|\^/| 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_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif
> ((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float or
omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre cos 1 $eq_no = 1
> array_tmp2[1] := cos(array_x[1]);
> array_tmp2_g[1] := sin(array_x[1]);
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h;
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp2[2] := -array_tmp2_g[1] * array_x[2] / 1;
> array_tmp2_g[2] := array_tmp2[1] * array_x[2] / 1;
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h;
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp2[3] := -array_tmp2_g[2] * array_x[2] / 2;
> array_tmp2_g[3] := array_tmp2[2] * array_x[2] / 2;
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp2[4] := -array_tmp2_g[3] * array_x[2] / 3;
> array_tmp2_g[4] := array_tmp2[3] * array_x[2] / 3;
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp2[5] := -array_tmp2_g[4] * array_x[2] / 4;
> array_tmp2_g[5] := array_tmp2[4] * array_x[2] / 4;
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (4.0);
> 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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit cos LINEAR $eq_no = 1
> array_tmp2[kkk] := -array_tmp2_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp2_g[kkk] := array_tmp2[kkk - 1] * array_x[2] / (kkk - 1);
> #emit div FULL FULL $eq_no = 1
> array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 2;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 1) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary / glob_h;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := cos(array_x[1]);
array_tmp2_g[1] := sin(array_x[1]);
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := -array_tmp2_g[1]*array_x[2];
array_tmp2_g[2] := array_tmp2[1]*array_x[2];
array_tmp3[2] :=
(array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := -1/2*array_tmp2_g[2]*array_x[2];
array_tmp2_g[3] := 1/2*array_tmp2[2]*array_x[2];
array_tmp3[3] :=
(array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := -1/3*array_tmp2_g[3]*array_x[2];
array_tmp2_g[4] := 1/3*array_tmp2[3]*array_x[2];
array_tmp3[4] :=
(array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := -1/4*array_tmp2_g[4]*array_x[2];
array_tmp2_g[5] := 1/4*array_tmp2[4]*array_x[2];
array_tmp3[5] :=
(array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := -array_tmp2_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2_g[kkk] := array_tmp2[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3[kkk] := (
array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 2;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 1 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary/glob_h
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error <> 0.0) 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 rel_error <> 0. then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(2.0 - ln(abs(cos(x))));
> end;
exact_soln_y := proc(x) return 2.0 - ln(abs(cos(x))) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_log10normmin := 0.1;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_hmax := 1.0;
> glob_hmin := 0.00000000001;
> glob_hmin_init := 0.001;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_log10_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-50;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_log10abserr := 0.0;
> glob_log10relerr := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/divpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
> 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 := -5.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> 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,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - ln(abs(cos(x))));");
> omniout_str(ALWAYS,"end;");
> 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;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2_g:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1_g[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_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1_g[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_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_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 := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05 ;
> glob_look_poles := true;
> glob_max_iter := 10000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #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;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_log10normmin := -glob_large_float ;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> 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 := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 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 ) = sin ( x ) / cos ( x ) ;");
> 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,"2012-12-14T21:36:31-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;")
> ;
> 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," 151 | ")
> ;
> logitem_str(html_log_file,"div diffeq.mxt")
> ;
> logitem_str(html_log_file,"div maple results")
> ;
> logitem_str(html_log_file,"Languages compared")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_log10normmin := 0.1;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_hmax := 1.0;
glob_hmin := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_log10_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-50);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_log10abserr := 0.;
glob_log10relerr := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/divpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
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 := -5.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
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, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(2.0 - ln(abs(cos(x))));");
omniout_str(ALWAYS, "end;");
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;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2_g := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[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_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_g[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_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 := -5.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_log10normmin := -glob_large_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
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 := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-12-14T21:36:31-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "div");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
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, " 151 | ");
logitem_str(html_log_file,
"div diffeq.mxt");
logitem_str(html_log_file,
"div maple results");
logitem_str(html_log_file, "Languages compared");
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/divpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05 ;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#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;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(2.0 - ln(abs(cos(x))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 10
estimated_steps = 10000
step_error = 1.0000000000000000000000000000000e-14
est_needed_step_err = 1.0000000000000000000000000000000e-14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 3.0677116042050893868093673224158e-63
max_value3 = 3.0677116042050893868093673224158e-63
value3 = 3.0677116042050893868093673224158e-63
best_h = 0.001
START of Soultion
x[1] = -5
y[1] (analytic) = 3.259971236628587709130758159876
y[1] (numeric) = 3.259971236628587709130758159876
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2881
Order of pole = 2.082
x[1] = -4.999
y[1] (analytic) = 3.2633579796165452273496192122587
y[1] (numeric) = 3.2633579796165555755010007360666
absolute error = 1.03481513815238079e-14
relative error = 3.1710132465270475976155012333618e-13 %
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2871
Order of pole = 2.082
x[1] = -4.998
y[1] (analytic) = 3.2667572350261429930154543198646
y[1] (numeric) = 3.2667572350261639079988415279477
absolute error = 2.09149833872080831e-14
relative error = 6.4023684291436813874155333406339e-13 %
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2861
Order of pole = 2.082
x[1] = -4.997
y[1] (analytic) = 3.2701690882135694479210400994238
y[1] (numeric) = 3.2701690882136011538275334890504
absolute error = 3.17059064933896266e-14
relative error = 9.6954945258533876725312699028381e-13 %
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.285
Order of pole = 2.082
x[1] = -4.996
y[1] (analytic) = 3.2735936254368717460848438747144
y[1] (numeric) = 3.2735936254369144725695484939883
absolute error = 4.27264847046192739e-14
relative error = 1.3051859697129415433921084429803e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.284
Order of pole = 2.082
x[1] = -4.995
y[1] (analytic) = 3.2770309338686958293469015044044
y[1] (numeric) = 3.2770309338687498117873736865034
absolute error = 5.39824404721820990e-14
relative error = 1.6472972505161304343360678005742e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.36
Real estimate of pole used
Radius of convergence = 0.283
Order of pole = 2.082
x[1] = -4.994
y[1] (analytic) = 3.2804811016092523049999538571674
y[1] (numeric) = 3.2804811016093177846597421800323
absolute error = 6.54796597883228649e-14
relative error = 1.9960383175565794988435826002571e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.282
Order of pole = 2.082
x[1] = -4.993
y[1] (analytic) = 3.2839442176995129449759701733792
y[1] (numeric) = 3.2839442176995901691734332792453
absolute error = 7.72241974631058661e-14
relative error = 2.3515684903199541802763797196982e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.281
Order of pole = 2.082
x[1] = -4.992
y[1] (analytic) = 3.2874203721346427465494558934324
y[1] (numeric) = 3.2874203721347319688320470309145
absolute error = 8.92222825911374821e-14
relative error = 2.7140515203780336185796365785140e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.28
Order of pole = 2.082
x[1] = -4.991
y[1] (analytic) = 3.2909096558776726184123840235942
y[1] (numeric) = 3.2909096558777740987365997165684
absolute error = 1.014803242156929742e-13
relative error = 3.0836557313096026697272387134140e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.279
Order of pole = 2.082
x[1] = -4.99
y[1] (analytic) = 3.2944121608734178834329202908972
y[1] (numeric) = 3.2944121608735318883501184079311
absolute error = 1.140049171981170339e-13
relative error = 3.4605541635656157537232803443863e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.278
Order of pole = 2.082
x[1] = -4.989
y[1] (analytic) = 3.2979279800626479205470823039834
y[1] (numeric) = 3.2979279800627747233953830150504
absolute error = 1.268028483007110670e-13
relative error = 3.8449247244720699332408591420123e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.277
Order of pole = 2.082
x[1] = -4.988
y[1] (analytic) = 3.3014572073965124031690229533277
y[1] (numeric) = 3.3014572073966522842715146333101
absolute error = 1.398811024916799824e-13
relative error = 4.2369503435723299614957929038167e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.276
Order of pole = 2.082
x[1] = -4.987
y[1] (analytic) = 3.3049999378512297303660594104908
y[1] (numeric) = 3.3049999378513829772355404986574
absolute error = 1.532468694810881666e-13
relative error = 4.6368191335193415343227420089939e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.275
Order of pole = 2.082
x[1] = -4.986
y[1] (analytic) = 3.3085562674430433899577171325453
y[1] (numeric) = 3.3085562674432102975082143018109
absolute error = 1.669075504971692656e-13
relative error = 5.0447245567372708946527877149332e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.274
Order of pole = 2.082
x[1] = -4.985
y[1] (analytic) = 3.3121262932434521397974764541921
y[1] (numeric) = 3.312126293243633010562789202471
absolute error = 1.808707653127482789e-13
relative error = 5.4608655980816394778097910044044e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.273
Order of pole = 2.082
x[1] = -4.984
y[1] (analytic) = 3.3157101133947200449200589667937
y[1] (numeric) = 3.3157101133949151892795909350806
absolute error = 1.951443595319682869e-13
relative error = 5.8854469437370035876817033990415e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.76
Real estimate of pole used
Radius of convergence = 0.272
Order of pole = 2.082
x[1] = -4.983
y[1] (analytic) = 3.3193078271256725641295404948193
y[1] (numeric) = 3.3193078271258823005416884637446
absolute error = 2.097364121479689253e-13
relative error = 6.3186791666016843689445674098939e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.271
Order of pole = 2.082
x[1] = -4.982
y[1] (analytic) = 3.3229195347677850401132108741722
y[1] (numeric) = 3.3229195347680096953565935147449
absolute error = 2.246552433826405727e-13
relative error = 6.7607789184200066028214406958351e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.27
Order of pole = 2.082
x[1] = -4.981
y[1] (analytic) = 3.3265453377715701124473342004681
y[1] (numeric) = 3.3265453377718100218701542787596
absolute error = 2.399094228200782915e-13
relative error = 7.2119691289339819144096350819104e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.269
Order of pole = 2.082
x[1] = -4.98
y[1] (analytic) = 3.3301853387232707430739725234632
y[1] (numeric) = 3.3301853387235262508518184075586
absolute error = 2.555077778458840954e-13
relative error = 7.6724792123384004277519276335943e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.268
Order of pole = 2.082
x[1] = -4.979
y[1] (analytic) = 3.3338396413618657191389935663622
y[1] (numeric) = 3.3338396413621371785413985827275
absolute error = 2.714594024050163653e-13
relative error = 8.1425452813359023005712604476081e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.267
Order of pole = 2.082
x[1] = -4.978
y[1] (analytic) = 3.3375083505963946786627059531727
y[1] (numeric) = 3.3375083505966824523287974157833
absolute error = 2.877736660914626106e-13
relative error = 8.6224103691018185463480674427480e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.266
Order of pole = 2.082
x[1] = -4.977
y[1] (analytic) = 3.3411915725236098905451743019884
y[1] (numeric) = 3.341191572523914350768757919665
absolute error = 3.044602235836176766e-13
relative error = 9.1123246594824298037695134703849e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.265
Order of pole = 2.082
x[1] = -4.976
y[1] (analytic) = 3.3448894144459622120738565919867
y[1] (numeric) = 3.3448894144462837410982964774677
absolute error = 3.215290244398854810e-13
relative error = 9.6125457257648267185663144967489e-12 %
Correct digits = 13
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.264
