|\^/| 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float or
omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[1] := array_m1[1] * array_const_3D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp4[1] / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp1[2] := array_m1[2] * array_const_3D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := (array_tmp1[2] - array_tmp2[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp4[2] - array_tmp5[1] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp1[3] := array_m1[3] * array_const_3D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp2[3] := (array_tmp1[3] - array_tmp2[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp4[3] - array_tmp5[2] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp1[4] := array_m1[4] * array_const_3D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp2[4] := (array_tmp1[4] - array_tmp2[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp4[4] - array_tmp5[3] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp1[5] := array_m1[5] * array_const_3D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp2[5] := (array_tmp1[5] - array_tmp2[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp4[5] - array_tmp5[4] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[kkk] := array_m1[kkk] * array_const_3D0[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp2[kkk] := -ats(kkk,array_x,array_tmp2,2) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := -ats(kkk,array_x,array_tmp3,2) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := -ats(kkk,array_x,array_tmp4,2) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := -ats(kkk,array_x,array_tmp5,2) / array_x[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_const_3D0[1];
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_tmp4[1]/array_x[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_m1[2]*array_const_3D0[1];
array_tmp2[2] := (array_tmp1[2] - array_tmp2[1]*array_x[2])/array_x[1];
array_tmp3[2] := (array_tmp2[2] - array_tmp3[1]*array_x[2])/array_x[1];
array_tmp4[2] := (array_tmp3[2] - array_tmp4[1]*array_x[2])/array_x[1];
array_tmp5[2] := (array_tmp4[2] - array_tmp5[1]*array_x[2])/array_x[1];
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_m1[3]*array_const_3D0[1];
array_tmp2[3] := (array_tmp1[3] - array_tmp2[2]*array_x[2])/array_x[1];
array_tmp3[3] := (array_tmp2[3] - array_tmp3[2]*array_x[2])/array_x[1];
array_tmp4[3] := (array_tmp3[3] - array_tmp4[2]*array_x[2])/array_x[1];
array_tmp5[3] := (array_tmp4[3] - array_tmp5[2]*array_x[2])/array_x[1];
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_m1[4]*array_const_3D0[1];
array_tmp2[4] := (array_tmp1[4] - array_tmp2[3]*array_x[2])/array_x[1];
array_tmp3[4] := (array_tmp2[4] - array_tmp3[3]*array_x[2])/array_x[1];
array_tmp4[4] := (array_tmp3[4] - array_tmp4[3]*array_x[2])/array_x[1];
array_tmp5[4] := (array_tmp4[4] - array_tmp5[3]*array_x[2])/array_x[1];
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_m1[5]*array_const_3D0[1];
array_tmp2[5] := (array_tmp1[5] - array_tmp2[4]*array_x[2])/array_x[1];
array_tmp3[5] := (array_tmp2[5] - array_tmp3[4]*array_x[2])/array_x[1];
array_tmp4[5] := (array_tmp3[5] - array_tmp4[4]*array_x[2])/array_x[1];
array_tmp5[5] := (array_tmp4[5] - array_tmp5[4]*array_x[2])/array_x[1];
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_m1[kkk]*array_const_3D0[1];
array_tmp2[kkk] := -ats(kkk, array_x, array_tmp2, 2)/array_x[1];
array_tmp3[kkk] := -ats(kkk, array_x, array_tmp3, 2)/array_x[1];
array_tmp4[kkk] := -ats(kkk, array_x, array_tmp4, 2)/array_x[1];
array_tmp5[kkk] := -ats(kkk, array_x, array_tmp5, 2)/array_x[1];
array_tmp6[kkk] := array_tmp5[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_tmp6[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(1.0/x/x/x);
> end;
exact_soln_y := proc(x) return 1.0/(x*x*x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_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/sing5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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 := -1.0;");
> omniout_str(ALWAYS,"x_end := -0.7;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0/x/x/x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_3D0[1] := 3.0;
> 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 := -1.0;
> x_end := -0.7;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_log10normmin := -glob_large_float ;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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,"2013-01-13T01:59:51-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing5")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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," 156 | ")
> ;
> logitem_str(html_log_file,"sing5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing5 maple results")
> ;
> logitem_str(html_log_file,"Languages compared - single equations")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year,
glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_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/sing5postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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 := -1.0;");
omniout_str(ALWAYS, "x_end := -0.7;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0/x/x/x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
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 := -1.0;
x_end := -0.7;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_log10normmin := -glob_large_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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, "2013-01-13T01:59:51-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing5");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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, " 156 | ");
logitem_str(html_log_file,
"sing5 diffeq.mxt");
logitem_str(html_log_file,
"sing5 maple results")
;
logitem_str(html_log_file,
"Languages compared - single equations");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/sing5postode.ode#################
diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := -0.7;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0/x/x/x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.3
estimated_steps = 300
step_error = 3.3333333333333333333333333333333e-13
est_needed_step_err = 3.3333333333333333333333333333333e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 4.0404069204059829059829059829059e-78
max_value3 = 4.0404069204059829059829059829059e-78
value3 = 4.0404069204059829059829059829059e-78
best_h = 0.001
START of Soultion
x[1] = -1
y[1] (analytic) = -1
y[1] (numeric) = -1
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = -1
y[1] (numeric) = -1
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.999
y[1] (analytic) = -1.0030060100150210280360450550661
y[1] (numeric) = -1.0030060100150210175150131366772
absolute error = 1.05210319183889e-17
relative error = 1.0489500375208456548311100000000e-15 %
Correct digits = 16
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.998
y[1] (analytic) = -1.0060240802406737966195482277442
y[1] (numeric) = -1.0060240802406737754822986403582
absolute error = 2.11372495873860e-17
relative error = 2.1010679567758735932911999999998e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used
Radius of convergence = 0.998
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -0.997
y[1] (analytic) = -1.0090542712201234910283314761
y[1] (numeric) = -1.0090542712201234591787206587356
absolute error = 3.18496108173644e-17
relative error = 3.1563823399560697169961200000000e-15 %
Correct digits = 16
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.996
y[1] (analytic) = -1.0120966438616192807876074547054
y[1] (numeric) = -1.0120966438616192381285234235307
absolute error = 4.26590840311747e-17
relative error = 4.2149219928652721990419200000005e-15 %
Correct digits = 16
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.8319
Order of pole = 4.877e-27
TOP MAIN SOLVE Loop
x[1] = -0.995
y[1] (analytic) = -1.0151512594410653301861952371894
y[1] (numeric) = -1.0151512594410652766195468446405
absolute error = 5.35666483925489e-17
relative error = 5.2767159469459058598887500000003e-15 %
Correct digits = 16
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.7904
Order of pole = 2.517e-27
TOP MAIN SOLVE Loop
x[1] = -0.994
y[1] (analytic) = -1.0182181796046125218370125452544
y[1] (numeric) = -1.0182181796046124572637186090651
absolute error = 6.45732939361893e-17
relative error = 6.3417934613251510827511200000000e-15 %
Correct digits = 16
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.993
y[1] (analytic) = -1.0212974663712710812022922527324
y[1] (numeric) = -1.0212974663712710055222705531658
absolute error = 7.56800216995666e-17
relative error = 7.4101840248818094738856200000005e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used
Radius of convergence = 0.993
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.992
y[1] (analytic) = -1.0243891821355442919002383270116
y[1] (numeric) = -1.0243891821355442050123944705604
absolute error = 8.68878438564512e-17
relative error = 8.4819173583340755327385599999993e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used
Radius of convergence = 0.992
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.991
y[1] (analytic) = -1.0274933896700834935271733588728
y[1] (numeric) = -1.0274933896700833953293895066732
absolute error = 9.81977838521996e-17
relative error = 9.5570234163481867049291599999994e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used
Radius of convergence = 0.991
Order of pole = 2.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = -1.0306101521283645556678920621376
y[1] (numeric) = -1.0306101521283644460570155213115
absolute error = 1.096108765408261e-16
relative error = 1.0635532389668702400389999999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
memory used=3.8MB, alloc=3.0MB, time=0.19
TOP MAIN SOLVE Loop
x[1] = -0.989
y[1] (analytic) = -1.0337395330473860237271816069859
y[1] (numeric) = -1.033739533047385902599013283106
absolute error = 1.211281683238799e-16
relative error = 1.1717474707270139261955310000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.8443
Order of pole = 6.53e-28
TOP MAIN SOLVE Loop
x[1] = -0.988
y[1] (analytic) = -1.0368815963503891341975628073193
y[1] (numeric) = -1.0368815963503890014468455161625
absolute error = 1.327507172911568e-16
relative error = 1.2802881038530545581864960000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.987
y[1] (analytic) = -1.040036406349599898982511894951
y[1] (numeric) = -1.0400364063495997545029185316821
absolute error = 1.444795933632689e-16
relative error = 1.3891782295426997113052670000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.2284
Order of pole = 3.678e-27
TOP MAIN SOLVE Loop
x[1] = -0.986
y[1] (analytic) = -1.0432040277489934604210102726637
y[1] (numeric) = -1.0432040277489933041051318365619
