|\^/| 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.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found_sing := 0;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float
and array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[1] := array_m1[1] * array_const_2D0[1];
> #emit pre mult FULL LINEAR $eq_no = 1 i = 1
> #emit pre mult LINEAR - FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] * array_tmp1[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp2[1] / (array_tmp4[1]));
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp9[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp1[2] := array_m1[2] * array_const_2D0[1];
> #emit pre mult LINEAR FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp5[2] := ((array_tmp2[2] - ats(2,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2];
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp9[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp1[3] := array_m1[3] * array_const_2D0[1];
> #emit pre mult LINEAR FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp5[3] := ((array_tmp2[3] - ats(3,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp6[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[3];
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp8[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp9[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp1[4] := array_m1[4] * array_const_2D0[1];
> #emit pre mult LINEAR FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp5[4] := ((array_tmp2[4] - ats(4,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[4];
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp8[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp9[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp1[5] := array_m1[5] * array_const_2D0[1];
> #emit pre mult LINEAR FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp5[5] := ((array_tmp2[5] - ats(5,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[5];
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp8[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp9[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1];
> #emit mult FULL LINEAR $eq_no = 1 i = 1
> array_tmp2[kkk] := array_tmp1[kkk-1] * array_x[2] + array_tmp1[kkk] * array_x[1];
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit div FULL FULL $eq_no = 1
> array_tmp5[kkk] := ((array_tmp2[kkk] - ats(kkk,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[kkk];
> #emit div FULL FULL $eq_no = 1
> array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp9[kkk] := array_tmp8[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp9[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_const_2D0[1];
array_tmp2[1] := array_x[1]*array_tmp1[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_x[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp9[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_m1[2]*array_const_2D0[1];
array_tmp2[2] :=
array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk];
array_tmp3[2] := 2*array_x[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(array_tmp2[2] - ats(2, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[2] := 2*array_x[1]*array_x[2];
array_tmp7[2] := array_tmp6[2];
array_tmp8[2] :=
(array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[2] := array_tmp8[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp9[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_m1[3]*array_const_2D0[1];
array_tmp2[3] :=
array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk];
array_tmp3[3] := array_x[2]*array_x[2];
array_tmp4[3] := array_tmp3[3];
array_tmp5[3] :=
(array_tmp2[3] - ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[3] := array_x[2]*array_x[2];
array_tmp7[3] := array_tmp6[3];
array_tmp8[3] :=
(array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[3] := array_tmp8[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp9[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_m1[4]*array_const_2D0[1];
array_tmp2[4] :=
array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk];
array_tmp4[4] := array_tmp3[4];
array_tmp5[4] :=
(array_tmp2[4] - ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[4] := array_tmp6[4];
array_tmp8[4] :=
(array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[4] := array_tmp8[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp9[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_m1[5]*array_const_2D0[1];
array_tmp2[5] :=
array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk];
array_tmp4[5] := array_tmp3[5];
array_tmp5[5] :=
(array_tmp2[5] - ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[5] := array_tmp6[5];
array_tmp8[5] :=
(array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[5] := array_tmp8[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp9[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_m1[kkk]*array_const_2D0[1];
array_tmp2[kkk] :=
array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk];
array_tmp4[kkk] := array_tmp3[kkk];
array_tmp5[kkk] := (
array_tmp2[kkk] - ats(kkk, array_tmp4, array_tmp5, 2))/
array_tmp4[1];
array_tmp7[kkk] := array_tmp6[kkk];
array_tmp8[kkk] := (
array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
array_tmp7[1];
array_tmp9[kkk] := array_tmp8[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp9[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 16
> # Begin Function number 17
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 26
> # Begin Function number 27
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 27
> # Begin Function number 28
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(1.0 / (x * x + 0.000001)) ;
> end;
exact_soln_y := proc(x) return 1.0/(x*x + 0.1*10^(-5)) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sing1postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.0;");
> omniout_str(ALWAYS,"x_end := -1.5;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 500;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0 / (x * x + 0.000001)) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_2D0[1] := 2.0;
> array_const_0D000001 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D000001[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D000001[1] := 0.000001;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -2.0;
> x_end := -1.5;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 500;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T19:00:08-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing1")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"sing1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing1 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_0D000001, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sing1postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.\
000001) /( x * x + 0.000001);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.0;");
omniout_str(ALWAYS, "x_end := -1.5;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 500;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0 / (x * x + 0.000001)) ;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_0D000001 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D000001[term] := 0.; term := term + 1
end do;
array_const_0D000001[1] := 0.1*10^(-5);
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := -2.0;
x_end := -1.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 500;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + \
0.000001) /( x * x + 0.000001);");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-01-28T19:00:08-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing1");
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x\
/ (x * x + 0.000001) /( x * x + 0.000001);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 165 | ");
logitem_str(html_log_file,
"sing1 diffeq.mxt");
logitem_str(html_log_file,
"sing1 maple results")
;
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/sing1postode.ode#################
diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.0;
x_end := -1.5;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 500;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0 / (x * x + 0.000001)) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.5
estimated_steps = 500
step_error = 2.0000000000000000000000000000000e-13
est_needed_step_err = 2.0000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.0060551788397984124943226430006e-85
max_value3 = 1.0060551788397984124943226430006e-85
value3 = 1.0060551788397984124943226430006e-85
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (analytic) = 0.24999993750001562499609375097656
y[1] (numeric) = 0.24999993750001562499609375097656
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.999
y[1] (analytic) = 0.25025012499993743746875001564063
y[1] (numeric) = 0.25025012499993743746875001564063
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.999
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.998
y[1] (analytic) = 0.2505006882506409686360613275785
y[1] (numeric) = 0.25050068825064096863606132757849
absolute error = 1e-32
relative error = 3.9920050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.998
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.997
y[1] (analytic) = 0.2507516280049448221042575118919
y[1] (numeric) = 0.25075162800494482210425751189189
absolute error = 1e-32
relative error = 3.9880099999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.997
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.996
y[1] (analytic) = 0.25100294501755389095980263136427
y[1] (numeric) = 0.25100294501755389095980263136427
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.996
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.995
y[1] (analytic) = 0.25125464004506503223848286418229
y[1] (numeric) = 0.25125464004506503223848286418229
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.995
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.994
y[1] (analytic) = 0.251506713845972761319877053458
y[1] (numeric) = 0.251506713845972761319877053458
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.994
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.993
y[1] (analytic) = 0.25175916718067496632721138958472
y[1] (numeric) = 0.25175916718067496632721138958472
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.993
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.992
y[1] (analytic) = 0.25201200081147864261296122921374
y[1] (numeric) = 0.25201200081147864261296122921373
absolute error = 1e-32
relative error = 3.9680649999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.992
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.991
y[1] (analytic) = 0.25226521550260564741092641373211
y[1] (numeric) = 0.2522652155026056474109264137321
absolute error = 1e-32
relative error = 3.9640820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.991
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (analytic) = 0.25251881202019847473587163559717
y[1] (numeric) = 0.25251881202019847473587163559717
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.99
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.989
y[1] (analytic) = 0.25277279113232605061219042284338
y[1] (numeric) = 0.25277279113232605061219042284338
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.989
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.18
x[1] = -1.988
y[1] (analytic) = 0.25302715360898954871342018068669
y[1] (numeric) = 0.25302715360898954871342018068669
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.988
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.987
y[1] (analytic) = 0.25328190022212822649480645463595
y[1] (numeric) = 0.25328190022212822649480645463594
absolute error = 1e-32
relative error = 3.9481699999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.987
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.986
y[1] (analytic) = 0.25353703174562528190148717216711
y[1] (numeric) = 0.25353703174562528190148717216711
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.986
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.985
y[1] (analytic) = 0.25379254895531373073524209017452
y[1] (numeric) = 0.25379254895531373073524209017452
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.985
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.984
y[1] (analytic) = 0.25404845262898230476312903349553
y[1] (numeric) = 0.25404845262898230476312903349552
absolute error = 1e-32
relative error = 3.9362569999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.984
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.983
y[1] (analytic) = 0.25430474354638137065170676628631
y[1] (numeric) = 0.25430474354638137065170676628631
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.983
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.982
y[1] (analytic) = 0.25456142248922886981092450344613
y[1] (numeric) = 0.25456142248922886981092450344612
absolute error = 1e-32
relative error = 3.9283249999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.982
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.981
y[1] (analytic) = 0.25481849024121627923214015424673
y[1] (numeric) = 0.25481849024121627923214015424672
absolute error = 1e-32
relative error = 3.9243620000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.981
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (analytic) = 0.25507594758801459340511340549092
y[1] (numeric) = 0.25507594758801459340511340549091
absolute error = 1e-32
relative error = 3.9204010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.98
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.979
y[1] (analytic) = 0.25533379531728032739920570762953
y[1] (numeric) = 0.25533379531728032739920570762952
absolute error = 1e-32
relative error = 3.9164420000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.979
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.978
y[1] (analytic) = 0.25559203421866154119440713510723
y[1] (numeric) = 0.25559203421866154119440713510722
absolute error = 1e-32
relative error = 3.9124850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.978
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.977
y[1] (analytic) = 0.2558506650838038853481999626458
y[1] (numeric) = 0.2558506650838038853481999626458
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.977
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.976
y[1] (analytic) = 0.25610968870635666808466064313753
y[1] (numeric) = 0.25610968870635666808466064313753
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.976
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.975
y[1] (analytic) = 0.25636910588197894389259570130538
y[1] (numeric) = 0.25636910588197894389259570130538
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.975
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.974
y[1] (analytic) = 0.2566289174083456237199028813525
y[1] (numeric) = 0.2566289174083456237199028813525
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.974
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.973
y[1] (analytic) = 0.25688912408515360685174671759922
y[1] (numeric) = 0.25688912408515360685174671759922
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.973
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.972
y[1] (analytic) = 0.25714972671412793456053754578872
y[1] (numeric) = 0.25714972671412793456053754578873
absolute error = 1e-32
relative error = 3.8887850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.972
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.971
y[1] (analytic) = 0.25741072609902796561610485059624
y[1] (numeric) = 0.25741072609902796561610485059625
absolute error = 1e-32
relative error = 3.8848420000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.971
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (analytic) = 0.25767212304565357374485976323539
y[1] (numeric) = 0.2576721230456535737448597632354
absolute error = 1e-32
relative error = 3.8809010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.97
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.969
y[1] (analytic) = 0.2579339183618513671271474933208
y[1] (numeric) = 0.25793391836185136712714749332081
absolute error = 1e-32
relative error = 3.8769620000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.969
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.968
y[1] (analytic) = 0.25819611285752093002239851279039
y[1] (numeric) = 0.2581961128575209300223985127904
absolute error = 1e-32
relative error = 3.8730250000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.968
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.967
y[1] (analytic) = 0.25845870734462108661209741825597
y[1] (numeric) = 0.25845870734462108661209741825598
absolute error = 1e-32
relative error = 3.8690900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.967
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.966
y[1] (analytic) = 0.25872170263717618715100059324886
y[1] (numeric) = 0.25872170263717618715100059324887
memory used=7.6MB, alloc=4.2MB, time=0.39
absolute error = 1e-32
relative error = 3.8651570000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.966
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.965
y[1] (analytic) = 0.25898509955128241651744808514187
y[1] (numeric) = 0.25898509955128241651744808514188
absolute error = 1e-32