Order of pole = 2.082
x[1] = -4.975
y[1] (analytic) = 3.3486019848899288445945304085993
y[1] (numeric) = 3.3486019848902678349178000986301
absolute error = 3.389903232696900308e-13
relative error = 1.0123338778371801829979617384995e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.263
Order of pole = 2.082
x[1] = -4.974
y[1] (analytic) = 3.3523293936246907115276399501667
y[1] (numeric) = 3.3523293936250475662179357326959
absolute error = 3.568546902957825292e-13
relative error = 1.0644976921851197905984970925957e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.262
Order of pole = 2.082
x[1] = -4.973
y[1] (analytic) = 3.3560717516811674926689727494922
y[1] (numeric) = 3.3560717516815426256912972171254
absolute error = 3.751330223244676332e-13
relative error = 1.1177741421545921299399371993276e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.261
Order of pole = 2.082
x[1] = -4.972
y[1] (analytic) = 3.3598291713714185649217225106776
y[1] (numeric) = 3.3598291713718124014758636559697
absolute error = 3.938365541411452921e-13
relative error = 1.1721921980348443664945662047363e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=1.18
Real estimate of pole used
Radius of convergence = 0.26
Order of pole = 2.082
x[1] = -4.971
y[1] (analytic) = 3.3636017663084183224905978606674
y[1] (numeric) = 3.3636017663088312993609472377496
absolute error = 4.129768703493770822e-13
relative error = 1.2277817025962105077871536100773e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.259
Order of pole = 2.082
x[1] = -4.97
y[1] (analytic) = 3.3673896514262145793604636100166
y[1] (numeric) = 3.3673896514266471452781361497354
absolute error = 4.325659176725397188e-13
relative error = 1.2845734009110944067200370794235e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.258
Order of pole = 2.082
x[1] = -4.969
y[1] (analytic) = 3.3711929430004789938238720638399
y[1] (numeric) = 3.3711929430009316098416100895623
absolute error = 4.526160177380257224e-13
relative error = 1.3425989713160164643192309393483e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.257
Order of pole = 2.082
x[1] = -4.968
y[1] (analytic) = 3.3750117586694586991650199349669
y[1] (numeric) = 3.375011758669931839045384829417
absolute error = 4.731398803648944501e-13
relative error = 1.4018910575630760031363271645682e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.256
Order of pole = 2.082
x[1] = -4.967
y[1] (analytic) = 3.3788462174553385766132636959101
y[1] (numeric) = 3.3788462174558327272306405643259
absolute error = 4.941506173768684158e-13
relative error = 1.4624833022114303264990475738742e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.255
Order of pole = 2.082
x[1] = -4.966
y[1] (analytic) = 3.3826964397860238666187306332596
y[1] (numeric) = 3.3826964397865395283756942459675
absolute error = 5.156617569636127079e-13
relative error = 1.5244103813117545120541042928079e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.254
Order of pole = 2.082
x[1] = -4.965
y[1] (analytic) = 3.3865625475173530826578845451794
y[1] (numeric) = 3.386562547517890769916498877406
absolute error = 5.376872586143322266e-13
relative error = 1.5877080404391292693635601282861e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.253
Order of pole = 2.082
x[1] = -4.964
y[1] (analytic) = 3.3904446639557514684414441314646
y[1] (numeric) = 3.3904446639563117099700930068932
absolute error = 5.602415286488754286e-13
relative error = 1.6524131321324143400397739935589e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.252
Order of pole = 2.082
x[1] = -4.963
y[1] (analytic) = 3.3943429138813355248757891142837
y[1] (numeric) = 3.3943429138819188643121618617825
absolute error = 5.833394363727474988e-13
relative error = 1.7185636548009089697012549410719e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.251
Order of pole = 2.082
x[1] = -4.962
y[1] (analytic) = 3.3982574235714794277390984225665
y[1] (numeric) = 3.3982574235720864240699821363279
absolute error = 6.069963308837137614e-13
relative error = 1.7861987931619863483942781379519e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.25
Order of pole = 2.082
x[1] = -4.961
y[1] (analytic) = 3.4021883208248544611048532366317
y[1] (numeric) = 3.4021883208254856891634122559441
absolute error = 6.312280585590193124e-13
relative error = 1.8553589602764235016435333272338e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.249
Order of pole = 2.082
memory used=15.2MB, alloc=3.9MB, time=1.60
x[1] = -4.96
y[1] (analytic) = 3.4061357349859529054212091224762
y[1] (numeric) = 3.4061357349866089564024627896099
absolute error = 6.560509812536671337e-13
relative error = 1.9260858412513402807709680333083e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.248
Order of pole = 2.082
x[1] = -4.959
y[1] (analytic) = 3.4100997969701081431921885401137
y[1] (numeric) = 3.4100997969707896251874302284995
absolute error = 6.814819952416883858e-13
relative error = 1.9984224386840196675272433656187e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.247
Order of pole = 2.082
x[1] = -4.958
y[1] (analytic) = 3.4140806392890230797772699690244
y[1] (numeric) = 3.414080639289730618328203878532
absolute error = 7.075385509339095076e-13
relative error = 2.0724131199234160366617261881720e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.246
Order of pole = 2.082
x[1] = -4.957
y[1] (analytic) = 3.4180783960768193223165158346681
y[1] (numeric) = 3.4180783960775535609899232104041
absolute error = 7.342386734073757360e-13
relative error = 2.1481036662298782137396586601309e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.245
Order of pole = 2.082
x[1] = -4.956
y[1] (analytic) = 3.4220932031166199166014953974361
y[1] (numeric) = 3.4220932031173815175852787320139
absolute error = 7.616009837833345778e-13
relative error = 2.2255413239175307565144525109849e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.244
Order of pole = 2.082
x[1] = -4.955
y[1] (analytic) = 3.4261251978676788102670887108869
y[1] (numeric) = 3.4261251978684684549885812316607
absolute error = 7.896447214925207738e-13
relative error = 2.3047748575678810582741241617105e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.243
Order of pole = 2.082
x[1] = -4.954
y[1] (analytic) = 3.4301745194930705914122849128146
y[1] (numeric) = 3.4301745194938889811797533347086
absolute error = 8.183897674684218940e-13
relative error = 2.3858546054075635790378189128618e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.242
Order of pole = 2.082
x[1] = -4.953
y[1] (analytic) = 3.434241308887954445123896919125
y[1] (numeric) = 3.4342413088888023017922081658402
absolute error = 8.478566683112467152e-13
relative error = 2.4688325369477083718517705493417e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.241
Order of pole = 2.082
x[1] = -4.952
y[1] (analytic) = 3.4383257087084266768492220405603
y[1] (numeric) = 3.4383257087093047435106895137334
absolute error = 8.780666614674731731e-13
relative error = 2.5537623129872425635098281613366e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.24
Order of pole = 2.082
x[1] = -4.951
y[1] (analytic) = 3.4424278634009765716354046686103
y[1] (numeric) = 3.4424278634018856133368767941478
absolute error = 9.090417014721255375e-13
relative error = 2.6406993480875148272305336620192e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.239
Order of pole = 2.082
x[1] = -4.95
y[1] (analytic) = 3.4465479192325607924386419292941
y[1] (numeric) = 3.4465479192335015969259452578382
absolute error = 9.408044873033285441e-13
relative error = 2.7297008756309893169492886909210e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.238
Order of pole = 2.082
x[1] = -4.949
y[1] (analytic) = 3.4506860243213119695411346297333
y[1] (numeric) = 3.4506860243222853480320358467405
absolute error = 9.733784909012170072e-13
relative error = 2.8208260155824031903287259808021e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.0MB, time=2.04
Real estimate of pole used
Radius of convergence = 0.237
Order of pole = 2.082
x[1] = -4.948
y[1] (analytic) = 3.4548423286678975971562321007678
y[1] (numeric) = 3.4548423286689043851431380516199
absolute error = 1.0067879869059508521e-12
relative error = 2.9141358450767378094617349991731e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.236
Order of pole = 2.082
x[1] = -4.947
y[1] (analytic) = 3.4590169841875458331347100628465
y[1] (numeric) = 3.4590169841885868912183824688688
absolute error = 1.0410580836724060223e-12
relative error = 3.0096934719646362838790542766646e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.235
Order of pole = 2.082
x[1] = -4.946
y[1] (analytic) = 3.4632101447427552939145820216199
y[1] (numeric) = 3.4632101447438315086702041119281
absolute error = 1.0762147556220903082e-12
relative error = 3.1075641114525285321639639570009e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.234
Order of pole = 2.082
x[1] = -4.945
y[1] (analytic) = 3.4674219661767064501163442102562
y[1] (numeric) = 3.4674219661778187349933401896751
absolute error = 1.1122848769959794189e-12
relative error = 3.2078151659817201949368970275841e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.233
Order of pole = 2.082
x[1] = -4.944
y[1] (analytic) = 3.4716526063473927591354337990077
y[1] (numeric) = 3.4716526063485420553925090917717
absolute error = 1.1492962570752927640e-12
relative error = 3.3105163084980854347118391241134e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.232
Order of pole = 2.082
x[1] = -4.943
y[1] (analytic) = 3.475902225162490220412855034866
y[1] (numeric) = 3.4759022251636774980897957761917
absolute error = 1.1872776769407413257e-12
relative error = 3.4157395692717993474388120354202e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.231
Order of pole = 2.082
x[1] = -4.942
y[1] (analytic) = 3.4801709846149846074922520855355
y[1] (numeric) = 3.4801709846162108664200965787901
absolute error = 1.2262589278444932546e-12
relative error = 3.5235594264347782215629158949706e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.23
Order of pole = 2.082
x[1] = -4.941
y[1] (analytic) = 3.4844590488195762192474108992633
y[1] (numeric) = 3.4844590488208424900986839280622
absolute error = 1.2662708512730287989e-12
relative error = 3.6340529004121918015249660083656e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.229
Order of pole = 2.082
x[1] = -4.94
y[1] (analytic) = 3.4887665840498826015713750005312
y[1] (numeric) = 3.4887665840511899469521582085666
absolute error = 1.3073453807832080354e-12
relative error = 3.7472996524335992374516227450040e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.228
Order of pole = 2.082
x[1] = -4.939
y[1] (analytic) = 3.4930937587764603211746638648537
y[1] (numeric) = 3.4930937587778098367603621315388
absolute error = 1.3495155856982666851e-12
relative error = 3.8633820873189696829946553996204e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.227
Order of pole = 2.082
x[1] = -4.938
y[1] (analytic) = 3.4974407437056675257992493507169
y[1] (numeric) = 3.4974407437070603415160044527768
absolute error = 1.3928157167551020599e-12
relative error = 3.9823854607451116160732314761142e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.226
Order of pole = 2.082
x[1] = -4.937
y[1] (analytic) = 3.5018077118193897010086645451231
y[1] (numeric) = 3.5018077118208269822624636740385
absolute error = 1.4372812537991289154e-12
relative error = 4.1043979912088861441092381592044e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.0MB, time=2.46
Real estimate of pole used
Radius of convergence = 0.225
Order of pole = 2.082
x[1] = -4.936
y[1] (analytic) = 3.5061948384156517336943677656552
y[1] (numeric) = 3.5061948384171346826499959564155
absolute error = 1.4829489556281907603e-12
relative error = 4.2295109769150552929899379958026e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.224
Order of pole = 2.082
x[1] = -4.935
y[1] (analytic) = 3.5106023011501401175174900779588
y[1] (numeric) = 3.510602301151669974429582602225
absolute error = 1.5298569120925242662e-12
relative error = 4.3578189178287555670229275570925e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.223
Order of pole = 2.082
x[1] = -4.934
y[1] (analytic) = 3.5150302800786598867004032251001
y[1] (numeric) = 3.5150302800802379312989668374084
absolute error = 1.5780445985636123083e-12
relative error = 4.4894196431454314079250593787616e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.222
Order of pole = 2.082
x[1] = -4.933
y[1] (analytic) = 3.5194789577005516429571999202808
y[1] (numeric) = 3.5194789577021791958900908659786
absolute error = 1.6275529328909456978e-12
relative error = 4.6244144444446569939327779385288e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.221
Order of pole = 2.082
x[1] = -4.932
y[1] (analytic) = 3.5239485190030948470175203081626
y[1] (numeric) = 3.5239485190047732713524925752633
absolute error = 1.6784243349722671007e-12
relative error = 4.7629082148086654652734092414354e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2199
Order of pole = 2.082
x[1] = -4.931
y[1] (analytic) = 3.5284391515069243823162487002367
y[1] (numeric) = 3.5284391515086550851053185170179
absolute error = 1.7307027890698167812e-12
relative error = 4.9050095942016427459156879077570e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2189
Order of pole = 2.082
x[1] = -4.93
y[1] (analytic) = 3.5329510453124882652077845351035
y[1] (numeric) = 3.5329510453142726991167969992288
absolute error = 1.7844339090124641253e-12
relative error = 5.0508311214219827373830354575672e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2179
Order of pole = 2.082
x[1] = -4.929
y[1] (analytic) = 3.5374843931475752747891809316696
y[1] (numeric) = 3.5374843931494149397956123502946
absolute error = 1.8396650064314186250e-12
relative error = 5.2004893929567995690648915801904e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2169
Order of pole = 2.082
x[1] = -4.928
y[1] (analytic) = 3.5420393904159422074115915199626
y[1] (numeric) = 3.542039390417838652573777018248
absolute error = 1.8964451621854982854e-12
relative error = 5.3541052290861125929771146406555e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2159
Order of pole = 2.082
x[1] = -4.927
y[1] (analytic) = 3.5466162352470714276161564098298
y[1] (numeric) = 3.5466162352490262529172971332826
absolute error = 1.9548253011407234528e-12
relative error = 5.5118038476033269730499675007537e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2149
Order of pole = 2.082
x[1] = -4.926
y[1] (analytic) = 3.5512151285470903900056897209194
y[1] (numeric) = 3.5512151285491052482761680541836
absolute error = 2.0148582704783332642e-12
relative error = 5.6737150455389977334414306748856e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2139
Order of pole = 2.082
x[1] = -4.925
y[1] (analytic) = 3.5558362740508858469826719773664
y[1] (numeric) = 3.5558362740529624459043872034339