absolute error = 1.563158784361018e-16
relative error = 1.4984209634753552359506080000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.985
y[1] (analytic) = -1.0463845256470809207085121942383
y[1] (numeric) = -1.0463845256470807524478456670545
absolute error = 1.682606665271838e-16
relative error = 1.6080194460361684881967499999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.985
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.984
y[1] (analytic) = -1.0495779655397188514815943321043
y[1] (numeric) = -1.04957796553971867116653040811
absolute error = 1.803150639239943e-16
relative error = 1.7179768425423436854174720000001e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.8016
Order of pole = 4.759e-27
TOP MAIN SOLVE Loop
x[1] = -0.983
y[1] (analytic) = -1.0527844133229416914289368831288
y[1] (numeric) = -1.0527844133229414989487475488867
absolute error = 1.924801893342421e-16
relative error = 1.8282963434717834166926270000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.982
y[1] (analytic) = -1.0560039352958172419101671644937
y[1] (numeric) = -1.0560039352958170371529931263562
absolute error = 2.047571740381375e-16
relative error = 1.9389811646940415423210000000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.981
y[1] (analytic) = -1.0592365981633254727067612653502
y[1] (numeric) = -1.0592365981633252555595992226599
absolute error = 2.171471620426903e-16
relative error = 2.0500345477036473568213229999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.981
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = -1.0624824690392608521959387670103
y[1] (numeric) = -1.06248246903926062254462852895
absolute error = 2.296513102380603e-16
relative error = 2.1614597598558044987760000000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.979
y[1] (analytic) = -1.0657416154491584184295952209222
y[1] (numeric) = -1.0657416154491581761588066649297
absolute error = 2.422707885559925e-16
relative error = 2.2732600946045173353095749999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.979
Order of pole = 2.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.978
y[1] (analytic) = -1.0690141053332438098160963061637
y[1] (numeric) = -1.0690141053332435548093161758011
absolute error = 2.550067801303626e-16
relative error = 2.3854388717431312679423520000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.977
y[1] (analytic) = -1.0723000070494074763435096902299
y[1] (numeric) = -1.0723000070494072084830282303612
absolute error = 2.678604814598687e-16
relative error = 2.4979994376473664910442709999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.976
y[1] (analytic) = -1.0755993893762032945488829461497
y[1] (numeric) = -1.0755993893762030137157803732551
absolute error = 2.808331025728946e-16
relative error = 2.6109451655208218297384959999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.975
y[1] (analytic) = -1.0789123215158718117297998954803
y[1] (numeric) = -1.0789123215158715178039327009
absolute error = 2.939258671945803e-16
relative error = 2.7242794556430170024531250000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.975
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.974
y[1] (analytic) = -1.0822388730973883472119790717858
y[1] (numeric) = -1.0822388730973880400719661556567
absolute error = 3.071400129161291e-16
relative error = 2.8380057356199792612973840000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.974
Order of pole = 1.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.973
y[1] (analytic) = -1.0855791141795361808304364754183
y[1] (numeric) = -1.0855791141795358603536451090342
absolute error = 3.204767913663841e-16
relative error = 2.9521274606374080538845970000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.972
y[1] (analytic) = -1.0889331152540050611520445424867
y[1] (numeric) = -1.0889331152540047272145761567797
absolute error = 3.339374683857070e-16
relative error = 3.0666481137164479182393600000002e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.971
y[1] (analytic) = -1.0923009472485152683645087474632
y[1] (numeric) = -1.0923009472485149208411845452694
absolute error = 3.475233242021938e-16
relative error = 3.1815712059721110705281180000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.971
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (analytic) = -1.0956826815299674691811853752658
y[1] (numeric) = -1.0956826815299671079455317650077
absolute error = 3.612356536102581e-16
relative error = 3.2969002768743509090130000000001e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.5668
Order of pole = 6.327e-27
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=0.42
x[1] = -0.969
y[1] (analytic) = -1.0990783899076186035631160806292
y[1] (numeric) = -1.0990783899076182284873499290099
absolute error = 3.750757661516193e-16
relative error = 3.4126388945118440065133370000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.969
Order of pole = 6.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.968
y[1] (analytic) = -1.1024881446362840455394987810185
y[1] (numeric) = -1.1024881446362836564945124822888
absolute error = 3.890449862987297e-16
relative error = 3.5287906558585030966359040000002e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.967
y[1] (analytic) = -1.1059120184195662829158966860222
y[1] (numeric) = -1.1059120184195658797712430453467
absolute error = 4.031446536406755e-16
relative error = 3.6453591870427482740305649999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.966
y[1] (analytic) = -1.1093500844131103631961590004675
y[1] (numeric) = -1.1093500844131099458200359288804
absolute error = 4.173761230715871e-16
relative error = 3.7623481436195627420342159999997e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.965
y[1] (analytic) = -1.1128024162278863556096439352199
y[1] (numeric) = -1.1128024162278859238688789536224
absolute error = 4.317407649815975e-16
relative error = 3.8797612108453854731968749999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.965
Order of pole = 5.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.964
y[1] (analytic) = -1.1162690879334990817302578077933
y[1] (numeric) = -1.1162690879334986354902923574094
absolute error = 4.462399654503839e-16
relative error = 3.9976021039558547829196159999998e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.963
y[1] (analytic) = -1.1197501740615253697984187777124
y[1] (numeric) = -1.1197501740615249089232923343826
absolute error = 4.608751264433298e-16
relative error = 4.1158745684464321370424059999998e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.962
y[1] (analytic) = -1.1232457496088790905116906474093
y[1] (numeric) = -1.1232457496088786148640246370609
absolute error = 4.756476660103484e-16
relative error = 4.2345823803559619183139519999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.961
y[1] (analytic) = -1.1267558900412042347348866939516
y[1] (numeric) = -1.126755890041203744175868206548
absolute error = 4.905590184874036e-16
relative error = 4.3537293465531774713265160000002e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = -1.1302806712962962962962962962964
y[1] (numeric) = -1.1302806712962957906856615955269
absolute error = 5.056106347007695e-16
relative error = 4.4733193050262000435199999999996e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.96
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.959
y[1] (analytic) = -1.1338201697875522257837239681508
y[1] (numeric) = -1.1338201697875517049797417940834
absolute error = 5.208039821740674e-16
relative error = 4.5933561251750551279892459999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.958
y[1] (analytic) = -1.1373744624074492240326423195072
y[1] (numeric) = -1.137374462407448687892096981384
absolute error = 5.361405453381232e-16
relative error = 4.7138437081072601390275840000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.958
Order of pole = 5.6e-29
TOP MAIN SOLVE Loop
x[1] = -0.957
y[1] (analytic) = -1.1409436265310526468093437893195
y[1] (numeric) = -1.1409436265310520951875180456358
absolute error = 5.516218257436837e-16
relative error = 4.8347859869364931312396410000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.956
y[1] (analytic) = -1.1445277400195532950349324516209
y[1] (numeric) = -1.1445277400195527277855901745853
absolute error = 5.672493422770356e-16
relative error = 4.9561869270843939656424960000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.955
y[1] (analytic) = -1.1481268812238343677717340059826
y[1] (numeric) = -1.1481268812238337847471026274124
absolute error = 5.830246313785702e-16
relative error = 5.0780505265855366475552500000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.955
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.954
y[1] (analytic) = -1.1517411289880683581026319837056
y[1] (numeric) = -1.1517411289880677591533847193699
absolute error = 5.989492472643357e-16
relative error = 5.2003808163955965504390479999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.954
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.953
y[1] (analytic) = -1.1553705626533441749763796331014
y[1] (numeric) = -1.1553705626533435599516174824792
absolute error = 6.150247621506222e-16
relative error = 5.3231818607027587907072939999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.952
y[1] (analytic) = -1.1590152620613247770685140096572
y[1] (numeric) = -1.1590152620613241458157475280329
absolute error = 6.312527664816243e-16
relative error = 5.4464577572424065216701440000002e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.951
y[1] (analytic) = -1.1626753075579356077185414125254
y[1] (numeric) = -1.1626753075579349600836722522996
absolute error = 6.476348691602258e-16
relative error = 5.5702126376151188243225580000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.951
Order of pole = 8.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = -1.1663507799970841230500072896924
y[1] (numeric) = -1.166350779997083458877309507739
absolute error = 6.641726977819534e-16
relative error = 5.6944506676080229632499999999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.949
y[1] (analytic) = -1.170041760744410708461350868743
y[1] (numeric) = -1.170041760744410027593451996597
absolute error = 6.808678988721460e-16
relative error = 5.8191760475195372819895399999998e-14 %
Correct digits = 15
h = 0.001
NO POLE
memory used=11.4MB, alloc=4.3MB, time=0.67
TOP MAIN SOLVE Loop
x[1] = -0.948
y[1] (analytic) = -1.1737483316810712817925229113796
y[1] (numeric) = -1.1737483316810705840703847849916
absolute error = 6.977221381263880e-16
relative error = 5.9443930124875505629209600000002e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.6453
Order of pole = 4.632e-27
TOP MAIN SOLVE Loop
x[1] = -0.947
y[1] (analytic) = -1.1774705752075518846256681452278
y[1] (numeric) = -1.1774705752075511698885674909741
absolute error = 7.147371006542537e-16
relative error = 6.0701058328210665430180510000003e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.946