relative error = 3.8612260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.965
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.964
y[1] (analytic) = 0.25924889890511412525403151481465
y[1] (numeric) = 0.25924889890511412525403151481466
absolute error = 1e-32
relative error = 3.8572970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.964
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.963
y[1] (analytic) = 0.25951310151893018319029836221282
y[1] (numeric) = 0.25951310151893018319029836221283
absolute error = 1e-32
relative error = 3.8533699999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.963
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.962
y[1] (analytic) = 0.25977770821508035573959362973104
y[1] (numeric) = 0.25977770821508035573959362973105
absolute error = 1e-32
relative error = 3.8494450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.962
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.961
y[1] (analytic) = 0.26004271981801170296256268979868
y[1] (numeric) = 0.26004271981801170296256268979869
absolute error = 1e-32
relative error = 3.8455220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.961
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (analytic) = 0.26030813715427500149026408520822
y[1] (numeric) = 0.26030813715427500149026408520823
absolute error = 1e-32
relative error = 3.8416010000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.96
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.959
y[1] (analytic) = 0.26057396105253118940026818272072
y[1] (numeric) = 0.26057396105253118940026818272072
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.959
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.958
y[1] (analytic) = 0.26084019234355783413954689450188
y[1] (numeric) = 0.26084019234355783413954689450188
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.958
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.957
y[1] (analytic) = 0.26110683186025562358839119025549
y[1] (numeric) = 0.26110683186025562358839119025549
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.957
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.956
y[1] (analytic) = 0.26137388043765488036002683787004
y[1] (numeric) = 0.26137388043765488036002683787004
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.956
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.955
y[1] (analytic) = 0.26164133891292209943103474439996
y[1] (numeric) = 0.26164133891292209943103474439996
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.955
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.954
y[1] (analytic) = 0.26190920812536650919812043475881
y[1] (numeric) = 0.26190920812536650919812043475881
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.954
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.953
y[1] (analytic) = 0.26217748891644665605721761518113
y[1] (numeric) = 0.26217748891644665605721761518113
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.953
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.952
y[1] (analytic) = 0.26244618212977701260135343496124
y[1] (numeric) = 0.26244618212977701260135343496125
absolute error = 1e-32
relative error = 3.8103050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.952
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.951
y[1] (analytic) = 0.26271528861113460953414799592896
y[1] (numeric) = 0.26271528861113460953414799592897
absolute error = 1e-32
relative error = 3.8064020000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.951
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (analytic) = 0.2629848092084656913962678773786
y[1] (numeric) = 0.26298480920846569139626787737861
absolute error = 1e-32
relative error = 3.8025010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.95
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.949
y[1] (analytic) = 0.26325474477189239620260295761441
y[1] (numeric) = 0.26325474477189239620260295761442
absolute error = 1e-32
relative error = 3.7986020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.949
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.948
y[1] (analytic) = 0.26352509615371945908838763487544
y[1] (numeric) = 0.26352509615371945908838763487545
absolute error = 1e-32
relative error = 3.7947050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.948
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.947
y[1] (analytic) = 0.26379586420844094006294169320013
y[1] (numeric) = 0.26379586420844094006294169320015
absolute error = 2e-32
relative error = 7.5816200000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.947
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.946
y[1] (analytic) = 0.26406704979274697597016253590982
y[1] (numeric) = 0.26406704979274697597016253590983
absolute error = 1e-32
relative error = 3.7869170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.946
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.945
y[1] (analytic) = 0.26433865376553055675535933403577
y[1] (numeric) = 0.26433865376553055675535933403578
absolute error = 1e-32
relative error = 3.7830260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.945
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.944
y[1] (analytic) = 0.26461067698789432613848082247349
y[1] (numeric) = 0.2646106769878943261384808224735
absolute error = 1e-32
relative error = 3.7791370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.944
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.61
x[1] = -1.943
y[1] (analytic) = 0.26488312032315740679425203628899
y[1] (numeric) = 0.264883120323157406794252036289
absolute error = 1e-32
relative error = 3.7752500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.943
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.942
y[1] (analytic) = 0.26515598463686225014020122687674
y[1] (numeric) = 0.26515598463686225014020122687675
absolute error = 1e-32
relative error = 3.7713650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.942
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.941
y[1] (analytic) = 0.26542927079678151083402654611223
y[1] (numeric) = 0.26542927079678151083402654611224
absolute error = 1e-32
relative error = 3.7674820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.941
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (analytic) = 0.26570297967292494608222284987171
y[1] (numeric) = 0.26570297967292494608222284987171
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.94
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.939
y[1] (analytic) = 0.26597711213754633986236216401106
y[1] (numeric) = 0.26597711213754633986236216401107
absolute error = 1e-32
relative error = 3.7597220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.939
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.938
y[1] (analytic) = 0.26625166906515045216189698989176
y[1] (numeric) = 0.26625166906515045216189698989176
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.938
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.937
y[1] (analytic) = 0.2665266513324999933368337166875
y[1] (numeric) = 0.2665266513324999933368337166875
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.937
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.936
y[1] (analytic) = 0.26680205981862262369410396796027
y[1] (numeric) = 0.26680205981862262369410396796027
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.936
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.935
y[1] (analytic) = 0.26707789540481797840194475440318
y[1] (numeric) = 0.26707789540481797840194475440318
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.935
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.934
y[1] (analytic) = 0.26735415897466471783308384734398
y[1] (numeric) = 0.26735415897466471783308384734398
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.934
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.933
y[1] (analytic) = 0.26763085141402760344601484280702
y[1] (numeric) = 0.26763085141402760344601484280702
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.933
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.932
y[1] (analytic) = 0.26790797361106459931013696795151
y[1] (numeric) = 0.26790797361106459931013696795151
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.932
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.931
y[1] (analytic) = 0.26818552645623399938102780493901
y[1] (numeric) = 0.26818552645623399938102780493901
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.931
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (analytic) = 0.26846351084230158063261278621902
y[1] (numeric) = 0.26846351084230158063261278621901
absolute error = 1e-32
relative error = 3.7249009999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.93
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.929
y[1] (analytic) = 0.26874192766434778215349356443706
y[1] (numeric) = 0.26874192766434778215349356443705
absolute error = 1e-32
relative error = 3.7210420000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.929
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.928
y[1] (analytic) = 0.26902077781977491031519819433254
y[1] (numeric) = 0.26902077781977491031519819433253
absolute error = 1e-32
relative error = 3.7171850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.928
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.927
y[1] (analytic) = 0.2693000622083143701206194978631
y[1] (numeric) = 0.26930006220831437012061949786309
absolute error = 1e-32
relative error = 3.7133300000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.927
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.926
y[1] (analytic) = 0.26957978173203392284141403222071
y[1] (numeric) = 0.2695797817320339228414140322207
absolute error = 1e-32
relative error = 3.7094770000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.926
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.925
y[1] (analytic) = 0.26985993729534497005364275833557
y[1] (numeric) = 0.26985993729534497005364275833555
absolute error = 2e-32
relative error = 7.4112520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.925
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.924
y[1] (analytic) = 0.27014052980500986418144582993519
y[1] (numeric) = 0.27014052980500986418144582993517
absolute error = 2e-32
relative error = 7.4035540000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.924
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.923
y[1] (analytic) = 0.27042156017014924565905790536868
y[1] (numeric) = 0.27042156017014924565905790536866
absolute error = 2e-32
relative error = 7.3958600000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.923
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.922
y[1] (analytic) = 0.27070302930224940682198704144599
y[1] (numeric) = 0.27070302930224940682198704144597
absolute error = 2e-32
relative error = 7.3881699999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.922
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.921
y[1] (analytic) = 0.27098493811516968263869957580018
y[1] (numeric) = 0.27098493811516968263869957580016
absolute error = 2e-32
relative error = 7.3804839999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.921
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=0.84
x[1] = -1.92
y[1] (analytic) = 0.27126728752514986839467545717354
y[1] (numeric) = 0.27126728752514986839467545717352
absolute error = 2e-32
relative error = 7.3728020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.92
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.919
y[1] (analytic) = 0.2715500784508176644412232570694
y[1] (numeric) = 0.27155007845081766444122325706938
absolute error = 2e-32
relative error = 7.3651240000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.919
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.918
y[1] (analytic) = 0.27183331181319614812197160701058
y[1] (numeric) = 0.27183331181319614812197160701056
absolute error = 2e-32
relative error = 7.3574500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.918
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.917
y[1] (analytic) = 0.27211698853571127299048406891091
y[1] (numeric) = 0.27211698853571127299048406891089
absolute error = 2e-32
relative error = 7.3497799999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.917
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.916
y[1] (analytic) = 0.27240110954419939543297747760386
y[1] (numeric) = 0.27240110954419939543297747760385
absolute error = 1e-32
relative error = 3.6710570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.916
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.915
y[1] (analytic) = 0.27268567576691482881065961028854
y[1] (numeric) = 0.27268567576691482881065961028853
absolute error = 1e-32
relative error = 3.6672260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.915
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.914
y[1] (analytic) = 0.27297068813453742523674065355188
y[1] (numeric) = 0.27297068813453742523674065355187
absolute error = 1e-32
relative error = 3.6633970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.914
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.913
y[1] (analytic) = 0.27325614758018018510371437081406
y[1] (numeric) = 0.27325614758018018510371437081405
absolute error = 1e-32
relative error = 3.6595700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.913
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.912
y[1] (analytic) = 0.27354205503939689447704913772706
y[1] (numeric) = 0.27354205503939689447704913772705
absolute error = 1e-32
relative error = 3.6557450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.912
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.911
y[1] (analytic) = 0.27382841145018979047197612654378
y[1] (numeric) = 0.27382841145018979047197612654377
absolute error = 1e-32
relative error = 3.6519219999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.911
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (analytic) = 0.27411521775301725473061189917713
y[1] (numeric) = 0.27411521775301725473061189917713
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.91
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.909
y[1] (analytic) = 0.27440247489080153511720552910011
y[1] (numeric) = 0.2744024748908015351172055291001
absolute error = 1e-32
relative error = 3.6442820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.909
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.908
y[1] (analytic) = 0.27469018380893649574985613101623
y[1] (numeric) = 0.27469018380893649574985613101622
absolute error = 1e-32
relative error = 3.6404650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.908
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.907
y[1] (analytic) = 0.2749783454552953954876053510786
y[1] (numeric) = 0.27497834545529539548760535107859
absolute error = 1e-32
relative error = 3.6366500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.907
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.906
y[1] (analytic) = 0.27526696078023869499237097618198
y[1] (numeric) = 0.27526696078023869499237097618196
absolute error = 2e-32
relative error = 7.2656739999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.906
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.905
y[1] (analytic) = 0.27555603073662189248575237543076
y[1] (numeric) = 0.27555603073662189248575237543075
absolute error = 1e-32
relative error = 3.6290260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.905
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.904
y[1] (analytic) = 0.27584555627980338832130600733694
y[1] (numeric) = 0.27584555627980338832130600733693
absolute error = 1e-32
relative error = 3.6252170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.904
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.903
y[1] (analytic) = 0.27613553836765237849345972977376
y[1] (numeric) = 0.27613553836765237849345972977375
absolute error = 1e-32
relative error = 3.6214100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.903
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.902
y[1] (analytic) = 0.27642597796055677720480815346065
y[1] (numeric) = 0.27642597796055677720480815346063
absolute error = 2e-32
relative error = 7.2352099999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.902
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.901
y[1] (analytic) = 0.27671687602143116861410780114683
y[1] (numeric) = 0.27671687602143116861410780114681
absolute error = 2e-32
relative error = 7.2276039999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.901
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (analytic) = 0.27700823351572478788787039117164
y[1] (numeric) = 0.27700823351572478788787039117162
absolute error = 2e-32
relative error = 7.2200019999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.9
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.899
y[1] (analytic) = 0.27730005141142953167903517329312
y[1] (numeric) = 0.2773000514114295316790351732931
absolute error = 2e-32
relative error = 7.2124040000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.899
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.898
y[1] (analytic) = 0.27759233067908799815678692429086
y[1] (numeric) = 0.27759233067908799815678692429083
absolute error = 3e-32