absolute error = 2.0765989217152260675e-12
relative error = 5.8399733892964636207908215702118e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=2.88
Real estimate of pole used
Radius of convergence = 0.2129
Order of pole = 2.082
x[1] = -4.924
y[1] (analytic) = 3.5604798783754465369443838864457
y[1] (numeric) = 3.5604798783775866411410152290405
absolute error = 2.1401041966313425948e-12
relative error = 6.0107184136308500533686927211815e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2119
Order of pole = 2.082
x[1] = -4.923
y[1] (analytic) = 3.5651461510744692681004889188765
y[1] (numeric) = 3.5651461510766747013177986013726
absolute error = 2.2054332173096824961e-12
relative error = 6.1860948299272545044718136948758e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2109
Order of pole = 2.082
x[1] = -4.922
y[1] (analytic) = 3.5698353046942644763195496222349
y[1] (numeric) = 3.5698353046965371237000561373223
absolute error = 2.2726473805065150874e-12
relative error = 6.3662527442597356716568062005301e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2099
Order of pole = 2.082
x[1] = -4.921
y[1] (analytic) = 3.5745475548309985431552278302606
y[1] (numeric) = 3.5745475548333403536118097913804
absolute error = 2.3418104565819611198e-12
relative error = 6.5513478857401292944854946422864e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2089
Order of pole = 2.082
x[1] = -4.92
y[1] (analytic) = 3.5792831201893114143748952609665
y[1] (numeric) = 3.5792831201917244030681297956616
absolute error = 2.4129886932345346951e-12
relative error = 6.7415418456948150357896171855631e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2079
Order of pole = 2.082
x[1] = -4.919
y[1] (analytic) = 3.5840422226423493619306208816665
y[1] (numeric) = 3.5840422226448356128549183792309
absolute error = 2.4862509242974975644e-12
relative error = 6.9370023282384748158094618070664e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2069
Order of pole = 2.082
x[1] = -4.918
y[1] (analytic) = 3.5888250872932540854904460637747
y[1] (numeric) = 3.5888250872958157541743161141109
absolute error = 2.5616686838700503362e-12
relative error = 7.1379034128467359391111212922996e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2059
Order of pole = 2.082
x[1] = -4.917
y[1] (analytic) = 3.5936319425381507556050877525451
y[1] (numeric) = 3.5936319425407900719311602818699
absolute error = 2.6393163260725293248e-12
relative error = 7.3444258295645138548065402934028e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2049
Order of pole = 2.082
x[1] = -4.916
y[1] (analytic) = 3.5984630201306790616490005282837
y[1] (numeric) = 3.5984630201333983327997324895327
absolute error = 2.7192711507319612490e-12
relative error = 7.5567572475240005505973713153039e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2039
Order of pole = 2.082
x[1] = -4.915
y[1] (analytic) = 3.6033185552481128462869414305977
y[1] (numeric) = 3.6033185552509144598222640537703
absolute error = 2.8016135353226231726e-12
relative error = 7.7750925774857369990302015031113e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2029
Order of pole = 2.082
x[1] = -4.914
y[1] (analytic) = 3.6081987865591154869404980979311
y[1] (numeric) = 3.6081987865620019140140038377209
absolute error = 2.8864270735057397898e-12
relative error = 7.9996342891582244651504613538143e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.2019
Order of pole = 2.082
x[1] = -4.913
y[1] (analytic) = 3.6131039562931798262535715035466
y[1] (numeric) = 3.6131039562961536249742047116577
absolute error = 2.9737987206332081111e-12
relative error = 8.2305927440962446972344896115718e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=3.30
Real estimate of pole used
Radius of convergence = 0.2009
Order of pole = 2.082
x[1] = -4.912
y[1] (analytic) = 3.6180343103118031607060936075718
y[1] (numeric) = 3.6180343103148669796526959684311
absolute error = 3.0638189466023608593e-12
relative error = 8.4681865450256609818639846556894e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1999
Order of pole = 2.082
x[1] = -4.911
y[1] (analytic) = 3.6229900981814495722677128113046
y[1] (numeric) = 3.6229900981846061541641851726507
absolute error = 3.1565818964723613461e-12
relative error = 8.7126429024931627436706540405000e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1989
Order of pole = 2.082
x[1] = -4.91
y[1] (analytic) = 3.6279715732483537354339393135843
y[1] (numeric) = 3.6279715732516059209932172821775
absolute error = 3.2521855592779685932e-12
relative error = 8.9641980197934130474000778521915e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1979
Order of pole = 2.082
x[1] = -4.909
y[1] (analytic) = 3.632978992715222254420545848507
y[1] (numeric) = 3.6329789927185729863660490828687
absolute error = 3.3507319455032343617e-12
relative error = 9.2230974971835947881318922091344e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1969
Order of pole = 2.082
x[1] = -4.908
y[1] (analytic) = 3.6380126177198905861490665942817
y[1] (numeric) = 3.63801261772334291342277290887
absolute error = 3.4523272737063145883e-12
relative error = 9.4895967564566790263212878193644e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1959
Order of pole = 2.082
x[1] = -4.907
y[1] (analytic) = 3.6430727134159956875546035605951
y[1] (numeric) = 3.6430727134195527697214206875667
absolute error = 3.5570821668171269716e-12
relative error = 9.7639614870101287061394297585413e-11 %
Correct digits = 12
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1949
Order of pole = 2.082
x[1] = -4.906
y[1] (analytic) = 3.6481595490557266944907814849447
y[1] (numeric) = 3.6481595490593918063494436896905
absolute error = 3.6651118586622047458e-12
relative error = 1.0046468114616494531682936858894e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1939
Order of pole = 2.082
x[1] = -4.905
y[1] (analytic) = 3.6532733980747181980965222535611
y[1] (numeric) = 3.6532733980784947345078281893029
absolute error = 3.7765364113059357418e-12
relative error = 1.0337404294176771381111909925144e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1929
Order of pole = 2.082
x[1] = -4.904
y[1] (analytic) = 3.6584145381791530371345377166248
y[1] (numeric) = 3.6584145381830445180783723159487
absolute error = 3.8914809438345993239e-12
relative error = 1.0637069427816801974668864224323e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1919
Order of pole = 2.082
x[1] = -4.903
y[1] (analytic) = 3.6635832514351439759415194075553
y[1] (numeric) = 3.6635832514391540518147688059692
absolute error = 4.0100758732493984139e-12
relative error = 1.0945775209771804908401077898283e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1909
Order of pole = 2.082
x[1] = -4.902
y[1] (analytic) = 3.6687798243604661919073877911694
y[1] (numeric) = 3.6687798243645986490755650114878
absolute error = 4.1324571681772203184e-12
relative error = 1.1263846199594660504816821752334e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1899
Order of pole = 2.082
x[1] = -4.901
y[1] (analytic) = 3.674004548018715158734656898665
y[1] (numeric) = 3.6740045480229739253508102532312
absolute error = 4.2587666161533545662e-12
relative error = 1.1591620425320335407964834890035e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.1MB, time=3.71
Real estimate of pole used
Radius of convergence = 0.1889
Order of pole = 2.082
x[1] = -4.9
y[1] (analytic) = 3.6792577181159672872889469504773
y[1] (numeric) = 3.6792577181203564393942260216153
absolute error = 4.3891521052790711380e-12
relative error = 1.1929450018322224369531401535921e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1879
Order of pole = 2.082
x[1] = -4.899
y[1] (analytic) = 3.6845396351000235800842244405324
y[1] (numeric) = 3.6845396351045473480053334996416
absolute error = 4.5237679211090591092e-12
relative error = 1.2277701881706730885684955780020e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1869
Order of pole = 2.082
x[1] = -4.898
y[1] (analytic) = 3.689850604262319574090396760456
y[1] (numeric) = 3.6898506042669823491500762646805
absolute error = 4.6627750596795042245e-12
relative error = 1.2636758394210632698327918737276e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1859
Order of pole = 2.082
x[1] = -4.897
y[1] (analytic) = 3.695190935842587995655401876947
y[1] (numeric) = 3.695190935847394337213049202996
absolute error = 4.8063415576473260490e-12
relative error = 1.3007018151692262455745655971170e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1849
Order of pole = 2.082
x[1] = -4.896
y[1] (analytic) = 3.7005609451363638372764364559467
y[1] (numeric) = 3.7005609451413184801170115620089
absolute error = 4.9546428405751060622e-12
relative error = 1.3388896748442903778330915368613e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1839
Order of pole = 2.082
x[1] = -4.895
y[1] (analytic) = 3.7059609526054249954612783054439
y[1] (numeric) = 3.7059609526105328575517431531062
absolute error = 5.1078620904648476623e-12
relative error = 1.3782827600689735568862204106353e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1829
Order of pole = 2.082
x[1] = -4.894
y[1] (analytic) = 3.71139128399126518908593644501
y[1] (numeric) = 3.711391283996531379719653720323
absolute error = 5.2661906337172753130e-12
relative error = 1.4189262814816885165077457968161e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1819
Order of pole = 2.082
x[1] = -4.893
y[1] (analytic) = 3.7168522704316996159660277638794
y[1] (numeric) = 3.7168522704371294443168000546644
absolute error = 5.4298283507722907850e-12
relative error = 1.4608674102997466953391488543957e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1809
Order of pole = 2.082
x[1] = -4.892
y[1] (analytic) = 3.7223442485807077097189515894089
y[1] (numeric) = 3.7223442485863066938277224695048
absolute error = 5.5989841087708800959e-12
relative error = 1.5041553749107746342632501960930e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1799
Order of pole = 2.082
x[1] = -4.891
y[1] (analytic) = 3.7278675607316214377459567274415
y[1] (numeric) = 3.727867560737395313964626388902
absolute error = 5.7738762186696614605e-12
relative error = 1.5488415627985710333241063251566e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1789
Order of pole = 2.082
x[1] = -4.89
y[1] (analytic) = 3.7334225549437718431198901069061
y[1] (numeric) = 3.7334225549497265760382269842237
absolute error = 5.9547329183368773176e-12
relative error = 1.5949796281301354280673114412979e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1779
Order of pole = 2.082
x[1] = -4.889
y[1] (analytic) = 3.7390095851727109876356757873001
y[1] (numeric) = 3.73900958517885278051893928707
absolute error = 6.1417928832634997699e-12
relative error = 1.6426256053526004211310152534225e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=4.13
Real estimate of pole used
Radius of convergence = 0.1769
Order of pole = 2.082
x[1] = -4.888
y[1] (analytic) = 3.744629011404131110104944464306
y[1] (numeric) = 3.7446290114104664158715802866346
absolute error = 6.3353057666358223286e-12
relative error = 1.6918380291724172479720153512772e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1759
Order of pole = 2.082
x[1] = -4.887
y[1] (analytic) = 3.7502811997916076835541259989703
y[1] (numeric) = 3.7502811997981432163247630850996
absolute error = 6.5355327706370861293e-12
relative error = 1.7426780613145080553737504211057e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1749
Order of pole = 2.082
x[1] = -4.886
y[1] (analytic) = 3.7559665227982981483145012655127
y[1] (numeric) = 3.755966522805040895565477291064
absolute error = 6.7427472509760255513e-12
relative error = 1.7952096244863476001547219223992e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1739
Order of pole = 2.082
x[1] = -4.885
y[1] (analytic) = 3.7616853593427334267062755973789
y[1] (numeric) = 3.7616853593496906620630560640899
absolute error = 6.9572353567804667110e-12
relative error = 1.8494995440012242115310756596685e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1729
Order of pole = 2.082
x[1] = -4.884
y[1] (analytic) = 3.767438094948844901425701695766
y[1] (numeric) = 3.7674380949560241981338467848913
absolute error = 7.1792967081450891253e-12
relative error = 1.9056176975464201188056719729448e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1719
Order of pole = 2.082
x[1] = -4.883
y[1] (analytic) = 3.7732251219003753768730428670853
y[1] (numeric) = 3.7732251219077846219868279220561
absolute error = 7.4092451137850549708e-12
relative error = 1.9636371736159244155958870885381e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1709
Order of pole = 2.082
x[1] = -4.882
y[1] (analytic) = 3.7790468393998286543040254502543
y[1] (numeric) = 3.7790468394074760636354478404358
absolute error = 7.6474093314223901815e-12
relative error = 2.0236344391637436243181422842298e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1699
Order of pole = 2.082
x[1] = -4.881
y[1] (analytic) = 3.7849036537321187524584000371182
y[1] (numeric) = 3.7849036537400128863321208596866
absolute error = 7.8941338737208225684e-12
relative error = 2.0856895170731179933538102165037e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1689
Order of pole = 2.082
x[1] = -4.88
y[1] (analytic) = 3.7907959784330865106954293243597
y[1] (numeric) = 3.7907959784412362905582177193519
absolute error = 8.1497798627883949922e-12
relative error = 2.1498861740792182223518453429843e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1679
Order of pole = 2.082
x[1] = -4.879
y[1] (analytic) = 3.7967242344630583380529677587405
y[1] (numeric) = 3.7967242344714730639894545906021
absolute error = 8.4147259364868318616e-12
relative error = 2.2163121198284399958834599533669e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1669
Order of pole = 2.082
x[1] = -4.878
y[1] (analytic) = 3.8026888503856292364373659040857
y[1] (numeric) = 3.8026888503943186056473896192418
absolute error = 8.6893692100237151561e-12
relative error = 2.2850592178065080225333481398977e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1659
Order of pole = 2.082
x[1] = -4.877
y[1] (analytic) = 3.8086902625518599477922431628017
y[1] (numeric) = 3.8086902625608340740888026810742
absolute error = 8.9741262965595182725e-12
relative error = 2.3562237089205477585008882939085e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=4.55
Real estimate of pole used
Radius of convergence = 0.1649
Order of pole = 2.082
x[1] = -4.876
y[1] (analytic) = 3.8147289152900861731558128080091
y[1] (numeric) = 3.8147289152993556075466508953217
absolute error = 9.2694343908380873126e-12
relative error = 2.4299064485774096086210486087527e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1639
Order of pole = 2.082
x[1] = -4.875
y[1] (analytic) = 3.8208052611015463067693723104409
y[1] (numeric) = 3.820805261111122059189520347861
