718884929 y[1] (numeric) = -1.0904078263291160373491718884929 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.918 y[1] (analytic) = -1.0901941804265272166868131049712 y[1] (numeric) = -1.0901941804265272166868131049712 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.917 y[1] (analytic) = -1.0899803592877499884907138915571 y[1] (numeric) = -1.0899803592877499884907138915571 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.162 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -1.916 y[1] (analytic) = -1.0897663627166737749355564314937 y[1] (numeric) = -1.0897663627166737749355564314936 absolute error = 1e-31 relative error = 9.1762788264734506583807129225455e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.161 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -1.915 y[1] (analytic) = -1.0895521905169303340508833907792 y[1] (numeric) = -1.0895521905169303340508833907791 absolute error = 1e-31 relative error = 9.1780825985541552593114430261943e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.16 Order of pole = 2.3e-29 TOP MAIN SOLVE Loop x[1] = -1.914 y[1] (analytic) = -1.0893378424918934180315803774641 y[1] (numeric) = -1.089337842491893418031580377464 absolute error = 1e-31 relative error = 9.1798885615914123713052762040903e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.913 y[1] (analytic) = -1.089123318444678431250887793451 y[1] (numeric) = -1.0891233184446784312508877934509 absolute error = 1e-31 relative error = 9.1816967194132717178587516586951e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.159 Order of pole = 6.5e-29 TOP MAIN SOLVE Loop x[1] = -1.912 memory used=15.2MB, alloc=4.2MB, time=1.81 y[1] (analytic) = -1.088908618178142087976676772703 y[1] (numeric) = -1.088908618178142087976676772703 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.911 y[1] (analytic) = -1.0886937414948820697917308102142 y[1] (numeric) = -1.0886937414948820697917308102142 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.157 Order of pole = 1.53e-28 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = -1.0884786881972366827187816331298 y[1] (numeric) = -1.0884786881972366827187816331298 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.156 Order of pole = 1.28e-28 TOP MAIN SOLVE Loop x[1] = -1.909 y[1] (analytic) = -1.0882634580872845140510548491992 y[1] (numeric) = -1.0882634580872845140510548491991 absolute error = 1e-31 relative error = 9.1889513754103713041870176103847e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.908 y[1] (analytic) = -1.0880480509668440888890879284541 y[1] (numeric) = -1.088048050966844088889087928454 absolute error = 1e-31 relative error = 9.1907705648789663351824837155424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.907 y[1] (analytic) = -1.0878324666374735263845901318031 y[1] (numeric) = -1.087832466637473526384590131803 absolute error = 1e-31 relative error = 9.1925919722825830598204883418474e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.153 Order of pole = 9.0e-29 TOP MAIN SOLVE Loop x[1] = -1.906 y[1] (analytic) = -1.0876167049004701956921210952779 y[1] (numeric) = -1.0876167049004701956921210952778 absolute error = 1e-31 relative error = 9.1944156015102015057258789205689e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.905 y[1] (analytic) = -1.0874007655568703716293719111304 y[1] (numeric) = -1.0874007655568703716293719111304 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.904 y[1] (analytic) = -1.0871846484074488900468397170265 y[1] (numeric) = -1.0871846484074488900468397170265 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.903 y[1] (analytic) = -1.0869683532527188029076940123762 y[1] (numeric) = -1.0869683532527188029076940123762 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.902 y[1] (analytic) = -1.0867518798929310330786401665586 y[1] (numeric) = -1.0867518798929310330786401665585 absolute error = 1e-31 relative error = 9.2017324147488201111130775904820e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.901 y[1] (analytic) = -1.0865352281280740288325928675998 y[1] (numeric) = -1.0865352281280740288325928675998 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = -1.0863183977578734180639795819257 y[1] (numeric) = -1.0863183977578734180639795819256 absolute error = 1e-31 relative error = 9.2054042540747552241846705235362e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.147 Order of pole = 4.9e-29 TOP MAIN SOLVE Loop x[1] = -1.899 y[1] (analytic) = -1.0861013885817916622175014562941 y[1] (numeric) = -1.086101388581791662217501456294 absolute error = 1e-31 relative error = 9.2072435457041350112918090220349e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.898 y[1] (analytic) = -1.0858842003990277099311864921022 y[1] (numeric) = -1.0858842003990277099311864921021 absolute error = 1e-31 relative error = 9.2090850905882228194692844273728e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.897 y[1] (analytic) = -1.085666833008516650394577260115 y[1] (numeric) = -1.0856668330085166503945772601149 absolute error = 1e-31 relative error = 9.2109288926960834390817176372048e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.144 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -1.896 y[1] (analytic) = -1.0854492862089293664229029004597 y[1] (numeric) = -1.0854492862089293664229029004597 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.895 y[1] (analytic) = -1.0852315597986721872480926686421 y[1] (numeric) = -1.0852315597986721872480926686421 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.894 y[1] (analytic) = -1.0850136535758865410274958435374 y[1] (numeric) = -1.0850136535758865410274958435373 absolute error = 1e-31 relative error = 9.2164738821884269280400018914311e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.142 Order of pole = 1.94e-28 TOP MAIN SOLVE Loop x[1] = -1.893 y[1] (analytic) = -1.0847955673384486070711804079716 y[1] (numeric) = -1.0847955673384486070711804079716 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.141 Order of pole = 2.99e-28 TOP MAIN SOLVE Loop x[1] = -1.892 y[1] (analytic) = -1.0845773008839689677886905468049 y[1] (numeric) = -1.0845773008839689677886905468048 absolute error = 1e-31 relative error = 9.2201819011421733813010714595852e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.891 y[1] (analytic) = -1.0843588540097922603561506815363 y[1] (numeric) = -1.0843588540097922603561506815363 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = -1.084140226512996828104611474551 y[1] (numeric) = -1.084140226512996828104611474551 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.138 Order of pole = 3.48e-28 TOP MAIN SOLVE Loop x[1] = -1.889 y[1] (analytic) = -1.0839214181903943716305409903873 y[1] (numeric) = -1.0839214181903943716305409903873 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.137 Order of pole = 2.89e-28 TOP MAIN SOLVE Loop x[1] = -1.888 y[1] (analytic) = -1.0837024288385295996293719960113 y[1] (numeric) = -1.0837024288385295996293719960113 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.136 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -1.887 y[1] (analytic) = -1.0834832582536798794530242172078 y[1] (numeric) = -1.0834832582536798794530242172078 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=2.30 x[1] = -1.886 y[1] (analytic) = -1.0832639062318548873923282440222 y[1] (numeric) = -1.0832639062318548873923282440222 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.135 Order of pole = 1.40e-28 TOP MAIN SOLVE Loop x[1] = -1.885 y[1] (analytic) = -1.0830443725687962586852856948912 y[1] (numeric) = -1.0830443725687962586852856948912 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.884 y[1] (analytic) = -1.0828246570599772372521082068612 y[1] (numeric) = -1.0828246570599772372521082068612 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.133 Order of pole = 1.84e-28 TOP MAIN SOLVE Loop x[1] = -1.883 y[1] (analytic) = -1.0826047595006023251579858182959 y[1] (numeric) = -1.0826047595006023251579858182959 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.132 Order of pole = 2.92e-28 TOP MAIN SOLVE Loop x[1] = -1.882 y[1] (analytic) = -1.0823846796856069318045433508962 y[1] (numeric) = -1.0823846796856069318045433508963 absolute error = 1e-31 relative error = 9.2388595179531120030967885518493e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.881 y[1] (analytic) = -1.0821644174096570228509514798842 y[1] (numeric) = -1.0821644174096570228509514798843 absolute error = 1e-31 relative error = 9.2407399828731071368025313317981e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.13 Order of pole = 5.5e-29 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = -1.0819439724671487688656673050121 y[1] (numeric) = -1.0819439724671487688656673050121 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.129 Order of pole = 1.12e-28 TOP MAIN SOLVE Loop x[1] = -1.879 y[1] (analytic) = -1.0817233446522081937097874008434 y[1] (numeric) = -1.0817233446522081937097874008434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.878 y[1] (analytic) = -1.0815025337586908226530045326886 y[1] (numeric) = -1.0815025337586908226530045326886 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.128 Order of pole = 2.44e-28 TOP MAIN SOLVE Loop x[1] = -1.877 y[1] (analytic) = -1.0812815395801813302231674748537 y[1] (numeric) = -1.0812815395801813302231674748537 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.876 y[1] (analytic) = -1.0810603619099931877904516606612 y[1] (numeric) = -1.0810603619099931877904516606612 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.126 Order of pole = 7.8e-29 TOP MAIN SOLVE Loop x[1] = -1.875 y[1] (analytic) = -1.0808390005411683108871567292172 y[1] (numeric) = -1.0808390005411683108871567292172 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.125 Order of pole = 9.7e-29 TOP MAIN SOLVE Loop x[1] = -1.874 y[1] (analytic) = -1.0806174552664767062641554123057 y[1] (numeric) = -1.0806174552664767062641554123057 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.124 Order of pole = 1.68e-28 TOP MAIN SOLVE Loop x[1] = -1.873 y[1] (analytic) = -1.0803957258784161186850266262912 y[1] (numeric) = -1.0803957258784161186850266262912 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.123 Order of pole = 1.52e-28 TOP MAIN SOLVE Loop x[1] = -1.872 y[1] (analytic) = -1.0801738121692116774589140986807 y[1] (numeric) = -1.0801738121692116774589140986807 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.871 y[1] (analytic) = -1.0799517139308155427131603672314 y[1] (numeric) = -1.0799517139308155427131603672314 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = -1.0797294309549065514067745413803 y[1] (numeric) = -1.0797294309549065514067745413803 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.121 Order of pole = 1.0e-29 TOP MAIN SOLVE Loop x[1] = -1.869 y[1] (analytic) = -1.0795069630328898630858008115048 y[1] (numeric) = -1.0795069630328898630858008115048 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.868 y[1] (analytic) = -1.0792843099558966053816633312927 y[1] (numeric) = -1.0792843099558966053816633312927 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.119 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -1.867 y[1] (analytic) = -1.0790614715147835192535717824957 y[1] (numeric) = -1.0790614715147835192535717824957 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.866 y[1] (analytic) = -1.07883844750013260397608065976 y[1] (numeric) = -1.07883844750013260397608065976 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.117 Order of pole = 7.8e-29 TOP MAIN SOLVE Loop x[1] = -1.865 y[1] (analytic) = -1.0786152377022507618729040862557 y[1] (numeric) = -1.0786152377022507618729040862557 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.864 y[1] (analytic) = -1.0783918419111694427980967886686 y[1] (numeric) = -1.0783918419111694427980967886686 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.863 y[1] (analytic) = -1.0781682599166442883657207229581 y[1] (numeric) = -1.0781682599166442883657207229581 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.114 Order of pole = 1.22e-28 TOP MAIN SOLVE Loop x[1] = -1.862 y[1] (analytic) = -1.0779444915081547759291257503268 y[1] (numeric) = -1.0779444915081547759291257503268 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.861 y[1] (analytic) = -1.0777205364749038623109817162831 y[1] (numeric) = -1.0777205364749038623109817162831 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.113 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=2.78 x[1] = -1.86 y[1] (analytic) = -1.0774963946058176272852082847049 y[1] (numeric) = -1.0774963946058176272852082847049 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.859 y[1] (analytic) = -1.0772720656895449168119579236318 y[1] (numeric) = -1.0772720656895449168119579236318 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.858 y[1] (analytic) = -1.0770475495144569860268165303173 y[1] (numeric) = -1.0770475495144569860268165303174 absolute error = 1e-31 relative error = 9.2846411511804586976718044742353e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.857 y[1] (analytic) = -1.0768228458686471419853953200687 y[1] (numeric) = -1.0768228458686471419853953200688 absolute error = 1e-31 relative error = 9.2865786033107795344102001548831e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.109 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -1.856 y[1] (analytic) = -1.0765979545399303861644967867803 y[1] (numeric) = -1.0765979545399303861644967867804 absolute error = 1e-31 relative error = 9.2885184834605831215698755590492e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.855 y[1] (analytic) = -1.0763728753158430567210467730395 y[1] (numeric) = -1.0763728753158430567210467730397 absolute