relative error = 1.0807215000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.898
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.06
x[1] = -1.897
y[1] (analytic) = 0.27788507229180155671217497867232
y[1] (numeric) = 0.2778850722918015567121749786723
absolute error = 2e-32
relative error = 7.1972200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.897
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.896
y[1] (analytic) = 0.27817827722523844746478054376621
y[1] (numeric) = 0.27817827722523844746478054376618
absolute error = 3e-32
relative error = 1.0784451000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.896
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.895
y[1] (analytic) = 0.2784719464576419106962745466059
y[1] (numeric) = 0.27847194645764191069627454660587
absolute error = 3e-32
relative error = 1.0773078000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.895
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.894
y[1] (analytic) = 0.27876608096983834633730640044134
y[1] (numeric) = 0.27876608096983834633730640044131
absolute error = 3e-32
relative error = 1.0761711000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.894
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.893
y[1] (analytic) = 0.27906068174524550363476537973182
y[1] (numeric) = 0.27906068174524550363476537973179
absolute error = 3e-32
relative error = 1.0750350000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.893
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.892
y[1] (analytic) = 0.27935574976988070112706077244658
y[1] (numeric) = 0.27935574976988070112706077244655
absolute error = 3e-32
relative error = 1.0738995000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.892
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.891
y[1] (analytic) = 0.27965128603236907705567465593104
y[1] (numeric) = 0.27965128603236907705567465593101
absolute error = 3e-32
relative error = 1.0727646000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.891
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (analytic) = 0.27994729152395187034185203609864
y[1] (numeric) = 0.27994729152395187034185203609861
absolute error = 3e-32
relative error = 1.0716303000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.89
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.889
y[1] (analytic) = 0.28024376723849473225790721801452
y[1] (numeric) = 0.28024376723849473225790721801448
absolute error = 4e-32
relative error = 1.4273288000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.889
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.888
y[1] (analytic) = 0.28054071417249606892324265789883
y[1] (numeric) = 0.2805407141724960689232426578988
absolute error = 3e-32
relative error = 1.0693635000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.888
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.887
y[1] (analytic) = 0.28083813332509541475579720116716
y[1] (numeric) = 0.28083813332509541475579720116713
absolute error = 3e-32
relative error = 1.0682310000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.887
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.886
y[1] (analytic) = 0.28113602569808183701026455743426
y[1] (numeric) = 0.28113602569808183701026455743423
absolute error = 3e-32
relative error = 1.0670991000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.886
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.885
y[1] (analytic) = 0.28143439229590237153505012065092
y[1] (numeric) = 0.28143439229590237153505012065089
absolute error = 3e-32
relative error = 1.0659678000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.885
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.884
y[1] (analytic) = 0.2817332341256704898805648300571
y[1] (numeric) = 0.28173323412567048988056483005707
absolute error = 3e-32
relative error = 1.0648371000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.884
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.883
y[1] (analytic) = 0.28203255219717459789208870487832
y[1] (numeric) = 0.28203255219717459789208870487828
absolute error = 4e-32
relative error = 1.4182760000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.883
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.882
y[1] (analytic) = 0.28233234752288656592107399224998
y[1] (numeric) = 0.28233234752288656592107399224994
absolute error = 4e-32
relative error = 1.4167700000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.882
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.881
y[1] (analytic) = 0.28263262111797029078939856343491
y[1] (numeric) = 0.28263262111797029078939856343488
absolute error = 3e-32
relative error = 1.0614486000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.881
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (analytic) = 0.28293337400029028964172429783717
y[1] (numeric) = 0.28293337400029028964172429783714
absolute error = 3e-32
relative error = 1.0603203000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.88
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.879
y[1] (analytic) = 0.28323460719042032582176272757193
y[1] (numeric) = 0.28323460719042032582176272757189
absolute error = 4e-32
relative error = 1.4122568000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.879
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.878
y[1] (analytic) = 0.28353632171165206690890119751565
y[1] (numeric) = 0.28353632171165206690890119751562
absolute error = 3e-32
relative error = 1.0580655000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.878
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.877
y[1] (analytic) = 0.28383851859000377505229724705021
y[1] (numeric) = 0.28383851859000377505229724705017
absolute error = 4e-32
relative error = 1.4092520000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.877
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.876
y[1] (analytic) = 0.28414119885422902974020686047559
y[1] (numeric) = 0.28414119885422902974020686047555
absolute error = 4e-32
relative error = 1.4077508000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.876
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.875
y[1] (analytic) = 0.28444436353582548314297368377637
y[1] (numeric) = 0.28444436353582548314297368377633
absolute error = 4e-32
relative error = 1.4062504000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.875
Order of pole = 1
memory used=22.8MB, alloc=4.3MB, time=1.29
TOP MAIN SOLVE Loop
x[1] = -1.874
y[1] (analytic) = 0.2847480136690436481687712866937
y[1] (numeric) = 0.28474801366904364816877128669365
absolute error = 5e-32
relative error = 1.7559385000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.874
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.873
y[1] (analytic) = 0.28505215029089571937185908161898
y[1] (numeric) = 0.28505215029089571937185908161894
absolute error = 4e-32
relative error = 1.4032520000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.873
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.872
y[1] (analytic) = 0.28535677444116442685378461556022
y[1] (numeric) = 0.28535677444116442685378461556018
absolute error = 4e-32
relative error = 1.4017540000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.872
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.871
y[1] (analytic) = 0.28566188716241192329864064934375
y[1] (numeric) = 0.28566188716241192329864064934371
absolute error = 4e-32
relative error = 1.4002568000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.871
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (analytic) = 0.28596748949998870428416475044618
y[1] (numeric) = 0.28596748949998870428416475044614
absolute error = 4e-32
relative error = 1.3987604000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.87
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.869
y[1] (analytic) = 0.28627358250204256201115207367995
y[1] (numeric) = 0.28627358250204256201115207367991
absolute error = 4e-32
relative error = 1.3972648000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.869
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.868
y[1] (analytic) = 0.28658016721952757259433860879658
y[1] (numeric) = 0.28658016721952757259433860879654
absolute error = 4e-32
relative error = 1.3957700000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.868
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.867
y[1] (analytic) = 0.28688724470621311705860245747614
y[1] (numeric) = 0.2868872447062131170586024574761
absolute error = 4e-32
relative error = 1.3942760000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.867
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.866
y[1] (analytic) = 0.28719481601869293618502468583041
y[1] (numeric) = 0.28719481601869293618502468583037
absolute error = 4e-32
relative error = 1.3927828000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.866
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.865
y[1] (analytic) = 0.28750288221639421935204900429127
y[1] (numeric) = 0.28750288221639421935204900429123
absolute error = 4e-32
relative error = 1.3912904000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.865
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.864
y[1] (analytic) = 0.28781144436158672751768097655574
y[1] (numeric) = 0.28781144436158672751768097655571
absolute error = 3e-32
relative error = 1.0423491000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.864
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.863
y[1] (analytic) = 0.28812050351939195048937267522769
y[1] (numeric) = 0.28812050351939195048937267522765
absolute error = 4e-32
relative error = 1.3883080000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.863
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.862
y[1] (analytic) = 0.28843006075779229862894770618783
y[1] (numeric) = 0.2884300607577922986289477061878
absolute error = 3e-32
relative error = 1.0401135000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.862
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.861
y[1] (analytic) = 0.28874011714764032914063433893816
y[1] (numeric) = 0.28874011714764032914063433893813
absolute error = 3e-32
relative error = 1.0389966000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.861
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (analytic) = 0.28905067376266800709099112874577
y[1] (numeric) = 0.28905067376266800709099112874574
absolute error = 3e-32
relative error = 1.0378803000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.86
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.859
y[1] (analytic) = 0.28936173167949600131022992104476
y[1] (numeric) = 0.28936173167949600131022992104473
absolute error = 3e-32
relative error = 1.0367646000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.859
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.858
y[1] (analytic) = 0.2896732919776430153251655120772
y[1] (numeric) = 0.28967329197764301532516551207718
absolute error = 2e-32
relative error = 6.9043300000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.858
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.857
y[1] (analytic) = 0.28998535573953515347474952514898
y[1] (numeric) = 0.28998535573953515347474952514896
absolute error = 2e-32
relative error = 6.8969000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.857
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.856
y[1] (analytic) = 0.29029792405051532235987827227449
y[1] (numeric) = 0.29029792405051532235987827227447
absolute error = 2e-32
relative error = 6.8894739999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.856
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.855
y[1] (analytic) = 0.2906109979988526677799005296676
y[1] (numeric) = 0.29061099799885266777990052966759
absolute error = 1e-32
relative error = 3.4410260000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.855
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.854
y[1] (analytic) = 0.29092457867575204730899128593609
y[1] (numeric) = 0.29092457867575204730899128593608
absolute error = 1e-32
relative error = 3.4373170000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.854
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.853
y[1] (analytic) = 0.29123866717536353866630164753714
y[1] (numeric) = 0.29123866717536353866630164753713
absolute error = 1e-32
relative error = 3.4336100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.853
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.852
y[1] (analytic) = 0.29155326459479198403454323078919
y[1] (numeric) = 0.29155326459479198403454323078918
absolute error = 1e-32
relative error = 3.4299050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
memory used=26.7MB, alloc=4.4MB, time=1.51
Complex estimate of poles used for equation 1
Radius of convergence = 1.852
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.851
y[1] (analytic) = 0.29186837203410657048241755740029
y[1] (numeric) = 0.29186837203410657048241755740028
absolute error = 1e-32
relative error = 3.4262020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.851
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (analytic) = 0.29218399059635044664705722511111
y[1] (numeric) = 0.2921839905963504466470572251111
absolute error = 1e-32
relative error = 3.4225010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.85
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.849
y[1] (analytic) = 0.29250012138755037583340597086348
y[1] (numeric) = 0.29250012138755037583340597086347
absolute error = 1e-32
relative error = 3.4188020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.849
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.848
y[1] (analytic) = 0.29281676551672642568822920525138
y[1] (numeric) = 0.29281676551672642568822920525137
absolute error = 1e-32
relative error = 3.4151050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.848
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.847
y[1] (analytic) = 0.2931339240959016946072151984077
y[1] (numeric) = 0.29313392409590169460721519840769
absolute error = 1e-32
relative error = 3.4114100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.847
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.846
y[1] (analytic) = 0.2934515982401120750343998636037
y[1] (numeric) = 0.29345159824011207503439986360369
absolute error = 1e-32
relative error = 3.4077170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.846
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.845
y[1] (analytic) = 0.29376978906741605381392504052554
y[1] (numeric) = 0.29376978906741605381392504052554
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.845
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.844
y[1] (analytic) = 0.29408849769890454975492135044262
y[1] (numeric) = 0.29408849769890454975492135044262
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.844
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.843
y[1] (analytic) = 0.29440772525871078857109210545685
y[1] (numeric) = 0.29440772525871078857109210545685
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.843
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.842
y[1] (analytic) = 0.29472747287402021535736442904657
y[1] (numeric) = 0.29472747287402021535736442904657
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.842
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.841
y[1] (analytic) = 0.29504774167508044476676771068327
y[1] (numeric) = 0.29504774167508044476676771068326
absolute error = 1e-32
relative error = 3.3892820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.841
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (analytic) = 0.29536853279521124905149779906138
y[1] (numeric) = 0.29536853279521124905149779906137
absolute error = 1e-32
relative error = 3.3856010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.84
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.839
y[1] (analytic) = 0.29568984737081458413292796226524
y[1] (numeric) = 0.29568984737081458413292796226524
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.839
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.838
y[1] (analytic) = 0.29601168654138465386613463499539
y[1] (numeric) = 0.29601168654138465386613463499539
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.838
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.837
y[1] (analytic) = 0.2963340514495180126653173589524
y[1] (numeric) = 0.2963340514495180126653173589524
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.837
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.836
y[1] (analytic) = 0.29665694324092370665730812896389
y[1] (numeric) = 0.29665694324092370665730812896389
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.836
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.835
y[1] (analytic) = 0.29698036306443345353118561094503
y[1] (numeric) = 0.29698036306443345353118561094503
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.835
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.834
y[1] (analytic) = 0.29730431207201186125283442498522
y[1] (numeric) = 0.29730431207201186125283442498521
absolute error = 1e-32
relative error = 3.3635570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.834
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.833
y[1] (analytic) = 0.29762879141876668581411891460732
y[1] (numeric) = 0.29762879141876668581411891460732