absolute error = 9.5757524201480374201e-12
relative error = 2.5062131581621952571719473233920e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1629
Order of pole = 2.082
x[1] = -4.874
y[1] (analytic) = 3.8269197608620430428955411873925
y[1] (numeric) = 3.8269197608719366051627868888941
absolute error = 9.8935622672457015016e-12
relative error = 2.5852546918875301112520056507651e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1619
Order of pole = 2.082
x[1] = -4.873
y[1] (analytic) = 3.8330728840298635701643666486975
y[1] (numeric) = 3.8330728840400869402345865183932
absolute error = 1.02233700702198696957e-11
relative error = 2.6671473200560772730062189096251e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1609
Order of pole = 2.082
x[1] = -4.872
y[1] (analytic) = 3.8392651088601928929718715572484
y[1] (numeric) = 3.8392651088707586005765284902676
absolute error = 1.05657076046569330192e-11
relative error = 2.7520130298565646666855275953202e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1599
Order of pole = 2.082
x[1] = -4.871
y[1] (analytic) = 3.8454969226262651381562904003335
y[1] (numeric) = 3.8454969226371862719101651607185
absolute error = 1.09211337538747603850e-11
relative error = 2.8399798448977096893055465716077e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1589
Order of pole = 2.082
x[1] = -4.87
y[1] (analytic) = 3.8517688218475085459921917581849
y[1] (numeric) = 3.8517688218587987820656292663155
absolute error = 1.12902360734375081306e-11
relative error = 2.9311821647754353106055545856806e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1579
Order of pole = 2.082
x[1] = -4.869
y[1] (analytic) = 3.8580813125249512373818705561678
y[1] (numeric) = 3.8580813125366248698385152273843
absolute error = 1.16736324566446712165e-11
relative error = 3.0257611260672917018471105753184e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1569
Order of pole = 2.082
x[1] = -4.868
y[1] (analytic) = 3.8644349103841668258127714556956
y[1] (numeric) = 3.8644349103962387987209808775412
absolute error = 1.20719729082094218456e-11
relative error = 3.1238649862547009621033763505127e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1559
Order of pole = 2.082
x[1] = -4.867
y[1] (analytic) = 3.8708301411260515370671312926252
y[1] (numeric) = 3.8708301411385374785010386557059
absolute error = 1.24859414339073630807e-11
relative error = 3.2256495321892671495366631429373e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1548
Order of pole = 2.082
x[1] = -4.866
y[1] (analytic) = 3.8772675406857377478917169128484
y[1] (numeric) = 3.8772675406986540059463082506494
absolute error = 1.29162580545913378010e-11
relative error = 3.3312785148447492417895666304884e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1538
Order of pole = 2.082
x[1] = -4.865
y[1] (analytic) = 3.8837476554999627952940004709596
y[1] (numeric) = 3.8837476555133264762476358397156
absolute error = 1.33636809536353687560e-11
relative error = 3.4409241122322698173483229006010e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=4.96
Real estimate of pole used
Radius of convergence = 0.1528
Order of pole = 2.082
x[1] = -4.864
y[1] (analytic) = 3.8902710427832265817855791307397
y[1] (numeric) = 3.8902710427970555905531752352973
absolute error = 1.38290087675961045576e-11
relative error = 3.5547674225039038347368532371308e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1518
Order of pole = 2.082
x[1] = -4.863
y[1] (analytic) = 3.8968382708130869524139757674471
y[1] (numeric) = 3.8968382708274000354446445152248
absolute error = 1.43130830306687477777e-11
relative error = 3.6729989894300335495228856979171e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1508
Order of pole = 2.082
x[1] = -4.862
y[1] (analytic) = 3.9034499192249580933893031377199
y[1] (numeric) = 3.9034499192397748841736754725714
absolute error = 1.48167907843723348515e-11
relative error = 3.7958193626099483626645361158083e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1498
Order of pole = 2.082
x[1] = -4.861
y[1] (analytic) = 3.9101065793167943492257021423985
y[1] (numeric) = 3.9101065793321354165905351669771
absolute error = 1.53410673648330245786e-11
relative error = 3.9234396949644121334083619451398e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1488
Order of pole = 2.082
x[1] = -4.86
y[1] (analytic) = 3.9168088543640599286379750350632
y[1] (numeric) = 3.9168088543799468280190260475168
absolute error = 1.58868993810510124536e-11
relative error = 4.0560823802647468667336372233369e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1478
Order of pole = 2.082
x[1] = -4.859
y[1] (analytic) = 3.9235573599454040256273061409402
y[1] (numeric) = 3.9235573599618593535259509958942
absolute error = 1.64553278986448549540e-11
relative error = 4.1939817336769684624290477893572e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1468
Order of pole = 2.082
x[1] = -4.858
y[1] (analytic) = 3.9303527242794809818007118907229
y[1] (numeric) = 3.9303527242965284336454871220913
absolute error = 1.70474518447752313684e-11
relative error = 4.3373847185433972843639585048896e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1458
Order of pole = 2.082
x[1] = -4.857
y[1] (analytic) = 3.937195588573376323713655995516
y[1] (numeric) = 3.9371955885910407553649242871661
absolute error = 1.76644316512682916501e-11
relative error = 4.4865517228898736429952117431896e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1448
Order of pole = 2.082
x[1] = -4.856
y[1] (analytic) = 3.9440866073831218941118210061904
y[1] (numeric) = 3.9440866074014293872662185797389
absolute error = 1.83074931543975735485e-11
relative error = 4.6417573894363559206324501853036e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1438
Order of pole = 2.082
x[1] = -4.855
y[1] (analytic) = 3.9510264489868069324202161763207
y[1] (numeric) = 3.9510264490057848641915711868834
absolute error = 1.89779317713550105627e-11
relative error = 4.8032915032046095807108022330734e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1428
Order of pole = 2.082
x[1] = -4.854
y[1] (analytic) = 3.9580157957708169269400075257417
y[1] (numeric) = 3.9580157957904940439151665944234
absolute error = 1.96771169751590686817e-11
relative error = 4.9714599411614988786189375998221e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1418
Order of pole = 2.082
x[1] = -4.853
y[1] (analytic) = 3.9650553446297584438367691949279
y[1] (numeric) = 3.9650553446501649409283954469176
absolute error = 2.04064970916262519897e-11
relative error = 5.1465856887129357040579947510769e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=5.38
Real estimate of pole used
Radius of convergence = 0.1408
Order of pole = 2.082
x[1] = -4.852
y[1] (analytic) = 3.9721458073806560270670559192939
y[1] (numeric) = 3.9721458074018236315111433310322
absolute error = 2.11676044440874117383e-11
relative error = 5.3290099282749949644036175718708e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1398
Order of pole = 2.082
x[1] = -4.851
y[1] (analytic) = 3.979287911192036756358782299909
y[1] (numeric) = 3.9792879112139988172325628729582
absolute error = 2.19620608737805730492e-11
relative error = 5.5190932055985893934365919020811e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1388
Order of pole = 2.082
x[1] = -4.85
y[1] (analytic) = 3.9864823990285492517577304021098
y[1] (numeric) = 3.9864823990513408354240478489078
absolute error = 2.27915836663174467980e-11
relative error = 5.7172166800163074141917762576434e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1378
Order of pole = 2.082
x[1] = -4.849
y[1] (analytic) = 3.9937300301117969352240453954106
y[1] (numeric) = 3.9937300301354549271413691383773
absolute error = 2.36579919173237429667e-11
relative error = 5.9237834653188818900576696713399e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1368
Order of pole = 2.082
x[1] = -4.848
y[1] (analytic) = 4.0010315803981003226950019230733
y[1] (numeric) = 4.0010315804226635360683205898757
absolute error = 2.45632133733186668024e-11
relative error = 6.1392200685590792842507378327410e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1358
Order of pole = 2.082
x[1] = -4.847
y[1] (analytic) = 4.0083878430739401532204133483018
y[1] (numeric) = 4.0083878430994494450075675299776
absolute error = 2.55092917871541816758e-11
relative error = 6.3639779347279165401397731343580e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1348
Order of pole = 2.082
x[1] = -4.846
y[1] (analytic) = 4.0157996290698724041630935165322
y[1] (numeric) = 4.0157996290963707989940040400165
absolute error = 2.64983948309105234843e-11
relative error = 6.5985351059579641124799117884782e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1338
Order of pole = 2.082
x[1] = -4.845
y[1] (analytic) = 4.0232677675937478424153430227217
y[1] (numeric) = 4.0232677676212806650284183577241
absolute error = 2.75328226130753350024e-11
relative error = 6.8433980046876860538641903693580e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1328
Order of pole = 2.082
x[1] = -4.844
y[1] (analytic) = 4.0307931066841128817975660629393
y[1] (numeric) = 4.0307931067127278986487239589749
absolute error = 2.86150168511578960356e-11
relative error = 7.0991033510766622770730188421758e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1318
Order of pole = 2.082
x[1] = -4.843
y[1] (analytic) = 4.0383765137847153292170779578661
y[1] (numeric) = 4.0383765138144628999727279037265
absolute error = 2.97475707556499458604e-11
relative error = 7.3662202259023389706272164298723e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1308
Order of pole = 2.082
x[1] = -4.842
y[1] (analytic) = 4.0460188763410882930066238854408
y[1] (numeric) = 4.0460188763720215326931121071363
absolute error = 3.09332396864882216955e-11
relative error = 7.6453522912038143276964311716042e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1298
Order of pole = 2.082
x[1] = -4.841
y[1] (analytic) = 4.0537211024202382967907754171883
y[1] (numeric) = 4.0537211024524132494397298162683
absolute error = 3.21749526489543990800e-11
relative error = 7.9371401820773087828710241344216e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=5.79
Real estimate of pole used
Radius of convergence = 0.1288
Order of pole = 2.082
x[1] = -4.84
y[1] (analytic) = 4.0614841213545197075655208706915
y[1] (numeric) = 4.0614841213879955322678461664978
absolute error = 3.34758247023252958063e-11
relative error = 8.2422640842828130198818673312358e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1278
Order of pole = 2.082
x[1] = -4.839
y[1] (analytic) = 4.0693088844108371807625632356911
y[1] (numeric) = 4.0693088844456763511241900685218
absolute error = 3.48391703616268328307e-11
relative error = 8.5614465137047267414463675196367e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1268
Order of pole = 2.082
x[1] = -4.838
y[1] (analytic) = 4.0771963654863811997494447284817
y[1] (numeric) = 4.0771963655226497178300689924199
absolute error = 3.62685180806242639382e-11
relative error = 8.8954553152353950236238458698134e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1258
Order of pole = 2.082
x[1] = -4.837
y[1] (analytic) = 4.0851475618321692144647937066179
y[1] (numeric) = 4.0851475618699368403775763687035
absolute error = 3.77676259127826620856e-11
relative error = 9.2451069003353361948985664652665e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1248
Order of pole = 2.082
x[1] = -4.836
y[1] (analytic) = 4.0931634948057366575950169062117
y[1] (numeric) = 4.0931634948450771560514669014006
absolute error = 3.93404984564499951889e-11
relative error = 9.6112697443855983998997904280268e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1238
Order of pole = 2.082
x[1] = -4.835
y[1] (analytic) = 4.1012452106543985546282769842906
y[1] (numeric) = 4.1012452106953899598293334402375
absolute error = 4.09914052010564559469e-11
relative error = 9.9948681670062416640313343555809e-10 %
Correct digits = 11
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.1218
Order of pole = 0.9933
x[1] = -4.834
y[1] (analytic) = 4.109393781330583890061298632229
y[1] (numeric) = 4.1093937813733087904641060483143
absolute error = 4.27249004028074160853e-11
relative error = 1.0396886420793065615385165388414e-09 %
Correct digits = 10
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1218
Order of pole = 2.082
x[1] = -4.833
y[1] (analytic) = 4.1176103053408317181599987244319
y[1] (numeric) = 4.1176103053853775627913066198922
absolute error = 4.45458446313078954603e-11
relative error = 1.0818373116447854519182124931017e-09 %
Correct digits = 10
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1208
Order of pole = 2.082
x[1] = -4.832
y[1] (analytic) = 4.1258959086301306161495541590161
y[1] (numeric) = 4.1258959086765900442924994650019
absolute error = 4.64594281429453059858e-11
relative error = 1.1260446015074249953715136493695e-09 %
Correct digits = 10
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1198
Order of pole = 2.082
x[1] = -4.831
y[1] (analytic) = 4.1342517455033819075465233669056
y[1] (numeric) = 4.1342517455518531037993687848187
absolute error = 4.84711962528454179131e-11
relative error = 1.1724297221514172406327857055660e-09 %
Correct digits = 10
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.04491
Order of pole = 0.5717
memory used=57.2MB, alloc=4.1MB, time=6.20
x[1] = -4.8296525755274864345490528200464
y[1] (analytic) = 4.1456237715032203184121785102041
y[1] (numeric) = 4.1456237715517445426877138258143
absolute error = 4.85242242755353156102e-11
relative error = 1.1704927159354895169062381743946e-09 %
Correct digits = 10
h = 0.00044914149083785515031572665119202
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1174
Order of pole = 2.082
x[1] = -4.828754292545810724248421366744
y[1] (analytic) = 4.1532786274171284382411765424338
y[1] (numeric) = 4.1532786274656900958650829196684
absolute error = 4.85616576239063772346e-11
relative error = 1.1692366917869475864279959038427e-09 %
Correct digits = 10
h = 0.00044914149083785515031572665119202
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1165
Order of pole = 2.082
x[1] = -4.8278560095641350139477899134416
y[1] (analytic) = 4.1609933456142907400109606593014
y[1] (numeric) = 4.1609933456628916034971471622267
absolute error = 4.86008634861865029253e-11
relative error = 1.1680110841179804625056811675407e-09 %
Correct digits = 10
h = 0.00044914149083785515031572665119202
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1156
Order of pole = 2.082
x[1] = -4.8269577265824593036471584601392
y[1] (analytic) = 4.1687688569267151589016117156764
y[1] (numeric) = 4.168768856975357099459830148688
absolute error = 4.86419405582184330116e-11
relative error = 1.1668178838314885646746588905358e-09 %
Correct digits = 10
h = 0.00044914149083785515031572665119202
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.09036