error = 2e-31 relative error = 1.8580921592000676278365345927323e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.854 y[1] (analytic) = -1.0761476079836424705099939644419 y[1] (numeric) = -1.076147607983642470509993964442 absolute error = 1e-31 relative error = 9.2924055453106585335090153478525e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.853 y[1] (analytic) = -1.0759221523303065648623874465032 y[1] (numeric) = -1.0759221523303065648623874465034 absolute error = 2e-31 relative error = 1.8588705471564664420487561209757e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.106 Order of pole = 1.28e-28 TOP MAIN SOLVE Loop x[1] = -1.852 y[1] (analytic) = -1.0756965081425335391248523335068 y[1] (numeric) = -1.0756965081425335391248523335069 absolute error = 1e-31 relative error = 9.2963023718163498232442498154181e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.851 y[1] (analytic) = -1.0754706752067414959616928969641 y[1] (numeric) = -1.0754706752067414959616928969642 absolute error = 1e-31 relative error = 9.2982544578239336591460294742795e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = -1.0752446533090680824208620873218 y[1] (numeric) = -1.075244653309068082420862087322 absolute error = 2e-31 relative error = 1.8600417996453133236468869531471e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.849 y[1] (analytic) = -1.0750184422353701307650458563007 y[1] (numeric) = -1.0750184422353701307650458563009 absolute error = 2e-31 relative error = 1.8604331994912042583880831782527e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.102 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -1.848 y[1] (analytic) = -1.0747920417712232990691202490252 y[1] (numeric) = -1.0747920417712232990691202490254 absolute error = 2e-31 relative error = 1.8608250919908778274663424217194e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.101 Order of pole = 4.5e-29 TOP MAIN SOLVE Loop x[1] = -1.847 y[1] (analytic) = -1.0745654517019217115852488450957 y[1] (numeric) = -1.074565451701921711585248845096 absolute error = 3e-31 relative error = 2.7918262170522329246914585753719e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.846 y[1] (analytic) = -1.0743386718124775988768977861754 y[1] (numeric) = -1.0743386718124775988768977861757 absolute error = 3e-31 relative error = 2.7924155377734000685555948314660e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.845 y[1] (analytic) = -1.0741117018876209377230553347201 y[1] (numeric) = -1.0741117018876209377230553347204 absolute error = 3e-31 relative error = 2.7930056014917853957333579491231e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.099 Order of pole = 1.33e-28 TOP MAIN SOLVE Loop x[1] = -1.844 y[1] (analytic) = -1.073884541711799090793952664386 y[1] (numeric) = -1.0738845417117990907939526643863 absolute error = 3e-31 relative error = 2.7935964095524870914733552053890e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.843 y[1] (analytic) = -1.0736571910691764460995923876043 y[1] (numeric) = -1.0736571910691764460995923876046 absolute error = 3e-31 relative error = 2.7941879633037432028566264928496e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.842 y[1] (analytic) = -1.0734296497436340562124011800399 y[1] (numeric) = -1.0734296497436340562124011800401 absolute error = 2e-31 relative error = 1.8631868427312937120652895760835e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.096 Order of pole = 3.38e-28 TOP MAIN SOLVE Loop x[1] = -1.841 y[1] (analytic) = -1.0732019175187692772653327653487 y[1] (numeric) = -1.0732019175187692772653327653489 absolute error = 2e-31 relative error = 1.8635822088577491838251468937032e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = -1.0729739941778954077267574770421 y[1] (numeric) = -1.0729739941778954077267574770423 absolute error = 2e-31 relative error = 1.8639780748203361025599096246503e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.094 Order of pole = 1.41e-28 TOP MAIN SOLVE Loop x[1] = -1.839 y[1] (analytic) = -1.0727458795040413269534846175545 y[1] (numeric) = -1.0727458795040413269534846175547 absolute error = 2e-31 relative error = 1.8643744415263125262072580928954e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.093 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -1.838 y[1] (analytic) = -1.0725175732799511335232738880207 y[1] (numeric) = -1.0725175732799511335232738880209 absolute error = 2e-31 relative error = 1.8647713098850597183044918728758e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.837 y[1] (analytic) = -1.0722890752880837833482022660042 y[1] (numeric) = -1.0722890752880837833482022660045 absolute error = 3e-31 relative error = 2.7977530212121323018938206931445e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.092 Order of pole = 8.1e-29 TOP MAIN SOLVE Loop x[1] = -1.836 y[1] (analytic) = -1.0720603853106127275702628626984 y[1] (numeric) = -1.0720603853106127275702628626987 absolute error = 3e-31 relative error = 2.7983498328135657449314193947025e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.835 memory used=26.7MB, alloc=4.3MB, time=3.26 y[1] (analytic) = -1.0718315031294255502405824961646 y[1] (numeric) = -1.0718315031294255502405824961649 absolute error = 3e-31 relative error = 2.7989474010055708285431928474344e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.09 Order of pole = 7.1e-29 TOP MAIN SOLVE Loop x[1] = -1.834 y[1] (analytic) = -1.0716024285261236057836549731896 y[1] (numeric) = -1.0716024285261236057836549731899 absolute error = 3e-31 relative error = 2.7995457271650497860459305013785e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.833 y[1] (analytic) = -1.0713731612820216562479973795565 y[1] (numeric) = -1.0713731612820216562479973795568 absolute error = 3e-31 relative error = 2.8001448126721353646042716422842e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.832 y[1] (analytic) = -1.0711437011781475083446470371482 y[1] (numeric) = -1.0711437011781475083446470371485 absolute error = 3e-31 relative error = 2.8007446589102000586806134943257e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.087 Order of pole = 8.5e-29 TOP MAIN SOLVE Loop x[1] = -1.831 y[1] (analytic) = -1.0709140479952416502749271965605 y[1] (numeric) = -1.0709140479952416502749271965608 absolute error = 3e-31 relative error = 2.8013452672658653745499550395080e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = -1.0706842015137568883489199960067 y[1] (numeric) = -1.0706842015137568883489199960071 absolute error = 4e-31 relative error = 3.7359288521720148346665977727177e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.085 Order of pole = 3.32e-28 TOP MAIN SOLVE Loop x[1] = -1.829 y[1] (analytic) = -1.0704541615138579833960957314775 y[1] (numeric) = -1.0704541615138579833960957314778 absolute error = 3e-31 relative error = 2.8025487758927847613369564835552e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.828 y[1] (analytic) = -1.0702239277754212869695580495882 y[1] (numeric) = -1.0702239277754212869695580495885 absolute error = 3e-31 relative error = 2.8031516789536107218194475717391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.827 y[1] (analytic) = -1.0699935000780343773453752935366 y[1] (numeric) = -1.0699935000780343773453752935369 absolute error = 3e-31 relative error = 2.8037553497111998316405861944994e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.083 Order of pole = 2.80e-28 TOP MAIN SOLVE Loop x[1] = -1.826 y[1] (analytic) = -1.0697628782009956953184789043136 y[1] (numeric) = -1.0697628782009956953184789043139 absolute error = 3e-31 relative error = 2.8043597895685587195824197938997e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.082 Order of pole = 1.05e-28 TOP MAIN SOLVE Loop x[1] = -1.825 y[1] (analytic) = -1.0695320619233141797966205039994 y[1] (numeric) = -1.0695320619233141797966205039997 absolute error = 3e-31 relative error = 2.8049649999319992724645945924283e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.824 y[1] (analytic) = -1.0693010510237089031938900658457 y[1] (numeric) = -1.069301051023708903193890065846 absolute error = 3e-31 relative error = 2.8055709822111481205110765585664e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.08 Order of pole = 6.29e-28 TOP MAIN SOLVE Loop x[1] = -1.823 y[1] (analytic) = -1.0690698452806087066253084071283 y[1] (numeric) = -1.0690698452806087066253084071286 absolute error = 3e-31 relative error = 2.8061777378189561547588959632361e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.079 Order of pole = 3.93e-28 TOP MAIN SOLVE Loop x[1] = -1.822 y[1] (analytic) = -1.068838444472151834904018125674 y[1] (numeric) = -1.0688384444721518349040181256743 absolute error = 3e-31 relative error = 2.8067852681717080766334799306703e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.078 Order of pole = 6.94e-28 TOP MAIN SOLVE Loop x[1] = -1.821 y[1] (analytic) = -1.068606848376185571342608039746 y[1] (numeric) = -1.0686068483761855713426080397463 absolute error = 3e-31 relative error = 2.8073935746890319798156859161509e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.078 Order of pole = 1.143e-27 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = -1.0683750567702658723601171838498 y[1] (numeric) = -1.0683750567702658723601171838501 absolute error = 3e-31 relative error = 2.8080026587939089645262002760789e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.819 y[1] (analytic) = -1.0681430694316570018962754602112 y[1] (numeric) = -1.0681430694316570018962754602115 absolute error = 3e-31 relative error = 2.8086125219126827843535200477993e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.076 Order of pole = 1.313e-25 TOP MAIN SOLVE Loop x[1] = -1.818 y[1] (analytic) = -1.0679108861373311656345491474241 y[1] (numeric) = -1.0679108861373311656345491474244 absolute error = 3e-31 relative error = 2.8092231654750695257522927423330e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.075 Order of pole = 4.296e-27 TOP MAIN SOLVE Loop x[1] = -1.817 y[1] (analytic) = -1.0676785066639681450355706242843 y[1] (numeric) = -1.0676785066639681450355706242846 absolute error = 3e-31 relative error = 2.8098345909141673203393483876693e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.816 y[1] (analytic) = -1.0674459307879549311825428783578 y[1] (numeric) = -1.0674459307879549311825428783581 absolute error = 3e-31 relative error = 2.8104467996664660901153202585791e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.815 y[1] (analytic) = -1.0672131582853853584402206356041 y[1] (numeric) = -1.0672131582853853584402206356044 absolute error = 3e-31 relative error = 2.8110597931718573257403157061688e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.072 Order of pole = 2.72e-28 TOP MAIN SOLVE Loop x[1] = -1.814 y[1] (analytic) = -1.0669801889320597379290812696193 y[1] (numeric) = -1.0669801889320597379290812696196 absolute error = 3e-31 relative error = 2.8116735728736438979926662718547e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.813 y[1] (analytic) = -1.0667470225034844908163100270173 y[1] (numeric) = -1.0667470225034844908163100270177 absolute error = 4e-31 relative error = 3.7497175202913998700538091352118e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.812 y[1] (analytic) = -1.0665136587748717814252355393604 y[1] (numeric) = -1.0665136587748717814252355393608 absolute error = 4e-31 relative error = 3.7505379955423073842070761075278e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.811 y[1] (analytic) = -1.0662800975211391501648630821168 y[1] (numeric) = -1.0662800975211391501648630821172 absolute error = 4e-31 relative error = 3.7513595248557093580016724809298e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = -1.0660463385169091462811645876063 y[1] (numeric) = -1.0660463385169091462811645876067 memory used=30.5MB, alloc=4.3MB, time=3.75 absolute error = 4e-31 relative error = 3.7521821101743353568354227243260e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.068 Order of pole = 3.14e-28 TOP MAIN SOLVE Loop x[1] = -1.809 y[1] (analytic) = -1.0658123815365089604317960220182 y[1] (numeric) = -1.0658123815365089604317960220186 absolute error = 4e-31 relative error = 3.7530057534455295323918643603915e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.808 y[1] (analytic) = -1.0655782263539700570859243966009 y[1] (numeric) = -1.0655782263539700570859243966013 absolute error = 4e-31 relative error = 3.7538304566212639737055677664421e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.807 y[1] (analytic) = -1.0653438727430278067508584002558 y[1] (numeric) = -1.0653438727430278067508584002562 absolute error = 4e-31 relative error = 3.7546562216581521036973481518940e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.065 Order of pole = 5.49e-28 TOP MAIN SOLVE Loop x[1] = -1.806 y[1] (analytic) = -1.0651093204771211180271884152658 y[1] (numeric) = -1.0651093204771211180271884152661 absolute error = 3e-31 relative error = 2.8166122878880965910182010904529e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.805 y[1] (analytic) = -1.0648745693293920694941535099859 y[1] (numeric) = -1.0648745693293920694941535099863 absolute error = 4e-31 relative error = 3.7563109451651304897567873866394e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.063 Order of pole = 4.9e-29 TOP MAIN SOLVE Loop x[1] = -1.804 y[1] (analytic) = -1.0646396190726855414269648922663 y[1] (numeric) = -1.0646396190726855414269648922667 absolute error = 4e-31 relative error = 3.7571399075717754700628783078964e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.063 Order of pole = 8.65e-28 TOP MAIN SOLVE Loop x[1] = -1.803 y[1] (analytic) = -1.0644044694795488473478272553968 y[1] (numeric) = -1.0644044694795488473478272553972 absolute error = 