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.833
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.832
y[1] (analytic) = 0.29795380226295912818717457858159
y[1] (numeric) = 0.29795380226295912818717457858159
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.832
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.831
y[1] (analytic) = 0.29827934576601417065515865180122
y[1] (numeric) = 0.29827934576601417065515865180122
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.831
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (analytic) = 0.29860542309253095269164421402723
y[1] (numeric) = 0.29860542309253095269164421402723
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.83
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.829
y[1] (analytic) = 0.29893203541029318656168970735152
y[1] (numeric) = 0.29893203541029318656168970735152
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.829
Order of pole = 1
memory used=30.5MB, alloc=4.4MB, time=1.74
TOP MAIN SOLVE Loop
x[1] = -1.828
y[1] (analytic) = 0.29925918389027961281846788275624
y[1] (numeric) = 0.29925918389027961281846788275624
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.828
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.827
y[1] (analytic) = 0.29958686970667449587019500109349
y[1] (numeric) = 0.2995868697066744958701950010935
absolute error = 1e-32
relative error = 3.3379300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.827
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.826
y[1] (analytic) = 0.29991509403687815979296261228446
y[1] (numeric) = 0.29991509403687815979296261228447
absolute error = 1e-32
relative error = 3.3342770000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.826
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.825
y[1] (analytic) = 0.30024385806151756456594045683904
y[1] (numeric) = 0.30024385806151756456594045683905
absolute error = 1e-32
relative error = 3.3306260000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.825
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.824
y[1] (analytic) = 0.30057316296445692290629000440941
y[1] (numeric) = 0.30057316296445692290629000440941
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.824
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.823
y[1] (analytic) = 0.30090300993280835788200389368495
y[1] (numeric) = 0.30090300993280835788200389368495
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.823
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.822
y[1] (analytic) = 0.301233400156942601481767095372
y[1] (numeric) = 0.301233400156942601481767095372
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.822
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.821
y[1] (analytic) = 0.30156433483049973432182101432973
y[1] (numeric) = 0.30156433483049973432182101432973
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.821
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (analytic) = 0.30189581515039996667070200739584
y[1] (numeric) = 0.30189581515039996667070200739584
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.82
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.819
y[1] (analytic) = 0.3022278423168544609736209494669
y[1] (numeric) = 0.3022278423168544609736209494669
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.819
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.818
y[1] (analytic) = 0.30256041753337619605915056162778
y[1] (numeric) = 0.30256041753337619605915056162777
absolute error = 1e-32
relative error = 3.3051249999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.818
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.817
y[1] (analytic) = 0.30289354200679087321179225137741
y[1] (numeric) = 0.3028935420067908732117922513774
absolute error = 1e-32
relative error = 3.3014900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.817
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.816
y[1] (analytic) = 0.30322721694724786429490423629648
y[1] (numeric) = 0.30322721694724786429490423629647
absolute error = 1e-32
relative error = 3.2978570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.816
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.815
y[1] (analytic) = 0.30356144356823120210938775906692
y[1] (numeric) = 0.30356144356823120210938775906692
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.815
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.814
y[1] (analytic) = 0.30389622308657061317444828400439
y[1] (numeric) = 0.30389622308657061317444828400439
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.814
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.813
y[1] (analytic) = 0.30423155672245259311767372382468
y[1] (numeric) = 0.30423155672245259311767372382468
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.813
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.812
y[1] (analytic) = 0.30456744569943152486260201105884
y[1] (numeric) = 0.30456744569943152486260201105885
absolute error = 1e-32
relative error = 3.2833450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.812
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.811
y[1] (analytic) = 0.30490389124444083980288573238829
y[1] (numeric) = 0.3049038912444408398028857323883
absolute error = 1e-32
relative error = 3.2797220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.811
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (analytic) = 0.30524089458780422215310211742556
y[1] (numeric) = 0.30524089458780422215310211742557
absolute error = 1e-32
relative error = 3.2761010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.81
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.809
y[1] (analytic) = 0.30557845696324685666720244756121
y[1] (numeric) = 0.30557845696324685666720244756122
absolute error = 1e-32
relative error = 3.2724820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.809
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.808
y[1] (analytic) = 0.30591657960790671991654595708296
y[1] (numeric) = 0.30591657960790671991654595708297
absolute error = 1e-32
relative error = 3.2688650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.808
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.807
y[1] (analytic) = 0.30625526376234591532041956971135
y[1] (numeric) = 0.30625526376234591532041956971136
absolute error = 1e-32
relative error = 3.2652500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.807
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.806
y[1] (analytic) = 0.30659451067056205212290638105957
y[1] (numeric) = 0.30659451067056205212290638105958
absolute error = 1e-32
relative error = 3.2616370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.806
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=1.96
x[1] = -1.805
y[1] (analytic) = 0.30693432157999966851093269360036
y[1] (numeric) = 0.30693432157999966851093269360037
absolute error = 1e-32
relative error = 3.2580260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.805
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.804
y[1] (analytic) = 0.30727469774156169906929566801058
y[1] (numeric) = 0.3072746977415616990692956680106
absolute error = 2e-32
relative error = 6.5088340000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.804
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.803
y[1] (analytic) = 0.3076156404096209867694513059822
y[1] (numeric) = 0.30761564040962098676945130598222
absolute error = 2e-32
relative error = 6.5016200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.803
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.802
y[1] (analytic) = 0.30795715084203183968982555767191
y[1] (numeric) = 0.30795715084203183968982555767192
absolute error = 1e-32
relative error = 3.2472050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.802
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.801
y[1] (analytic) = 0.30829923030014163266639988506605
y[1] (numeric) = 0.30829923030014163266639988506606
absolute error = 1e-32
relative error = 3.2436020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.801
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (analytic) = 0.30864188004880245407331664403807
y[1] (numeric) = 0.30864188004880245407331664403809
absolute error = 2e-32
relative error = 6.4800020000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.8
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.799
y[1] (analytic) = 0.30898510135638279793424920637177
y[1] (numeric) = 0.30898510135638279793424920637178
absolute error = 1e-32
relative error = 3.2364020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.799
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.798
y[1] (analytic) = 0.30932889549477930156628686233781
y[1] (numeric) = 0.30932889549477930156628686233783
absolute error = 2e-32
relative error = 6.4656100000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.798
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.797
y[1] (analytic) = 0.30967326373942852895909525859266
y[1] (numeric) = 0.30967326373942852895909525859267
absolute error = 1e-32
relative error = 3.2292100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.797
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.796
y[1] (analytic) = 0.31001820736931880009312946949374
y[1] (numeric) = 0.31001820736931880009312946949375
absolute error = 1e-32
relative error = 3.2256170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.796
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.795
y[1] (analytic) = 0.31036372766700206640169880689976
y[1] (numeric) = 0.31036372766700206640169880689976
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.795
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.794
y[1] (analytic) = 0.31070982591860583258271017888497
y[1] (numeric) = 0.31070982591860583258271017888497
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.794
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.793
y[1] (analytic) = 0.31105650341384512496695024651228
y[1] (numeric) = 0.31105650341384512496695024651228
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.793
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.792
y[1] (analytic) = 0.31140376144603450665080583508368
y[1] (numeric) = 0.31140376144603450665080583508368
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.792
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.791
y[1] (analytic) = 0.31175160131210013960236706755844
y[1] (numeric) = 0.31175160131210013960236706755844
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.791
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (analytic) = 0.31210002431259189395090853877578
y[1] (numeric) = 0.31210002431259189395090853877577
absolute error = 1e-32
relative error = 3.2041010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.79
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.789
y[1] (analytic) = 0.3124490317516955046708005756561
y[1] (numeric) = 0.31244903175169550467080057565609
absolute error = 1e-32
relative error = 3.2005220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.789
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.788
y[1] (analytic) = 0.31279862493724477587196526684069
y[1] (numeric) = 0.31279862493724477587196526684068
absolute error = 1e-32
relative error = 3.1969450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.788
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.787
y[1] (analytic) = 0.31314880518073383291006053166404
y[1] (numeric) = 0.31314880518073383291006053166403
absolute error = 1e-32
relative error = 3.1933700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.787
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.786
y[1] (analytic) = 0.31349957379732942253065006958123
y[1] (numeric) = 0.31349957379732942253065006958122
absolute error = 1e-32
relative error = 3.1897970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.786
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.785
y[1] (analytic) = 0.31385093210588326126269762408567
y[1] (numeric) = 0.31385093210588326126269762408566
absolute error = 1e-32
relative error = 3.1862260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.785
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.784
y[1] (analytic) = 0.31420288142894443227781064689032
y[1] (numeric) = 0.3142028814289444322778106468903
absolute error = 2e-32
relative error = 6.3653140000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.784
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.783
y[1] (analytic) = 0.314555423092771830932751196097
y[1] (numeric) = 0.31455542309277183093275119609698
absolute error = 2e-32
relative error = 6.3581799999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.783
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.19
x[1] = -1.782
y[1] (analytic) = 0.31490855842734665921383078388613
y[1] (numeric) = 0.31490855842734665921383078388611
absolute error = 2e-32
relative error = 6.3510500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.782
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.781
y[1] (analytic) = 0.3152622887663849693029109428171
y[1] (numeric) = 0.31526228876638496930291094281708
absolute error = 2e-32
relative error = 6.3439239999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.781
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (analytic) = 0.31561661544735025648584254328919
y[1] (numeric) = 0.31561661544735025648584254328917
absolute error = 2e-32
relative error = 6.3368019999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.78
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.779
y[1] (analytic) = 0.31597153981146610162529440648222
y[1] (numeric) = 0.3159715398114661016252944064822
absolute error = 2e-32
relative error = 6.3296840000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.779
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.778
y[1] (analytic) = 0.31632706320372886342104555584201
y[1] (numeric) = 0.31632706320372886342104555584199
absolute error = 2e-32
relative error = 6.3225699999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.778
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.777
y[1] (analytic) = 0.31668318697292042068194557482749
y[1] (numeric) = 0.31668318697292042068194557482747
absolute error = 2e-32
relative error = 6.3154599999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.777
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.776
y[1] (analytic) = 0.31703991247162096483488402838522
y[1] (numeric) = 0.3170399124716209648348840283852
absolute error = 2e-32
relative error = 6.3083539999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.776
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.775
y[1] (analytic) = 0.31739724105622184289725279991976
y[1] (numeric) = 0.31739724105622184289725279991974
absolute error = 2e-32
relative error = 6.3012520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.775
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.774
y[1] (analytic) = 0.31775517408693845114053453410895
y[1] (numeric) = 0.31775517408693845114053453410893
absolute error = 2e-32
relative error = 6.2941540000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.774
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.773
y[1] (analytic) = 0.31811371292782317967380619876381
y[1] (numeric) = 0.31811371292782317967380619876379
absolute error = 2e-32
relative error = 6.2870600000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.773
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.772
y[1] (analytic) = 0.31847285894677840817710912631748
y[1] (numeric) = 0.31847285894677840817710912631746
absolute error = 2e-32
relative error = 6.2799700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.772
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.771
y[1] (analytic) = 0.31883261351556955301580580798242
y[1] (numeric) = 0.3188326135155695530158058079824
absolute error = 2e-32
relative error = 6.2728840000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.771
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (analytic) = 0.31919297800983816596821923195147
y[1] (numeric) = 0.31919297800983816596821923195145
absolute error = 2e-32
relative error = 6.2658020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.77
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.769
y[1] (analytic) = 0.31955395380911508480003272232487
y[1] (numeric) = 0.31955395380911508480003272232485
absolute error = 2e-32
relative error = 6.2587240000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.769
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.768
y[1] (analytic) = 0.31991554229683363592011708908848
y[1] (numeric) = 0.31991554229683363592011708908846
absolute error = 2e-32
relative error = 6.2516500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.768
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.767
y[1] (analytic) = 0.32027774486034288935364748309734
y[1] (numeric) = 0.32027774486034288935364748309732
absolute error = 2e-32
relative error = 6.2445800000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.767
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.766
y[1] (analytic) = 0.32064056289092096626957470556379
y[1] (numeric) = 0.32064056289092096626957470556377
absolute error = 2e-32
relative error = 6.2375139999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.766