Order of pole = 0.8111
x[1] = -4.8256103021099457381962112801856
y[1] (analytic) = 4.1805482014481943307448482941916
y[1] (numeric) = 4.180548201496901627018840761854
absolute error = 4.87072962739924676624e-11
relative error = 1.1650935218763809332639858689307e-09 %
Correct digits = 10
h = 0.00044914149083785515031572665119202
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.03124
Order of pole = 0.5381
memory used=61.0MB, alloc=4.1MB, time=6.60
x[1] = -4.8249855924239036540539159454918
y[1] (analytic) = 4.1860575453708736478825215815762
y[1] (numeric) = 4.1860575454195861476351685288687
absolute error = 4.87124997526469472925e-11
relative error = 1.1636844268066828118331861968711e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1128
Order of pole = 2.082
x[1] = -4.8237361730518194857693252761042
y[1] (analytic) = 4.1971693182529418539565180065317
y[1] (numeric) = 4.197169318301665295612628024083
absolute error = 4.87234416561100175513e-11
relative error = 1.1608643340695865103716171115032e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1115
Order of pole = 2.082
x[1] = -4.8227991085227563595558822740635
y[1] (analytic) = 4.2055859679257372228757730224932
y[1] (numeric) = 4.2055859679744693673223525108243
absolute error = 4.87321444465794883311e-11
relative error = 1.1587480274625076168735652021170e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1106
Order of pole = 2.082
x[1] = -4.8218620439936932333424392720228
y[1] (analytic) = 4.2140749448907615994166456129243
y[1] (numeric) = 4.2140749449395029009214510471979
absolute error = 4.87413015048054342736e-11
relative error = 1.1566311027263640559403457584431e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.03321
Order of pole = 0.546
memory used=64.8MB, alloc=4.1MB, time=7.00
x[1] = -4.8209249794646301071289962699821
y[1] (analytic) = 4.222637487646454711842528171673
y[1] (numeric) = 4.2226374876952056525791801133608
absolute error = 4.87509407366519416878e-11
relative error = 1.1545139946129723631362970536442e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1087
Order of pole = 2.082
x[1] = -4.8199879149355669809155532679414
y[1] (analytic) = 4.231274866909928562203916051582
y[1] (numeric) = 4.2312748669586896542283568300405
absolute error = 4.87610920244407784585e-11
relative error = 1.1523971748035048927717644232617e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1078
Order of pole = 2.082
x[1] = -4.8187384955634828126309625985538
y[1] (analytic) = 4.2429100438253052609351545350066
y[1] (numeric) = 4.2429100438740807402095860693739
absolute error = 4.87754792744315343673e-11
relative error = 1.1495760874170393633159255524535e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1065
Order of pole = 2.082
x[1] = -4.8178014310344196864175195965131
y[1] (analytic) = 4.251727172808752471922931520367
y[1] (numeric) = 4.2517271728575394258124616335199
absolute error = 4.87869538895301131529e-11
relative error = 1.1474620055947932733035595309582e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=7.39
Real estimate of pole used
Radius of convergence = 0.1056
Order of pole = 2.082
x[1] = -4.8168643665053565602040765944724
y[1] (analytic) = 4.2606236215658305769481458922821
y[1] (numeric) = 4.2606236216146296335410001493482
absolute error = 4.87990565928542570661e-11
relative error = 1.1453500925510058338321952597996e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1046
Order of pole = 2.082
x[1] = -4.8159273019762934339906335924317
y[1] (analytic) = 4.269600814113245227620592647929
y[1] (numeric) = 4.2696008141620570554828676879187
absolute error = 4.88118278622750399897e-11
relative error = 1.1432410191820891407408107144902e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.07113
Order of pole = 0.736
x[1] = -4.814990237447230307777190590391
y[1] (analytic) = 4.2786602133087501668176714810901
y[1] (numeric) = 4.2786602133575754780022559980735
absolute error = 4.88253111845845169834e-11
relative error = 1.1411355132317738731051978151030e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1028
Order of pole = 2.082
memory used=72.4MB, alloc=4.1MB, time=7.79
x[1] = -4.8137408180751461394925999210034
y[1] (analytic) = 4.2908698932218013359670051790857
y[1] (numeric) = 4.2908698932706458138587433494499
absolute error = 4.88444778917381703642e-11
relative error = 1.1383350953823322536911212837718e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.1015
Order of pole = 2.082
x[1] = -4.8128037535460830132791569189627
y[1] (analytic) = 4.3001270258108467016623750142362
y[1] (numeric) = 4.3001270258597065123009592476873
absolute error = 4.88598106385842334511e-11
relative error = 1.1362411004444934964499926835777e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.0525
Order of pole = 0.6367
x[1] = -4.811866689017019887065713916922
y[1] (analytic) = 4.3094715405637443841840956899506
y[1] (numeric) = 4.3094715406126204097556181144336
absolute error = 4.88760255715224244830e-11
relative error = 1.1341535757103224167460203581481e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.09963
Order of pole = 2.082
x[1] = -4.8109296244879567608522709148813
y[1] (analytic) = 4.3189050859976427763802211422487
y[1] (numeric) = 4.3189050860465359588593366151983
absolute error = 4.88931824791154729496e-11
relative error = 1.1320735581254715828896408526553e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.09869
Order of pole = 2.082
memory used=76.2MB, alloc=4.1MB, time=8.19
x[1] = -4.8099925599588936346388279128406
y[1] (analytic) = 4.3284293578855401391704696185213
y[1] (numeric) = 4.3284293579344514849964457913206
absolute error = 4.89113458259761727993e-11
relative error = 1.1300021735798782953026583049571e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.08708
Order of pole = 0.898
x[1] = -4.808743140586809466354237243453
y[1] (analytic) = 4.3412725402097656853675785887477
y[1] (numeric) = 4.3412725402587029355718080515979
absolute error = 4.89372502042294628502e-11
relative error = 1.1272558852493713010853792436056e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0965
Order of pole = 2.082
x[1] = -4.8078060760577463401407942414123
y[1] (analytic) = 4.3510153811153538095176910135373
y[1] (numeric) = 4.3510153811643118515845183040517
absolute error = 4.89580420668272905144e-11
relative error = 1.1252095839357208283394938661424e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.09556
Order of pole = 2.082
x[1] = -4.8068690115286832139273512393716
y[1] (analytic) = 4.3608549664334686750478339456202
y[1] (numeric) = 4.3608549664824487697240250241311
absolute error = 4.89800946761910785109e-11
relative error = 1.1231764196058443409003950514589e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.1MB, time=8.58
Real estimate of pole used
Radius of convergence = 0.09463
Order of pole = 2.082
x[1] = -4.8059319469996200877139082373309
y[1] (analytic) = 4.3707932189653530485951100860079
y[1] (numeric) = 4.3707932190143565467233460279013
absolute error = 4.90034981282359418934e-11
relative error = 1.1211580066429216486604420509281e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.09369
Order of pole = 2.082
x[1] = -4.8049948824705569615004652352902
y[1] (analytic) = 4.3808321195903408873484256836359
y[1] (numeric) = 4.3808321196393692373011743850645
absolute error = 4.90283499527487014286e-11
relative error = 1.1191561012690307425486248897121e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.09275
Order of pole = 2.082
x[1] = -4.8037454630984727932158745659026
y[1] (analytic) = 4.3943774213456147706087868871104
y[1] (numeric) = 4.3943774213946786932413493716998
absolute error = 4.90639226325624845894e-11
relative error = 1.1165159003920624031772108914837e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0915
Order of pole = 2.082
memory used=83.9MB, alloc=4.1MB, time=8.98
x[1] = -4.8028083985694096670024315638619
y[1] (analytic) = 4.4046592151217763403213765174026
y[1] (numeric) = 4.4046592151708689207243671139052
absolute error = 4.90925804029905965026e-11
relative error = 1.1145602419013323333649882873723e-09 %
Correct digits = 10
h = 0.000312354843021042071147667346868
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.0666
Order of pole = 0.7712
x[1] = -4.8019758043950241983254860920317
y[1] (analytic) = 4.4138850144784348769910455009565
y[1] (numeric) = 4.4138850145275484752144236104715
absolute error = 4.91135982233781095150e-11
relative error = 1.1127067891953592281967445721427e-09 %
Correct digits = 10
h = 0.00020788448834338453465013713644828
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08972
Order of pole = 2.082
x[1] = -4.8009363819533072756522354063497
y[1] (analytic) = 4.4255243748341590096840007387642
y[1] (numeric) = 4.4255243748832773043263329577351
absolute error = 4.91182946423322189709e-11
relative error = 1.1098864333827754733224109349636e-09 %
Correct digits = 10
h = 0.00020788448834338453465013713644828
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08868
Order of pole = 2.082
memory used=87.7MB, alloc=4.1MB, time=9.37
x[1] = -4.7998969595115903529789847206677
y[1] (analytic) = 4.4373019000899706146098712130298
y[1] (numeric) = 4.4373019001390939481529052719705
absolute error = 4.91233335430340589407e-11
relative error = 1.1070541209296134559615093998818e-09 %
Correct digits = 10
h = 0.00020788448834338453465013713644828
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08764
Order of pole = 2.082
x[1] = -4.7988575370698734303057340349857
y[1] (analytic) = 4.4492208835924681838098421861586
y[1] (numeric) = 4.4492208836415969282299951732577
absolute error = 4.91287444201529870991e-11
relative error = 1.1042100562219017579297930609766e-09 %
Correct digits = 10
h = 0.00020788448834338453465013713644828
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0866
Order of pole = 2.082
memory used=91.5MB, alloc=4.1MB, time=9.77
x[1] = -4.7978764186806806087824004848729
y[1] (analytic) = 4.4606041482166051812243696708491
y[1] (numeric) = 4.4606041482657383227508683000673
absolute error = 4.91331415264986292182e-11
relative error = 1.1014907374406347615268609386859e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08562
Order of pole = 2.082
x[1] = -4.7969827563702739389839426381139
y[1] (analytic) = 4.471087554104553105333282292957
y[1] (numeric) = 4.4710875541536887516191998735538
absolute error = 4.91356462859175805968e-11
relative error = 1.0989640818106998654128686377732e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08472
Order of pole = 2.082
x[1] = -4.7959103615977859352257932220031
memory used=95.3MB, alloc=4.1MB, time=10.15
y[1] (analytic) = 4.4838155247894101117752900742547
y[1] (numeric) = 4.4838155248385489810910566151963
absolute error = 4.91388693157665409416e-11
relative error = 1.0959163918340380438867313742311e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08365
Order of pole = 2.082
x[1] = -4.7948379668252979314676438058923
y[1] (analytic) = 4.4967087524678636520854264520144
y[1] (numeric) = 4.4967087525170060023978755833313
absolute error = 4.91423503124491313169e-11
relative error = 1.0928515280310081386828216208155e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08258
Order of pole = 2.082
x[1] = -4.7939443045148912616691859591333
y[1] (analytic) = 4.5075824563757587900072686873683
y[1] (numeric) = 4.507582456424904255742633770964
absolute error = 4.91454657353650835957e-11
relative error = 1.0902843422387356177886636705606e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.1MB, time=10.55
Real estimate of pole used
Radius of convergence = 0.08168
Order of pole = 2.082
x[1] = -4.7928719097424032579110365430225
y[1] (analytic) = 4.5207899915622685804963513689908
y[1] (numeric) = 4.520789991611418065493945821968
absolute error = 4.91494849975944529772e-11
relative error = 1.0871879713352855147799766644342e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.08061
Order of pole = 2.082
x[1] = -4.7919782474319965881125786962635
y[1] (analytic) = 4.5319319962248598560425267729474
y[1] (numeric) = 4.5319319962740129444621044337642
absolute error = 4.91530884195776608168e-11
relative error = 1.0845945715982196089523842761978e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07971
Order of pole = 2.082
memory used=103.0MB, alloc=4.1MB, time=10.94
x[1] = -4.7909058526595085843544292801527
y[1] (analytic) = 4.545469438283810713543332912954
y[1] (numeric) = 4.5454694383329684591359965042215
absolute error = 4.91577455926635912675e-11
relative error = 1.0814668596963135594238532302032e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07864
Order of pole = 2.082
x[1] = -4.7898334578870205805962798640419
y[1] (analytic) = 4.5591938264671337022021662420929
y[1] (numeric) = 4.5591938265162965024559477620791
absolute error = 4.91628002537815199862e-11
relative error = 1.0783222237313214299131478108287e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.03871
Order of pole = 0.6249
memory used=106.8MB, alloc=4.1MB, time=11.33
x[1] = -4.7889397955766139107978220172829
y[1] (analytic) = 4.5707773698578924001524925962967
y[1] (numeric) = 4.5707773699070597450882418929207
absolute error = 4.91673449357492966240e-11
relative error = 1.0756889027233004854376898042795e-09 %
Correct digits = 10
h = 0.00017873246208133395969156935178515
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07667
Order of pole = 2.082
x[1] = -4.7879604475285427281907921453889
y[1] (analytic) = 4.5836285081428735975127276162216
y[1] (numeric) = 4.5836285081920451440829893760695
absolute error = 4.91715465702617598479e-11
relative error = 1.0727646554014551999527559775832e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.02087
Order of pole = 0.5381
memory used=110.6MB, alloc=4.1MB, time=11.71
x[1] = -4.7869027747295593411177377674417
y[1] (analytic) = 4.5976965673304483222934767688554
y[1] (numeric) = 4.597696567379621260353945306272
absolute error = 4.91729380604685374166e-11
relative error = 1.0695124686973356631925403094274e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07463
Order of pole = 2.082
memory used=114.4MB, alloc=4.1MB, time=12.09
x[1] = -4.7859773110304488774288151867379
y[1] (analytic) = 4.6101715201996327530273049796206
y[1] (numeric) = 4.6101715202488070096413550845975
absolute error = 4.91742566140501049769e-11
relative error = 1.0666470086544790461166977898925e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0737
Order of pole = 2.082
x[1] = -4.7849196382314654903557608087907
y[1] (analytic) = 4.6246228761746640023269824900898
y[1] (numeric) = 4.6246228762238398928912526524551
absolute error = 4.91758905642701623653e-11
relative error = 1.0633492044857686269429124211369e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07264
Order of pole = 2.082
memory used=118.2MB, alloc=4.1MB, time=12.49
x[1] = -4.7839941745323550266668382280869
y[1] (analytic) = 4.6374423604219961062395308548146
y[1] (numeric) = 4.6374423604711735484797074478754