4e-31 relative error = 3.7579699397127107017463919551986e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.062 Order of pole = 2.80e-28 TOP MAIN SOLVE Loop x[1] = -1.802 y[1] (analytic) = -1.0641691203222313654124114547175 y[1] (numeric) = -1.0641691203222313654124114547179 absolute error = 4e-31 relative error = 3.7588010435679588291544294668560e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.801 y[1] (analytic) = -1.0639335713726841696335440179519 y[1] (numeric) = -1.0639335713726841696335440179523 absolute error = 4e-31 relative error = 3.7596332211222651746359474721922e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.06 Order of pole = 3.83e-28 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = -1.0636978224025596609438911160525 y[1] (numeric) = -1.063697822402559660943891116053 absolute error = 5e-31 relative error = 4.7005830929563893230016305303638e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.059 Order of pole = 4.33e-28 TOP MAIN SOLVE Loop x[1] = -1.799 y[1] (analytic) = -1.0634618731832111980994268041349 y[1] (numeric) = -1.0634618731832111980994268041354 absolute error = 5e-31 relative error = 4.7016260066134119566249209805795e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.058 Order of pole = 6.78e-28 TOP MAIN SOLVE Loop x[1] = -1.798 y[1] (analytic) = -1.0632257234856927284254875841644 y[1] (numeric) = -1.0632257234856927284254875841648 absolute error = 4e-31 relative error = 3.7621362158981153587008401710518e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.797 y[1] (analytic) = -1.0629893730807584184072276426995 y[1] (numeric) = -1.0629893730807584184072276426999 absolute error = 4e-31 relative error = 3.7629727081910425416613541789994e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.796 y[1] (analytic) = -1.0627528217388622841263014784297 y[1] (numeric) = -1.0627528217388622841263014784301 absolute error = 4e-31 relative error = 3.7638102841780765655705772834783e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.056 Order of pole = 1.155e-27 TOP MAIN SOLVE Loop x[1] = -1.795 y[1] (analytic) = -1.0625160692301578215456130557209 y[1] (numeric) = -1.0625160692301578215456130557213 absolute error = 4e-31 relative error = 3.7646489458725885864545700835308e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.055 Order of pole = 1.72e-28 TOP MAIN SOLVE Loop x[1] = -1.794 y[1] (analytic) = -1.0622791153244976366439831021563 y[1] (numeric) = -1.0622791153244976366439831021567 absolute error = 4e-31 relative error = 3.7654886952927694691313411430901e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.054 Order of pole = 4.69e-28 TOP MAIN SOLVE Loop x[1] = -1.793 y[1] (analytic) = -1.0620419597914330754025987103692 y[1] (numeric) = -1.0620419597914330754025987103696 absolute error = 4e-31 relative error = 3.7663295344616438394044498699751e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.792 y[1] (analytic) = -1.061804602400213853645122007572 y[1] (numeric) = -1.0618046024002138536451220075723 absolute error = 3e-31 relative error = 2.8253785990553131383636789462704e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.052 Order of pole = 3.3e-29 TOP MAIN SOLVE Loop x[1] = -1.791 y[1] (analytic) = -1.0615670429197876867333473203349 y[1] (numeric) = -1.0615670429197876867333473203352 absolute error = 3e-31 relative error = 2.8260108676213687513739159726227e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = -1.061329281118799919120308987613 y[1] (numeric) = -1.0613292811187999191203089876133 absolute error = 3e-31 relative error = 2.8266439580726077474527569644484e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.05 Order of pole = 6.6e-29 TOP MAIN SOLVE Loop x[1] = -1.789 y[1] (analytic) = -1.0610913167655931537627547620153 y[1] (numeric) = -1.0610913167655931537627547620156 absolute error = 3e-31 relative error = 2.8272778719409059959332584798323e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.788 y[1] (analytic) = -1.0608531496282068813949125881078 y[1] (numeric) = -1.0608531496282068813949125881081 absolute error = 3e-31 relative error = 2.8279126107618179280495052171179e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.787 y[1] (analytic) = -1.0606147794743771096654914573981 y[1] (numeric) = -1.0606147794743771096654914573984 absolute error = 3e-31 relative error = 2.8285481760745872952654185695514e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.048 Order of pole = 2.06e-28 TOP MAIN SOLVE Loop x[1] = -1.786 y[1] (analytic) = -1.0603762060715359921398700128174 y[1] (numeric) = -1.0603762060715359921398700128177 absolute error = 3e-31 relative error = 2.8291845694221579646418197554602e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.047 Order of pole = 6.1e-29 TOP MAIN SOLVE Loop x[1] = -1.785 y[1] (analytic) = -1.0601374291868114571694396112554 y[1] (numeric) = -1.0601374291868114571694396112556 absolute error = 2e-31 relative error = 1.8865478615674565009256863159005e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.046 memory used=34.3MB, alloc=4.3MB, time=4.24 Order of pole = 2.9e-29 TOP MAIN SOLVE Loop x[1] = -1.784 y[1] (analytic) = -1.0598984485870268366300816512671 y[1] (numeric) = -1.0598984485870268366300816512673 absolute error = 2e-31 relative error = 1.8869732309413628591659634640842e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.045 Order of pole = 3.95e-28 TOP MAIN SOLVE Loop x[1] = -1.783 y[1] (analytic) = -1.0596592640387004945317721347226 y[1] (numeric) = -1.0596592640387004945317721347229 absolute error = 3e-31 relative error = 2.8310987331588459353651996807241e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.044 Order of pole = 2.26e-28 TOP MAIN SOLVE Loop x[1] = -1.782 y[1] (analytic) = -1.0594198753080454555013196561638 y[1] (numeric) = -1.0594198753080454555013196561641 absolute error = 3e-31 relative error = 2.8317384541494427202726701073615e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.781 y[1] (analytic) = -1.0591802821609690331402563022281 y[1] (numeric) = -1.0591802821609690331402563022284 absolute error = 3e-31 relative error = 2.8323790109454423256732763898785e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = -1.0589404843630724582599142959644 y[1] (numeric) = -1.0589404843630724582599142959647 absolute error = 3e-31 relative error = 2.8330204051122181076376797600840e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.779 y[1] (analytic) = -1.0587004816796505069957346374499 y[1] (numeric) = -1.0587004816796505069957346374502 absolute error = 3e-31 relative error = 2.8336626382189201548871686384311e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.041 Order of pole = 3.6e-29 TOP MAIN SOLVE Loop x[1] = -1.778 y[1] (analytic) = -1.0584602738756911288028674730938 y[1] (numeric) = -1.0584602738756911288028674730941 absolute error = 3e-31 relative error = 2.8343057118384863858066981396865e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.04 Order of pole = 3.20e-28 TOP MAIN SOLVE Loop x[1] = -1.777 y[1] (analytic) = -1.0582198607158750743351374716394 y[1] (numeric) = -1.0582198607158750743351374716397 absolute error = 3e-31 relative error = 2.8349496275476536838412323221305e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.776 y[1] (analytic) = -1.0579792419645755232094610954174 y[1] (numeric) = -1.0579792419645755232094610954177 absolute error = 3e-31 relative error = 2.8355943869269690714282244963984e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.775 y[1] (analytic) = -1.057738417385857711657816331125 y[1] (numeric) = -1.0577384173858577116578163311254 absolute error = 4e-31 relative error = 3.7816533220810678968263474455773e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.774 y[1] (analytic) = -1.0574973867434785600688791855726 y[1] (numeric) = -1.0574973867434785600688791855729 absolute error = 3e-31 relative error = 2.8368864430373502145485836770791e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.036 Order of pole = 1.57e-28 TOP MAIN SOLVE Loop x[1] = -1.773 y[1] (analytic) = -1.057256149800886300421455058718 y[1] (numeric) = -1.0572561498008863004214550587183 absolute error = 3e-31 relative error = 2.8375337429486618178929146114313e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.772 y[1] (analytic) = -1.0570147063212201036118469791709 y[1] (numeric) = -1.0570147063212201036118469791712 absolute error = 3e-31 relative error = 2.8381818928906358264956835658017e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.035 Order of pole = 2.13e-28 TOP MAIN SOLVE Loop x[1] = -1.771 y[1] (analytic) = -1.0567730560673097066773166264532 y[1] (numeric) = -1.0567730560673097066773166264535 absolute error = 3e-31 relative error = 2.8388308944630389262944914234223e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = -1.0565311988016750399178080699299 y[1] (numeric) = -1.0565311988016750399178080699302 absolute error = 3e-31 relative error = 2.8394807492695158037193269426314e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.033 Order of pole = 1.57e-28 TOP MAIN SOLVE Loop x[1] = -1.769 y[1] (analytic) = -1.0562891342865258539181182267354 y[1] (numeric) = -1.0562891342865258539181182267358 absolute error = 4e-31 relative error = 3.7868419452234674582877022184918e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.032 Order of pole = 2.00e-28 TOP MAIN SOLVE Loop x[1] = -1.768 y[1] (analytic) = -1.0560468622837613464727121804917 y[1] (numeric) = -1.0560468622837613464727121804921 absolute error = 4e-31 relative error = 3.7877107000249711567362386299793e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.031 Order of pole = 4.3e-29 TOP MAIN SOLVE Loop x[1] = -1.767 y[1] (analytic) = -1.055804382554969789415395709414 y[1] (numeric) = -1.0558043825549697894153957094144 absolute error = 4e-31 relative error = 3.7885805989176622140931891369171e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.03 Order of pole = 2.75e-28 TOP MAIN SOLVE Loop x[1] = -1.766 y[1] (analytic) = -1.0555616948614281553560716468066 y[1] (numeric) = -1.055561694861428155356071646807 absolute error = 4e-31 relative error = 3.7894516440605693867154208397767e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.029 Order of pole = 2.24e-28 TOP MAIN SOLVE Loop x[1] = -1.765 y[1] (analytic) = -1.0553187989641017443268210392272 y[1] (numeric) = -1.0553187989641017443268210392275 absolute error = 3e-31 relative error = 2.8427428782134767132630374264652e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.029 Order of pole = 8.2e-29 TOP MAIN SOLVE Loop x[1] = -1.764 y[1] (analytic) = -1.0550756946236438103395644780314 y[1] (numeric) = -1.0550756946236438103395644780317 absolute error = 3e-31 relative error = 2.8433978863195501761451931728028e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.763 y[1] (analytic) = -1.0548323816003951878575734588655 y[1] (numeric) = -1.0548323816003951878575734588659 absolute error = 4e-31 relative error = 3.7920716786596812030571677804760e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.762 y[1] (analytic) = -1.0545888596543839181831161712323 y[1] (numeric) = -1.0545888596543839181831161712327 absolute error = 4e-31 relative error = 3.7929473304989240972115401056360e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.026 Order of pole = 2.49e-28 TOP MAIN SOLVE Loop x[1] = -1.761 y[1] (analytic) = -1.0543451285453248757635367367935 y[1] (numeric) = -1.0543451285453248757635367367939 absolute error = 4e-31 relative error = 3.7938241394625511301066851748945e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.025 Order of pole = 1.60e-28 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = -1.0541011880326193944180816008678 y[1] (numeric) = -1.0541011880326193944180816008681 absolute error = 3e-31 relative error = 2.8460265808059826761492516831447e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=38.1MB, alloc=4.3MB, time=4.74 TOP MAIN SOLVE Loop x[1] = -1.759 y[1] (analytic) = -1.0538570378753548934878015369111 y[1] (numeric) = -1.0538570378753548934878015369115 absolute error = 4e-31 relative error = 3.7955812375312908691015353878470e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.758 y[1] (analytic) = -1.0536126778323045039108725489141 y[1] (numeric) = -1.0536126778323045039108725489145 absolute error = 4e-31 relative error = 3.7964615310339398742789472009923e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.023 Order of pole = 1.36e-28 TOP MAIN SOLVE Loop x[1] = -1.757 y[1] (analytic) = -1.0533681076619266942256938518897 y[1] (numeric) = -1.0533681076619266942256938518901 absolute error = 4e-31 relative error = 3.7973429904560773905093162026308e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.756 y[1] (analytic) = -1.053123327122364896504136076245 y[1] (numeric) = -1.0531233271223648965041360762454 absolute error = 4e-31 relative error = 3.7982256180099128270025099635819e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.755 y[1] (analytic) = -1.0528783359714471322173278781071 y[1] (numeric) = -1.0528783359714471322173278781075 absolute error = 4e-31 relative error = 3.7991094159130608883992369836028e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.02 Order of pole = 3.42e-28 TOP MAIN SOLVE Loop x[1] = -1.754 y[1] (analytic) = -1.0526331339666856380363842448938 y[1] (numeric) = -1.0526331339666856380363842448942 absolute error = 4e-31 relative error = 3.7999943863885576572092365430905e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.753 y[1] (analytic) = -1.0523877208652764915704949638652 y[1] (numeric) = -1.0523877208652764915704949638656 absolute error = 4e-31 relative error = 3.8008805316648767325814271866611e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.752 y[1] (analytic) = -1.0521420964240992370448069713523 y[1] (numeric) = -1.0521420964240992370448069713527 