y[1] (analytic) = -1.1812085742475155663682023490042
y[1] (numeric) = -1.1812085742475148344537111225913
absolute error = 7.319144912264129e-16
relative error = 6.1963188143353619436831440000005e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.945
y[1] (analytic) = -1.1849624122516818689938143480878
y[1] (numeric) = -1.1849624122516811197377798229402
absolute error = 7.492560345251476e-16
relative error = 6.3230362986906983903804999999997e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.944
y[1] (analytic) = -1.1887321732017392235817683404827
y[1] (numeric) = -1.1887321732017384568182929421531
absolute error = 7.667634753983296e-16
relative error = 6.4502626637346215902576640000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.943
y[1] (analytic) = -1.1925179416142905730978515695743
y[1] (numeric) = -1.1925179416142897886592724526611
absolute error = 7.844385791169132e-16
relative error = 6.5780023238479119725415239999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.942
y[1] (analytic) = -1.196319802544832539201892566443
y[1] (numeric) = -1.1963198025448317369187609304517
absolute error = 8.022831316359913e-16
relative error = 6.7062597302941947646507439999998e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.941
y[1] (analytic) = -1.2001378415917684542474589010426
y[1] (numeric) = -1.2001378415917676339485190415709
absolute error = 8.202989398594717e-16
relative error = 6.8350393715732827362482569999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.941
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = -1.2039721449004555830596303323926
y[1] (numeric) = -1.2039721449004547445717984239661
absolute error = 8.384878319084265e-16
relative error = 6.9643457737782851607600000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.94
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -0.939
y[1] (analytic) = -1.207822799167286862537140083043
y[1] (numeric) = -1.2078227991672860056854826898745
absolute error = 8.568516573931685e-16
relative error = 7.0941835009565184568620150000003e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.938
y[1] (analytic) = -1.2116898916438074906261973616586
y[1] (numeric) = -1.2116898916438066152339096725464
absolute error = 8.753922876891122e-16
relative error = 7.2245571554742780195799840000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.938
Order of pole = 2.9e-29
TOP MAIN SOLVE Loop
x[1] = -0.937
y[1] (analytic) = -1.2155735101408666997554690332752
y[1] (numeric) = -1.2155735101408658056438528168003
absolute error = 8.941116162164749e-16
relative error = 7.3554713783855062963497969999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.937
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.936
y[1] (analytic) = -1.2194737430328050534055355444793
y[1] (numeric) = -1.2194737430328041403939768206038
absolute error = 9.130115587238755e-16
relative error = 7.4869308498044027452492799999995e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.936
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -0.935
y[1] (analytic) = -1.2233906792616776081121812551163
y[1] (numeric) = -1.2233906792616766760181276792253
absolute error = 9.320940535758910e-16
relative error = 7.6189402892820339435912499999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.935
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.934
y[1] (analytic) = -1.2273244083415132868716750738552
y[1] (numeric) = -1.2273244083415123355106130292266
absolute error = 9.513610620446286e-16
relative error = 7.7515044561869776120081440000002e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.933
y[1] (analytic) = -1.2312750203626108136282941788923
y[1] (numeric) = -1.2312750203626098428137255735179
absolute error = 9.708145686053744e-16
relative error = 7.8846281500900526442413280000003e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.932
y[1] (analytic) = -1.2352426059958715622802997500976
y[1] (numeric) = -1.2352426059958705718237185137174
absolute error = 9.904565812363802e-16
relative error = 8.0183162111531838783535359999998e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.7155
Order of pole = 2.932e-27
TOP MAIN SOLVE Loop
x[1] = -0.931
y[1] (analytic) = -1.2392272564971696774409549695412
y[1] (numeric) = -1.2392272564971686671518232466902
absolute error = 1.0102891317228510e-15
relative error = 8.1525735205224518177384099999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.931
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = -1.2432290637117598280365559073895
y[1] (numeric) = -1.2432290637117587977222799421926
absolute error = 1.0303142759651969e-15
relative error = 8.2874050007253788289329999999992e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.929
y[1] (analytic) = -1.2472481200787229587144071821765
y[1] (numeric) = -1.2472481200787219081803128905642
absolute error = 1.0505340942916123e-15
relative error = 8.4228156160724892766299470000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.929
Order of pole = 4.3e-29
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=0.91
x[1] = -0.928
y[1] (analytic) = -1.2512845186354504079708065111321
y[1] (numeric) = -1.2512845186354493370201147360807
absolute error = 1.0709506917750514e-15
relative error = 8.5588103730632224258785279999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.928
Order of pole = 4.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.927
y[1] (analytic) = -1.2553383530221667658930037737743
y[1] (numeric) = -1.2553383530221656743268052191133
absolute error = 1.0915661985546610e-15
relative error = 8.6953943207962046784876300000000e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.926
y[1] (analytic) = -1.2594097174864918484403777354619
y[1] (numeric) = -1.259409717486490736057607573717
absolute error = 1.1123827701617449e-15
relative error = 8.8325725513839865450184239999995e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.925
y[1] (analytic) = -1.2634987068880421692693423884075
y[1] (numeric) = -1.2634987068880410358667545380843
absolute error = 1.1334025878503232e-15
relative error = 8.9703502003722532889999999999993e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.925
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.924
y[1] (analytic) = -1.2676054167030722942343789029571
y[1] (numeric) = -1.2676054167030711396065199705978
absolute error = 1.1546278589323593e-15
relative error = 9.1087324471635861019432319999998e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.923
y[1] (analytic) = -1.2717299430291564678747211762303
y[1] (numeric) = -1.2717299430291552918139040585049
absolute error = 1.1760608171177254e-15
relative error = 9.2477245154458260775976180000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.923
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.922
y[1] (analytic) = -1.2758723825899109054232445840927
y[1] (numeric) = -1.2758723825899097077195217251154
absolute error = 1.1977037228589773e-15
relative error = 9.3873316736250849208393040000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.922
Order of pole = 4.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.921
y[1] (analytic) = -1.280032832739757148151669518471
y[1] (numeric) = -1.2800328327397559285928058174583
absolute error = 1.2195588637010127e-15
relative error = 9.5275592352634646728150470000001e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = -1.2842113914687268841949535629161
y[1] (numeric) = -1.2842113914687256425663989272272
absolute error = 1.2416285546356889e-15
relative error = 9.6684125595215531816319999999999e-14 %
Correct digits = 15
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.919
y[1] (analytic) = -1.288408157407308641378378008257
y[1] (numeric) = -1.2884081574073073774632395467841
absolute error = 1.2639151384614729e-15
relative error = 9.8098970516057305277125110000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.919
Order of pole = 1.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.918
y[1] (analytic) = -1.2926232298313367630040146085453
y[1] (numeric) = -1.2926232298313354765830284603415
absolute error = 1.2864209861482038e-15
relative error = 9.9520181632203666942080159999995e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used
Radius of convergence = 0.918
Order of pole = 6.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.917
y[1] (analytic) = -1.2968567086669230820396754298098
y[1] (numeric) = -1.2968567086669217728911782227665
absolute error = 1.3091484972070433e-15
relative error = 1.0094781393024949585137228999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.917
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.916
y[1] (analytic) = -1.3011086944954317136938005355821
y[1] (numeric) = -1.3011086944954303815937004698861
absolute error = 1.3321001000656960e-15
relative error = 1.0238192287096219226460160000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.915
y[1] (analytic) = -1.3053792885584973909547331992383
y[1] (numeric) = -1.3053792885584960356764807502589
absolute error = 1.3552782524489794e-15
relative error = 1.0382256439395360520209750000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.914
y[1] (analytic) = -1.3096685927630877723231885321479
y[1] (numeric) = -1.3096685927630863936377467673233
absolute error = 1.3786854417648246e-15
relative error = 1.0526979492240306141490224000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.914
Order of pole = 2.9e-29
TOP MAIN SOLVE Loop
x[1] = -0.913
y[1] (analytic) = -1.3139767096866101556731673040805
y[1] (numeric) = -1.3139767096866087533489818082857
absolute error = 1.4023241854957948e-15
relative error = 1.0672367136783238323604156000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.912
y[1] (analytic) = -1.3183037425820630369398411387039
y[1] (numeric) = -1.3183037425820616107428095425013
absolute error = 1.4261970315962026e-15
relative error = 1.0818425113493321650249728000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.911
y[1] (analytic) = -1.3226497953832329571537875774513
y[1] (numeric) = -1.3226497953832315068472286825362
absolute error = 1.4503065588949151e-15
relative error = 1.0965159212644750464181680999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.911
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (analytic) = -1.3270149727099370862201438218827
y[1] (numeric) = -1.3270149727099356115647663179501
absolute error = 1.4746553775039326e-15
relative error = 1.1112575274810159933146000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.91
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.909
y[1] (analytic) = -1.3313993798733119967795472727922
y[1] (numeric) = -1.3313993798733104975334180399582
absolute error = 1.4992461292328340e-15
relative error = 1.1260679191359494971117860000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.908
y[1] (analytic) = -1.335803122881149086485921319016
y[1] (numeric) = -1.335803122881147562404433309843
absolute error = 1.5240814880091730e-15
relative error = 1.1409476904964352859109760000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.908