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.765
y[1] (analytic) = 0.3210039977837883993007248912278
y[1] (numeric) = 0.32100399778378839930072489122778
absolute error = 2e-32
relative error = 6.2304519999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.765
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.764
y[1] (analytic) = 0.32136805093812154589601751070236
y[1] (numeric) = 0.32136805093812154589601751070234
absolute error = 2e-32
relative error = 6.2233940000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.764
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.763
y[1] (analytic) = 0.32173272375706605494551456323174
y[1] (numeric) = 0.32173272375706605494551456323172
absolute error = 2e-32
relative error = 6.2163400000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.763
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.762
y[1] (analytic) = 0.32209801764775038692024369936015
y[1] (numeric) = 0.32209801764775038692024369936013
absolute error = 2e-32
relative error = 6.2092900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.762
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.761
y[1] (analytic) = 0.32246393402129938776997486716098
y[1] (numeric) = 0.32246393402129938776997486716096
absolute error = 2e-32
relative error = 6.2022440000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.761
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (analytic) = 0.32283047429284791682337395939632
y[1] (numeric) = 0.3228304742928479168233739593963
absolute error = 2e-32
relative error = 6.1952020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.76
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=2.41
x[1] = -1.759
y[1] (analytic) = 0.32319763988155452893620789623546
y[1] (numeric) = 0.32319763988155452893620789623544
absolute error = 2e-32
relative error = 6.1881640000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.759
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.758
y[1] (analytic) = 0.32356543221061521113453365323169
y[1] (numeric) = 0.32356543221061521113453365323167
absolute error = 2e-32
relative error = 6.1811300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.758
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.757
y[1] (analytic) = 0.32393385270727717400106898171393
y[1] (numeric) = 0.32393385270727717400106898171391
absolute error = 2e-32
relative error = 6.1741000000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.757
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.756
y[1] (analytic) = 0.32430290280285269805421501347316
y[1] (numeric) = 0.32430290280285269805421501347314
absolute error = 2e-32
relative error = 6.1670740000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.756
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.755
y[1] (analytic) = 0.3246725839327330353704806387998
y[1] (numeric) = 0.32467258393273303537048063879978
absolute error = 2e-32
relative error = 6.1600520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.755
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.754
y[1] (analytic) = 0.32504289753640236670234554205291
y[1] (numeric) = 0.32504289753640236670234554205289
absolute error = 2e-32
relative error = 6.1530340000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.754
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.753
y[1] (analytic) = 0.32541384505745181434489311782259
y[1] (numeric) = 0.32541384505745181434489311782257
absolute error = 2e-32
relative error = 6.1460200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.753
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.752
y[1] (analytic) = 0.32578542794359351100584621950445
y[1] (numeric) = 0.32578542794359351100584621950443
absolute error = 2e-32
relative error = 6.1390100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.752
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.751
y[1] (analytic) = 0.32615764764667472493494785717687
y[1] (numeric) = 0.32615764764667472493494785717685
absolute error = 2e-32
relative error = 6.1320040000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.751
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (analytic) = 0.32653050562269204156994560981368
y[1] (numeric) = 0.32653050562269204156994560981366
absolute error = 2e-32
relative error = 6.1250020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.75
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.749
y[1] (analytic) = 0.32690400333180560195776269515352
y[1] (numeric) = 0.3269040033318056019577626951535
absolute error = 2e-32
relative error = 6.1180040000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.749
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.748
y[1] (analytic) = 0.32727814223835339821077039638292
y[1] (numeric) = 0.3272781422383533982107703963829
absolute error = 2e-32
relative error = 6.1110100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.748
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.747
y[1] (analytic) = 0.32765292381086562625941592589801
y[1] (numeric) = 0.32765292381086562625941592589799
absolute error = 2e-32
relative error = 6.1040200000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.747
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.746
y[1] (analytic) = 0.32802834952207909616380686084414
y[1] (numeric) = 0.32802834952207909616380686084412
absolute error = 2e-32
relative error = 6.0970340000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.746
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.745
y[1] (analytic) = 0.32840442084895170024820806127764
y[1] (numeric) = 0.32840442084895170024820806127762
absolute error = 2e-32
relative error = 6.0900520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.745
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.744
y[1] (analytic) = 0.32878113927267693932376952836674
y[1] (numeric) = 0.32878113927267693932376952836673
absolute error = 1e-32
relative error = 3.0415370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.744
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.743
y[1] (analytic) = 0.32915850627869850726617402610227
y[1] (numeric) = 0.32915850627869850726617402610226
absolute error = 1e-32
relative error = 3.0380500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.743
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.742
y[1] (analytic) = 0.32953652335672493421627152491378
y[1] (numeric) = 0.32953652335672493421627152491378
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.742
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.741
y[1] (analytic) = 0.32991519200074428867315367911525
y[1] (numeric) = 0.32991519200074428867315367911524
absolute error = 1e-32
relative error = 3.0310820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.741
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (analytic) = 0.33029451370903893875051567230953
y[1] (numeric) = 0.33029451370903893875051567230952
absolute error = 1e-32
relative error = 3.0276010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.74
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.739
y[1] (analytic) = 0.33067448998420037286855490618434
y[1] (numeric) = 0.33067448998420037286855490618433
absolute error = 1e-32
relative error = 3.0241220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.739
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.738
y[1] (analytic) = 0.33105512233314408015506621930084
y[1] (numeric) = 0.33105512233314408015506621930083
absolute error = 1e-32
relative error = 3.0206450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.738
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.737
y[1] (analytic) = 0.33143641226712449083081165463
y[1] (numeric) = 0.33143641226712449083081165462999
absolute error = 1e-32
relative error = 3.0171700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.737
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=2.64
x[1] = -1.736
y[1] (analytic) = 0.33181836130174997685566929920294
y[1] (numeric) = 0.33181836130174997685566929920293
absolute error = 1e-32
relative error = 3.0136970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.736
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.735
y[1] (analytic) = 0.33220097095699791311350044813911
y[1] (numeric) = 0.3322009709569979131135004481391
absolute error = 1e-32
relative error = 3.0102260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.735
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.734
y[1] (analytic) = 0.33258424275722979941511735068714
y[1] (numeric) = 0.33258424275722979941511735068713
absolute error = 1e-32
relative error = 3.0067570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.734
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.733
y[1] (analytic) = 0.3329681782312064436001851303071
y[1] (numeric) = 0.33296817823120644360018513030709
absolute error = 1e-32
relative error = 3.0032900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.733
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.732
y[1] (analytic) = 0.33335277891210320602035118715258
y[1] (numeric) = 0.33335277891210320602035118715258
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.732
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.731
y[1] (analytic) = 0.3337380463375253056873635428563
y[1] (numeric) = 0.3337380463375253056873635428563
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.731
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (analytic) = 0.33412398204952318837141622793403
y[1] (numeric) = 0.33412398204952318837141622793403
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.73
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.729
y[1] (analytic) = 0.33451058759460795693644499542055
y[1] (numeric) = 0.33451058759460795693644499542055
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.729
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.728
y[1] (analytic) = 0.33489786452376686420059042493516
y[1] (numeric) = 0.33489786452376686420059042493516
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.728
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.727
y[1] (analytic) = 0.33528581439247886861154791401931
y[1] (numeric) = 0.33528581439247886861154791401931
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.727
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.726
y[1] (analytic) = 0.33567443876073025302803519345086
y[1] (numeric) = 0.33567443876073025302803519345086
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.726
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.725
y[1] (analytic) = 0.33606373919303030690012790585914
y[1] (numeric) = 0.33606373919303030690012790585914
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.725
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.724
y[1] (analytic) = 0.33645371725842707214274250826919
y[1] (numeric) = 0.33645371725842707214274250826919
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.724
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.723
y[1] (analytic) = 0.33684437453052315299808335550892
y[1] (numeric) = 0.33684437453052315299808335550892
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.723
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.722
y[1] (analytic) = 0.33723571258749159018441734942847
y[1] (numeric) = 0.33723571258749159018441734942847
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.722
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.721
y[1] (analytic) = 0.33762773301209179963009505571195
y[1] (numeric) = 0.33762773301209179963009505571195
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.721
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (analytic) = 0.3380204373916855760933017532106
y[1] (numeric) = 0.3380204373916855760933017532106
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.72
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.719
y[1] (analytic) = 0.33841382731825316196959554809842
y[1] (numeric) = 0.33841382731825316196959554809842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.719
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.718
y[1] (analytic) = 0.33880790438840938159087251505578
y[1] (numeric) = 0.33880790438840938159087251505578
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.718
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.717
y[1] (analytic) = 0.3392026702034198413209908788402
y[1] (numeric) = 0.3392026702034198413209908788402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.717
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.716
y[1] (analytic) = 0.33959812636921719575488758113424
y[1] (numeric) = 0.33959812636921719575488758113424
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.716
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.715
y[1] (analytic) = 0.33999427449641748032963124900977
y[1] (numeric) = 0.33999427449641748032963124900977
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.715
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.714
y[1] (analytic) = 0.34039111620033651065747565267444
y[1] (numeric) = 0.34039111620033651065747565267444
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.714
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.713
y[1] (analytic) = 0.34078865310100634889260727174828
y[1] (numeric) = 0.34078865310100634889260727174828
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.713
Order of pole = 1
memory used=49.5MB, alloc=4.4MB, time=2.87
TOP MAIN SOLVE Loop
x[1] = -1.712
y[1] (analytic) = 0.34118688682319183744491964195848
y[1] (numeric) = 0.34118688682319183744491964195848
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.712
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.711
y[1] (analytic) = 0.34158581899640720035579578906666
y[1] (numeric) = 0.34158581899640720035579578906666
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.711
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (analytic) = 0.34198545125493271265253833571412
y[1] (numeric) = 0.34198545125493271265253833571412
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.71
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.709
y[1] (analytic) = 0.34238578523783143799975485177777
y[1] (numeric) = 0.34238578523783143799975485177777
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.709
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.708
y[1] (analytic) = 0.34278682258896603496768377230043
y[1] (numeric) = 0.34278682258896603496768377230043
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.708
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.707
y[1] (analytic) = 0.34318856495701563223913379206205
y[1] (numeric) = 0.34318856495701563223913379206205
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.707
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.706
y[1] (analytic) = 0.34359101399549277307840712580276
y[1] (numeric) = 0.34359101399549277307840712580276
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.706
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.705
y[1] (analytic) = 0.34399417136276042938728446185208
y[1] (numeric) = 0.34399417136276042938728446185208
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.705
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.704
y[1] (analytic) = 0.34439803872204908567486689876798
y[1] (numeric) = 0.34439803872204908567486689876799
absolute error = 1e-32
relative error = 2.9036170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.704
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.703
y[1] (analytic) = 0.34480261774147389326979770430417
y[1] (numeric) = 0.34480261774147389326979770430418
absolute error = 1e-32
relative error = 2.9002100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.703
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.702
y[1] (analytic) = 0.34520791009405189510512443882139
y[1] (numeric) = 0.3452079100940518951051244388214
absolute error = 1e-32
relative error = 2.8968050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.702
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.701
y[1] (analytic) = 0.34561391745771932140780990681558
y[1] (numeric) = 0.34561391745771932140780990681558
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.701
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (analytic) = 0.34602064151534895662665860669252
y[1] (numeric) = 0.34602064151534895662665860669253
absolute error = 1e-32
relative error = 2.8900010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.7
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.699
y[1] (analytic) = 0.34642808395476757793419390688429
y[1] (numeric) = 0.34642808395476757793419390688429
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.699
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.698
y[1] (analytic) = 0.34683624646877346563980015295478
y[1] (numeric) = 0.34683624646877346563980015295479
absolute error = 1e-32
relative error = 2.8832050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.698
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.697
y[1] (analytic) = 0.34724513075515398585323337303503
y[1] (numeric) = 0.34724513075515398585323337303503
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.697
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.696
y[1] (analytic) = 0.34765473851670324573940426579317
y[1] (numeric) = 0.34765473851670324573940426579318
absolute error = 1e-32
relative error = 2.8764170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.696