absolute error = 4e-31 relative error = 3.8017678539759454256332011881731e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.751 y[1] (analytic) = -1.0518962603997165109205496221103 y[1] (numeric) = -1.0518962603997165109205496221107 absolute error = 4e-31 relative error = 3.8026563555611610115670909960087e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.016 Order of pole = 2.34e-28 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = -1.0516502125483736674598673120863 y[1] (numeric) = -1.0516502125483736674598673120867 absolute error = 4e-31 relative error = 3.8035460386654070388040776269875e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.016 Order of pole = 3.46e-28 TOP MAIN SOLVE Loop x[1] = -1.749 y[1] (analytic) = -1.0514039526259984042378393540978 y[1] (numeric) = -1.0514039526259984042378393540982 absolute error = 4e-31 relative error = 3.8044369055390696953638602974722e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.015 Order of pole = 5.89e-28 TOP MAIN SOLVE Loop x[1] = -1.748 y[1] (analytic) = -1.0511574803882003876041825447895 y[1] (numeric) = -1.0511574803882003876041825447899 absolute error = 4e-31 relative error = 3.8053289584380542327234612814242e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.747 y[1] (analytic) = -1.0509107955902708780971474730531 y[1] (numeric) = -1.0509107955902708780971474730536 absolute error = 5e-31 relative error = 4.7577777495297518092332501225537e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.746 y[1] (analytic) = -1.0506638979871823558121353051524 y[1] (numeric) = -1.0506638979871823558121353051528 absolute error = 4e-31 relative error = 3.8071166313633042203973366869802e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.012 Order of pole = 2.64e-28 TOP MAIN SOLVE Loop x[1] = -1.745 y[1] (analytic) = -1.0504167873335881457275775403811 y[1] (numeric) = -1.0504167873335881457275775403815 absolute error = 4e-31 relative error = 3.8080122559291241150325542579905e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.744 y[1] (analytic) = -1.0501694633838220429906370634934 y[1] (numeric) = -1.0501694633838220429906370634938 absolute error = 4e-31 relative error = 3.8089090755994080329089290354394e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.743 y[1] (analytic) = -1.0499219258918979381653047266663 y[1] (numeric) = -1.0499219258918979381653047266667 absolute error = 4e-31 relative error = 3.8098070926579049287411161878086e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.742 y[1] (analytic) = -1.0496741746115094424454816746877 y[1] (numeric) = -1.0496741746115094424454816746881 absolute error = 4e-31 relative error = 3.8107063093939825839889688697394e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.009 Order of pole = 3.59e-28 TOP MAIN SOLVE Loop x[1] = -1.741 y[1] (analytic) = -1.0494262092960295128356536826984 y[1] (numeric) = -1.0494262092960295128356536826988 absolute error = 4e-31 relative error = 3.8116067281026444396327005411097e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.008 Order of pole = 6.60e-28 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = -1.0491780296985100773017799064475 y[1] (numeric) = -1.0491780296985100773017799064479 absolute error = 4e-31 relative error = 3.8125083510845464883159995961140e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.007 Order of pole = 6.29e-28 TOP MAIN SOLVE Loop x[1] = -1.739 y[1] (analytic) = -1.0489296355716816598950346509516 y[1] (numeric) = -1.048929635571681659895034650952 absolute error = 4e-31 relative error = 3.8134111806460142260982098675114e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.006 Order of pole = 1.76e-28 TOP MAIN SOLVE Loop x[1] = -1.738 y[1] (analytic) = -1.048681026667953005851057044964 y[1] (numeric) = -1.0486810266679530058510570449644 absolute error = 4e-31 relative error = 3.8143152190990596640578007995642e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.005 Order of pole = 7.47e-28 TOP MAIN SOLVE Loop x[1] = -1.737 y[1] (analytic) = -1.0484322027394107066673798660733 y[1] (numeric) = -1.0484322027394107066673798660737 absolute error = 4e-31 relative error = 3.8152204687613983999904670402652e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.004 Order of pole = 7.31e-28 TOP MAIN SOLVE Loop x[1] = -1.736 y[1] (analytic) = -1.0481831635378188251617251948455 y[1] (numeric) = -1.0481831635378188251617251948459 absolute error = 4e-31 relative error = 3.8161269319564667504463189221229e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.003 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -1.735 y[1] (analytic) = -1.0479339088146185205138710865148 y[1] (numeric) = -1.0479339088146185205138710865152 absolute error = 4e-31 relative error = 3.8170346110134389433517528140051e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.003 Order of pole = 1.296e-27 memory used=41.9MB, alloc=4.3MB, time=5.22 TOP MAIN SOLVE Loop x[1] = -1.734 y[1] (analytic) = -1.0476844383209276732938100356012 y[1] (numeric) = -1.0476844383209276732938100356016 absolute error = 4e-31 relative error = 3.8179435082672443714627236676171e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.002 Order of pole = 3.393e-27 TOP MAIN SOLVE Loop x[1] = -1.733 y[1] (analytic) = -1.0474347518075405104789366728037 y[1] (numeric) = -1.0474347518075405104789366728041 absolute error = 4e-31 relative error = 3.8188536260585849068972812845094e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2.001 Order of pole = 3.249e-27 TOP MAIN SOLVE Loop x[1] = -1.732 y[1] (analytic) = -1.0471848490249272304630188748779 y[1] (numeric) = -1.0471848490249272304630188748783 absolute error = 4e-31 relative error = 3.8197649667339522769963769267513e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 2 Order of pole = 2.934e-26 TOP MAIN SOLVE Loop x[1] = -1.731 y[1] (analytic) = -1.0469347297232336280597232872656 y[1] (numeric) = -1.046934729723233628059723287266 absolute error = 4e-31 relative error = 3.8206775326456455017630979204307e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.999 Order of pole = 2.252e-27 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = -1.0466843936522807195034831563044 y[1] (numeric) = -1.0466843936522807195034831563048 absolute error = 4e-31 relative error = 3.8215913261517883931316448900140e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.998 Order of pole = 2.31e-28 TOP MAIN SOLVE Loop x[1] = -1.729 y[1] (analytic) = -1.0464338405615643674505133432104 y[1] (numeric) = -1.0464338405615643674505133432108 absolute error = 4e-31 relative error = 3.8225063496163471163185292476433e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.728 y[1] (analytic) = -1.0461830702002549059827944460079 y[1] (numeric) = -1.0461830702002549059827944460084 absolute error = 5e-31 relative error = 4.7792782567614347668870469739315e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.727 y[1] (analytic) = -1.0459320823171967656178650884773 y[1] (numeric) = -1.0459320823171967656178650884777 absolute error = 4e-31 relative error = 3.8243400959058942901379846526326e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.996 Order of pole = 3.47e-28 TOP MAIN SOLVE Loop x[1] = -1.726 y[1] (analytic) = -1.0456808766609080983272786473166 y[1] (numeric) = -1.0456808766609080983272786473171 absolute error = 5e-31 relative error = 4.7815735293602322050101974513059e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.995 Order of pole = 6.12e-28 TOP MAIN SOLVE Loop x[1] = -1.725 y[1] (analytic) = -1.0454294529795804025665979803791 y[1] (numeric) = -1.0454294529795804025665979803796 absolute error = 5e-31 relative error = 4.7827234881794183469058050399155e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.724 y[1] (analytic) = -1.0451778110210781483198190903494 y[1] (numeric) = -1.0451778110210781483198190903499 absolute error = 5e-31 relative error = 4.7838749993317307166030252896632e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.723 y[1] (analytic) = -1.0449259505329384021611321098912 y[1] (numeric) = -1.0449259505329384021611321098918 absolute error = 6e-31 relative error = 5.7420336789796920499190932397685e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.722 y[1] (analytic) = -1.0446738712623704523369455264271 y[1] (numeric) = -1.0446738712623704523369455264277 absolute error = 6e-31 relative error = 5.7434192287681870230172340091213e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.991 Order of pole = 3.6e-29 TOP MAIN SOLVE Loop x[1] = -1.721 y[1] (analytic) = -1.0444215729562554338711171776211 y[1] (numeric) = -1.0444215729562554338711171776216 absolute error = 5e-31 relative error = 4.7873388768171490671404385032056e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = -1.0441690553611459536963532426421 y[1] (numeric) = -1.0441690553611459536963532426426 absolute error = 5e-31 relative error = 4.7884966273690746550011717184458e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.99 Order of pole = 1.29e-28 TOP MAIN SOLVE Loop x[1] = -1.719 y[1] (analytic) = -1.0439163182232657158147542296939 y[1] (numeric) = -1.0439163182232657158147542296944 absolute error = 5e-31 relative error = 4.7896559453251443827517487773139e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.718 y[1] (analytic) = -1.0436633612885091464905048174304 y[1] (numeric) = -1.043663361288509146490504817431 absolute error = 6e-31 relative error = 5.7489802004665435689014153575557e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.717 y[1] (analytic) = -1.0434101843024410194777223470474 y[1] (numeric) = -1.043410184302441019477722347048 absolute error = 6e-31 relative error = 5.7503751547252012213688962444618e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.716 y[1] (analytic) = -1.0431567870102960812864967833629 y[1] (numeric) = -1.0431567870102960812864967833635 absolute error = 6e-31 relative error = 5.7517720008284615493165304171181e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.986 Order of pole = 5.21e-28 TOP MAIN SOLVE Loop x[1] = -1.715 y[1] (analytic) = -1.0429031691569786764901730673983 y[1] (numeric) = -1.0429031691569786764901730673989 absolute error = 6e-31 relative error = 5.7531707424477821979161718333440e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.985 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.714 y[1] (analytic) = -1.0426493304870623730769449701572 y[1] (numeric) = -1.0426493304870623730769449701578 absolute error = 6e-31 relative error = 5.7545713832637909104366471811133e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.713 y[1] (analytic) = -1.0423952707447895878488478277957 y[1] (numeric) = -1.0423952707447895878488478277964 absolute error = 7e-31 relative error = 6.7153029147940323154098600135898e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.712 y[1] (analytic) = -1.0421409896740712118712558925046 y[1] (numeric) = -1.0421409896740712118712558925053 absolute error = 7e-31 relative error = 6.7169414401301349671634699667004e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.711 y[1] (analytic) = -1.0418864870184862359760084715006 y[1] (numeric) = -1.0418864870184862359760084715013 absolute error = 7e-31 relative error = 6.7185821941424207223976352897077e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.982 Order of pole = 1.03e-28 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = -1.0416317625212813763213075488757 y[1] (numeric) = -1.0416317625212813763213075488764 absolute error = 7e-31 relative error = 6.7202251811680755644734239599977e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.981 Order of pole = 1.93e-28 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=5.70 x[1] = -1.709 y[1] (analytic) = -1.0413768159253707000115481919974 y[1] (numeric) = -1.041376815925370700011548191998 absolute error = 6e-31 relative error = 5.7616032047615552197799028329262e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.98 Order of pole = 3.14e-28 TOP MAIN SOLVE Loop x[1] = -1.708 y[1] (analytic) = -1.0411216469733352507802617360203 y[1] (numeric) = -1.041121646973335250780261736021 absolute error = 7e-31 relative error = 6.7235178716625809605535087668396e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.707 y[1] (analytic) = -1.0408662554074226747393705171791 y[1] (numeric) = -1.0408662554074226747393705171798 absolute error = 7e-31 relative error = 6.7251675838602474771488754777273e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.706 y[1] (analytic) = -1.0406106409695468461979717882109 y[1] (numeric) = -1.0406106409695468461979717882116 absolute error = 7e-31 relative error = 6.7268195465289816023022358730615e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.977 Order of pole = 4.8e-29 TOP MAIN SOLVE Loop x[1] = -1.705 y[1] (analytic) = -1.0403548034012874935538873978328 y[1] (numeric) = -1.0403548034012874935538873978335 absolute error = 7e-31 relative error = 6.7284737640606131058319593706494e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.704 y[1] (analytic) = -1.0400987424438898252612348509983 y[1] (numeric) = -1.040098742443889825261234850999 absolute error = 7e-31 relative error = 6.7301302408580008295021950822365e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.703 y[1] (analytic) = -1.0398424578382641558772944880061 y[1] (numeric) = -1.0398424578382641558772944880069 absolute error = 8e-31 relative error = 7.6934731215257901784438578874278e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.975 Order of pole = 2.60e-28 TOP MAIN SOLVE Loop x[1] = -1.702 y[1] (analytic) = -1.0395859493249855321919667287672 y[1] (numeric) = -1.039585949324985532191966728768 absolute error = 8e-31 relative error = 7.6953714170478035430006282420110e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.974 Order of pole = 1.66e-28 TOP MAIN SOLVE