Order of pole = 2.8e-29
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.16
x[1] = -0.907
y[1] (analytic) = -1.3402263084432771120950394467669
y[1] (numeric) = -1.340226308443275562930879141842
absolute error = 1.5491641603049249e-15
relative error = 1.1558974410107923508025107000001e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.6633
Order of pole = 1.674e-27
TOP MAIN SOLVE Loop
x[1] = -0.906
y[1] (analytic) = -1.3446690439769923038781642926751
y[1] (numeric) = -1.344669043976990729381278723603
absolute error = 1.5744968855690721e-15
relative error = 1.1709177753600552288456935999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.905
y[1] (analytic) = -1.3491314376125365340577269732354
y[1] (numeric) = -1.34913143761253493397529030681
absolute error = 1.6000824366664254e-15
relative error = 1.1860093035101007522276750000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.904
y[1] (analytic) = -1.3536135981986240182078138633596
y[1] (numeric) = -1.3536135981986223922841935405788
absolute error = 1.6259236203227808e-15
relative error = 1.2011726407643542773645312000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.903
y[1] (analytic) = -1.3581156353080170338720028735771
y[1] (numeric) = -1.3581156353080153818487252970725
absolute error = 1.6520232775765046e-15
relative error = 1.2164084078170781755614042000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.902
y[1] (analytic) = -1.3626376592431511460256912140318
y[1] (numeric) = -1.3626376592431494676414069773793
absolute error = 1.6783842842366525e-15
relative error = 1.2317172308072538333902200000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.902
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.901
y[1] (analytic) = -1.3671797810418104344503459655956
y[1] (numeric) = -1.3671797810418087294407946178744
absolute error = 1.7050095513477212e-15
relative error = 1.2470997413730619075109611999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.901
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = -1.3717421124828532235939643347051
y[1] (numeric) = -1.3717421124828514916919386735676
absolute error = 1.7319020256611375e-15
relative error = 1.2625565767069692375000000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.9
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.899
y[1] (analytic) = -1.3763247660919888210663417729105
y[1] (numeric) = -1.3763247660919870620016516593205
absolute error = 1.7590646901135900e-15
relative error = 1.2780883796114297028794100000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.898
y[1] (analytic) = -1.3809278551476057765604156102339
y[1] (numeric) = -1.3809278551476039900598512979243
absolute error = 1.7865005643123096e-15
relative error = 1.2936957985552059321892031999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.897
y[1] (analytic) = -1.3855514936866521787028949919356
y[1] (numeric) = -1.3855514936866503644901899645265
absolute error = 1.8142127050274091e-15
relative error = 1.3093794877303205518620843000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.897
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -0.896
y[1] (analytic) = -1.3901957965105685131195335276968
y[1] (numeric) = -1.3901957965105666709153268363052
absolute error = 1.8422042066913916e-15
relative error = 1.3251401071096439899160576000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.895
y[1] (analytic) = -1.3948608791912736108536914731631
y[1] (numeric) = -1.3948608791912717403754895672234
absolute error = 1.8704782019059397e-15
relative error = 1.3409783225051262866322875000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.895
Order of pole = 3.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.894
y[1] (analytic) = -1.399546858077204222202225496714
y[1] (numeric) = -1.3995468580772023231643635406119
absolute error = 1.8990378619561021e-15
relative error = 1.3568948056266824128880664000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.893
y[1] (analytic) = -1.4042538502994087570312061028052
y[1] (numeric) = -1.4042538502994068291448087708139
absolute error = 1.9278863973319913e-15
relative error = 1.3728902341417372232629741000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.892
y[1] (analytic) = -1.4089819737776957387064797029497
y[1] (numeric) = -1.4089819737776937816794214448367
absolute error = 1.9570270582581130e-15
relative error = 1.3889652917354398340525439999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.892
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -0.891
y[1] (analytic) = -1.413731347226837524921662636677
y[1] (numeric) = -1.4137313472268355384585274062318
absolute error = 1.9864631352304452e-15
relative error = 1.4051206681715540296466892000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.891
Order of pole = 4.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = -1.4185020901628298549297912390473
y[1] (numeric) = -1.4185020901628278387318316776546
absolute error = 2.0161979595613927e-15
relative error = 1.4213570593540354503263000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.89
Order of pole = 5.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.889
y[1] (analytic) = -1.4232943229092077889855832511187
y[1] (numeric) = -1.4232943229092057427506793183812
absolute error = 2.0462349039327375e-15
relative error = 1.4376751673893012549926375000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.889
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -0.888
y[1] (analytic) = -1.4281081666034186121841344631703
y[1] (numeric) = -1.4281081666034165356067515064556
absolute error = 2.0765773829567147e-15
relative error = 1.4540757006492030371203584000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.887
y[1] (analytic) = -1.4329437432032522813399387588215
y[1] (numeric) = -1.4329437432032501741110850134809
absolute error = 2.1072288537453406e-15
relative error = 1.4705593738347103082484818000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.887
Order of pole = 9.8e-29
memory used=22.8MB, alloc=4.3MB, time=1.41
TOP MAIN SOLVE Loop
x[1] = -0.886
y[1] (analytic) = -1.4378011754933300000884535283164
y[1] (numeric) = -1.4378011754933278618956370401895
absolute error = 2.1381928164881269e-15
relative error = 1.4871269080403155062972663999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.885
y[1] (analytic) = -1.4426805870916515140121253696644
y[1] (numeric) = -1.4426805870916493445393103313561
absolute error = 2.1694728150383083e-15
relative error = 1.5037790308191654311667375000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.884
y[1] (analytic) = -1.4475821024562017242949487676374
y[1] (numeric) = -1.447582102456199523222511259911
absolute error = 2.2010724375077264e-15
relative error = 1.5205164762489334520083456000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.884
Order of pole = 6.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.883
y[1] (analytic) = -1.4525058468916172251953750000215
y[1] (numeric) = -1.45250584689161499220005812952
absolute error = 2.2329953168705015e-15
relative error = 1.5373399849984374440815805000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.883
Order of pole = 4.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.882
y[1] (analytic) = -1.4574519465559133774978583909607
y[1] (numeric) = -1.4574519465559111122527268153255
absolute error = 2.2652451315756352e-15
relative error = 1.5542503043950147937204736000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.881
y[1] (analytic) = -1.4624205284672725370596775546123
y[1] (numeric) = -1.4624205284672702392340713859272
absolute error = 2.2978256061686851e-15
relative error = 1.5712481884926631531888690999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.881
Order of pole = 5.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = -1.4674117205108940646130728775357
y[1] (numeric) = -1.4674117205108917338725609548776
absolute error = 2.3307405119226581e-15
relative error = 1.5883343981409576607232000000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.879
y[1] (analytic) = -1.4724256514459067501143879634775
y[1] (numeric) = -1.4724256514459043861207204852097
absolute error = 2.3639936674782678e-15
relative error = 1.6055097010547530775973642000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.879
Order of pole = 2.6e-29
TOP MAIN SOLVE Loop
x[1] = -0.878
y[1] (analytic) = -1.4774624509123442921529995342211
y[1] (numeric) = -1.477462450912341894564060040515
absolute error = 2.3975889394937061e-15
relative error = 1.6227748718846808649429272000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.878
Order of pole = 1.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.877
y[1] (analytic) = -1.4825222494381844802445926880049
y[1] (numeric) = -1.4825222494381820487143493839216
absolute error = 2.4315302433040833e-15
relative error = 1.6401306922884524514588789000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.877
Order of pole = 5.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.876
y[1] (analytic) = -1.4876051784464527352370300107803
y[1] (numeric) = -1.4876051784464502694154864200913
absolute error = 2.4658215435906890e-15
relative error = 1.6575779510029769403680640000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.876
Order of pole = 3.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.875
y[1] (analytic) = -1.4927113702623906705539358600583
y[1] (numeric) = -1.4927113702623881700870807998244
absolute error = 2.5004668550602339e-15
relative error = 1.6751174439173051322265625000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.875
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.874
y[1] (analytic) = -1.4978409581206903445924520343095
y[1] (numeric) = -1.4978409581206878091222089000778
absolute error = 2.5354702431342317e-15
relative error = 1.6927499741464094229364808000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.874
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.873
y[1] (analytic) = -1.5029940761727948822787179358928
y[1] (numeric) = -1.5029940761727923114428932872085
absolute error = 2.5708358246486843e-15
relative error = 1.7104763521058101230316131000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.873
Order of pole = 2.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.872
y[1] (analytic) = -1.5081708594942661515688065672661
y[1] (numeric) = -1.5081708594942635450010380030288
absolute error = 2.6065677685642373e-15
relative error = 1.7282973955870595411874304000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.872
Order of pole = 2.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.871
y[1] (analytic) = -1.513371444092220188565446317884
y[1] (numeric) = -1.5133714440922175458951496309106
absolute error = 2.6426702966869734e-15
relative error = 1.7462139298340938050071274000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = -1.5185959669128310729032365835843
y[1] (numeric) = -1.5185959669128283937555521835669
absolute error = 2.6791476844000174e-15