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.695
y[1] (analytic) = 0.34806507146123982170714779469451
y[1] (numeric) = 0.34806507146123982170714779469452
absolute error = 1e-32
relative error = 2.8730260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.695
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.694
y[1] (analytic) = 0.34847613130162456087651504354035
y[1] (numeric) = 0.34847613130162456087651504354036
absolute error = 1e-32
relative error = 2.8696370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.694
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.693
y[1] (analytic) = 0.34888791975577845617095508068033
y[1] (numeric) = 0.34888791975577845617095508068034
absolute error = 1e-32
relative error = 2.8662500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.693
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.692
y[1] (analytic) = 0.34930043854670059538259750285116
y[1] (numeric) = 0.34930043854670059538259750285117
absolute error = 1e-32
relative error = 2.8628650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.692
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.691
y[1] (analytic) = 0.34971368940248618456070015478328
y[1] (numeric) = 0.34971368940248618456070015478328
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.691
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (analytic) = 0.3501276740563446460751913185143
y[1] (numeric) = 0.3501276740563446460751913185143
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.69
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=3.10
x[1] = -1.689
y[1] (analytic) = 0.35054239424661779170911150823669
y[1] (numeric) = 0.3505423942466177917091115082367
absolute error = 1e-32
relative error = 2.8527220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.689
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.688
y[1] (analytic) = 0.3509578517167980711356469644778
y[1] (numeric) = 0.35095785171679807113564696447781
absolute error = 1e-32
relative error = 2.8493450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.688
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.687
y[1] (analytic) = 0.35137404821554689613734508796649
y[1] (numeric) = 0.3513740482155468961373450879665
absolute error = 1e-32
relative error = 2.8459700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.687
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.686
y[1] (analytic) = 0.3517909854967130409270114617021
y[1] (numeric) = 0.35179098549671304092701146170211
absolute error = 1e-32
relative error = 2.8425970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.686
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.685
y[1] (analytic) = 0.35220866531935111893170885304657
y[1] (numeric) = 0.35220866531935111893170885304658
absolute error = 1e-32
relative error = 2.8392260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.685
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.684
y[1] (analytic) = 0.35262708944774013640321074017484
y[1] (numeric) = 0.35262708944774013640321074017485
absolute error = 1e-32
relative error = 2.8358570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.684
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.683
y[1] (analytic) = 0.35304625965140212322020554353237
y[1] (numeric) = 0.35304625965140212322020554353238
absolute error = 1e-32
relative error = 2.8324900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.683
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.682
y[1] (analytic) = 0.3534661777051208412495029381876
y[1] (numeric) = 0.35346617770512084124950293818761
absolute error = 1e-32
relative error = 2.8291250000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.682
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.681
y[1] (analytic) = 0.35388684538896057063546045279114
y[1] (numeric) = 0.35388684538896057063546045279115
absolute error = 1e-32
relative error = 2.8257620000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.681
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (analytic) = 0.35430826448828497438882710146432
y[1] (numeric) = 0.35430826448828497438882710146433
absolute error = 1e-32
relative error = 2.8224010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.68
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.679
y[1] (analytic) = 0.35473043679377604164819112308366
y[1] (numeric) = 0.35473043679377604164819112308367
absolute error = 1e-32
relative error = 2.8190420000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.679
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.678
y[1] (analytic) = 0.35515336410145310998922109539952
y[1] (numeric) = 0.35515336410145310998922109539953
absolute error = 1e-32
relative error = 2.8156850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.678
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.677
y[1] (analytic) = 0.35557704821269196715890382707577
y[1] (numeric) = 0.35557704821269196715890382707578
absolute error = 1e-32
relative error = 2.8123300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.677
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.676
y[1] (analytic) = 0.35600149093424403261400858746796
y[1] (numeric) = 0.35600149093424403261400858746797
absolute error = 1e-32
relative error = 2.8089770000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.676
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.675
y[1] (analytic) = 0.35642669407825561924504549073897
y[1] (numeric) = 0.35642669407825561924504549073897
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.675
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.674
y[1] (analytic) = 0.35685265946228727566903628727638
y[1] (numeric) = 0.35685265946228727566903628727639
absolute error = 1e-32
relative error = 2.8022770000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.674
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.673
y[1] (analytic) = 0.35727938890933320947647851143115
y[1] (numeric) = 0.35727938890933320947647851143116
absolute error = 1e-32
relative error = 2.7989300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.673
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.672
y[1] (analytic) = 0.35770688424784079181995897102038
y[1] (numeric) = 0.35770688424784079181995897102038
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.672
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.671
y[1] (analytic) = 0.35813514731173014373396002208978
y[1] (numeric) = 0.35813514731173014373396002208978
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.671
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (analytic) = 0.35856417994041380457750203395531
y[1] (numeric) = 0.35856417994041380457750203395531
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.67
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.669
y[1] (analytic) = 0.35899398397881648299337799697153
y[1] (numeric) = 0.35899398397881648299337799697153
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.669
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.668
y[1] (analytic) = 0.35942456127739489077986144183163
y[1] (numeric) = 0.35942456127739489077986144183163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.668
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.667
y[1] (analytic) = 0.35985591369215766007290680811403
y[1] (numeric) = 0.35985591369215766007290680811403
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.667
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=3.33
x[1] = -1.666
y[1] (analytic) = 0.36028804308468534423901220547804
y[1] (numeric) = 0.36028804308468534423901220547803
absolute error = 1e-32
relative error = 2.7755570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.666
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.665
y[1] (analytic) = 0.36072095132215050288107823821002
y[1] (numeric) = 0.36072095132215050288107823821001
absolute error = 1e-32
relative error = 2.7722260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.665
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.664
y[1] (analytic) = 0.36115464027733787136177329817613
y[1] (numeric) = 0.36115464027733787136177329817613
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.664
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.663
y[1] (analytic) = 0.36158911182866461525110555870942
y[1] (numeric) = 0.36158911182866461525110555870941
absolute error = 1e-32
relative error = 2.7655700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.663
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.662
y[1] (analytic) = 0.36202436786020067010710490923144
y[1] (numeric) = 0.36202436786020067010710490923143
absolute error = 1e-32
relative error = 2.7622450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.662
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.661
y[1] (analytic) = 0.36246041026168916700073434479119
y[1] (numeric) = 0.36246041026168916700073434479118
absolute error = 1e-32
relative error = 2.7589220000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.661
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (analytic) = 0.36289724092856694419837995413705
y[1] (numeric) = 0.36289724092856694419837995413704
absolute error = 1e-32
relative error = 2.7556010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.66
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.659
y[1] (analytic) = 0.36333486176198514541751172299931
y[1] (numeric) = 0.36333486176198514541751172299931
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.659
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.658
y[1] (analytic) = 0.36377327466882990507336397516884
y[1] (numeric) = 0.36377327466882990507336397516883
absolute error = 1e-32
relative error = 2.7489650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.658
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.657
y[1] (analytic) = 0.3642124815617431209367545025768
y[1] (numeric) = 0.3642124815617431209367545025768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.657
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.656
y[1] (analytic) = 0.36465248435914331462544537742808
y[1] (numeric) = 0.36465248435914331462544537742808
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.656
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.655
y[1] (analytic) = 0.36509328498524658035374618568791
y[1] (numeric) = 0.3650932849852465803537461856879
absolute error = 1e-32
relative error = 2.7390260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.655
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.654
y[1] (analytic) = 0.36553488537008762236737206370396
y[1] (numeric) = 0.36553488537008762236737206370395
absolute error = 1e-32
relative error = 2.7357170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.654
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.653
y[1] (analytic) = 0.36597728744954088149289455096417
y[1] (numeric) = 0.36597728744954088149289455096416
absolute error = 1e-32
relative error = 2.7324100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.653
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.652
y[1] (analytic) = 0.36642049316534175123346298511783
y[1] (numeric) = 0.36642049316534175123346298511782
absolute error = 1e-32
relative error = 2.7291050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.652
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.651
y[1] (analytic) = 0.3668645044651078838448280542754
y[1] (numeric) = 0.36686450446510788384482805427539
absolute error = 1e-32
relative error = 2.7258020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.651
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (analytic) = 0.36730932330236058682806728078337
y[1] (numeric) = 0.36730932330236058682806728078336
absolute error = 1e-32
relative error = 2.7225010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.65
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.649
y[1] (analytic) = 0.36775495163654631027779473536721
y[1] (numeric) = 0.36775495163654631027779473536721
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.649
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.648
y[1] (analytic) = 0.36820139143305822552703426666249
y[1] (numeric) = 0.36820139143305822552703426666249
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.648
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.647
y[1] (analytic) = 0.36864864466325789553234707532598
y[1] (numeric) = 0.36864864466325789553234707532597
absolute error = 1e-32
relative error = 2.7126100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.647
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.646
y[1] (analytic) = 0.36909671330449703744523066145453
y[1] (numeric) = 0.36909671330449703744523066145452
absolute error = 1e-32
relative error = 2.7093170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.646
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.645
y[1] (analytic) = 0.36954559934013937781824712696774
y[1] (numeric) = 0.36954559934013937781824712696773
absolute error = 1e-32
relative error = 2.7060260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.645
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.644
y[1] (analytic) = 0.36999530475958260089679461967628
y[1] (numeric) = 0.36999530475958260089679461967627
absolute error = 1e-32
relative error = 2.7027370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.644
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.643
y[1] (analytic) = 0.37044583155828039044990646242753
y[1] (numeric) = 0.37044583155828039044990646242753
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
memory used=61.0MB, alloc=4.4MB, time=3.55
Complex estimate of poles used for equation 1
Radius of convergence = 1.643
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.642
y[1] (analytic) = 0.3708971817377645655959483191867
y[1] (numeric) = 0.3708971817377645655959483191867
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.642
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.641
y[1] (analytic) = 0.37134935730566731108158471110134
y[1] (numeric) = 0.37134935730566731108158471110134
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.641
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (analytic) = 0.37180236027574350247490241117549
y[1] (numeric) = 0.37180236027574350247490241117549
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.64
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.639
y[1] (analytic) = 0.37225619266789312673610981855489
y[1] (numeric) = 0.37225619266789312673610981855489
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.639
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.638
y[1] (analytic) = 0.37271085650818379863177844575846
y[1] (numeric) = 0.37271085650818379863177844575846
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.638
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.637
y[1] (analytic) = 0.37316635382887337346115524839818
y[1] (numeric) = 0.37316635382887337346115524839819
absolute error = 1e-32
relative error = 2.6797700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.637
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.636
y[1] (analytic) = 0.37362268666843265656565279169003
y[1] (numeric) = 0.37362268666843265656565279169004
absolute error = 1e-32
relative error = 2.6764970000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.636
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.635
y[1] (analytic) = 0.374079857071568210095218286819
y[1] (numeric) = 0.374079857071568210095218286819
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.635
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.634
y[1] (analytic) = 0.37453786708924525750789244920424
y[1] (numeric) = 0.37453786708924525750789244920424
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.634
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.633
y[1] (analytic) = 0.37499671877871068628149503691843
y[1] (numeric) = 0.37499671877871068628149503691843
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.633
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.632
y[1] (analytic) = 0.37545641420351614931901592873837
y[1] (numeric) = 0.37545641420351614931901592873838
absolute error = 1e-32
relative error = 2.6634250000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.632
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.631
y[1] (analytic) = 0.37591695543354126553194880612534
y[1] (numeric) = 0.37591695543354126553194880612535
absolute error = 1e-32
relative error = 2.6601620000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.631
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (analytic) = 0.37637834454501692008847902123564
y[1] (numeric) = 0.37637834454501692008847902123565
absolute error = 1e-32
relative error = 2.6569010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.63
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.629
y[1] (analytic) = 0.37684058362054866481612817403403
y[1] (numeric) = 0.37684058362054866481612817403403
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.629
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.628
y[1] (analytic) = 0.37730367474914021925116539672538
y[1] (numeric) = 0.37730367474914021925116539672539
absolute error = 1e-32
relative error = 2.6503850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.628
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.627