Loop x[1] = -1.701 y[1] (analytic) = -1.0393292166442933594431326239748 y[1] (numeric) = -1.0393292166442933594431326239756 absolute error = 8e-31 relative error = 7.6972723097593540226204367943251e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = -1.0390722595360910276212503379073 y[1] (numeric) = -1.0390722595360910276212503379081 absolute error = 8e-31 relative error = 7.6991758047430856596457476662046e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.972 Order of pole = 1.47e-28 TOP MAIN SOLVE Loop x[1] = -1.699 y[1] (analytic) = -1.0388150777399455378665396584461 y[1] (numeric) = -1.0388150777399455378665396584469 absolute error = 8e-31 relative error = 7.7010819070944412237296847526919e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.698 y[1] (analytic) = -1.038557670995087128962126188953 y[1] (numeric) = -1.0385576709950871289621261889538 absolute error = 8e-31 relative error = 7.7029906219217014473637763950644e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.971 Order of pole = 3.24e-28 TOP MAIN SOLVE Loop x[1] = -1.697 y[1] (analytic) = -1.038300039040408903926536524248 y[1] (numeric) = -1.0383000390404089039265365242489 absolute error = 9e-31 relative error = 8.6680146986392774534114016289536e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.696 y[1] (analytic) = -1.0380421816144664567089554494038 y[1] (numeric) = -1.0380421816144664567089554494047 absolute error = 9e-31 relative error = 8.6701678981891706504053602752383e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.969 Order of pole = 1.03e-28 TOP MAIN SOLVE Loop x[1] = -1.695 y[1] (analytic) = -1.037784098455477498990676025748 y[1] (numeric) = -1.0377840984554774989906760257489 absolute error = 9e-31 relative error = 8.6723240541020041043266583237422e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.694 y[1] (analytic) = -1.0375257893013214870961933436928 y[1] (numeric) = -1.0375257893013214870961933436937 absolute error = 9e-31 relative error = 8.6744831721828090682447329456986e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.967 Order of pole = 1.76e-28 TOP MAIN SOLVE Loop x[1] = -1.693 y[1] (analytic) = -1.0372672538895392490174127271123 y[1] (numeric) = -1.0372672538895392490174127271132 absolute error = 9e-31 relative error = 8.6766452582512826065132309356567e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.966 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -1.692 y[1] (analytic) = -1.0370084919573326115544632693128 y[1] (numeric) = -1.0370084919573326115544632693137 absolute error = 9e-31 relative error = 8.6788103181418327007193782847749e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.691 y[1] (analytic) = -1.0367495032415640275766277665203 y[1] (numeric) = -1.0367495032415640275766277665212 absolute error = 9e-31 relative error = 8.6809783577036235189857361992371e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.965 Order of pole = 1.68e-28 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = -1.0364902874787562034069203915875 y[1] (numeric) = -1.0364902874787562034069203915884 absolute error = 9e-31 relative error = 8.6831493828006208493058755591423e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.964 Order of pole = 3.14e-28 TOP MAIN SOLVE Loop x[1] = -1.689 y[1] (analytic) = -1.0362308444050917263338638186339 y[1] (numeric) = -1.0362308444050917263338638186348 absolute error = 9e-31 relative error = 8.6853233993116376975987275640567e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.688 y[1] (analytic) = -1.0359711737564126922540379689265 y[1] (numeric) = -1.0359711737564126922540379689274 absolute error = 9e-31 relative error = 8.6875004131303800511696111823296e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.962 Order of pole = 1.02e-28 TOP MAIN SOLVE Loop x[1] = -1.687 y[1] (analytic) = -1.0357112752682203334489930998183 y[1] (numeric) = -1.0357112752682203334489930998192 absolute error = 9e-31 relative error = 8.6896804301654928082691981132353e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.961 Order of pole = 1.05e-28 TOP MAIN SOLVE Loop x[1] = -1.686 y[1] (analytic) = -1.0354511486756746465001406023373 y[1] (numeric) = -1.0354511486756746465001406023382 absolute error = 9e-31 relative error = 8.6918634563406058744449533855470e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.96 Order of pole = 2.53e-28 TOP MAIN SOLVE Loop x[1] = -1.685 y[1] (analytic) = -1.0351907937135940203452556094 y[1] (numeric) = -1.0351907937135940203452556094008 absolute error = 8e-31 relative error = 7.7280439978616714901181196049292e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=6.19 x[1] = -1.684 y[1] (analytic) = -1.034930210116454864480246345955 y[1] (numeric) = -1.0349302101164548644802463459558 absolute error = 8e-31 relative error = 7.7299898310049380835028842974328e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.959 Order of pole = 7.9e-29 TOP MAIN SOLVE Loop x[1] = -1.683 y[1] (analytic) = -1.0346693976183912373098660749934 y[1] (numeric) = -1.0346693976183912373098660749942 absolute error = 8e-31 relative error = 7.7319383548159944987352582000105e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.682 y[1] (analytic) = -1.034408355953194474651064509632 y[1] (numeric) = -1.0344083559531944746510645096329 absolute error = 9e-31 relative error = 8.7006257714407300863845404765298e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.957 Order of pole = 1.20e-28 TOP MAIN SOLVE Loop x[1] = -1.681 y[1] (analytic) = -1.0341470848543128183926966717421 y[1] (numeric) = -1.034147084854312818392696671743 absolute error = 9e-31 relative error = 8.7028239326980164439368522511271e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = -1.0338855840548510453153283821921 y[1] (numeric) = -1.033885584054851045315328382193 absolute error = 9e-31 relative error = 8.7050251389543702851670104034777e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.955 Order of pole = 6.3e-29 TOP MAIN SOLVE Loop x[1] = -1.679 y[1] (analytic) = -1.0336238532875700960748988670659 y[1] (numeric) = -1.0336238532875700960748988670668 absolute error = 9e-31 relative error = 8.7072293962396214224916773582519e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.678 y[1] (analytic) = -1.0333618922848867043540223585378 y[1] (numeric) = -1.0333618922848867043540223585386 absolute error = 8e-31 relative error = 7.7417215205324084759155327089157e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.953 Order of pole = 2.09e-28 TOP MAIN SOLVE Loop x[1] = -1.677 y[1] (analytic) = -1.0330997007788730261847320588002 y[1] (numeric) = -1.0330997007788730261847320588011 absolute error = 9e-31 relative error = 8.7116470880929817997658988712602e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.676 y[1] (analytic) = -1.0328372785012562694464914208908 y[1] (numeric) = -1.0328372785012562694464914208917 absolute error = 9e-31 relative error = 8.7138605347977406910077425187299e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.675 y[1] (analytic) = -1.0325746251834183235433193818035 y[1] (numeric) = -1.0325746251834183235433193818044 absolute error = 9e-31 relative error = 8.7160770568047919620012700987214e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.674 y[1] (analytic) = -1.0323117405563953892638979612579 y[1] (numeric) = -1.0323117405563953892638979612588 absolute error = 9e-31 relative error = 8.7182966602212427963069179800391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.673 y[1] (analytic) = -1.0320486243508776088285525142806 y[1] (numeric) = -1.0320486243508776088285525142815 absolute error = 9e-31 relative error = 8.7205193511698001375547789031812e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.672 y[1] (analytic) = -1.0317852762972086961270168976902 y[1] (numeric) = -1.0317852762972086961270168976911 absolute error = 9e-31 relative error = 8.7227451357888191956946728991485e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.948 Order of pole = 1.87e-28 TOP MAIN SOLVE Loop x[1] = -1.671 y[1] (analytic) = -1.0315216961253855671509178800198 y[1] (numeric) = -1.0315216961253855671509178800207 absolute error = 9e-31 relative error = 8.7249740202323521308621534548575e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.947 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = -1.0312578835650579706249352917186 y[1] (numeric) = -1.0312578835650579706249352917196 absolute error = 1.0e-30 relative error = 9.6968955674113299062331856211358e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.947 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -1.669 y[1] (analytic) = -1.0309938383455281188406166780065 y[1] (numeric) = -1.0309938383455281188406166780075 absolute error = 1.0e-30 relative error = 9.6993790147643848625080804012649e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.668 y[1] (analytic) = -1.0307295601957503186968475808608 y[1] (numeric) = -1.0307295601957503186968475808618 absolute error = 1.0e-30 relative error = 9.7018659269855971267948139373768e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.945 Order of pole = 6.5e-29 TOP MAIN SOLVE Loop x[1] = -1.667 y[1] (analytic) = -1.0304650488443306029510010396658 y[1] (numeric) = -1.0304650488443306029510010396668 absolute error = 1.0e-30 relative error = 9.7043563109831115637182458424735e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.944 Order of pole = 1.63e-28 TOP MAIN SOLVE Loop x[1] = -1.666 y[1] (analytic) = -1.0302003040195263616848124624 y[1] (numeric) = -1.0302003040195263616848124624011 absolute error = 1.1e-30 relative error = 1.0677535191051066304050735111573e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.943 Order of pole = 1.75e-28 TOP MAIN SOLVE Loop x[1] = -1.665 y[1] (analytic) = -1.0299353254492459739890486812413 y[1] (numeric) = -1.0299353254492459739890486812423 absolute error = 1.0e-30 relative error = 9.7093475220282542650610227557985e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.942 Order of pole = 1.1e-29 TOP MAIN SOLVE Loop x[1] = -1.664 y[1] (analytic) = -1.0296701128610484398710627684934 y[1] (numeric) = -1.0296701128610484398710627684944 absolute error = 1.0e-30 relative error = 9.7118483629809661978329853148130e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.941 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -1.663 y[1] (analytic) = -1.0294046659821430123893490511472 y[1] (numeric) = -1.0294046659821430123893490511482 absolute error = 1.0e-30 relative error = 9.7143527035202588404356958804048e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.941 Order of pole = 1.76e-28 TOP MAIN SOLVE Loop x[1] = -1.662 y[1] (analytic) = -1.0291389845393888300192357255379 y[1] (numeric) = -1.0291389845393888300192357255389 absolute error = 1.0e-30 relative error = 9.7168605506434045997895920567524e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.661 y[1] (analytic) = -1.0288730682592945492538755378225 y[1] (numeric) = -1.0288730682592945492538755378235 absolute error = 1.0e-30 relative error = 9.7193719113656689099103332099530e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = -1.0286069168680179774447181617342 y[1] (numeric) = -1.0286069168680179774447181617352 absolute error = 1.0e-30 relative error = 9.7218867927203665517998028665419e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.938 Order of pole = 1.94e-28 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=6.68 x[1] = -1.659 y[1] (analytic) = -1.0283405300913657058856711726431 y[1] (numeric) = -1.0283405300913657058856711726441 absolute error = 1.0e-30 relative error = 9.7244052017589181809482933071420e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.658 y[1] (analytic) = -1.0280739076547927431451798867289 y[1] (numeric) = -1.0280739076547927431451798867299 absolute error = 1.0e-30 relative error = 9.7269271455509070633298420408727e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.936 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop x[1] = -1.657 y[1] (analytic) = -1.0278070492834021486504798064199 y[1] (numeric) = -1.0278070492834021486504798064209 absolute error = 1.0e-30 relative error = 9.7294526311841360207769421554954e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.935 Order of pole = 5.0e-29 TOP MAIN SOLVE Loop x[1] = -1.656 y[1] (analytic) = -1.0275399547019446665282989885398 y[1] (numeric) = -1.0275399547019446665282989885408 absolute error = 1.0e-30 relative error = 9.7319816657646845866251238467509e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.655 y[1] (analytic) = -1.0272726236348183597063113302 y[1] (numeric) = -1.027272623634818359706311330201 absolute error = 1.0e-30 relative error = 9.7345142564169663725222028761654e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.934 Order of pole = 1.13e-28 TOP MAIN SOLVE Loop x[1] = -1.654 y[1] (analytic) = -1.0270050558060682442796655497461 y[1] (numeric) = -1.0270050558060682442796655497471 absolute error = 1.0e-30 relative error = 9.7370504102837866473013134289214e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.653 y[1] (analytic) = -1.0267372509393859241469385263886 y[1] (numeric) = -1.0267372509393859241469385263896 absolute error = 1.0e-30 relative error = 9.7395901345264001288211879822197e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.932 Order of pole = 9.1e-29 TOP MAIN SOLVE Loop x[1] = -1.652 y[1] (analytic) = -1.0264692087581092259198856528828 y[1] (numeric) = -1.0264692087581092259198856528838 absolute error = 1.0e-30 relative error = 9.7421334363245689896815154909437e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.651 y[1] (analytic) = -1.0262009289852218341113849511525 y[1] (numeric) = -1.0262009289852218341113849511535 absolute error = 1.0e-30 relative error = 9.7446803228766210777256015932192e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = -1.0259324113433529266059959014387 