relative error = 1.7642267876204646579522000000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.869
y[1] (analytic) = -1.5238445658489039631386022470804
y[1] (numeric) = -1.5238445658489012471343408409567
absolute error = 2.7160042614061237e-15
relative error = 1.7823368093274597983122433000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.868
y[1] (analytic) = -1.529117379747518010066828056647
y[1] (numeric) = -1.5291173797475152568224155752164
absolute error = 2.7532444124814306e-15
relative error = 1.8005448430231273317489791999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.868
Order of pole = 3e-30
TOP MAIN SOLVE Loop
x[1] = -0.867
y[1] (analytic) = -1.5344145484177398741785901072737
y[1] (numeric) = -1.5344145484177370833060118667187
absolute error = 2.7908725782405550e-15
relative error = 1.8188517445422109625914650000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.66
x[1] = -0.866
y[1] (analytic) = -1.5397362126384085818639004496732
y[1] (numeric) = -1.539736212638405752970644536455
absolute error = 2.8288932559132182e-15
relative error = 1.8372583775670119036337072000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.865
y[1] (analytic) = -1.5450825141659924634737665268303
y[1] (numeric) = -1.545082514165989596162766394246
absolute error = 2.8673110001325843e-15
relative error = 1.8557656137091854980053875000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.865
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.864
y[1] (analytic) = -1.5504535957425189249606259208454
y[1] (numeric) = -1.5504535957425160188302021853392
absolute error = 2.9061304237355062e-15
relative error = 1.8743743325924874169417728000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.3368
Order of pole = 2.717e-27
TOP MAIN SOLVE Loop
x[1] = -0.863
y[1] (analytic) = -1.5558496011035778135392574546282
y[1] (numeric) = -1.5558496011035748681830588797571
absolute error = 2.9453561985748711e-15
relative error = 1.8930854219364802544001016999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.863
Order of pole = 2.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.862
y[1] (analytic) = -1.561270674986399146641923482474
y[1] (numeric) = -1.5612706749863961616488671382321
absolute error = 2.9849930563442419e-15
relative error = 1.9118997776412122571321831999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.861
y[1] (analytic) = -1.5667169631380059823865198193511
y[1] (numeric) = -1.5667169631380029573407304043533
absolute error = 3.0250457894149978e-15
relative error = 1.9308183038728823179047618000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = -1.5721886123234432188360773265248
y[1] (numeric) = -1.5721886123234401533168256403491
absolute error = 3.0655192516861757e-15
relative error = 1.9498419131505021710391999999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.86
Order of pole = 5.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.859
y[1] (analytic) = -1.5776857703340831185036747275529
y[1] (numeric) = -1.5776857703340800120853152803317
absolute error = 3.1064183594472212e-15
relative error = 1.9689715264335692475721148000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.859
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -0.858
y[1] (analytic) = -1.5832085859960083638503121118408
y[1] (numeric) = -1.5832085859960052161022198579789
absolute error = 3.1477480922538619e-15
relative error = 1.9882080732107639689228728000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.857
y[1] (analytic) = -1.5887572091784734589362098299482
y[1] (numeric) = -1.5887572091784702694227160126327
absolute error = 3.1895134938173155e-15
relative error = 2.0075524915896829537721914999999e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.333
Order of pole = 5.130e-27
TOP MAIN SOLVE Loop
x[1] = -0.856
y[1] (analytic) = -1.594331790802445301920014236235
y[1] (numeric) = -1.5943317908024420702003413291813
absolute error = 3.2317196729070537e-15
relative error = 2.0270057283876228023342592000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.856
Order of pole = 4.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.855
y[1] (analytic) = -1.5999324828492237627572116456687
y[1] (numeric) = -1.599932482849220488385407378324
absolute error = 3.2743718042673447e-15
relative error = 2.0465687392234279887164624999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.855
Order of pole = 6.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.854
y[1] (analytic) = -1.6055594383691431102304025318619
y[1] (numeric) = -1.6055594383691397927552729840631
absolute error = 3.3174751295477988e-15
relative error = 2.0662424886104151948961632000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.853
y[1] (analytic) = -1.6112128114903551423517233516925
y[1] (numeric) = -1.6112128114903517813167651035404
absolute error = 3.3610349582481521e-15
relative error = 2.0860279500503906852335517000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.852
y[1] (analytic) = -1.6168927574276948842134041806586
y[1] (numeric) = -1.6168927574276914791567355031416
absolute error = 3.4050566686775170e-15
relative error = 2.1059261061287710239135360000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.852
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.851
y[1] (analytic) = -1.6225994324916297275280245597819
y[1] (numeric) = -1.622599432491626277982315631437
absolute error = 3.4495457089283449e-15
relative error = 2.1259379486108254754910898999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = -1.6283329940972928963973132505598
y[1] (numeric) = -1.6283329940972894018897153852203
absolute error = 3.4945075978653395e-15
relative error = 2.1460644785390516204374999999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.849
y[1] (analytic) = -1.6340936007736021342791937713569
y[1] (numeric) = -1.6340936007735985943312676417861
absolute error = 3.5399479261295708e-15
relative error = 2.1663067063317005271169691999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.849
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.848
y[1] (analytic) = -1.6398814121724645176890990549246
y[1] (numeric) = -1.6398814121724609318167418968841
absolute error = 3.5858723571580405e-15
relative error = 2.1866656518824656712437759999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.847
y[1] (analytic) = -1.6456965890780683128752868101502
y[1] (numeric) = -1.6456965890780646805886585911944
absolute error = 3.6322866282189558e-15
relative error = 2.2071423446613511337093033999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.846
y[1] (analytic) = -1.6515392934162628025509332405935
y[1] (numeric) = -1.6515392934162591233543817776216
absolute error = 3.6791965514629719e-15
relative error = 2.2277378238167340473378183999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.91
x[1] = -0.845
y[1] (analytic) = -1.6574096882640270207501477684324
y[1] (numeric) = -1.6574096882640232941421327777629
absolute error = 3.7266080149906695e-15
relative error = 2.2484531382786373073281875000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.844
y[1] (analytic) = -1.6633079378590283450027469863256
y[1] (numeric) = -1.6633079378590245704757630497878
absolute error = 3.7745269839365378e-15
relative error = 2.2692893468632284462138751999999e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.5773
Order of pole = 8.694e-27
TOP MAIN SOLVE Loop
x[1] = -0.843
y[1] (analytic) = -1.6692342076092719062956949212883
y[1] (numeric) = -1.6692342076092680833361933515528
absolute error = 3.8229595015697355e-15
relative error = 2.2902475183785591020951985000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.842
y[1] (analytic) = -1.6751886641028417887096331295281
y[1] (numeric) = -1.6751886641028379167979427176127
absolute error = 3.8719116904119154e-15
relative error = 2.3113287317315646656815952000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.841
y[1] (analytic) = -1.6811714751177350021889945367492
y[1] (numeric) = -1.6811714751177310807992411643579
absolute error = 3.9213897533723913e-15
relative error = 2.3325340760363367427775073000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = -1.6871828096317892236259583198358
y[1] (numeric) = -1.6871828096317852522259834188941
absolute error = 3.9713999749009417e-15
relative error = 2.3538646507236877493568000000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.839
y[1] (analytic) = -1.6932228378327053133141317009617
y[1] (numeric) = -1.6932228378327012913654095424168
absolute error = 4.0219487221585449e-15
relative error = 2.3753215656520241059398831000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.839
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.838
y[1] (analytic) = -1.699291731128165625859544239898
y[1] (numeric) = -1.6992917311281615528170980335537
absolute error = 4.0730424462063443e-15
relative error = 2.3969059412195441030585095999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.837
y[1] (analytic) = -1.7053896621560491468265513132913
y[1] (numeric) = -1.705389662156045022138868100139
absolute error = 4.1246876832131523e-15
relative error = 2.4186189084777792459923319000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.837
Order of pole = 4.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.836
y[1] (analytic) = -1.7115168047947444987468410876636
y[1] (numeric) = -1.7115168047947403218557854058593
absolute error = 4.1768910556818043e-15
relative error = 2.4404616092464966891721408000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.835
y[1] (analytic) = -1.7176733341735618726332340160297
y[1] (numeric) = -1.7176733341735576429739603213517
absolute error = 4.2296592736946780e-15
relative error = 2.4624351962299795102392500000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.835
Order of pole = 8e-30
TOP MAIN SOLVE Loop
x[1] = -0.834
y[1] (analytic) = -1.7238594266832449538187023660578
y[1] (numeric) = -1.7238594266832406708195661873553
absolute error = 4.2829991361787025e-15
relative error = 2.4845408331347039391390599999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.834
Order of pole = 3.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.833
y[1] (analytic) = -1.7300752599865839237874028365729
y[1] (numeric) = -1.7300752599865795868698706463862
absolute error = 4.3369175321901867e-15
relative error = 2.5067796947884324104105579000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.7266
Order of pole = 3.64e-28
TOP MAIN SOLVE Loop
x[1] = -0.832
y[1] (analytic) = -1.7363210130291306326809285389167
y[1] (numeric) = -1.7363210130291262412594863191159
absolute error = 4.3914214422198008e-15
relative error = 2.5291529672607406116306944000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.832
Order of pole = 2.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.831
y[1] (analytic) = -1.7425968660500170503519060230893
y[1] (numeric) = -1.7425968660500126038339665050387
absolute error = 4.4465179395180506e-15