y[1] (analytic) = 0.37776762002621707282981946485439
y[1] (numeric) = 0.3777676200262170728298194648544
absolute error = 1e-32
relative error = 2.6471300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.627
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.626
y[1] (analytic) = 0.37823242155365018871906673419376
y[1] (numeric) = 0.37823242155365018871906673419377
absolute error = 1e-32
relative error = 2.6438770000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.626
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.625
y[1] (analytic) = 0.3786980814397798097875276544274
y[1] (numeric) = 0.37869808143977980978752765442741
absolute error = 1e-32
relative error = 2.6406260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.625
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.624
y[1] (analytic) = 0.37916460179943936721977934895163
y[1] (numeric) = 0.37916460179943936721977934895164
absolute error = 1e-32
relative error = 2.6373770000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.624
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.623
y[1] (analytic) = 0.37963198475397949228018359002783
y[1] (numeric) = 0.37963198475397949228018359002784
absolute error = 1e-32
relative error = 2.6341300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.623
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.622
y[1] (analytic) = 0.38010023243129213173513855603723
y[1] (numeric) = 0.38010023243129213173513855603724
absolute error = 1e-32
relative error = 2.6308850000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.622
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.621
y[1] (analytic) = 0.38056934696583476744548914958735
y[1] (numeric) = 0.38056934696583476744548914958736
absolute error = 1e-32
relative error = 2.6276420000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.621
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (analytic) = 0.38103933049865474064367449943816
y[1] (numeric) = 0.38103933049865474064367449943817
absolute error = 1e-32
relative error = 2.6244010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.62
Order of pole = 1
memory used=64.8MB, alloc=4.4MB, time=3.78
TOP MAIN SOLVE Loop
x[1] = -1.619
y[1] (analytic) = 0.38151018517741368141305268426751
y[1] (numeric) = 0.38151018517741368141305268426752
absolute error = 1e-32
relative error = 2.6211620000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.619
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.618
y[1] (analytic) = 0.38198191315641204388972182167174
y[1] (numeric) = 0.38198191315641204388972182167175
absolute error = 1e-32
relative error = 2.6179250000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.618
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.617
y[1] (analytic) = 0.38245451659661374771005358187778
y[1] (numeric) = 0.38245451659661374771005358187778
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.617
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.616
y[1] (analytic) = 0.38292799766567092623007003370149
y[1] (numeric) = 0.3829279976656709262300700337015
absolute error = 1e-32
relative error = 2.6114570000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.616
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.615
y[1] (analytic) = 0.3834023585379487820457276324981
y[1] (numeric) = 0.38340235853794878204572763249811
absolute error = 1e-32
relative error = 2.6082260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.615
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.614
y[1] (analytic) = 0.3838776013945505503461232392974
y[1] (numeric) = 0.3838776013945505503461232392974
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.614
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.613
y[1] (analytic) = 0.38435372842334257063460644099978
y[1] (numeric) = 0.38435372842334257063460644099978
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.613
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.612
y[1] (analytic) = 0.38483074181897946735577024835052
y[1] (numeric) = 0.38483074181897946735577024835052
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.612
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.611
y[1] (analytic) = 0.38530864378292943996929860726338
y[1] (numeric) = 0.38530864378292943996929860726338
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.611
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (analytic) = 0.38578743652349966301467419672304
y[1] (numeric) = 0.38578743652349966301467419672305
absolute error = 1e-32
relative error = 2.5921010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.61
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.609
y[1] (analytic) = 0.38626712225586179671379383069603
y[1] (numeric) = 0.38626712225586179671379383069604
absolute error = 1e-32
relative error = 2.5888820000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.609
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.608
y[1] (analytic) = 0.38674770320207760866160156091373
y[1] (numeric) = 0.38674770320207760866160156091374
absolute error = 1e-32
relative error = 2.5856650000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.608
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.607
y[1] (analytic) = 0.38722918159112470715793142171194
y[1] (numeric) = 0.38722918159112470715793142171195
absolute error = 1e-32
relative error = 2.5824500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.607
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.606
y[1] (analytic) = 0.38771155965892238673685279793986
y[1] (numeric) = 0.38771155965892238673685279793987
absolute error = 1e-32
relative error = 2.5792370000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.606
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.605
y[1] (analytic) = 0.38819483964835758645293176388748
y[1] (numeric) = 0.38819483964835758645293176388749
absolute error = 1e-32
relative error = 2.5760260000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.605
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.604
y[1] (analytic) = 0.3886790238093109614869615678068
y[1] (numeric) = 0.38867902380931096148696156780682
absolute error = 2e-32
relative error = 5.1456340000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.604
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.603
y[1] (analytic) = 0.38916411439868306863687485649573
y[1] (numeric) = 0.38916411439868306863687485649575
absolute error = 2e-32
relative error = 5.1392200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.603
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.602
y[1] (analytic) = 0.3896501136804206662627293821513
y[1] (numeric) = 0.38965011368042066626272938215131
absolute error = 1e-32
relative error = 2.5664050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.602
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.601
y[1] (analytic) = 0.3901370239255431292578579448674
y[1] (numeric) = 0.39013702392554312925785794486741
absolute error = 1e-32
relative error = 2.5632020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.601
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (analytic) = 0.39062484741216897962149233535456
y[1] (numeric) = 0.39062484741216897962149233535457
absolute error = 1e-32
relative error = 2.5600010000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.6
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.599
y[1] (analytic) = 0.39111358642554253321141019132494
y[1] (numeric) = 0.39111358642554253321141019132496
absolute error = 2e-32
relative error = 5.1136040000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.599
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.598
y[1] (analytic) = 0.39160324325806066325841310617735
y[1] (numeric) = 0.39160324325806066325841310617736
absolute error = 1e-32
relative error = 2.5536050000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.598
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.597
y[1] (analytic) = 0.39209382020929968122772416983936
y[1] (numeric) = 0.39209382020929968122772416983937
absolute error = 1e-32
relative error = 2.5504100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.597
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=4.00
x[1] = -1.596
y[1] (analytic) = 0.39258531958604233561569351963339
y[1] (numeric) = 0.3925853195860423356156935196334
absolute error = 1e-32
relative error = 2.5472170000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.596
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.595
y[1] (analytic) = 0.39307774370230492927352157564427
y[1] (numeric) = 0.39307774370230492927352157564429
absolute error = 2e-32
relative error = 5.0880520000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.595
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.594
y[1] (analytic) = 0.3935710948793645558530515731627
y[1] (numeric) = 0.39357109487936455585305157316272
absolute error = 2e-32
relative error = 5.0816740000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.594
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.593
y[1] (analytic) = 0.39406537544578645597304592831951
y[1] (numeric) = 0.39406537544578645597304592831953
absolute error = 2e-32
relative error = 5.0753000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.593
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.592
y[1] (analytic) = 0.39456058773745149370774502705699
y[1] (numeric) = 0.39456058773745149370774502705701
absolute error = 2e-32
relative error = 5.0689300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.592
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.591
y[1] (analytic) = 0.39505673409758375400291235824377
y[1] (numeric) = 0.39505673409758375400291235824379
absolute error = 2e-32
relative error = 5.0625640000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.591
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (analytic) = 0.39555381687677826162799666627243
y[1] (numeric) = 0.39555381687677826162799666627245
absolute error = 2e-32
relative error = 5.0562020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.59
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.589
y[1] (analytic) = 0.39605183843302882227649012523951
y[1] (numeric) = 0.39605183843302882227649012523953
absolute error = 2e-32
relative error = 5.0498440000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.589
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.588
y[1] (analytic) = 0.39655080113175598643003158527131
y[1] (numeric) = 0.39655080113175598643003158527133
absolute error = 2e-32
relative error = 5.0434900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.588
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.587
y[1] (analytic) = 0.39705070734583513660529586233458
y[1] (numeric) = 0.3970507073458351366052958623346
absolute error = 2e-32
relative error = 5.0371400000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.587
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.586
y[1] (analytic) = 0.39755155945562469860622398770453
y[1] (numeric) = 0.39755155945562469860622398770455
absolute error = 2e-32
relative error = 5.0307939999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.586
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.585
y[1] (analytic) = 0.39805335984899447740768545505062
y[1] (numeric) = 0.39805335984899447740768545505065
absolute error = 3e-32
relative error = 7.5366780000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.585
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.584
y[1] (analytic) = 0.39855611092135411830022195589817
y[1] (numeric) = 0.3985561109213541183002219558982
absolute error = 3e-32
relative error = 7.5271710000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.584
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.583
y[1] (analytic) = 0.39905981507568169392910303325365
y[1] (numeric) = 0.39905981507568169392910303325368
absolute error = 3e-32
relative error = 7.5176700000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.583
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.582
y[1] (analytic) = 0.39956447472255241786452766484532
y[1] (numeric) = 0.39956447472255241786452766484534
absolute error = 2e-32
relative error = 5.0054500000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.582
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.581
y[1] (analytic) = 0.40007009228016748534343216931606
y[1] (numeric) = 0.40007009228016748534343216931609
absolute error = 3e-32
relative error = 7.4986860000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.581
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (analytic) = 0.40057667017438304182701416959855
y[1] (numeric) = 0.40057667017438304182701416959858
absolute error = 3e-32
relative error = 7.4892030000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.58
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.579
y[1] (analytic) = 0.40108421083873928002175480759589
y[1] (numeric) = 0.40108421083873928002175480759592
absolute error = 3e-32
relative error = 7.4797260000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.579
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.578
y[1] (analytic) = 0.40159271671448966601541714439467
y[1] (numeric) = 0.4015927167144896660154171443947
absolute error = 3e-32
relative error = 7.4702550000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.578
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.577
y[1] (analytic) = 0.4021021902506302951832178629877
y[1] (numeric) = 0.40210219025063029518321786298773
absolute error = 3e-32
relative error = 7.4607900000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.577
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.576
y[1] (analytic) = 0.40261263390392937852311217955557
y[1] (numeric) = 0.4026126339039293785231121795556
absolute error = 3e-32
relative error = 7.4513310000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.576
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.575
y[1] (analytic) = 0.40312405013895686008289842967058
y[1] (numeric) = 0.4031240501389568600828984296706
absolute error = 2e-32
relative error = 4.9612519999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.575
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.574
y[1] (analytic) = 0.40363644142811416614563929352321
y[1] (numeric) = 0.40363644142811416614563929352323
absolute error = 2e-32
relative error = 4.9549540000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.574
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=4.22
x[1] = -1.573
y[1] (analytic) = 0.40414981025166408684371122687758
y[1] (numeric) = 0.4041498102516640868437112268776
absolute error = 2e-32
relative error = 4.9486600000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.573
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.572
y[1] (analytic) = 0.40466415909776079087563254066369
y[1] (numeric) = 0.40466415909776079087563254066371
absolute error = 2e-32
relative error = 4.9423700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.572
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.571
y[1] (analytic) = 0.40517949046247997400368389192728
y[1] (numeric) = 0.40517949046247997400368389192731
absolute error = 3e-32
relative error = 7.4041260000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.571
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (analytic) = 0.40569580684984914201422288359654
y[1] (numeric) = 0.40569580684984914201422288359657
absolute error = 3e-32
relative error = 7.3947030000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.57
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.569
y[1] (analytic) = 0.40621311077187802882650719281555
y[1] (numeric) = 0.40621311077187802882650719281558
absolute error = 3e-32
relative error = 7.3852860000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.569
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.568
y[1] (analytic) = 0.40673140474858915043977833138441
y[1] (numeric) = 0.40673140474858915043977833138444
absolute error = 3e-32
relative error = 7.3758750000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.568
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.567
y[1] (analytic) = 0.40725069130804849541232096241483
y[1] (numeric) = 0.40725069130804849541232096241486
absolute error = 3e-32
relative error = 7.3664700000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.567
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.566
y[1] (analytic) = 0.40777097298639635257020083128191
y[1] (numeric) = 0.40777097298639635257020083128193
absolute error = 2e-32
relative error = 4.9047139999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.566
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.565
y[1] (analytic) = 0.40829225232787827664739799430514
y[1] (numeric) = 0.40829225232787827664739799430516
absolute error = 2e-32
relative error = 4.8984520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.565
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.564
y[1] (analytic) = 0.40881453188487619256309132466946
y[1] (numeric) = 0.40881453188487619256309132466948
absolute error = 2e-32
relative error = 4.8921940000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.564
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.563
y[1] (analytic) = 0.40933781421793963904591542262083
y[1] (numeric) = 0.40933781421793963904591542262084