absolute error = 4.91774422401765930608e-11
relative error = 1.0604432016207650296504936833716e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.07172
Order of pole = 2.082
memory used=122.0MB, alloc=4.1MB, time=12.87
x[1] = -4.7829365017333716395937838501397
y[1] (analytic) = 4.652298364341036903406680138397
y[1] (numeric) = 4.652298364390216272802176187922
absolute error = 4.91793693954960495250e-11
relative error = 1.0570983532020723603632710183719e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.04091
Order of pole = 0.6682
x[1] = -4.7818788289343882525207294721925
y[1] (analytic) = 4.6673795372039081579881344508504
y[1] (numeric) = 4.6673795372530896358506625953148
absolute error = 4.91814778625281444644e-11
relative error = 1.0537278460108119427484070807882e-09 %
Correct digits = 10
h = 0.00013220909987292338413179724343189
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0696
Order of pole = 2.082
memory used=125.8MB, alloc=4.1MB, time=13.25
x[1] = -4.780926006575447998780726606947
y[1] (analytic) = 4.6811641613601374533251724633761
y[1] (numeric) = 4.6811641614093204906689543043986
absolute error = 4.91830373437818410225e-11
relative error = 1.0506582475734293558891955702907e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06864
Order of pole = 2.082
memory used=129.7MB, alloc=4.1MB, time=13.65
x[1] = -4.779953417043529209382913676852
y[1] (analytic) = 4.6954344606143572600019049687235
y[1] (numeric) = 4.6954344606635407933887525828339
absolute error = 4.91835333868476141104e-11
relative error = 1.0474756659772942781042499859976e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.03844
Order of pole = 0.6618
memory used=133.5MB, alloc=4.1MB, time=14.03
x[1] = -4.778980827511610419985100746757
y[1] (analytic) = 4.7099123127365110978560252714518
y[1] (numeric) = 4.7099123127856951720197446529608
absolute error = 4.91840741637193815090e-11
relative error = 1.0442673004912673403844102932084e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06669
Order of pole = 2.082
memory used=137.3MB, alloc=4.2MB, time=14.42
x[1] = -4.7779109790264997516475065236525
y[1] (analytic) = 4.7260849600747256038467699382884
y[1] (numeric) = 4.7260849601239103302523302590532
absolute error = 4.91847264055603207648e-11
relative error = 1.0407076220818223655022908812609e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06562
Order of pole = 2.082
x[1] = -4.7769383894945809622496935935575
y[1] (analytic) = 4.7410188498992334779600689209844
y[1] (numeric) = 4.7410188499484188553450027605326
absolute error = 4.91853773849338395482e-11
relative error = 1.0374431940083772283027775007295e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06465
Order of pole = 2.082
memory used=141.1MB, alloc=4.2MB, time=14.80
x[1] = -4.7759657999626621728518806634625
y[1] (analytic) = 4.7561801065704029677413261981475
y[1] (numeric) = 4.7561801066195890576792855169644
absolute error = 4.91860899379593188169e-11
relative error = 1.0341511220319731543383105274473e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06367
Order of pole = 2.082
memory used=144.9MB, alloc=4.2MB, time=15.19
x[1] = -4.7749932104307433834540677333675
y[1] (analytic) = 4.7715757308341501592652679116245
y[1] (numeric) = 4.7715757308833370302328297148952
absolute error = 4.91868709675618032707e-11
relative error = 1.0308307725205720823792574786291e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0627
Order of pole = 2.082
memory used=148.7MB, alloc=4.2MB, time=15.58
x[1] = -4.773923361945632715116473510263
y[1] (analytic) = 4.7887903702989104704196640058069
y[1] (numeric) = 4.7887903703480982889515402943915
absolute error = 4.91878185318762885846e-11
relative error = 1.0271449516134498236104748702885e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06163
Order of pole = 2.082
memory used=152.5MB, alloc=4.2MB, time=15.97
x[1] = -4.772950772413713925718660580168
y[1] (analytic) = 4.8047024425171297379246968921607
y[1] (numeric) = 4.8047024425663185079183051351341
absolute error = 4.91887699936082429734e-11
relative error = 1.0237630858954669811441984416467e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.06066
Order of pole = 2.082
memory used=156.4MB, alloc=4.2MB, time=16.36
x[1] = -4.771978182881795136320847650073
y[1] (analytic) = 4.8208727697191888669031330563427
y[1] (numeric) = 4.8208727697683786845685190000501
absolute error = 4.91898176653859437074e-11
relative error = 1.0203508786698638091491612337817e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05968
Order of pole = 2.082
memory used=160.2MB, alloc=4.2MB, time=16.75
x[1] = -4.7709083343966844679832534269685
y[1] (analytic) = 4.8389685592787224432501578347124
y[1] (numeric) = 4.8389685593279135383009391746689
absolute error = 4.91910950507813399565e-11
relative error = 1.0165615760502806502031323993199e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05861
Order of pole = 2.082
x[1] = -4.7699357448647656785854404968735
y[1] (analytic) = 4.8557093657089410120089295569022
y[1] (numeric) = 4.855709365758133396275818992283
absolute error = 4.91923842668894353808e-11
relative error = 1.0130833738585437734013356144937e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05764
Order of pole = 2.082
memory used=164.0MB, alloc=4.2MB, time=17.14
x[1] = -4.7689631553328468891876275667785
y[1] (analytic) = 4.8727361673662536651335877169504
y[1] (numeric) = 4.8727361674154474761610996469443
absolute error = 4.91938110275119299939e-11
relative error = 1.0095726371760758047226488555555e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05666
Order of pole = 2.082
memory used=167.8MB, alloc=4.2MB, time=17.53
x[1] = -4.7679905658009280997898146366835
y[1] (analytic) = 4.8900588726099097297793661545893
y[1] (numeric) = 4.8900588726591051225401949621953
absolute error = 4.91953927608288076060e-11
relative error = 1.0060286397855240595880719143819e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05569
Order of pole = 2.082
memory used=171.6MB, alloc=4.2MB, time=17.91
x[1] = -4.766920717315817431452220413579
y[1] (analytic) = 4.9094680853147499109687477587319
y[1] (numeric) = 4.9094680853639472465845623950937
absolute error = 4.91973356158146363618e-11
relative error = 1.0020909548831613592917240717859e-09 %
Correct digits = 10
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05462
Order of pole = 2.082
memory used=175.4MB, alloc=4.2MB, time=18.30
x[1] = -4.765948127783898642054407483484
y[1] (analytic) = 4.9274468196653139905600385091078
y[1] (numeric) = 4.9274468197145133020465824831694
absolute error = 4.91993114865439740616e-11
relative error = 9.9847473320647079660283455197793e-10 %
Correct digits = 11
h = 9.7258953191878939781293009462920e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.03463
Order of pole = 0.709
memory used=179.2MB, alloc=4.2MB, time=18.69
x[1] = -4.7649629575947850625611077705289
y[1] (analytic) = 4.9459947244679556294482724970461
y[1] (numeric) = 4.945994724517156310715430214634
absolute error = 4.92006812671577175879e-11
relative error = 9.9475806198823375933377813286720e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05265
Order of pole = 2.082
memory used=183.1MB, alloc=4.2MB, time=19.08
x[1] = -4.7639675100460034908409806372033
y[1] (analytic) = 4.9650932150325797591063129647465
y[1] (numeric) = 4.9650932150817805907782997376101
absolute error = 4.92008316719867728636e-11
relative error = 9.9093470235410129605536870893077e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05166
Order of pole = 2.082
memory used=186.9MB, alloc=4.2MB, time=19.47
memory used=190.7MB, alloc=4.2MB, time=19.85
x[1] = -4.7629720624972219191208535038777
y[1] (analytic) = 4.9845645819391607257921096731994
y[1] (numeric) = 4.9845645819883617263324355752286
absolute error = 4.92010005403259020292e-11
relative error = 9.8706716969017749464849584331990e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.05066
Order of pole = 2.082
memory used=194.5MB, alloc=4.2MB, time=20.23
x[1] = -4.7619766149484403474007263705521
y[1] (analytic) = 5.0044236353290151790991988436285
y[1] (numeric) = 5.0044236353782163696705315978719
absolute error = 4.92011905713327542434e-11
relative error = 9.8315398848319179891674198222066e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04966
Order of pole = 2.082
memory used=198.3MB, alloc=4.2MB, time=20.62
memory used=202.1MB, alloc=4.2MB, time=21.00
x[1] = -4.7609811673996587756805992372265
y[1] (analytic) = 5.0246860864261692919734952574697
y[1] (numeric) = 5.0246860864753706968981652811796
absolute error = 4.92014049246700237099e-11
relative error = 9.7919360689186347806323865451345e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04867
Order of pole = 2.082
memory used=206.0MB, alloc=4.2MB, time=21.39
x[1] = -4.7599857198508772039604721039009
y[1] (analytic) = 5.0453686221517126502856328299268
y[1] (numeric) = 5.0453686222009142975964380468218
absolute error = 4.92016473108052168950e-11
relative error = 9.7518439177635450893055210596804e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.02628
Order of pole = 0.6524
memory used=209.8MB, alloc=4.2MB, time=21.78
memory used=213.6MB, alloc=4.2MB, time=22.16
x[1] = -4.7589902723020956322403449705753
y[1] (analytic) = 5.0664889876247768287438720819154
y[1] (numeric) = 5.066488987673978750845291556813
absolute error = 4.92019221014194748976e-11
relative error = 9.7112462341472199616326985362822e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.02399
Order of pole = 0.6325
memory used=217.4MB, alloc=4.2MB, time=22.55
x[1] = -4.7579948247533140605202178372497
y[1] (analytic) = 5.088066077572106801325083512935
y[1] (numeric) = 5.0880660776213090357900462352278
absolute error = 4.92022344649627222928e-11
relative error = 9.6701248990934395973186584658369e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04568
Order of pole = 2.082
memory used=221.2MB, alloc=4.2MB, time=22.94
memory used=225.0MB, alloc=4.2MB, time=23.32
x[1] = -4.7569993772045324888000907039241
y[1] (analytic) = 5.1101200378261108153178729639308
y[1] (numeric) = 5.110120037875313405851673737827
absolute error = 4.92025905338007738962e-11
relative error = 9.6284608129737752153977522321888e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04468
Order of pole = 2.082
memory used=228.8MB, alloc=4.2MB, time=23.71
x[1] = -4.7559486270141519408732898409693
y[1] (analytic) = 5.1339403536946814660176078116677
y[1] (numeric) = 5.1339403537438844879076745997165
absolute error = 4.92030218900667880488e-11
relative error = 9.5838709646592285831621039681422e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04363
Order of pole = 2.082
memory used=232.7MB, alloc=4.2MB, time=24.10
memory used=236.5MB, alloc=4.2MB, time=24.49
x[1] = -4.7549531794653703691531627076437
y[1] (analytic) = 5.15704374628325282057010677678
y[1] (numeric) = 5.1570437463324563128864843372105
absolute error = 4.92034923163775604305e-11
relative error = 9.5410267465423663856984946092281e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04263
Order of pole = 2.082
memory used=240.3MB, alloc=4.2MB, time=24.87
x[1] = -4.7539577319165887974330355743181
y[1] (analytic) = 5.1806945691865597957759048039201
y[1] (numeric) = 5.1806945692357638293831274494537
absolute error = 4.92040336072226455336e-11
relative error = 9.4975746881268769001264484861421e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04163
Order of pole = 2.082
memory used=244.1MB, alloc=4.2MB, time=25.27
memory used=247.9MB, alloc=4.2MB, time=25.65
x[1] = -4.7529622843678072257129084409925
y[1] (analytic) = 5.2049193465648025800120400162962
y[1] (numeric) = 5.2049193466140072385466797110155
absolute error = 4.92046585346396947193e-11
relative error = 9.4534910645857179005557677496700e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.04064
Order of pole = 2.082
memory used=251.7MB, alloc=4.2MB, time=26.04
x[1] = -4.7519668368190256539927813076669
y[1] (analytic) = 5.2297465794920829781040153002736
y[1] (numeric) = 5.2297465795412883606743543908972
absolute error = 4.92053825703390906236e-11
relative error = 9.4087508490933331868315506690462e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03964
Order of pole = 2.082
memory used=255.5MB, alloc=4.2MB, time=26.43
memory used=259.4MB, alloc=4.2MB, time=26.81
x[1] = -4.7509713892702440822726541743413
y[1] (analytic) = 5.2552069474317547393761881064212
y[1] (numeric) = 5.2552069474809609639211230307251
absolute error = 4.92062245449349243039e-11
relative error = 9.3633276552471917738951212104855e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03864
Order of pole = 2.082
memory used=263.2MB, alloc=4.2MB, time=27.20
x[1] = -4.7499759417214625105525270410157
y[1] (analytic) = 5.2813335360507826117696616713128
y[1] (numeric) = 5.281333536099989819260642004297
absolute error = 4.92072074909803329842e-11
relative error = 9.3171936888833490167803510972901e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03764
Order of pole = 2.082
memory used=267.0MB, alloc=4.2MB, time=27.60
memory used=270.8MB, alloc=4.3MB, time=27.99
x[1] = -4.7489804941726809388323999076901
y[1] (analytic) = 5.3081620956162802068441426996382
y[1] (numeric) = 5.3081620956654885665719233712144
absolute error = 4.92083597277806715762e-11
relative error = 9.2703197154471140965511375234982e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03665
Order of pole = 2.082
memory used=274.6MB, alloc=4.3MB, time=28.37
x[1] = -4.7479850466238993671122727743645
y[1] (analytic) = 5.3357313350369474763502010963423
y[1] (numeric) = 5.3357313350861571926166896603939
absolute error = 4.92097162664885640516e-11
relative error = 9.2226750517504850126116515352391e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03565
Order of pole = 2.082
memory used=278.4MB, alloc=4.3MB, time=28.76
memory used=282.3MB, alloc=4.3MB, time=29.14
x[1] = -4.7469895990751177953921456410389
y[1] (analytic) = 5.3640832576177311017463400165026
y[1] (numeric) = 5.3640832576669424223889690395983
absolute error = 4.92113206426290230957e-11
relative error = 9.1742275947604325888480449756715e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03465
Order of pole = 2.082
memory used=286.1MB, alloc=4.3MB, time=29.52
x[1] = -4.7459941515263362236720185077133
y[1] (analytic) = 5.3932635458365931021653769268239
y[1] (numeric) = 5.3932635458858063294888976622766
absolute error = 4.92132273235207354527e-11
relative error = 9.1249439055340786843903796223954e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03366
Order of pole = 2.082
memory used=289.9MB, alloc=4.3MB, time=29.91
memory used=293.7MB, alloc=4.3MB, time=30.29
x[1] = -4.7449987039775546519518913743877
y[1] (analytic) = 5.4233220039914180266548651836933
y[1] (numeric) = 5.4233220040406335315502040137178
absolute error = 4.92155048953388300245e-11
relative error = 9.0747893743203062860257798414926e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03266