y[1] (numeric) = -1.0259324113433529266059959014397 absolute error = 1.0e-30 relative error = 9.7472308013995083522469707765860e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.649 y[1] (analytic) = -1.0256636555547768104175782417792 y[1] (numeric) = -1.0256636555547768104175782417802 absolute error = 1.0e-30 relative error = 9.7497848791288655368209906697059e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.648 y[1] (analytic) = -1.025394661341412557738440406758 y[1] (numeric) = -1.025394661341412557738440406759 absolute error = 1.0e-30 relative error = 9.7523425633190689896870629796178e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.928 Order of pole = 2.86e-28 TOP MAIN SOLVE Loop x[1] = -1.647 y[1] (analytic) = -1.0251254284248236422845117928801 y[1] (numeric) = -1.0251254284248236422845117928812 absolute error = 1.1e-30 relative error = 1.0730394247367625371872555648869e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.927 Order of pole = 1.27e-28 TOP MAIN SOLVE Loop x[1] = -1.646 y[1] (analytic) = -1.0248559565262175759410576630018 y[1] (numeric) = -1.0248559565262175759410576630029 absolute error = 1.1e-30 relative error = 1.0733215658212941365081535728946e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.926 Order of pole = 1.23e-28 TOP MAIN SOLVE Loop x[1] = -1.645 y[1] (analytic) = -1.0245862453664455457134802343583 y[1] (numeric) = -1.0245862453664455457134802343593 absolute error = 1.0e-30 relative error = 9.7600373274808874633558339411926e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.644 y[1] (analytic) = -1.0243162946660020509877743342532 y[1] (numeric) = -1.0243162946660020509877743342542 absolute error = 1.0e-30 relative error = 9.7626095104351449895587055214438e-29 % Correct digits = 30 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.924 Order of pole = 1.3e-29 TOP MAIN SOLVE Loop x[1] = -1.643 y[1] (analytic) = -1.0240461041450245411052309547881 y[1] (numeric) = -1.0240461041450245411052309547891 absolute error = 1.0e-30 relative error = 9.7651853364053309046916568504042e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.642 y[1] (analytic) = -1.0237756735232930532560070934894 y[1] (numeric) = -1.0237756735232930532560070934905 absolute error = 1.1e-30 relative error = 1.0744541294035471948950020036250e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.923 Order of pole = 6e-30 TOP MAIN SOLVE Loop x[1] = -1.641 y[1] (analytic) = -1.0235050025202298506962054307213 y[1] (numeric) = -1.0235050025202298506962054307224 absolute error = 1.1e-30 relative error = 1.0747382741573441456396784230304e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = -1.0232340908548990612931326677265 y[1] (numeric) = -1.0232340908548990612931326677276 absolute error = 1.1e-30 relative error = 1.0750228220806873220325624945279e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.921 Order of pole = 4.8e-29 TOP MAIN SOLVE Loop x[1] = -1.639 y[1] (analytic) = -1.0229629382460063164034307314038 y[1] (numeric) = -1.022962938246006316403430731405 absolute error = 1.2e-30 relative error = 1.1730630261713539088378233753015e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.92 Order of pole = 2.77e-28 TOP MAIN SOLVE Loop x[1] = -1.638 y[1] (analytic) = -1.022691544411898390088800543882 y[1] (numeric) = -1.0226915444118983900888005438832 absolute error = 1.2e-30 relative error = 1.1733743244059608698648345655191e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.919 Order of pole = 1.53e-28 TOP MAIN SOLVE Loop x[1] = -1.637 y[1] (analytic) = -1.0224199090705628386740636569746 y[1] (numeric) = -1.0224199090705628386740636569758 absolute error = 1.2e-30 relative error = 1.1736860651421268240692871100263e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.636 y[1] (analytic) = -1.0221480319396276406523327640814 y[1] (numeric) = -1.0221480319396276406523327640827 absolute error = 1.3e-30 relative error = 1.2718314367177527026997045257713e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.635 y[1] (analytic) = -1.0218759127363608369420879254161 y[1] (numeric) = -1.0218759127363608369420879254174 absolute error = 1.3e-30 relative error = 1.2721701175232553554191825692513e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.634 y[1] (analytic) = -1.0216035511776701715009812769787 y[1] (numeric) = -1.02160355117767017150098127698 memory used=57.2MB, alloc=4.3MB, time=7.16 absolute error = 1.3e-30 relative error = 1.2725092806318104290473006868527e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.916 Order of pole = 1.49e-28 TOP MAIN SOLVE Loop x[1] = -1.633 y[1] (analytic) = -1.0213309469801027323012190398388 y[1] (numeric) = -1.0213309469801027323012190398401 absolute error = 1.3e-30 relative error = 1.2728489270239710222362449007390e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.915 Order of pole = 7.9e-29 TOP MAIN SOLVE Loop x[1] = -1.632 y[1] (analytic) = -1.0210580998598445926713958044295 y[1] (numeric) = -1.0210580998598445926713958044309 absolute error = 1.4e-30 relative error = 1.3711266775046109697232453997719e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.631 y[1] (analytic) = -1.0207850095327204530096823350723 y[1] (numeric) = -1.0207850095327204530096823350737 absolute error = 1.4e-30 relative error = 1.3714934946398466988415858830250e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.913 Order of pole = 8.5e-29 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = -1.0205116757141932828732945232312 y[1] (numeric) = -1.0205116757141932828732945232326 absolute error = 1.4e-30 relative error = 1.3718608354188855373035156497589e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.629 y[1] (analytic) = -1.0202380981193639634491976144342 y[1] (numeric) = -1.0202380981193639634491976144355 absolute error = 1.3e-30 relative error = 1.2742123651296003276895416834180e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.628 y[1] (analytic) = -1.0199642764629709304110264437729 y[1] (numeric) = -1.0199642764629709304110264437742 absolute error = 1.3e-30 relative error = 1.2745544427380693319361400016283e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.911 Order of pole = 1.54e-28 TOP MAIN SOLVE Loop x[1] = -1.627 y[1] (analytic) = -1.0196902104593898171672291388033 y[1] (numeric) = -1.0196902104593898171672291388046 absolute error = 1.3e-30 relative error = 1.2748970095675678752154615819022e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.626 y[1] (analytic) = -1.0194158998226330985054685868957 y[1] (numeric) = -1.019415899822633098505468586897 absolute error = 1.3e-30 relative error = 1.2752400666167610091989880941140e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.909 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -1.625 y[1] (analytic) = -1.0191413442663497346383429170231 y[1] (numeric) = -1.0191413442663497346383429170244 absolute error = 1.3e-30 relative error = 1.2755836148869343118964339065388e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.624 y[1] (analytic) = -1.0188665435038248156555133140183 y[1] (numeric) = -1.0188665435038248156555133140196 absolute error = 1.3e-30 relative error = 1.2759276553820022572253522241694e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.623 y[1] (analytic) = -1.0185914972479792063873546668637 y[1] (numeric) = -1.0185914972479792063873546668651 absolute error = 1.4e-30 relative error = 1.3744469728860948173045707541970e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.906 Order of pole = 9.9e-29 TOP MAIN SOLVE Loop x[1] = -1.622 y[1] (analytic) = -1.018316205211369191685271852 y[1] (numeric) = -1.0183162052113691916852718520013 absolute error = 1.3e-30 relative error = 1.2766172170756748889557476582648e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.621 y[1] (analytic) = -1.0180406671061861221238518683366 y[1] (numeric) = -1.018040667106186122123851868338 absolute error = 1.4e-30 relative error = 1.3751906433949694451615490816207e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.905 Order of pole = 7.3e-29 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = -1.0177648826442560601300495730236 y[1] (numeric) = -1.017764882644256060130049573025 absolute error = 1.4e-30 relative error = 1.3755632797652228492974160066266e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.619 y[1] (analytic) = -1.0174888515370394265446324164765 y[1] (numeric) = -1.0174888515370394265446324164778 absolute error = 1.3e-30 relative error = 1.2776552765528521186305682270860e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.618 y[1] (analytic) = -1.0172125734956306476211373420518 y[1] (numeric) = -1.0172125734956306476211373420532 absolute error = 1.4e-30 relative error = 1.3763101602145243086425397765465e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.902 Order of pole = 8.2e-29 TOP MAIN SOLVE Loop x[1] = -1.617 y[1] (analytic) = -1.0169360482307578024676209005257 y[1] (numeric) = -1.016936048230757802467620900527 absolute error = 1.3e-30 relative error = 1.2783498060293077623065708313905e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.616 y[1] (analytic) = -1.016659275452782270936511632536 y[1] (numeric) = -1.0166592754527822709365116325374 absolute error = 1.4e-30 relative error = 1.3770591916121475525887027587768e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.9 Order of pole = 1.3e-29 TOP MAIN SOLVE Loop x[1] = -1.615 y[1] (analytic) = -1.0163822548716983819679018938144 y[1] (numeric) = -1.0163822548716983819679018938158 absolute error = 1.4e-30 relative error = 1.3774345166786949435900350176530e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.614 y[1] (analytic) = -1.0161049861971330623916445387347 y[1] (numeric) = -1.0161049861971330623916445387361 absolute error = 1.4e-30 relative error = 1.3778103828026959606348201617706e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.613 y[1] (analytic) = -1.0158274691383454861936482378634 y[1] (numeric) = -1.0158274691383454861936482378648 absolute error = 1.4e-30 relative error = 1.3781867910970362609086096703912e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.898 Order of pole = 1.89e-28 TOP MAIN SOLVE Loop x[1] = -1.612 y[1] (analytic) = -1.015549703404226724251793685188 y[1] (numeric) = -1.0155497034042267242517936851894 absolute error = 1.4e-30 relative error = 1.3785637426775434684216179327237e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.611 y[1] (analytic) = -1.015271688703299394546921550942 y[1] (numeric) = -1.0152716887032993945469215509434 absolute error = 1.4e-30 relative error = 1.3789412386629966399028871688824e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.896 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = -1.0149934247437173128543717568226 y[1] (numeric) = -1.014993424743717312854371756824 absolute error = 1.4e-30 relative error = 1.3793192801751357665741110277636e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.895 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -1.609 y[1] (analytic) = -1.0147149112332651439215824923232 y[1] (numeric) = -1.0147149112332651439215824923246 absolute error = 1.4e-30 relative error = 1.3796978683386713119599355762587e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 memory used=61.0MB, alloc=4.3MB, time=7.65 TOP MAIN SOLVE Loop x[1] = -1.608 y[1] (analytic) = -1.0144361478793580531372863542673 y[1] (numeric) = -1.0144361478793580531372863542687 absolute error = 1.4e-30 relative error = 1.3800770042812937858923348199567e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.894 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -1.607 y[1] (analytic) = -1.0141571343890413586978700768424 y[1] (numeric) = -1.0141571343890413586978700768439 absolute error = 1.5e-30 relative error = 1.4790607383575178802151149914799e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.893 Order of pole = 6.8e-29 TOP MAIN SOLVE Loop x[1] = -1.606 y[1] (analytic) = -1.0138778704689901842764935268911 y[1] (numeric) = -1.0138778704689901842764935268926 absolute error = 1.5e-30 relative error = 1.4794681328887708809792796158084e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.605 y[1] (analytic) = -1.0135983558255091122005929693204 y[1] (numeric) = -1.0135983558255091122005929693219 absolute error = 1.5e-30 relative error = 1.4798761179701685483571904321267e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.891 Order of pole = 1.0e-29 TOP MAIN SOLVE Loop x[1] = -1.604 y[1] (analytic) = -1.0133185901645318371434230606528 y[1] (numeric) = -1.0133185901645318371434230606542 absolute error = 1.4e-30 relative error = 1.3815990485013039880719796069428e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.89 Order of pole = 7.9e-29 TOP MAIN SOLVE Loop x[1] = -1.603 y[1] (analytic) = -1.0130385731916208203353216053524 y[1] (numeric) = -1.0130385731916208203353216053538 absolute error = 1.4e-30 relative error = 1.3819809403596951470874505915554e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.889 Order of pole = 9.0e-29 TOP MAIN SOLVE Loop x[1] = -1.602 y[1] (analytic) = -1.0127583046119669443004108100369 y[1] (numeric) = -1.0127583046119669443004108100384 absolute error = 1.5e-30 relative error = 1.4811036287426121545048654929333e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.888 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -1.601 y[1] (analytic) = -1.0124777841303891681244785954202 y[1] (numeric) = -1.0124777841303891681244785954216 absolute error = 1.4e-30 relative error = 1.3827463890503545592903573581796e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = -1.0121970114513341832598134752381 y[1] (numeric) = -1.0121970114513341832598134752395 absolute error = 1.4e-30 relative error = 1.3831299481833247327130182554885e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.887 