absolute error = 1e-32
relative error = 2.4429700000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.563
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.562
y[1] (analytic) = 0.40986210189581715231910223805201
y[1] (numeric) = 0.40986210189581715231910223805202
absolute error = 1e-32
relative error = 2.4398450000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.562
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.561
y[1] (analytic) = 0.41038739749548779056453711174274
y[1] (numeric) = 0.41038739749548779056453711174276
absolute error = 2e-32
relative error = 4.8734440000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.561
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (analytic) = 0.41091370360219279988790274165732
y[1] (numeric) = 0.41091370360219279988790274165734
absolute error = 2e-32
relative error = 4.8672020000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.56
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.559
y[1] (analytic) = 0.41144102280946742251125496917895
y[1] (numeric) = 0.41144102280946742251125496917897
absolute error = 2e-32
relative error = 4.8609640000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.559
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.558
y[1] (analytic) = 0.41196935771917284792357144475594
y[1] (numeric) = 0.41196935771917284792357144475596
absolute error = 2e-32
relative error = 4.8547300000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.558
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.557
y[1] (analytic) = 0.41249871094152830772403836238012
y[1] (numeric) = 0.41249871094152830772403836238014
absolute error = 2e-32
relative error = 4.8485000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.557
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.556
y[1] (analytic) = 0.41302908509514331489709173830312
y[1] (numeric) = 0.41302908509514331489709173830314
absolute error = 2e-32
relative error = 4.8422740000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.556
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.555
y[1] (analytic) = 0.41356048280705004826250834358274
y[1] (numeric) = 0.41356048280705004826250834358276
absolute error = 2e-32
relative error = 4.8360520000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.555
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.554
y[1] (analytic) = 0.41409290671273588284814757608647
y[1] (numeric) = 0.41409290671273588284814757608649
absolute error = 2e-32
relative error = 4.8298340000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.554
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.553
y[1] (analytic) = 0.41462635945617606693727947060506
y[1] (numeric) = 0.41462635945617606693727947060509
absolute error = 3e-32
relative error = 7.2354300000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.553
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.552
y[1] (analytic) = 0.41516084368986654654679589239861
y[1] (numeric) = 0.41516084368986654654679589239864
absolute error = 3e-32
relative error = 7.2261150000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.552
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.551
y[1] (analytic) = 0.41569636207485693809699193798475
y[1] (numeric) = 0.41569636207485693809699193798478
absolute error = 3e-32
relative error = 7.2168060000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.551
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=4.45
x[1] = -1.55
y[1] (analytic) = 0.4162329172807836500380228769936
y[1] (numeric) = 0.41623291728078365003802287699363
absolute error = 3e-32
relative error = 7.2075030000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.55
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.549
y[1] (analytic) = 0.41677051198590315420258881171225
y[1] (numeric) = 0.41677051198590315420258881171228
absolute error = 3e-32
relative error = 7.1982060000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.549
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.548
y[1] (analytic) = 0.41730914887712540765887480934188
y[1] (numeric) = 0.41730914887712540765887480934191
absolute error = 3e-32
relative error = 7.1889150000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.548
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.547
y[1] (analytic) = 0.41784883065004742584227878038283
y[1] (numeric) = 0.41784883065004742584227878038286
absolute error = 3e-32
relative error = 7.1796300000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.547
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.546
y[1] (analytic) = 0.41838956000898700774899304092645
y[1] (numeric) = 0.41838956000898700774899304092648
absolute error = 3e-32
relative error = 7.1703510000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.546
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.545
y[1] (analytic) = 0.41893133966701661397906851454488
y[1] (numeric) = 0.41893133966701661397906851454491
absolute error = 3e-32
relative error = 7.1610780000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.545
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.544
y[1] (analytic) = 0.41947417234599739842118311012413
y[1] (numeric) = 0.41947417234599739842118311012417
absolute error = 4e-32
relative error = 9.5357480000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.544
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.543
y[1] (analytic) = 0.42001806077661339437595816620115
y[1] (numeric) = 0.42001806077661339437595816620118
absolute error = 3e-32
relative error = 7.1425499999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.543
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.542
y[1] (analytic) = 0.42056300769840585591931919260314
y[1] (numeric) = 0.42056300769840585591931919260317
absolute error = 3e-32
relative error = 7.1332950000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.542
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.541
y[1] (analytic) = 0.42110901585980775531207968056354
y[1] (numeric) = 0.42110901585980775531207968056358
absolute error = 4e-32
relative error = 9.4987280000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.541
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (analytic) = 0.42165608801817843726663970878744
y[1] (numeric) = 0.42165608801817843726663970878747
absolute error = 3e-32
relative error = 7.1148030000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.54
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.539
y[1] (analytic) = 0.42220422693983843088643466262927
y[1] (numeric) = 0.4222042269398384308864346626293
absolute error = 3e-32
relative error = 7.1055660000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.539
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.538
y[1] (analytic) = 0.42275343540010442009854382579176
y[1] (numeric) = 0.4227534354001044200985438257918
absolute error = 4e-32
relative error = 9.4617800000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.538
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.537
y[1] (analytic) = 0.4233037161833243734046741196341
y[1] (numeric) = 0.42330371618332437340467411963413
absolute error = 3e-32
relative error = 7.0871099999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.537
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.536
y[1] (analytic) = 0.42385507208291283378057107689282
y[1] (numeric) = 0.42385507208291283378057107689285
absolute error = 3e-32
relative error = 7.0778910000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.536
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.535
y[1] (analytic) = 0.4244075059013863695587774687148
y[1] (numeric) = 0.42440750590138636955877746871483
absolute error = 3e-32
relative error = 7.0686780000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.535
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.534
y[1] (analytic) = 0.42496102045039918713456008247643
y[1] (numeric) = 0.42496102045039918713456008247646
absolute error = 3e-32
relative error = 7.0594710000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.534
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.533
y[1] (analytic) = 0.42551561855077890633975720078805
y[1] (numeric) = 0.42551561855077890633975720078808
absolute error = 3e-32
relative error = 7.0502700000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.533
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.532
y[1] (analytic) = 0.42607130303256249933426358901162
y[1] (numeric) = 0.42607130303256249933426358901165
absolute error = 3e-32
relative error = 7.0410750000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.532
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.531
y[1] (analytic) = 0.42662807673503239386986649100967
y[1] (numeric) = 0.4266280767350323938698664910097
absolute error = 3e-32
relative error = 7.0318859999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.531
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (analytic) = 0.42718594250675274178617549396578
y[1] (numeric) = 0.42718594250675274178617549396582
absolute error = 4e-32
relative error = 9.3636040000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.53
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.529
y[1] (analytic) = 0.42774490320560585360345138807499
y[1] (numeric) = 0.42774490320560585360345138807502
absolute error = 3e-32
relative error = 7.0135259999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.529
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.528
y[1] (analytic) = 0.42830496169882880008223455264618
y[1] (numeric) = 0.42830496169882880008223455264621
absolute error = 3e-32
relative error = 7.0043549999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.528
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=4.68
x[1] = -1.527
y[1] (analytic) = 0.42886612086305018162480218550175
y[1] (numeric) = 0.42886612086305018162480218550179
absolute error = 4e-32
relative error = 9.3269200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.527
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.526
y[1] (analytic) = 0.42942838358432706639864609819224
y[1] (numeric) = 0.42942838358432706639864609819227
absolute error = 3e-32
relative error = 6.9860309999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.526
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.525
y[1] (analytic) = 0.42999175275818209806735906805307
y[1] (numeric) = 0.42999175275818209806735906805311
absolute error = 4e-32
relative error = 9.3025040000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.525
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.524
y[1] (analytic) = 0.43055623128964077401954811401301
y[1] (numeric) = 0.43055623128964077401954811401305
absolute error = 4e-32
relative error = 9.2903080000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.524
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.523
y[1] (analytic) = 0.4311218220932688949916577927425
y[1] (numeric) = 0.43112182209326889499165779274253
absolute error = 3e-32
relative error = 6.9585899999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.523
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.522
y[1] (analytic) = 0.43168852809321018698588594357399
y[1] (numeric) = 0.43168852809321018698588594357403
absolute error = 4e-32
relative error = 9.2659400000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.522
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.521
y[1] (analytic) = 0.43225635222322409638970849496119
y[1] (numeric) = 0.43225635222322409638970849496123
absolute error = 4e-32
relative error = 9.2537680000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.521
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (analytic) = 0.43282529742672375920889923437533
y[1] (numeric) = 0.43282529742672375920889923437537
absolute error = 4e-32
relative error = 9.2416040000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.52
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.519
y[1] (analytic) = 0.4333953666568141453313350917628
y[1] (numeric) = 0.43339536665681414533133509176284
absolute error = 4e-32
relative error = 9.2294480000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.519
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.518
y[1] (analytic) = 0.43396656287633037874431775031734
y[1] (numeric) = 0.43396656287633037874431775031738
absolute error = 4e-32
relative error = 9.2173000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.518
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.517
y[1] (analytic) = 0.43453888905787623463361853569085
y[1] (numeric) = 0.43453888905787623463361853569089
absolute error = 4e-32
relative error = 9.2051600000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.517
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.516
y[1] (analytic) = 0.43511234818386281429796580626101
y[1] (numeric) = 0.43511234818386281429796580626104
absolute error = 3e-32
relative error = 6.8947709999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.516
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.515
y[1] (analytic) = 0.43568694324654739881824273513806
y[1] (numeric) = 0.4356869432465473988182427351381
absolute error = 4e-32
relative error = 9.1809040000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.515
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.514
y[1] (analytic) = 0.43626267724807248242624870375452
y[1] (numeric) = 0.43626267724807248242624870375456
absolute error = 4e-32
relative error = 9.1687880000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.514
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.513
y[1] (analytic) = 0.43683955320050498652349978376442
y[1] (numeric) = 0.43683955320050498652349978376446
absolute error = 4e-32
relative error = 9.1566800000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.513
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.512
y[1] (analytic) = 0.43741757412587565530620323732747
y[1] (numeric) = 0.4374175741258756553062032373275
absolute error = 3e-32
relative error = 6.8584349999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.512
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.511
y[1] (analytic) = 0.43799674305621863395823788654308
y[1] (numeric) = 0.43799674305621863395823788654311
absolute error = 3e-32
relative error = 6.8493659999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.511
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (analytic) = 0.43857706303361123037970686386261
y[1] (numeric) = 0.43857706303361123037970686386264
absolute error = 3e-32
relative error = 6.8403030000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.51
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.509
y[1] (analytic) = 0.43915853711021386142440193194624
y[1] (numeric) = 0.43915853711021386142440193194627
absolute error = 3e-32
relative error = 6.8312459999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.509
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.508
y[1] (analytic) = 0.43974116834831018462532953103803
y[1] (numeric) = 0.43974116834831018462532953103806
absolute error = 3e-32
relative error = 6.8221950000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.508
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.507
y[1] (analytic) = 0.44032495982034741639329825411153
y[1] (numeric) = 0.44032495982034741639329825411156
absolute error = 3e-32
relative error = 6.8131500000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.507
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.506
y[1] (analytic) = 0.44090991460897683767945584661979
y[1] (numeric) = 0.44090991460897683767945584661981
absolute error = 2e-32
relative error = 4.5360740000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.506
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.505
y[1] (analytic) = 0.44149603580709448809859136274815
y[1] (numeric) = 0.44149603580709448809859136274818
absolute error = 3e-32
relative error = 6.7950780000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.505
Order of pole = 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=4.90
x[1] = -1.504
y[1] (analytic) = 0.4420833265178820495159850699619
y[1] (numeric) = 0.44208332651788204951598506996192
absolute error = 2e-32
relative error = 4.5240340000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.504
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.503
y[1] (analytic) = 0.44267178985484792010659536699705
y[1] (numeric) = 0.44267178985484792010659536699707
absolute error = 2e-32
relative error = 4.5180200000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.503
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.502
y[1] (analytic) = 0.44326142894186847990141865820333
y[1] (numeric) = 0.44326142894186847990141865820335
absolute error = 2e-32
relative error = 4.5120100000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.502
Order of pole = 1
TOP MAIN SOLVE Loop
x[1] = -1.501
y[1] (analytic) = 0.44385224691322954884194510257869
y[1] (numeric) = 0.44385224691322954884194510257871
absolute error = 2e-32
relative error = 4.5060040000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.501
Order of pole = 1
Finished!
diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);
Iterations = 500
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Time to Timeout = 2 Minutes 55 Seconds
Percent Done = 100.2 %
> quit
memory used=84.5MB, alloc=4.4MB, time=4.95