relative error = 2.5516618479849968930612646000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = -1.7489030005928781172009856817312
y[1] (numeric) = -1.7489030005928736149867942401365
absolute error = 4.5022141914415947e-15
relative error = 2.5743075458818151087288999999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.83
Order of pole = 9.6e-29
TOP MAIN SOLVE Loop
x[1] = -0.829
y[1] (analytic) = -1.7552395995168801295747360388632
y[1] (numeric) = -1.755239599516875571057275218109
absolute error = 4.5585174608207542e-15
relative error = 2.5970912814839983119074638000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.829
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.828
y[1] (analytic) = -1.7616068470078558082235302646312
y[1] (numeric) = -1.761606847007851192788422916052
absolute error = 4.6154351073485792e-15
relative error = 2.6200142870629957708253183999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.827
y[1] (analytic) = -1.7680049285895472122228234362272
y[1] (numeric) = -1.768004928589542539248234444395
absolute error = 4.6729745889918322e-15
relative error = 2.6430778067568899034983125999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.827
Order of pole = 5.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.826
y[1] (analytic) = -1.774434031134957674850919505327
y[1] (numeric) = -1.7744340311349529437074560810586
absolute error = 4.7311434634242684e-15
relative error = 2.6662830966999375773215584000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.825
y[1] (analytic) = -1.7808943428778139521941174833737
y[1] (numeric) = -1.7808943428778091622447280007863
absolute error = 4.7899493894825874e-15
relative error = 2.6896314251536834905281250000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.16
x[1] = -0.824
y[1] (analytic) = -1.7873860534241397897187495138309
y[1] (numeric) = -1.787386053424134940318620868386
absolute error = 4.8494001286454449e-15
relative error = 2.7131240726396677474520576000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.824
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.823
y[1] (analytic) = -1.7939093537639421267118651337083
y[1] (numeric) = -1.7939093537639372172083185977888
absolute error = 4.9095035465359195e-15
relative error = 2.7367623320737496950497564999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.823
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.822
y[1] (analytic) = -1.8004644362830111733510061160912
y[1] (numeric) = -1.8004644362830062030833916682595
absolute error = 4.9702676144478317e-15
relative error = 2.7605475089020674832226616000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.821
y[1] (analytic) = -1.8070514947748356102215296773666
y[1] (numeric) = -1.8070514947748305785211187810365
absolute error = 5.0317004108963301e-15
relative error = 2.7844809212386590275228961000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = -1.8136707244526341753601950058762
y[1] (numeric) = -1.8136707244526290815500718127241
absolute error = 5.0938101231931521e-15
relative error = 2.8085639000047618870728000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.82
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -0.819
y[1] (analytic) = -1.8203223219615049193691959147911
y[1] (numeric) = -1.8203223219614997627641468677999
absolute error = 5.1566050490469912e-15
relative error = 2.8327977890698194598643208000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.818
y[1] (analytic) = -1.8270064853906934248185150415763
y[1] (numeric) = -1.8270064853906882047249168521809
absolute error = 5.2200935981893954e-15
relative error = 2.8571839453942126642410128000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.818
Order of pole = 9.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.817
y[1] (analytic) = -1.8337234142859813020394545286774
y[1] (numeric) = -1.8337234142859760177551605020371
absolute error = 5.2842842940266403e-15
relative error = 2.8817237391737428035878738999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.816
y[1] (analytic) = -1.8404733096621962895115754875575
y[1] (numeric) = -1.8404733096621909403258001695356
absolute error = 5.3491857753180219e-15
relative error = 2.9064185539858879408410624000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.815
y[1] (analytic) = -1.8472563740158453033622144170508
y[1] (numeric) = -1.8472563740158398885554165360236
absolute error = 5.4148067978810272e-15
relative error = 2.9312697869378581129148000000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.814
y[1] (analytic) = -1.8540728113378717970354503022977
y[1] (numeric) = -1.8540728113378663158792139784549
absolute error = 5.4811562363238428e-15
relative error = 2.9562788488164716163417632000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.813
y[1] (analytic) = -1.8609228271265388089491339578728
y[1] (numeric) = -1.8609228271265332607060481521953
absolute error = 5.5482430858056775e-15
relative error = 2.9814471642398788882674675000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.813
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.812
y[1] (analytic) = -1.867806628400439092947676191544
y[1] (numeric) = -1.8678066284004334768712123661636
absolute error = 5.6160764638253804e-15
relative error = 3.0067761718111590709395712000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.811
y[1] (analytic) = -1.8747244237116337435780916486818
y[1] (numeric) = -1.8747244237116280589124796098396
absolute error = 5.6846656120388422e-15
relative error = 3.0322673242738132571378482000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.811
Order of pole = 7.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = -1.8816764231589207456707329694172
y[1] (numeric) = -1.8816764231589149916508348637361
absolute error = 5.7540198981056811e-15
relative error = 3.0579220886691812694650999999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.809
y[1] (analytic) = -1.888662838401234895397702429192
y[1] (numeric) = -1.8886628384012290712488848634697
absolute error = 5.8241488175657223e-15
relative error = 3.0837419464958082807706766999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.809
Order of pole = 6.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.808
y[1] (analytic) = -1.8956838826711805579146288317687
y[1] (numeric) = -1.8956838826711746628526330859799
absolute error = 5.8950619957457888e-15
relative error = 3.1097283938707875565715455999998e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.6907
Order of pole = 2.319e-27
TOP MAIN SOLVE Loop
x[1] = -0.807
y[1] (analytic) = -1.9027397707886987448689363638825
y[1] (numeric) = -1.9027397707886927780997466665519
absolute error = 5.9667691896973306e-15
relative error = 3.1358829416931058627269558000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.806
y[1] (analytic) = -1.909830719174870013483557663832
y[1] (numeric) = -1.9098307191748639742032674983996
absolute error = 6.0392802901654324e-15
relative error = 3.1622071158090201391407584000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.806
Order of pole = 4.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.805
y[1] (analytic) = -1.9169569458658547076029627528077
y[1] (numeric) = -1.9169569458658485949976391630628
absolute error = 6.1126053235897449e-15
relative error = 3.1887024571794917732521125000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.805
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.804
y[1] (analytic) = -1.924118670526972080022155995597
y[1] (numeric) = -1.9241186705269658932677018576974
absolute error = 6.1867544541378996e-15
relative error = 3.2153705220497076242982143999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.804
Order of pole = 3.6e-29
memory used=38.1MB, alloc=4.4MB, time=2.41
TOP MAIN SOLVE Loop
x[1] = -0.803
y[1] (analytic) = -1.931316114466919854612763229623
y[1] (numeric) = -1.9313161144669135928747774576471
absolute error = 6.2617379857719759e-15
relative error = 3.2422128821207165325067893000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.802
y[1] (analytic) = -1.9385495006521358062173810937547
y[1] (numeric) = -1.9385495006521294686510167451552
absolute error = 6.3375663643485995e-15
relative error = 3.2692311247232102274239960000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.802
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.801
y[1] (analytic) = -1.9458190537213029560079440864848
y[1] (numeric) = -1.9458190537212965417577643332249
absolute error = 6.4142501797532599e-15
relative error = 3.2964268529934769153850198999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = -1.953125
y[1] (numeric) = -1.9531249999999935081998319305478
absolute error = 6.4918001680694522e-15
relative error = 3.3238016860515595264000000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.8
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.799
y[1] (analytic) = -1.9604675675154986086865545815472
y[1] (numeric) = -1.9604675675154920384593407982931
absolute error = 6.5702272137832541e-15
relative error = 3.3513572591816481173545858999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.798
y[1] (analytic) = -1.9678469860117092563067016414472
y[1] (numeric) = -1.9678469860117026067643496174867
absolute error = 6.6495423520239605e-15
relative error = 3.3790952240147363815091160000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.797
y[1] (analytic) = -1.975263486964277259099813210591
y[1] (numeric) = -1.9752634869642705293430423691756
absolute error = 6.7297567708414154e-15
relative error = 3.4070172487135754939504242000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.797
Order of pole = 6.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.796
y[1] (analytic) = -1.9827173035958307230199125726357
y[1] (numeric) = -1.9827173035958239121380990519507
absolute error = 6.8108818135206850e-15
relative error = 3.4351250181599549881801599999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.795
y[1] (analytic) = -1.9902086708913821228013480678431
y[1] (numeric) = -1.9902086708913752298723671331076
absolute error = 6.8929289809347355e-15
relative error = 3.4634202341443445824880625000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.795
Order of pole = 1.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.794
y[1] (analytic) = -1.9977378256138852559804559230874
y[1] (numeric) = -1.9977378256138782800705219872994
absolute error = 6.9759099339357880e-15
relative error = 3.4919046155579295001929919999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.794
Order of pole = 4.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.793
y[1] (analytic) = -2.0053050063199493374930471312832
y[1] (numeric) = -2.0053050063199422776565513452511
absolute error = 7.0598364957860321e-15
relative error = 3.5205798985870705465419496999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.793
Order of pole = 4.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.792
y[1] (analytic) = -2.0129104533757120227888516838625
y[1] (numeric) = -2.0129104533757048780681970554581
absolute error = 7.1447206546284044e-15