Order of pole = 2.082
memory used=297.5MB, alloc=4.3MB, time=30.67
x[1] = -4.7439479537871741040250905114329
y[1] (analytic) = 5.4560633122834929664165089056153
y[1] (numeric) = 5.4560633123327113742223442221244
absolute error = 4.92184078058353165091e-11
relative error = 9.0208644930911250529697372494008e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03161
Order of pole = 2.082
memory used=301.3MB, alloc=4.3MB, time=31.06
memory used=305.1MB, alloc=4.3MB, time=31.46
x[1] = -4.7429525062383925323049633781073
y[1] (analytic) = 5.4881036395785260216837704598778
y[1] (numeric) = 5.4881036396277477692763736884278
absolute error = 4.92217475926032285500e-11
relative error = 8.9688079572023803326856165211990e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.03061
Order of pole = 2.082
memory used=309.0MB, alloc=4.3MB, time=31.84
x[1] = -4.7419570586896109605848362447817
y[1] (analytic) = 5.5212056513492200517335011836232
y[1] (numeric) = 5.5212056513984458600287043935806
absolute error = 4.92258082952032099574e-11
relative error = 8.9157715549272960333975089944484e-10 %
Correct digits = 11
h = 5.5302641598976206673729629206565e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02961
Order of pole = 2.082
memory used=312.8MB, alloc=4.3MB, time=32.22
memory used=316.6MB, alloc=4.3MB, time=32.59
x[1] = -4.7409841226076536412929619798753
y[1] (analytic) = 5.5546547120012488436773303547305
y[1] (numeric) = 5.5546547120504789898859298521535
absolute error = 4.92301462085994974230e-11
relative error = 8.8628634471615432235747167706726e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.02085
Order of pole = 0.7659
memory used=320.4MB, alloc=4.3MB, time=32.97
x[1] = -4.7399868371509806928832616794161
y[1] (analytic) = 5.5901441061754117183446464583163
y[1] (numeric) = 5.5901441062246465702856165786169
absolute error = 4.92348519409701203006e-11
relative error = 8.8074387718521530957137996907168e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02764
Order of pole = 2.082
memory used=324.2MB, alloc=4.3MB, time=33.35
memory used=328.0MB, alloc=4.3MB, time=33.72
x[1] = -4.7389895516943077444735613789569
y[1] (analytic) = 5.6269405201339813854204269250456
y[1] (numeric) = 5.6269405201832220828042189375895
absolute error = 4.92406973837920125439e-11
relative error = 8.7508828656713003843704186596063e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02664
Order of pole = 2.082
memory used=331.8MB, alloc=4.3MB, time=34.10
memory used=335.7MB, alloc=4.3MB, time=34.48
x[1] = -4.7379922662376347960638610784977
y[1] (analytic) = 5.6651438391977432666342005957168
y[1] (numeric) = 5.6651438392469912845605184599593
absolute error = 4.92480179263178642425e-11
relative error = 8.6931628435566805781208066290577e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.01398
Order of pole = 0.6491
memory used=339.5MB, alloc=4.3MB, time=34.86
x[1] = -4.7369949807809618476541607780385
y[1] (analytic) = 5.7048658584853326924906001739418
y[1] (numeric) = 5.7048658585345899591201829558528
absolute error = 4.92572666295827819110e-11
relative error = 8.6342550116788908515877369211294e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02464
Order of pole = 2.082
memory used=343.3MB, alloc=4.3MB, time=35.24
memory used=347.1MB, alloc=4.3MB, time=35.62
x[1] = -4.7359976953242888992444604775793
y[1] (analytic) = 5.7462322549777423128725907064105
y[1] (numeric) = 5.7462322550270113756417554053571
absolute error = 4.92690627691646989466e-11
relative error = 8.5741509536940114015475866482689e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02365
Order of pole = 2.082
memory used=350.9MB, alloc=4.3MB, time=36.00
x[1] = -4.7349479211593700061816180560433
y[1] (analytic) = 5.7917086240051430868574342786901
y[1] (numeric) = 5.7917086240544282657675870223865
absolute error = 4.92851789101527436964e-11
relative error = 8.5096095314391938297648997219027e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02259
Order of pole = 2.082
memory used=354.7MB, alloc=4.3MB, time=36.38
memory used=358.5MB, alloc=4.3MB, time=36.75
x[1] = -4.7339506357026970577719177555841
y[1] (analytic) = 5.8369162439796400460902742592316
y[1] (numeric) = 5.8369162440289453187478870712977
absolute error = 4.93052726576128120661e-11
relative error = 8.4471441077242902323890323612577e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.02159
Order of pole = 2.082
memory used=362.4MB, alloc=4.3MB, time=37.13
x[1] = -4.7329533502460241093622174551249
y[1] (analytic) = 5.8842658022968526600500685173149
y[1] (numeric) = 5.8842658023461844584185813465295
absolute error = 4.93317983685128292146e-11
relative error = 8.3836794641834080194479328520902e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0206
Order of pole = 2.082
memory used=366.2MB, alloc=4.3MB, time=37.51
memory used=370.0MB, alloc=4.3MB, time=37.89
x[1] = -4.7319560647893511609525171546657
y[1] (analytic) = 5.9339703041855679610180754283681
y[1] (numeric) = 5.9339703042349352517840590730855
absolute error = 4.93672907659836447174e-11
relative error = 8.3194367742558598079533876648905e-10 %
Correct digits = 11
h = 5.2488708245944653142121076783578e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0196
Order of pole = 2.082
memory used=373.8MB, alloc=4.3MB, time=38.27
x[1] = -4.7309798152051447929397390238625
y[1] (analytic) = 5.9851441751469122056768395591791
y[1] (numeric) = 5.9851441751963151751038961451668
absolute error = 4.94029694270565859877e-11
relative error = 8.2542655584138762418820174330728e-10 %
Correct digits = 11
h = 4.3298135656879021884084735185316e-05
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.3MB, time=38.65
Real estimate of pole used
Radius of convergence = 0.01862
Order of pole = 2.082
memory used=381.4MB, alloc=4.3MB, time=39.03
x[1] = -4.7299839580850365754364050749529
y[1] (analytic) = 6.040193373334376600361833343574
y[1] (numeric) = 6.0401933733838047935946586457528
absolute error = 4.94281932328253021788e-11
relative error = 8.1832137115072833940397514033446e-10 %
Correct digits = 11
h = 4.3298135656879021884084735185316e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01762
Order of pole = 2.082
memory used=385.3MB, alloc=4.3MB, time=39.41
memory used=389.1MB, alloc=4.3MB, time=39.80
x[1] = -4.7289881009649283579330711260433
y[1] (analytic) = 6.098451484339484181775442705819
y[1] (numeric) = 6.0984514843889478153899451647163
absolute error = 4.94636336145024588973e-11
relative error = 8.1108513762096124194312367683334e-10 %
Correct digits = 11
h = 4.3298135656879021884084735185316e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01662
Order of pole = 2.082
memory used=392.9MB, alloc=4.3MB, time=40.19
memory used=396.7MB, alloc=4.3MB, time=40.57
x[1] = -4.7279929840991768443010604133752
y[1] (analytic) = 6.1602683304420055280100557575989
y[1] (numeric) = 6.1602683304915197247437923912666
absolute error = 4.95141967337366336677e-11
relative error = 8.0376688283290964394183185720311e-10 %
Correct digits = 11
h = 4.3051384204644398109672654727477e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.006662
Order of pole = 0.5911
memory used=400.5MB, alloc=4.3MB, time=40.95
memory used=404.3MB, alloc=4.3MB, time=41.34
x[1] = -4.7269851836894433413612729412016
y[1] (analytic) = 6.2270293401497046676902319592127
y[1] (numeric) = 6.2270293401992908547599463819462
absolute error = 4.95861870697144227335e-11
relative error = 7.9630565974693666678270925352183e-10 %
Correct digits = 11
h = 1.7618573026681783265001115523024e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01462
Order of pole = 2.082
memory used=408.1MB, alloc=4.3MB, time=41.72
memory used=412.0MB, alloc=4.3MB, time=42.11
memory used=415.8MB, alloc=4.3MB, time=42.50
memory used=419.6MB, alloc=4.3MB, time=42.90
memory used=423.4MB, alloc=4.3MB, time=43.28
x[1] = -4.7259985435999491614984328787336
y[1] (analytic) = 6.2970134259868076249899414610283
y[1] (numeric) = 6.2970134260363950617680426641197
absolute error = 4.95874367781012030914e-11
relative error = 7.8747548120925810155630734384344e-10 %
Correct digits = 11
h = 1.7618573026681783265001115523024e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01363
Order of pole = 2.082
memory used=427.2MB, alloc=4.3MB, time=43.67
memory used=431.0MB, alloc=4.3MB, time=44.06
memory used=434.8MB, alloc=4.3MB, time=44.45
memory used=438.7MB, alloc=4.3MB, time=44.84
x[1] = -4.7249942849374282998523278151501
y[1] (analytic) = 6.3736640397937534947522494470501
y[1] (numeric) = 6.373664039843342908056937166632
absolute error = 4.95894133046877195819e-11
relative error = 7.7803619699874221873439707845527e-10 %
Correct digits = 11
h = 1.7618573026681783265001115523024e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01262
Order of pole = 2.082
memory used=442.5MB, alloc=4.3MB, time=45.23
memory used=446.3MB, alloc=4.3MB, time=45.61
memory used=450.1MB, alloc=4.3MB, time=46.00
memory used=453.9MB, alloc=4.3MB, time=46.38
memory used=457.7MB, alloc=4.3MB, time=46.77
x[1] = -4.7239900262749074382062227515666
y[1] (analytic) = 6.456682452796047159421662832135
y[1] (numeric) = 6.4566824528456397664302477275913
absolute error = 4.95926070085848954563e-11
relative error = 7.6808186512423209359569760134097e-10 %
Correct digits = 11
h = 1.7618573026681783265001115523024e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01162
Order of pole = 2.082
memory used=461.5MB, alloc=4.3MB, time=47.15
memory used=465.4MB, alloc=4.3MB, time=47.54
memory used=469.2MB, alloc=4.3MB, time=47.93
memory used=473.0MB, alloc=4.3MB, time=48.31
memory used=476.8MB, alloc=4.3MB, time=48.70
memory used=480.6MB, alloc=4.3MB, time=49.09
memory used=484.4MB, alloc=4.3MB, time=49.47
x[1] = -4.7229969637576144986885993091561
y[1] (analytic) = 6.5461671679044798626213222026821
y[1] (numeric) = 6.5461671679540733433744256092548
absolute error = 4.95934807531034065727e-11
relative error = 7.5759569655137568009660741100843e-10 %
Correct digits = 11
h = 1.0024869800935120605922746941677e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.01062
Order of pole = 2.082
memory used=488.3MB, alloc=4.3MB, time=49.86
memory used=492.1MB, alloc=4.3MB, time=50.24
memory used=495.9MB, alloc=4.3MB, time=50.63
memory used=499.7MB, alloc=4.3MB, time=51.03
memory used=503.5MB, alloc=4.3MB, time=51.42
memory used=507.3MB, alloc=4.3MB, time=51.81
memory used=511.1MB, alloc=4.3MB, time=52.21
memory used=515.0MB, alloc=4.3MB, time=52.60
memory used=518.8MB, alloc=4.3MB, time=52.99
memory used=522.6MB, alloc=4.3MB, time=53.39
x[1] = -4.7219965967783425751783065104262
y[1] (analytic) = 6.6452145051540442839687407649135
y[1] (numeric) = 6.645214505203637967804265017016
absolute error = 4.95936838355242521025e-11
relative error = 7.4630674144618314659548805197333e-10 %
Correct digits = 11
h = 7.4018747485616897726593803398376e-06
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.3MB, time=53.78
Real estimate of pole used
Radius of convergence = 0.009622
Order of pole = 2.082
memory used=530.2MB, alloc=4.3MB, time=54.17
memory used=534.0MB, alloc=4.3MB, time=54.56
memory used=537.8MB, alloc=4.3MB, time=54.95
memory used=541.7MB, alloc=4.3MB, time=55.34
memory used=545.5MB, alloc=4.3MB, time=55.72
memory used=549.3MB, alloc=4.3MB, time=56.11
memory used=553.1MB, alloc=4.3MB, time=56.50
memory used=556.9MB, alloc=4.3MB, time=56.89
memory used=560.7MB, alloc=4.3MB, time=57.28
memory used=564.5MB, alloc=4.3MB, time=57.68
x[1] = -4.7209973436872867470589974940857
y[1] (analytic) = 6.7550334219096229834510093720759
y[1] (numeric) = 6.7550334219592168986356459224286
absolute error = 4.95939151846365503527e-11
relative error = 7.3417719923903106043810740742646e-10 %
Correct digits = 11
h = 7.4018747485616897726593803398376e-06
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.008622
Order of pole = 2.082
memory used=568.4MB, alloc=4.3MB, time=58.07
memory used=572.2MB, alloc=4.3MB, time=58.46
memory used=576.0MB, alloc=4.3MB, time=58.85
memory used=579.8MB, alloc=4.3MB, time=59.24
memory used=583.6MB, alloc=4.3MB, time=59.63
memory used=587.4MB, alloc=4.3MB, time=60.02
memory used=591.3MB, alloc=4.3MB, time=60.43
memory used=595.1MB, alloc=4.3MB, time=60.82
memory used=598.9MB, alloc=4.3MB, time=61.21
memory used=602.7MB, alloc=4.3MB, time=61.60
memory used=606.5MB, alloc=4.3MB, time=61.99
x[1] = -4.7199980905962309189396884777452
y[1] (analytic) = 6.8784186873049523298209435611473
y[1] (numeric) = 6.8784186873545467120925982331782
absolute error = 4.95943822716546720309e-11
relative error = 7.2101429887057880005657801551500e-10 %
Correct digits = 11
h = 7.4018747485616897726593803398376e-06
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.007621
Order of pole = 2.082
memory used=610.3MB, alloc=4.3MB, time=62.39
memory used=614.1MB, alloc=4.3MB, time=62.78
memory used=618.0MB, alloc=4.3MB, time=63.17
memory used=621.8MB, alloc=4.3MB, time=63.56
memory used=625.6MB, alloc=4.3MB, time=63.96
memory used=629.4MB, alloc=4.3MB, time=64.35
memory used=633.2MB, alloc=4.3MB, time=64.73
memory used=637.0MB, alloc=4.3MB, time=65.12
memory used=640.8MB, alloc=4.3MB, time=65.50
memory used=644.7MB, alloc=4.3MB, time=65.89
memory used=648.5MB, alloc=4.3MB, time=66.29
x[1] = -4.7189988375051750908203794614047
y[1] (analytic) = 7.0192005227249552414036362756673
y[1] (numeric) = 7.0192005227745506599128321604946
absolute error = 4.95954185091958848273e-11
relative error = 7.0656791109797537882219576295106e-10 %
Correct digits = 11
h = 7.4018747485616897726593803398376e-06
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.00662
Order of pole = 2.082
memory used=652.3MB, alloc=4.3MB, time=66.69
memory used=656.1MB, alloc=4.3MB, time=67.07
memory used=659.9MB, alloc=4.3MB, time=67.45
memory used=663.7MB, alloc=4.3MB, time=67.84
memory used=667.5MB, alloc=4.3MB, time=68.22
memory used=671.4MB, alloc=4.3MB, time=68.61
memory used=675.2MB, alloc=4.3MB, time=69.01
memory used=679.0MB, alloc=4.3MB, time=69.40
memory used=682.8MB, alloc=4.3MB, time=69.79
memory used=686.6MB, alloc=4.3MB, time=70.18
x[1] = -4.7179995844141192627010704450642
y[1] (analytic) = 7.1831021415986267633341966659173
y[1] (numeric) = 7.1831021416482247839212188116595
absolute error = 4.95980205870221457422e-11
relative error = 6.9048190613622427474943593099295e-10 %
Correct digits = 11
h = 7.4018747485616897726593803398376e-06
TOP MAIN SOLVE Loop
memory used=690.4MB, alloc=4.3MB, time=70.59
Real estimate of pole used
Radius of convergence = 0.005619
Order of pole = 2.082
memory used=694.3MB, alloc=4.3MB, time=71.00
memory used=698.1MB, alloc=4.3MB, time=71.41
memory used=701.9MB, alloc=4.3MB, time=71.82
memory used=705.7MB, alloc=4.3MB, time=72.22
memory used=709.5MB, alloc=4.3MB, time=72.63
memory used=713.3MB, alloc=4.3MB, time=73.03
memory used=717.1MB, alloc=4.3MB, time=73.44
memory used=721.0MB, alloc=4.3MB, time=73.84