Order of pole = 2.8e-29 TOP MAIN SOLVE Loop x[1] = -1.599 y[1] (analytic) = -1.0119159862788760698727965858925 y[1] (numeric) = -1.0119159862788760698727965858939 absolute error = 1.4e-30 relative error = 1.3835140653802963389818486513479e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.886 Order of pole = 6.2e-29 TOP MAIN SOLVE Loop x[1] = -1.598 y[1] (analytic) = -1.0116347083167159537400846505073 y[1] (numeric) = -1.0116347083167159537400846505087 absolute error = 1.4e-30 relative error = 1.3838987417992949982013993268947e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.597 y[1] (analytic) = -1.011353177268181663699247986941 y[1] (numeric) = -1.0113531772681816636992479869424 absolute error = 1.4e-30 relative error = 1.3842839786014341255057462450085e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.596 y[1] (analytic) = -1.0110713928362273896597581214427 y[1] (numeric) = -1.0110713928362273896597581214442 absolute error = 1.5e-30 relative error = 1.4835747610188481628289499893797e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.595 y[1] (analytic) = -1.0107893547234333411802501484831 y[1] (numeric) = -1.0107893547234333411802501484845 absolute error = 1.4e-30 relative error = 1.3850561380150865838596201021123e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.883 Order of pole = 5.5e-29 TOP MAIN SOLVE Loop x[1] = -1.594 y[1] (analytic) = -1.0105070626320054066180156832441 y[1] (numeric) = -1.0105070626320054066180156832456 absolute error = 1.5e-30 relative error = 1.4844032817475243931882971323650e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.593 y[1] (analytic) = -1.0102245162637748128567130867272 y[1] (numeric) = -1.0102245162637748128567130867287 absolute error = 1.5e-30 relative error = 1.4848184496131771675664712562815e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.592 y[1] (analytic) = -1.0099417153201977856183126048325 y[1] (numeric) = -1.009941715320197785618312604834 absolute error = 1.5e-30 relative error = 1.4852342241595905267657615121840e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.88 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -1.591 y[1] (analytic) = -1.0096586595023552103653251525016 y[1] (numeric) = -1.0096586595023552103653251525032 absolute error = 1.6e-30 relative error = 1.5846939804276176886604799138806e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.879 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = -1.0093753485109522937993946924935 y[1] (numeric) = -1.0093753485109522937993946924951 absolute error = 1.6e-30 relative error = 1.5851387715782312811861420427006e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.878 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -1.589 y[1] (analytic) = -1.0090917820463182259623655059993 y[1] (numeric) = -1.0090917820463182259623655060008 absolute error = 1.5e-30 relative error = 1.4864852005415981502776741995469e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.877 Order of pole = 6.7e-29 TOP MAIN SOLVE Loop x[1] = -1.588 y[1] (analytic) = -1.008807959808405842945967129505 y[1] (numeric) = -1.0088079598084058429459671295065 absolute error = 1.5e-30 relative error = 1.4869034144862239254329945223074e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.877 Order of pole = 8.1e-29 TOP MAIN SOLVE Loop x[1] = -1.587 y[1] (analytic) = -1.0085238814967912902162913394908 y[1] (numeric) = -1.0085238814967912902162913394923 absolute error = 1.5e-30 relative error = 1.4873222414662001094395701636065e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.586 y[1] (analytic) = -1.0082395468106736865592673041213 y[1] (numeric) = -1.0082395468106736865592673041228 absolute error = 1.5e-30 relative error = 1.4877416827626864036801875947434e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.875 Order of pole = 4.2e-29 TOP MAIN SOLVE Loop x[1] = -1.585 y[1] (analytic) = -1.0079549554488747886533728894521 y[1] (numeric) = -1.0079549554488747886533728894536 absolute error = 1.5e-30 relative error = 1.4881617396602824514394643625479e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.874 Order of pole = 4.9e-29 TOP MAIN SOLVE Loop x[1] = -1.584 y[1] (analytic) = -1.0076701071098386562758521072564 y[1] (numeric) = -1.0076701071098386562758521072579 absolute error = 1.5e-30 relative error = 1.4885824134470390793790931666164e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.873 Order of pole = 4.0e-29 memory used=64.8MB, alloc=4.3MB, time=8.14 TOP MAIN SOLVE Loop x[1] = -1.583 y[1] (analytic) = -1.0073850014916313181487408227815 y[1] (numeric) = -1.007385001491631318148740822783 absolute error = 1.5e-30 relative error = 1.4890037054144695822989774161978e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.582 y[1] (analytic) = -1.0070996382919404384310351039872 y[1] (numeric) = -1.0070996382919404384310351039886 absolute error = 1.4e-30 relative error = 1.3901305757337236479514149816216e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.872 Order of pole = 6.1e-29 TOP MAIN SOLVE Loop x[1] = -1.581 y[1] (analytic) = -1.0068140172080749838633689895111 y[1] (numeric) = -1.0068140172080749838633689895125 absolute error = 1.4e-30 relative error = 1.3905249391364666963387812526720e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.871 Order of pole = 4.6e-29 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = -1.0065281379369648915716009811645 y[1] (numeric) = -1.0065281379369648915716009811659 absolute error = 1.4e-30 relative error = 1.3909198831435716759357711401764e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.579 y[1] (analytic) = -1.0062420001751607375357412285954 y[1] (numeric) = -1.0062420001751607375357412285968 absolute error = 1.4e-30 relative error = 1.3913154089734836816783270409033e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.869 Order of pole = 6e-30 TOP MAIN SOLVE Loop x[1] = -1.578 y[1] (analytic) = -1.0059556036188334057306841692848 y[1] (numeric) = -1.0059556036188334057306841692862 absolute error = 1.4e-30 relative error = 1.3917115178479327199647238789628e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.868 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop x[1] = -1.577 y[1] (analytic) = -1.0056689479637737579452443166746 y[1] (numeric) = -1.0056689479637737579452443166761 absolute error = 1.5e-30 relative error = 1.4915445117770833792504439656851e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.867 Order of pole = 4.3e-29 TOP MAIN SOLVE Loop x[1] = -1.576 y[1] (analytic) = -1.0053820329053923042860259533815 y[1] (numeric) = -1.0053820329053923042860259533829 absolute error = 1.4e-30 relative error = 1.3925054896338511906183207418525e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.866 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -1.575 y[1] (analytic) = -1.0050948581387188743726906855402 y[1] (numeric) = -1.0050948581387188743726906855416 absolute error = 1.4e-30 relative error = 1.3929033550053024094604611731702e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.866 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -1.574 y[1] (analytic) = -1.0048074233584022892312201487656 y[1] (numeric) = -1.004807423358402289231220148767 absolute error = 1.4e-30 relative error = 1.3933018083412760002077412369442e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.573 y[1] (analytic) = -1.0045197282587100338918046264291 y[1] (numeric) = -1.0045197282587100338918046264305 absolute error = 1.4e-30 relative error = 1.3937008508800890425456882794909e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.572 y[1] (analytic) = -1.004231772533527930698021947339 y[1] (numeric) = -1.0042317725335279306980219473404 absolute error = 1.4e-30 relative error = 1.3941004838634088283548594502460e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.863 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -1.571 y[1] (analytic) = -1.0039435558763598133340047729067 y[1] (numeric) = -1.0039435558763598133340047729081 absolute error = 1.4e-30 relative error = 1.3945007085362638932156124836620e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.862 Order of pole = 2.2e-29 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = -1.0036550779803272015763282638849 y[1] (numeric) = -1.0036550779803272015763282638863 absolute error = 1.4e-30 relative error = 1.3949015261470550907178921127193e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.569 y[1] (analytic) = -1.0033663385381689767773841342047 y[1] (numeric) = -1.003366338538168976777384134206 absolute error = 1.3e-30 relative error = 1.2956384423798833733556789835119e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.861 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop x[1] = -1.568 y[1] (analytic) = -1.0030773372422410580870412547239 y[1] (numeric) = -1.0030773372422410580870412547252 absolute error = 1.3e-30 relative error = 1.2960117348220506611480591337277e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.86 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -1.567 y[1] (analytic) = -1.0027880737845160794194272632517 y[1] (numeric) = -1.0027880737845160794194272632531 absolute error = 1.4e-30 relative error = 1.3961075491418725510702726147951e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.566 y[1] (analytic) = -1.0024985478565830671717000694497 y[1] (numeric) = -1.0024985478565830671717000694511 absolute error = 1.4e-30 relative error = 1.3965107510562531892846525598510e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.565 y[1] (analytic) = -1.0022087591496471187017127145426 y[1] (numeric) = -1.002208759149647118701712714544 absolute error = 1.4e-30 relative error = 1.3969145522015496196541870792763e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.564 y[1] (analytic) = -1.001918707354529081571509756627 y[1] (numeric) = -1.0019187073545290815715097566285 absolute error = 1.5e-30 relative error = 1.4971274505499624132290265103813e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.563 y[1] (analytic) = -1.0016283921616652335636282031507 y[1] (numeric) = -1.0016283921616652335636282031522 absolute error = 1.5e-30 relative error = 1.4975613827826641612177568731801e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.856 Order of pole = 4.5e-29 TOP MAIN SOLVE Loop x[1] = -1.562 y[1] (analytic) = -1.0013378132611069634772110032747 y[1] (numeric) = -1.0013378132611069634772110032762 absolute error = 1.5e-30 relative error = 1.4979959611381047719268574988990e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.855 Order of pole = 4.5e-29 TOP MAIN SOLVE Loop x[1] = -1.561 y[1] (analytic) = -1.0010469703425204527109762447437 y[1] (numeric) = -1.0010469703425204527109762447453 absolute error = 1.6e-30 relative error = 1.5983265994527114442746498497754e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = -1.0007558630951863576401204729864 y[1] (numeric) = -1.0007558630951863576401204729879 absolute error = 1.5e-30 relative error = 1.4988670617034679354256225631317e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.853 Order of pole = 8e-30 TOP MAIN SOLVE Loop x[1] = -1.559 y[1] (analytic) = -1.0004644912079994927942699648733 y[1] (numeric) = -1.0004644912079994927942699648749 absolute error = 1.6e-30 relative error = 1.5992571591102630368692017763526e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=8.61 x[1] = -1.558 y[1] (analytic) = -1.0001728543694685148436293462945 y[1] (numeric) = -1.0001728543694685148436293462961 absolute error = 1.6e-30 relative error = 1.5997234808064012317074721774728e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.557 y[1] (analytic) = -0.99988095226771560740051264188759 y[1] (numeric) = -0.99988095226771560740051264188919 absolute error = 1.60e-30 relative error = 1.6001904990501349490556788548400e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.85 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -1.556 y[1] (analytic) = -0.99958878459047616664347768728934 y[1] (numeric) = -0.99958878459047616664347768729095 absolute error = 1.61e-30 relative error = 1.6106623291692939625011439359222e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.85 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.555 y[1] (analytic) = -0.99929635102509848777132081959536 y[1] (numeric) = -0.99929635102509848777132081959696 absolute error = 1.60e-30 relative error = 1.6011266311126699419206450725263e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.849 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -1.554 y[1] (analytic) = -0.99900365125854345229422489073047 y[1] (numeric) = -0.99900365125854345229422489073207 absolute error = 1.60e-30 relative error = 1.6015957479077500450057706464663e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.553 y[1] (analytic) = -0.99871068497738421616938992156386 y[1] (numeric) = -0.99871068497738421616938992156546 absolute error = 1.60e-30 relative error = 1.6020655672030103177982190154784e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.847 Order of pole = 3.3e-29 TOP MAIN SOLVE Loop x[1] = -1.552 y[1] (analytic) = -0.99841745186780589878851213227124 y[1] (numeric) = -0.99841745186780589878851213227284 absolute error = 1.60e-30 relative error = 1.6025360904967893311045555018496e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.846 Order of pole = 1.4e-29 TOP MAIN SOLVE Loop x[1] = -1.551 y[1] (analytic) = -0.99812395161560527282451364706925 y[1] (numeric) = -0.99812395161560527282451364707085 absolute error = 1.60e-30 relative error = 1.6030073192915297970520752896770e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.845 Order of pole = 1.0e-29 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = -0.9978301839061904549449618794427 y[1] (numeric) = -0.99783018390619045494496187944431 absolute error = 1.61e-30 relative