relative error = 3.5494478369102265143887871999998e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.791
y[1] (analytic) = -2.020554408972873170036153638601
y[1] (numeric) = -2.0205544089728659394615876404651
absolute error = 7.2305745659981359e-15
relative error = 3.5785102018973692174258888999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.791
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = -2.0282371171448911749374795908639
y[1] (numeric) = -2.0282371171448838575269242150648
absolute error = 7.3174105553757991e-15
relative error = 3.6077687828119286124649000000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.79
Order of pole = 4.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.789
y[1] (analytic) = -2.0359588237833437349451661012474
y[1] (numeric) = -2.0359588237833363297040453186549
absolute error = 7.4052411207825925e-15
relative error = 3.6372253870153025096313824999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.789
Order of pole = 5.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.788
y[1] (analytic) = -2.0437197766544549232588128793716
y[1] (numeric) = -2.0437197766544474291798774607581
absolute error = 7.4940789354186135e-15
relative error = 3.6668818401739655264214720000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.787
y[1] (analytic) = -2.0515202254157904769099931792492
y[1] (numeric) = -2.051520225415782892973142834355
absolute error = 7.5839368503448942e-15
relative error = 3.6967399864692169525229625999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.786
y[1] (analytic) = -2.0593604216331232274981882982627
y[1] (numeric) = -2.0593604216331155526702910882884
absolute error = 7.6748278972099743e-15
relative error = 3.7268016888096003601572408000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.786
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -0.785
y[1] (analytic) = -2.0672406187974706277408703548134
y[1] (numeric) = -2.067240618797462860975579332998
absolute error = 7.7667652910218154e-15
relative error = 3.7570688290460357829690250000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.784
y[1] (analytic) = -2.0751610723423063519451929043171
y[1] (numeric) = -2.0751610723422984921827599384507
absolute error = 7.8597624329658664e-15
relative error = 3.7875433081897009811193856000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.783
y[1] (analytic) = -2.0831220396609479738041654095807
y[1] (numeric) = -2.0831220396609400199712521394716
absolute error = 7.9538329132701091e-15
relative error = 3.8182270466327007498017516999999e-13 %
Correct digits = 14
h = 0.001
memory used=41.9MB, alloc=4.4MB, time=2.66
Complex estimate of poles used
Radius of convergence = 0.7022
Order of pole = 7.134e-27
TOP MAIN SOLVE Loop
x[1] = -0.782
y[1] (analytic) = -2.0911237801241227505718763491408
y[1] (numeric) = -2.0911237801241147015813622312116
absolute error = 8.0489905141179292e-15
relative error = 3.8491219843715638832308256000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.781
y[1] (analytic) = -2.0991665550977135686857719189918
y[1] (numeric) = -2.0991665550977054234365593093185
absolute error = 8.1452492126096733e-15
relative error = 3.8802300812336075788139553000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = -2.1072506279606871322847654208601
y[1] (numeric) = -2.1072506279606788896615816470916
absolute error = 8.2426231837737685e-15
relative error = 3.9115533171062093892120000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.78
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -0.779
y[1] (analytic) = -2.1153762641232065028257122097987
y[1] (numeric) = -2.1153762641231981616989085814988
absolute error = 8.3411268036282999e-15
relative error = 3.9430936921690282877607861000003e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.779
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.778
y[1] (analytic) = -2.1235437310449301251332969635414
y[1] (numeric) = -2.1235437310449216843586446695825
absolute error = 8.4407746522939589e-15
relative error = 3.9748532271292171694478728000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.8045
Order of pole = 8.9e-29
TOP MAIN SOLVE Loop
x[1] = -0.777
y[1] (analytic) = -2.1317532982534995027355010062484
y[1] (numeric) = -2.1317532982534909611539838469609
absolute error = 8.5415815171592875e-15
relative error = 4.0068339634596672183589874999998e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.1538
Order of pole = 2.302e-27
TOP MAIN SOLVE Loop
x[1] = -0.776
y[1] (analytic) = -2.140005237363217713244502686066
y[1] (numeric) = -2.1400052373632090696821065868942
absolute error = 8.6435623960991718e-15
relative error = 4.0390379636403299452013568000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.775
y[1] (analytic) = -2.1482998220939209828471686079689
y[1] (numeric) = -2.1482998220939122361146678604218
absolute error = 8.7467325007475471e-15
relative error = 4.0714673114026589946265624999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.775
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -0.774
y[1] (analytic) = -2.1566373282900455676763749335044
y[1] (numeric) = -2.156637328290036716569115108207
absolute error = 8.8511072598252974e-15
relative error = 4.1041241119772152956666576000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.1896
Order of pole = 7.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.773
y[1] (analytic) = -2.1650180339398922189505167310244
y[1] (numeric) = -2.1650180339398832622481942066649
absolute error = 8.9567023225243595e-15
relative error = 4.1370104923444836399331615000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.772
y[1] (analytic) = -2.1734422191950905383000858109763
y[1] (numeric) = -2.173442219195081474766523861928
absolute error = 9.0635335619490483e-15
relative error = 4.1701286014889433167649984000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.771
y[1] (analytic) = -2.1819101663902655596535974109681
y[1] (numeric) = -2.1819101663902563880365187953174
absolute error = 9.1716170786156507e-15
relative error = 4.2034806106564411996919577000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = -2.1904221600629089244370067443099
y[1] (numeric) = -2.1904221600628996434678027329588
absolute error = 9.2809692040113511e-15
relative error = 4.2370687136149141517362999999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.77
Order of pole = 6.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.769
y[1] (analytic) = -2.1989784869734570476577724679092
y[1] (numeric) = -2.1989784869734476560512682543366
absolute error = 9.3916065042135726e-15
relative error = 4.2708951269185084873513134000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.769
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -0.768
y[1] (analytic) = -2.2075794361255787037037037037036
y[1] (numeric) = -2.2075794361255692001579201328625
absolute error = 9.5035457835708411e-15
relative error = 4.3049620901751458157821952000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.767
y[1] (analytic) = -2.2162252987866744923945940476183
y[1] (numeric) = -2.2162252987866648755905056013203
absolute error = 9.6168040884462980e-15
relative error = 4.3392718663175838845615739999998e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.766
y[1] (analytic) = -2.224916368508590677988441363673
y[1] (numeric) = -2.2249163685085809465897303386606
absolute error = 9.7313987110250124e-15
relative error = 4.3738267418780232066431903999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.765
y[1] (analytic) = -2.2336529411485499264709372435661
y[1] (numeric) = -2.2336529411485400791237440572985
absolute error = 9.8473471931862676e-15
relative error = 4.4086290272663115940006500000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.764
y[1] (analytic) = -2.2424353148903014995541679804348
y[1] (numeric) = -2.2424353148902915348868375384218
absolute error = 9.9646673304420130e-15
relative error = 4.4436810570517964521166719999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.764
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.763
y[1] (analytic) = -2.251263790265493497385507179126
y[1] (numeric) = -2.2512637902654834140083312364231
absolute error = 1.00833771759427029e-14
relative error = 4.4789851902488785897022463000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=2.91
x[1] = -0.762
y[1] (analytic) = -2.2601386701752697760280326626562
y[1] (numeric) = -2.2601386701752595725329881108885
absolute error = 1.02034950445517677e-14
relative error = 4.5145438106063220525518855999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.761
y[1] (analytic) = -2.2690602599120942003271299638595
y[1] (numeric) = -2.2690602599120838752876129738788
absolute error = 1.03250395169899807e-14
relative error = 4.5503593269003722604661366999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.761
Order of pole = 6.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = -2.2780288671818049278320454876804
y[1] (numeric) = -2.2780288671817944798026014366624
absolute error = 1.04480294440510180e-14
relative error = 4.5864341732317396775680000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.76
Order of pole = 4.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.759
y[1] (analytic) = -2.2870448021259014550039521392055
y[1] (numeric) = -2.287044802125890882520001249678
absolute error = 1.05724839508895275e-14
relative error = 4.6227708093265039278211725000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.759
Order of pole = 3.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.758
y[1] (analytic) = -2.2961083773440671930216527244822
y[1] (numeric) = -2.2961083773440564945992113414295
absolute error = 1.06984224413830527e-14
relative error = 4.6593717208409957169742824000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.757
y[1] (analytic) = -2.3052199079169303771005742987441
y[1] (numeric) = -2.3052199079169195512359717295603
absolute error = 1.08258646025691838e-14
relative error = 4.6962394196707148330064934000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.6282
Order of pole = 7.061e-27
TOP MAIN SOLVE Loop
x[1] = -0.756
y[1] (analytic) = -2.3143797114290661503785436486089
y[1] (numeric) = -2.314379711429055195548134489276
absolute error = 1.09548304091593329e-14
relative error = 4.7333764442633420971808064000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.755
y[1] (analytic) = -2.3235881079922427011014678977424
y[1] (numeric) = -2.3235881079922316157613397671786
absolute error = 1.10853401281305638e-14
relative error = 4.7707853599359065957217249999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.755
Order of pole = 1.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.754
y[1] (analytic) = -2.3328454202689143700721089984511
y[1] (numeric) = -2.3328454202689031526577856015231
absolute error = 1.12174143233969280e-14
relative error = 4.8084687591961672508113919999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.754
Order of pole = 8e-30
TOP MAIN SOLVE Loop
x[1] = -0.753