memory used=724.8MB, alloc=4.3MB, time=74.24
memory used=728.6MB, alloc=4.3MB, time=74.64
x[1] = -4.7169936008708515074926050232893
y[1] (analytic) = 7.3806985598570312191783175925078
y[1] (numeric) = 7.3806985599066370375591692258577
absolute error = 4.96058183808516333499e-11
relative error = 6.7210194236428115691500425329160e-10 %
Correct digits = 11
h = 7.1780672363501562339080650281135e-06
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.004612
Order of pole = 2.082
memory used=732.4MB, alloc=4.3MB, time=75.04
memory used=736.2MB, alloc=4.3MB, time=75.44
memory used=740.0MB, alloc=4.3MB, time=75.81
memory used=743.8MB, alloc=4.3MB, time=76.20
memory used=747.7MB, alloc=4.3MB, time=76.58
memory used=751.5MB, alloc=4.3MB, time=76.97
memory used=755.3MB, alloc=4.3MB, time=77.35
memory used=759.1MB, alloc=4.3MB, time=77.75
memory used=762.9MB, alloc=4.3MB, time=78.15
memory used=766.7MB, alloc=4.3MB, time=78.55
memory used=770.6MB, alloc=4.3MB, time=78.93
x[1] = -4.7159958495249988357760918022543
y[1] (analytic) = 7.6249173253415716821830046569482
y[1] (numeric) = 7.6249173253912030949886541689929
absolute error = 4.96314128056495120447e-11
relative error = 6.5091083205188962447076720745528e-10 %
Correct digits = 11
h = 7.1780672363501562339080650281135e-06
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.003612
Order of pole = 2.082
memory used=774.4MB, alloc=4.3MB, time=79.32
memory used=778.2MB, alloc=4.3MB, time=79.71
memory used=782.0MB, alloc=4.3MB, time=80.09
memory used=785.8MB, alloc=4.3MB, time=80.48
memory used=789.6MB, alloc=4.3MB, time=80.86
memory used=793.4MB, alloc=4.3MB, time=81.25
memory used=797.3MB, alloc=4.3MB, time=81.63
memory used=801.1MB, alloc=4.3MB, time=82.01
memory used=804.9MB, alloc=4.3MB, time=82.40
memory used=808.7MB, alloc=4.3MB, time=82.79
memory used=812.5MB, alloc=4.3MB, time=83.17
memory used=816.3MB, alloc=4.3MB, time=83.56
memory used=820.1MB, alloc=4.3MB, time=83.94
x[1] = -4.7149947765985868566853158310973
y[1] (analytic) = 7.9500181338446667189489927543672
y[1] (numeric) = 7.9500181338943634682180205879029
absolute error = 4.96967492690278335357e-11
relative error = 6.2511491712779588795355432351531e-10 %
Correct digits = 11
h = 6.0128808010874226107974205801600e-06
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 0.0008903
Order of pole = 0.5584
memory used=824.0MB, alloc=4.3MB, time=84.33
memory used=827.8MB, alloc=4.3MB, time=84.72
memory used=831.6MB, alloc=4.3MB, time=85.11
memory used=835.4MB, alloc=4.3MB, time=85.50
memory used=839.2MB, alloc=4.3MB, time=85.89
memory used=843.0MB, alloc=4.3MB, time=86.28
memory used=846.8MB, alloc=4.3MB, time=86.67
memory used=850.7MB, alloc=4.3MB, time=87.05
memory used=854.5MB, alloc=4.3MB, time=87.44
memory used=858.3MB, alloc=4.3MB, time=87.83
memory used=862.1MB, alloc=4.3MB, time=88.22
memory used=865.9MB, alloc=4.3MB, time=88.61
memory used=869.7MB, alloc=4.3MB, time=88.99
memory used=873.6MB, alloc=4.3MB, time=89.39
memory used=877.4MB, alloc=4.3MB, time=89.79
memory used=881.2MB, alloc=4.3MB, time=90.19
memory used=885.0MB, alloc=4.3MB, time=90.59
memory used=888.8MB, alloc=4.3MB, time=90.99
memory used=892.6MB, alloc=4.3MB, time=91.39
memory used=896.4MB, alloc=4.3MB, time=91.80
memory used=900.3MB, alloc=4.3MB, time=92.19
memory used=904.1MB, alloc=4.3MB, time=92.58
memory used=907.9MB, alloc=4.3MB, time=92.97
memory used=911.7MB, alloc=4.3MB, time=93.37
memory used=915.5MB, alloc=4.3MB, time=93.77
memory used=919.3MB, alloc=4.3MB, time=94.16
memory used=923.1MB, alloc=4.3MB, time=94.55
memory used=927.0MB, alloc=4.3MB, time=94.93
memory used=930.8MB, alloc=4.3MB, time=95.33
memory used=934.6MB, alloc=4.3MB, time=95.73
memory used=938.4MB, alloc=4.3MB, time=96.12
memory used=942.2MB, alloc=4.3MB, time=96.50
memory used=946.0MB, alloc=4.3MB, time=96.88
memory used=949.8MB, alloc=4.3MB, time=97.26
memory used=953.7MB, alloc=4.3MB, time=97.64
memory used=957.5MB, alloc=4.3MB, time=98.02
memory used=961.3MB, alloc=4.3MB, time=98.39
memory used=965.1MB, alloc=4.3MB, time=98.77
memory used=968.9MB, alloc=4.3MB, time=99.15
memory used=972.7MB, alloc=4.3MB, time=99.53
memory used=976.6MB, alloc=4.3MB, time=99.91
memory used=980.4MB, alloc=4.3MB, time=100.30
memory used=984.2MB, alloc=4.3MB, time=100.69
memory used=988.0MB, alloc=4.3MB, time=101.07
memory used=991.8MB, alloc=4.3MB, time=101.46
memory used=995.6MB, alloc=4.3MB, time=101.86
memory used=999.4MB, alloc=4.3MB, time=102.25
memory used=1003.3MB, alloc=4.3MB, time=102.64
memory used=1007.1MB, alloc=4.3MB, time=103.02
memory used=1010.9MB, alloc=4.3MB, time=103.42
memory used=1014.7MB, alloc=4.3MB, time=103.81
memory used=1018.5MB, alloc=4.3MB, time=104.20
memory used=1022.3MB, alloc=4.3MB, time=104.59
memory used=1026.1MB, alloc=4.3MB, time=104.98
memory used=1030.0MB, alloc=4.3MB, time=105.37
memory used=1033.8MB, alloc=4.3MB, time=105.75
memory used=1037.6MB, alloc=4.3MB, time=106.14
memory used=1041.4MB, alloc=4.3MB, time=106.53
memory used=1045.2MB, alloc=4.3MB, time=106.91
memory used=1049.0MB, alloc=4.3MB, time=107.30
memory used=1052.8MB, alloc=4.3MB, time=107.68
memory used=1056.7MB, alloc=4.3MB, time=108.08
memory used=1060.5MB, alloc=4.3MB, time=108.47
memory used=1064.3MB, alloc=4.3MB, time=108.86
memory used=1068.1MB, alloc=4.3MB, time=109.25
memory used=1071.9MB, alloc=4.3MB, time=109.64
memory used=1075.7MB, alloc=4.3MB, time=110.04
memory used=1079.6MB, alloc=4.3MB, time=110.43
memory used=1083.4MB, alloc=4.3MB, time=110.82
memory used=1087.2MB, alloc=4.3MB, time=111.22
memory used=1091.0MB, alloc=4.3MB, time=111.61
memory used=1094.8MB, alloc=4.3MB, time=112.00
memory used=1098.6MB, alloc=4.3MB, time=112.40
memory used=1102.4MB, alloc=4.3MB, time=112.79
memory used=1106.3MB, alloc=4.3MB, time=113.19
memory used=1110.1MB, alloc=4.3MB, time=113.59
memory used=1113.9MB, alloc=4.3MB, time=113.99
memory used=1117.7MB, alloc=4.3MB, time=114.39
memory used=1121.5MB, alloc=4.3MB, time=114.79
memory used=1125.3MB, alloc=4.3MB, time=115.18
memory used=1129.1MB, alloc=4.3MB, time=115.57
memory used=1133.0MB, alloc=4.3MB, time=115.96
memory used=1136.8MB, alloc=4.3MB, time=116.35
memory used=1140.6MB, alloc=4.3MB, time=116.73
memory used=1144.4MB, alloc=4.3MB, time=117.13
memory used=1148.2MB, alloc=4.3MB, time=117.54
memory used=1152.0MB, alloc=4.3MB, time=117.94
memory used=1155.9MB, alloc=4.3MB, time=118.33
memory used=1159.7MB, alloc=4.3MB, time=118.73
memory used=1163.5MB, alloc=4.3MB, time=119.12
memory used=1167.3MB, alloc=4.3MB, time=119.51
memory used=1171.1MB, alloc=4.3MB, time=119.91
memory used=1174.9MB, alloc=4.3MB, time=120.31
memory used=1178.7MB, alloc=4.3MB, time=120.69
memory used=1182.6MB, alloc=4.3MB, time=121.09
memory used=1186.4MB, alloc=4.3MB, time=121.48
memory used=1190.2MB, alloc=4.3MB, time=121.87
x[1] = -4.7139996865112451801785718190537
y[1] (analytic) = 8.4310830406105166121529591692184
y[1] (numeric) = 8.4310830406602573330214607326495
absolute error = 4.97407208685015634311e-11
relative error = 5.8996834248829446582897726334475e-10 %
Correct digits = 11
h = 6.0671232888829560077972685025699e-07
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.001613
Order of pole = 2.082
memory used=1194.0MB, alloc=4.3MB, time=122.26
memory used=1197.8MB, alloc=4.3MB, time=122.66
memory used=1201.6MB, alloc=4.3MB, time=123.06
memory used=1205.4MB, alloc=4.3MB, time=123.46
memory used=1209.3MB, alloc=4.3MB, time=123.87
memory used=1213.1MB, alloc=4.3MB, time=124.27
memory used=1216.9MB, alloc=4.3MB, time=124.68
memory used=1220.7MB, alloc=4.3MB, time=125.08
memory used=1224.5MB, alloc=4.3MB, time=125.49
memory used=1228.3MB, alloc=4.3MB, time=125.89
memory used=1232.1MB, alloc=4.3MB, time=126.28
memory used=1236.0MB, alloc=4.3MB, time=126.68
memory used=1239.8MB, alloc=4.3MB, time=127.08
memory used=1243.6MB, alloc=4.3MB, time=127.48
memory used=1247.4MB, alloc=4.3MB, time=127.88
memory used=1251.2MB, alloc=4.3MB, time=128.27
memory used=1255.0MB, alloc=4.3MB, time=128.67
memory used=1258.9MB, alloc=4.3MB, time=129.07
memory used=1262.7MB, alloc=4.3MB, time=129.47
memory used=1266.5MB, alloc=4.3MB, time=129.87
memory used=1270.3MB, alloc=4.3MB, time=130.27
memory used=1274.1MB, alloc=4.3MB, time=130.68
memory used=1277.9MB, alloc=4.3MB, time=131.07
memory used=1281.7MB, alloc=4.3MB, time=131.46
memory used=1285.6MB, alloc=4.3MB, time=131.85
memory used=1289.4MB, alloc=4.3MB, time=132.24
memory used=1293.2MB, alloc=4.3MB, time=132.64
memory used=1297.0MB, alloc=4.3MB, time=133.03
memory used=1300.8MB, alloc=4.3MB, time=133.42
memory used=1304.6MB, alloc=4.3MB, time=133.81
memory used=1308.4MB, alloc=4.3MB, time=134.20
memory used=1312.3MB, alloc=4.3MB, time=134.60
memory used=1316.1MB, alloc=4.3MB, time=135.00
memory used=1319.9MB, alloc=4.3MB, time=135.40
memory used=1323.7MB, alloc=4.3MB, time=135.79
memory used=1327.5MB, alloc=4.3MB, time=136.18
memory used=1331.3MB, alloc=4.3MB, time=136.57
memory used=1335.1MB, alloc=4.3MB, time=136.98
memory used=1339.0MB, alloc=4.3MB, time=137.41
memory used=1342.8MB, alloc=4.3MB, time=137.83
memory used=1346.6MB, alloc=4.3MB, time=138.24
memory used=1350.4MB, alloc=4.3MB, time=138.65
memory used=1354.2MB, alloc=4.3MB, time=139.06
memory used=1358.0MB, alloc=4.3MB, time=139.47
memory used=1361.9MB, alloc=4.3MB, time=139.88
memory used=1365.7MB, alloc=4.3MB, time=140.28
memory used=1369.5MB, alloc=4.3MB, time=140.67
memory used=1373.3MB, alloc=4.3MB, time=141.08
memory used=1377.1MB, alloc=4.3MB, time=141.48
memory used=1380.9MB, alloc=4.3MB, time=141.88
memory used=1384.7MB, alloc=4.3MB, time=142.28
memory used=1388.6MB, alloc=4.3MB, time=142.69
memory used=1392.4MB, alloc=4.3MB, time=143.09
memory used=1396.2MB, alloc=4.3MB, time=143.50
memory used=1400.0MB, alloc=4.3MB, time=143.90
memory used=1403.8MB, alloc=4.3MB, time=144.31
memory used=1407.6MB, alloc=4.3MB, time=144.71
memory used=1411.4MB, alloc=4.3MB, time=145.12
memory used=1415.3MB, alloc=4.3MB, time=145.52
memory used=1419.1MB, alloc=4.3MB, time=145.93
memory used=1422.9MB, alloc=4.3MB, time=146.34
memory used=1426.7MB, alloc=4.3MB, time=146.75
memory used=1430.5MB, alloc=4.3MB, time=147.16
memory used=1434.3MB, alloc=4.3MB, time=147.56
memory used=1438.2MB, alloc=4.3MB, time=147.97
memory used=1442.0MB, alloc=4.3MB, time=148.37
memory used=1445.8MB, alloc=4.3MB, time=148.77
memory used=1449.6MB, alloc=4.3MB, time=149.18
memory used=1453.4MB, alloc=4.3MB, time=149.58
memory used=1457.2MB, alloc=4.3MB, time=149.97
memory used=1461.0MB, alloc=4.3MB, time=150.37
memory used=1464.9MB, alloc=4.3MB, time=150.77
memory used=1468.7MB, alloc=4.3MB, time=151.17
memory used=1472.5MB, alloc=4.3MB, time=151.56
memory used=1476.3MB, alloc=4.3MB, time=151.96
memory used=1480.1MB, alloc=4.3MB, time=152.35
memory used=1483.9MB, alloc=4.3MB, time=152.75
memory used=1487.7MB, alloc=4.3MB, time=153.16
memory used=1491.6MB, alloc=4.3MB, time=153.55
memory used=1495.4MB, alloc=4.3MB, time=153.95
memory used=1499.2MB, alloc=4.3MB, time=154.35
memory used=1503.0MB, alloc=4.3MB, time=154.75
memory used=1506.8MB, alloc=4.3MB, time=155.15
memory used=1510.6MB, alloc=4.3MB, time=155.55
memory used=1514.4MB, alloc=4.3MB, time=155.95
memory used=1518.3MB, alloc=4.3MB, time=156.35
memory used=1522.1MB, alloc=4.3MB, time=156.76
memory used=1525.9MB, alloc=4.3MB, time=157.16
memory used=1529.7MB, alloc=4.3MB, time=157.57
memory used=1533.5MB, alloc=4.3MB, time=157.97
memory used=1537.3MB, alloc=4.3MB, time=158.38
memory used=1541.2MB, alloc=4.3MB, time=158.78
memory used=1545.0MB, alloc=4.3MB, time=159.18
memory used=1548.8MB, alloc=4.3MB, time=159.58
memory used=1552.6MB, alloc=4.3MB, time=159.98
memory used=1556.4MB, alloc=4.3MB, time=160.37
memory used=1560.2MB, alloc=4.3MB, time=160.76
memory used=1564.0MB, alloc=4.3MB, time=161.16
memory used=1567.9MB, alloc=4.3MB, time=161.55
memory used=1571.7MB, alloc=4.3MB, time=161.95
memory used=1575.5MB, alloc=4.3MB, time=162.34
memory used=1579.3MB, alloc=4.3MB, time=162.74
memory used=1583.1MB, alloc=4.3MB, time=163.13
memory used=1586.9MB, alloc=4.3MB, time=163.52
memory used=1590.7MB, alloc=4.3MB, time=163.91
memory used=1594.6MB, alloc=4.3MB, time=164.31
memory used=1598.4MB, alloc=4.3MB, time=164.72
memory used=1602.2MB, alloc=4.3MB, time=165.11
memory used=1606.0MB, alloc=4.3MB, time=165.51
memory used=1609.8MB, alloc=4.3MB, time=165.90
memory used=1613.6MB, alloc=4.3MB, time=166.30
memory used=1617.4MB, alloc=4.3MB, time=166.69
memory used=1621.3MB, alloc=4.3MB, time=167.09
memory used=1625.1MB, alloc=4.3MB, time=167.48
memory used=1628.9MB, alloc=4.3MB, time=167.87
memory used=1632.7MB, alloc=4.3MB, time=168.26
memory used=1636.5MB, alloc=4.3MB, time=168.65
memory used=1640.3MB, alloc=4.3MB, time=169.04
memory used=1644.2MB, alloc=4.3MB, time=169.43
memory used=1648.0MB, alloc=4.3MB, time=169.82
memory used=1651.8MB, alloc=4.3MB, time=170.21
memory used=1655.6MB, alloc=4.3MB, time=170.60
memory used=1659.4MB, alloc=4.3MB, time=170.99
memory used=1663.2MB, alloc=4.3MB, time=171.37
memory used=1667.0MB, alloc=4.3MB, time=171.76
memory used=1670.9MB, alloc=4.3MB, time=172.14
memory used=1674.7MB, alloc=4.3MB, time=172.53
x[1] = -4.7129998245932372690284868291225
y[1] (analytic) = 9.400668671320971091078683888934
y[1] (numeric) = 9.4006686713707129291421200970322
absolute error = 4.97418380634362080982e-11
relative error = 5.2913085018287898591904428043226e-10 %
Correct digits = 11
h = 6.0671232888829560077972685025699e-07
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.0006118
Order of pole = 2.082
memory used=1678.5MB, alloc=4.3MB, time=172.92
memory used=1682.3MB, alloc=4.3MB, time=173.30
memory used=1686.1MB, alloc=4.3MB, time=173.68
memory used=1689.9MB, alloc=4.3MB, time=174.06
memory used=1693.7MB, alloc=4.3MB, time=174.44
memory used=1697.6MB, alloc=4.3MB, time=174.83
memory used=1701.4MB, alloc=4.3MB, time=175.21
memory used=1705.2MB, alloc=4.3MB, time=175.59
memory used=1709.0MB, alloc=4.3MB, time=175.98
memory used=1712.8MB, alloc=4.3MB, time=176.37
memory used=1716.6MB, alloc=4.3MB, time=176.76
memory used=1720.5MB, alloc=4.3MB, time=177.14
memory used=1724.3MB, alloc=4.3MB, time=177.52
memory used=1728.1MB, alloc=4.3MB, time=177.90
memory used=1731.9MB, alloc=4.3MB, time=178.28
memory used=1735.7MB, alloc=4.3MB, time=178.66
memory used=1739.5MB, alloc=4.3MB, time=179.04
memory used=1743.3MB, alloc=4.3MB, time=179.43
memory used=1747.2MB, alloc=4.3MB, time=179.82
Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
Iterations = 5786
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 2 Minutes 59 Seconds
Expected Time Remaining = 1 Hours 41 Minutes 29 Seconds
Optimized Time Remaining = 1 Hours 41 Minutes 27 Seconds
Expected Total Time = 1 Hours 44 Minutes 27 Seconds
Time to Timeout Unknown
Percent Done = 2.872 %
> quit
memory used=1750.5MB, alloc=4.3MB, time=180.12