error = 1.6135010004381284529241597820835e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.549 y[1] (analytic) = -0.99753614842458059739965445777235 y[1] (numeric) = -0.99753614842458059739965445777395 absolute error = 1.60e-30 relative error = 1.6039518994142687893315113032413e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.548 y[1] (analytic) = -0.99724184485540558048988255126777 y[1] (numeric) = -0.99724184485540558048988255126937 absolute error = 1.60e-30 relative error = 1.6044252537677968559531589495527e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.843 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -1.547 y[1] (analytic) = -0.99694727288290570592692260273558 y[1] (numeric) = -0.99694727288290570592692260273717 absolute error = 1.59e-30 relative error = 1.5948686989254145082955844787212e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.546 y[1] (analytic) = -0.99665243219093139108734376838494 y[1] (numeric) = -0.99665243219093139108734376838654 absolute error = 1.60e-30 relative error = 1.6053740986541672233920452628235e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.545 y[1] (analytic) = -0.9963573224629428641727558060101 y[1] (numeric) = -0.9963573224629428641727558060117 absolute error = 1.60e-30 relative error = 1.6058495922375360336227880499818e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.544 y[1] (analytic) = -0.99606194338200986028165974190967 y[1] (numeric) = -0.99606194338200986028165974191127 absolute error = 1.60e-30 relative error = 1.6063258019550373533630037941782e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.543 y[1] (analytic) = -0.99576629463081131840110138422489 y[1] (numeric) = -0.99576629463081131840110138422649 absolute error = 1.60e-30 relative error = 1.6068027293424441336764153856554e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.839 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -1.542 y[1] (analytic) = -0.99547037589163507932586563642001 y[1] (numeric) = -0.99547037589163507932586563642161 absolute error = 1.60e-30 relative error = 1.6072803759397585633827086330784e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.838 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -1.541 y[1] (analytic) = -0.9951741868463775845129875998069 y[1] (numeric) = -0.9951741868463775845129875998085 absolute error = 1.60e-30 relative error = 1.6077587432912262440592841345728e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = -0.99487772717654357587939463874932 y[1] (numeric) = -0.99487772717654357587939463875092 absolute error = 1.60e-30 relative error = 1.6082378329453504210445544821359e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.836 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.539 y[1] (analytic) = -0.99458099656324579655053191688854 y[1] (numeric) = -0.99458099656324579655053191689014 absolute error = 1.60e-30 relative error = 1.6087176464549062706981476748627e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.538 y[1] (analytic) = -0.99428399468720469256786239782779 y[1] (numeric) = -0.99428399468720469256786239782939 absolute error = 1.60e-30 relative error = 1.6091981853769552441747014861439e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.537 y[1] (analytic) = -0.99398672122874811556317093961612 y[1] (numeric) = -0.99398672122874811556317093961773 absolute error = 1.61e-30 relative error = 1.6197399478433148396440730184757e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.536 y[1] (analytic) = -0.99368917586781102640764089949904 y[1] (numeric) = -0.99368917586781102640764089950065 absolute error = 1.61e-30 relative error = 1.6202249547439730527529991657919e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.833 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -1.535 y[1] (analytic) = -0.99339135828393519984371060417091 y[1] (numeric) = -0.99339135828393519984371060417252 absolute error = 1.61e-30 relative error = 1.6207106963173553041441823714637e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.534 y[1] (analytic) = -0.99309326815626893010775613158899 y[1] (numeric) = -0.9930932681562689301077561315906 absolute error = 1.61e-30 relative error = 1.6211971741476524157670845866080e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.831 Order of pole = 1e-30 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=9.10 x[1] = -1.533 y[1] (analytic) = -0.99279490516356673755168609370703 y[1] (numeric) = -0.99279490516356673755168609370864 absolute error = 1.61e-30 relative error = 1.6216843898234413028319106590675e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.532 y[1] (analytic) = -0.99249626898418907627157350567385 y[1] (numeric) = -0.99249626898418907627157350567546 absolute error = 1.61e-30 relative error = 1.6221723449376997539324480070386e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.531 y[1] (analytic) = -0.99219735929610204275148937653489 y[1] (numeric) = -0.9921973592961020427514893765365 absolute error = 1.61e-30 relative error = 1.6226610410878212698816886153014e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.829 Order of pole = 6.2e-29 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = -0.99189817577687708553074235968741 y[1] (numeric) = -0.99189817577687708553074235968902 absolute error = 1.61e-30 relative error = 1.6231504798756299615294631599976e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.828 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -1.529 y[1] (analytic) = -0.99159871810369071590276865868826 y[1] (numeric) = -0.99159871810369071590276865868988 absolute error = 1.62e-30 relative error = 1.6337253875217271559434831342807e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.827 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -1.528 y[1] (analytic) = -0.9912989859533242196539563959113 y[1] (numeric) = -0.99129898595332421965395639591291 absolute error = 1.61e-30 relative error = 1.6241315917938481674505009651609e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.527 y[1] (analytic) = -0.99099897900216336985072881841382 y[1] (numeric) = -0.99099897900216336985072881841543 absolute error = 1.61e-30 relative error = 1.6246232681501938651370612057585e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.825 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -1.526 y[1] (analytic) = -0.99069869692619814068325103761255 y[1] (numeric) = -0.99069869692619814068325103761416 absolute error = 1.61e-30 relative error = 1.6251156935961293182080590226054e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.525 y[1] (analytic) = -0.99039813940102242237416547740178 y[1] (numeric) = -0.99039813940102242237416547740339 absolute error = 1.61e-30 relative error = 1.6256088697558572383561161586224e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.824 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -1.524 y[1] (analytic) = -0.99009730610183373716080183958421 y[1] (numeric) = -0.99009730610183373716080183958583 absolute error = 1.62e-30 relative error = 1.6362028156385866911251814406580e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.523 y[1] (analytic) = -0.98979619670343295635934818633987 y[1] (numeric) = -0.98979619670343295635934818634149 absolute error = 1.62e-30 relative error = 1.6367005706785832897791131225197e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.822 Order of pole = 1.9e-29 TOP MAIN SOLVE Loop x[1] = -1.522 y[1] (analytic) = -0.98949481088022401851951068734359 y[1] (numeric) = -0.98949481088022401851951068734522 absolute error = 1.63e-30 relative error = 1.6473052532231092250798714781341e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.521 y[1] (analytic) = -0.98919314830621364867823068446841 y[1] (numeric) = -0.98919314830621364867823068447004 absolute error = 1.63e-30 relative error = 1.6478076124880505325338848840615e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = -0.9888912086550110787210689901915 y[1] (numeric) = -0.98889120865501107872106899019313 absolute error = 1.63e-30 relative error = 1.6483107400832895301365860198905e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.819 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.519 y[1] (analytic) = -0.98858899159982776885990875726318 y[1] (numeric) = -0.9885889915998277688599087572648 absolute error = 1.62e-30 relative error = 1.6386992104558675069847737452605e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.819 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -1.518 y[1] (analytic) = -0.9882864968134771302356698373165 y[1] (numeric) = -0.98828649681347713023566983731812 absolute error = 1.62e-30 relative error = 1.6392007836020736750766286527804e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.818 Order of pole = 6.9e-29 TOP MAIN SOLVE Loop x[1] = -1.517 y[1] (analytic) = -0.98798372396837424865476928529662 y[1] (numeric) = -0.98798372396837424865476928529825 absolute error = 1.63e-30 relative error = 1.6498247495949406422548486447027e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.817 Order of pole = 1.0e-29 TOP MAIN SOLVE Loop x[1] = -1.516 y[1] (analytic) = -0.98768067273653560946810456528295 y[1] (numeric) = -0.98768067273653560946810456528458 absolute error = 1.63e-30 relative error = 1.6503309672789389921271235897473e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.816 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -1.515 y[1] (analytic) = -0.98737734278957882360137807187295 y[1] (numeric) = -0.98737734278957882360137807187458 absolute error = 1.63e-30 relative error = 1.6508379617004957606613032126865e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.514 y[1] (analytic) = -0.98707373379872235474562380020178 y[1] (numeric) = -0.98707373379872235474562380020341 absolute error = 1.63e-30 relative error = 1.6513457345552049518441849529639e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.513 y[1] (analytic) = -0.98676984543478524771683937729389 y[1] (numeric) = -0.98676984543478524771683937729551 absolute error = 1.62e-30 relative error = 1.6417202121597101205239995322559e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.512 y[1] (analytic) = -0.98646567736818685799366920818855 y[1] (numeric) = -0.98646567736818685799366920819017 absolute error = 1.62e-30 relative error = 1.6422264222329894742844163397107e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.511 y[1] (analytic) = -0.98616122926894658244212719255684 y[1] (numeric) = -0.98616122926894658244212719255847 absolute error = 1.63e-30 relative error = 1.6528737407455563802317643672053e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.812 Order of pole = 3.8e-29 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = -0.98585650080668359123639033173802 y[1] (numeric) = -0.98585650080668359123639033173965 absolute error = 1.63e-30 relative error = 1.6533846443840880872349491979335e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.811 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -1.509 y[1] (analytic) = -0.98555149165061656098473757267363 y[1] (numeric) = -0.98555149165061656098473757267526 absolute error = 1.63e-30 relative error = 1.6538963350053393144261040859491e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.508 y[1] (analytic) = -0.98524620146956340906975142451197 y[1] (numeric) = -0.9852462014695634090697514245136 absolute error = 1.63e-30 relative error = 1.6544088143336572552249226731848e-28 % Correct digits = 29 h = 0.001 memory used=76.2MB, alloc=4.3MB, time=9.59 Complex estimate of poles used for equation 1 Radius of convergence = 1.809 Order of pole = 4.1e-29 TOP MAIN SOLVE Loop x[1] = -1.507 y[1] (analytic) = -0.98494062993194102921194323609649 y[1] (numeric) = -0.98494062993194102921194323609812 absolute error = 1.63e-30 relative error = 1.6549220840982387880355306825292e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.809 Order of pole = 5.5e-29 TOP MAIN SOLVE Loop x[1] = -1.506 y[1] (analytic) = -0.9846347767057650282660065385424 y[1] (numeric) = -0.98463477670576502826600653854403 absolute error = 1.63e-30 relative error = 1.6554361460331470778789017956323e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.505 y[1] (analytic) = -0.98432864145864946425894653704764 y[1] (numeric) = -0.98432864145864946425894653704926 absolute error = 1.62e-30 relative error = 1.6457917932768538386274590761773e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.504 y[1] (analytic) = -0.98402222385780658567937768037798 y[1] (numeric) = -0.9840222238578065856793776803796 absolute error = 1.62e-30 relative error = 1.6463042812680352905974205766580e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.806 Order of pole = 8e-30 TOP MAIN SOLVE Loop x[1] = -1.503 y[1] (analytic) = -0.9837155235700465720273252455123 y[1] (numeric) = -0.98371552357004657202732524551392 absolute error = 1.62e-30 relative error = 1.6468175617690616580411006200903e-28 % Correct digits = 29 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = -1.502 y[1] (analytic) = -0.98340854026177727563391104913087 y[1] (numeric) = -0.98340854026177727563391104913249 absolute error = 1.62e-30 relative error = 1.6473316365228697445778648181251e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.804 Order of pole = 1.17e-28 TOP MAIN SOLVE Loop x[1] = -1.501 y[1] (analytic) = -0.98310127359900396476034773737684 y[1] (numeric) = -0.98310127359900396476034773737846 absolute error = 1.62e-30 relative error = 1.6478465072773162901035083204430e-28 % Correct digits = 29 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 1.804 Order of pole = 1.0e-29 Finished! diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; Iterations = 500 Total Elapsed Time = 9 Seconds Elapsed Time(since restart) = 9 Seconds Time to Timeout = 2 Minutes 50 Seconds Percent Done = 100.2 % > quit memory used=77.4MB, alloc=4.3MB, time=9.73