y[1] (analytic) = -2.342151973495964684114420054234
y[1] (numeric) = -2.3421519734959533330405594924399
absolute error = 1.13510738605617941e-14
relative error = 4.8464292620682715800677157000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.753
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -0.752
y[1] (analytic) = -2.3515080955087023106633404929544
y[1] (numeric) = -2.3515080955086908243234287402701
absolute error = 1.14863399117526843e-14
relative error = 4.8846695164227540667551743999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.751
y[1] (analytic) = -2.3609141167651129685246164405216
y[1] (numeric) = -2.3609141167651013452906559003607
absolute error = 1.16232339605401609e-14
relative error = 4.9231921983109370771084358999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.751
Order of pole = 4.9e-29
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = -2.3703703703703703703703703703703
y[1] (numeric) = -2.3703703703703586085925634280284
absolute error = 1.17617778069423419e-14
relative error = 4.9620000123038004890625000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.75
Order of pole = 4.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.749
y[1] (analytic) = -2.3798771921016093136531990931554
y[1] (numeric) = -2.3798771921015974116596265765046
absolute error = 1.19019935725166508e-14
relative error = 5.0010956918353847979726492000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.749
Order of pole = 4.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.748
y[1] (analytic) = -2.3894349204329640783441040138989
y[1] (numeric) = -2.3894349204329520344403984734598
absolute error = 1.20439037055404391e-14
relative error = 5.0404819995507939829783872000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.747
y[1] (analytic) = -2.3990438965608753322372917444871
y[1] (numeric) = -2.3990438965608631447063054623287
absolute error = 1.21875309862821584e-14
relative error = 5.0801617276588677321893232000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.747
Order of pole = 1.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.746
y[1] (analytic) = -2.4087044644296687875277359910374
y[1] (numeric) = -2.4087044644296564546292036262524
absolute error = 1.23328985323647850e-14
relative error = 5.1201376982895904340387600000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.746
Order of pole = 4.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.745
y[1] (analytic) = -2.4184169707574088959654456583219
y[1] (numeric) = -2.4184169707573964159356414350822
absolute error = 1.24800298042232397e-14
relative error = 5.1604127638563076927969124999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.745
Order of pole = 5.7e-29
TOP MAIN SOLVE Loop
x[1] = -0.744
y[1] (analytic) = -2.4281817650620309141338982566198
y[1] (numeric) = -2.4281817650620182851852875990414
absolute error = 1.26289486106575784e-14
relative error = 5.2009898074228212680134656000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.743
y[1] (analytic) = -2.4379991996877547152995106274908
y[1] (numeric) = -2.4379991996877419356203961437222
absolute error = 1.27796791144837686e-14
relative error = 5.2418717430754359290930202000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.742
y[1] (analytic) = -2.4478696298317837698449525251352
y[1] (numeric) = -2.4478696298317708375991142412395
absolute error = 1.29322458382838957e-14
relative error = 5.2830615163000295861137015999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=3.15
x[1] = -0.741
y[1] (analytic) = -2.4577934135712927625423710988308
y[1] (numeric) = -2.4577934135712796758687008411395
absolute error = 1.30866736702576913e-14
relative error = 5.3245621043642236769512173000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.741
Order of pole = 3e-30
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = -2.4677709118907073618541843523582
y[1] (numeric) = -2.4677709118906941188663141750519
absolute error = 1.32429878701773063e-14
relative error = 5.3663765167047287681112000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.74
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -0.739
y[1] (analytic) = -2.4778024887092797040802114816317
y[1] (numeric) = -2.4778024887092663028661360343396
absolute error = 1.34012140754472921e-14
relative error = 5.4085077953199421000096899000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.738
y[1] (analytic) = -2.4878885109089632035119273057289
y[1] (numeric) = -2.4878885109089496421336200339312
absolute error = 1.35613783072717977e-14
relative error = 5.4509590151678768480508743999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.738
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -0.737
y[1] (analytic) = -2.4980293483625903488191476787313
y[1] (numeric) = -2.4980293483625766253121707477075
absolute error = 1.37235069769310238e-14
relative error = 5.4937332845695010353531614000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.736
y[1] (analytic) = -2.5082253739623571956932686775704
y[1] (numeric) = -2.5082253739623433080663765085432
absolute error = 1.38876268921690272e-14
relative error = 5.5368337456175695115845632000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.735
y[1] (analytic) = -2.51847696364861831631629929958
y[1] (numeric) = -2.518476963648604262551035604581
absolute error = 1.40537652636949990e-14
relative error = 5.5802635745910286635596250000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.734
y[1] (analytic) = -2.5287844964389960175285630760685
y[1] (numeric) = -2.5287844964389817955788512758727
absolute error = 1.42219497118001958e-14
relative error = 5.6240259823750796957038032000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.734
Order of pole = 4.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.733
y[1] (analytic) = -2.5391483544578076916425330983765
y[1] (numeric) = -2.5391483544577932994342600056367
absolute error = 1.43922082730927398e-14
relative error = 5.6681242148869844795368125999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.733
Order of pole = 2.9e-29
TOP MAIN SOLVE Loop
x[1] = -0.732
y[1] (analytic) = -2.5495689229658152167084632797622
y[1] (numeric) = -2.5495689229658006521390559272089
absolute error = 1.45645694073525533e-14
relative error = 5.7125615535077009482148544000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.732
Order of pole = 2.4e-29
TOP MAIN SOLVE Loop
x[1] = -0.731
y[1] (analytic) = -2.5600465903903003766921674358228
y[1] (numeric) = -2.5600465903902856376301629270852
absolute error = 1.47390620045087376e-14
relative error = 5.7573413155194355723844016000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = -2.5705817483554703264895878586282
y[1] (numeric) = -2.5705817483554554107741961168725
absolute error = 1.49157153917417557e-14
relative error = 5.8024668545492025771469000000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.729
y[1] (analytic) = -2.5811747917131971819900315081167
y[1] (numeric) = -2.5811747917131820874306907952913
absolute error = 1.50945593407128254e-14
relative error = 5.8479415610184804250396206000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.728
y[1] (analytic) = -2.5918261185740958715237184021148
y[1] (numeric) = -2.591826118574080595899643479134
absolute error = 1.52756240749229808e-14
relative error = 5.8937688625990582089916415999998e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.1331
Order of pole = 3.096e-27
TOP MAIN SOLVE Loop
x[1] = -0.727
y[1] (analytic) = -2.6025361303389444420034101395271
y[1] (numeric) = -2.6025361303389289830631329352176
absolute error = 1.54589402772043095e-14
relative error = 5.9399522246751654923924385000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.726
y[1] (analytic) = -2.6133052317304510709084415550069
y[1] (numeric) = -2.6133052317304354263693442090798
absolute error = 1.56445390973459271e-14
relative error = 5.9864951508119815591878696000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.725
y[1] (analytic) = -2.6241338308253720939767928164335
y[1] (numeric) = -2.6241338308253562615246329591332
absolute error = 1.58324521598573003e-14
relative error = 6.0334011832306202658859375000003e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.725
Order of pole = 7.3e-29
TOP MAIN SOLVE Loop
x[1] = -0.724
y[1] (analytic) = -2.6350223390869854180814979946004
y[1] (numeric) = -2.6350223390869693953699261230123
absolute error = 1.60227115718715881e-14
relative error = 6.0806739032896897722676544000001e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.584
Order of pole = 5.829e-27
TOP MAIN SOLVE Loop
x[1] = -0.723
y[1] (analytic) = -2.6459711713979237492865370258804
y[1] (numeric) = -2.6459711713979075339366058341575
absolute error = 1.62153499311917229e-14
relative error = 6.1283169319735268006111342999998e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.4073
Order of pole = 6.249e-27
TOP MAIN SOLVE Loop
x[1] = -0.722
y[1] (analytic) = -2.6569807460933721275195165332327
y[1] (numeric) = -2.6569807460933557171191820512192
absolute error = 1.64104003344820135e-14
relative error = 6.1763339303872080300911480000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.722
Order of pole = 3.1e-29
TOP MAIN SOLVE Loop
x[1] = -0.721
y[1] (analytic) = -2.6680514849946343216792995658351
y[1] (numeric) = -2.6680514849946177137829139577272
absolute error = 1.66078963856081079e-14
relative error = 6.2247286002584420859864519000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.721
Order of pole = 6e-30
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=3.40
x[1] = -0.72
y[1] (analytic) = -2.6791838134430727023319615912208
y[1] (numeric) = -2.6791838134430558944597574630096
absolute error = 1.68078722041282112e-14
relative error = 6.2735046844464465739776000000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.719
y[1] (analytic) = -2.6903781603344262734539803107741
y[1] (numeric) = -2.6903781603344092630915463722542
absolute error = 1.70103624339385199e-14
relative error = 6.3226659674579183627511841000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.719
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.718
y[1] (analytic) = -2.7016349581535116099736495494029
y[1] (numeric) = -2.7016349581534943945713974735105
absolute error = 1.72154022520758924e-14
relative error = 6.3722162759702057498974368000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.718
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -0.717
y[1] (analytic) = -2.7129546430093115141568769223607
y[1] (numeric) = -2.7129546430092940911294992415222
absolute error = 1.74230273776808385e-14
relative error = 6.4221594793617928064602004999999e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.716
y[1] (analytic) = -2.7243376546704562711986161585216
y[1] (numeric) = -2.7243376546704386379245350345439
absolute error = 1.76332740811239777e-14
relative error = 6.4724994902502088408281792000004e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.715
y[1] (analytic) = -2.7357844366011024527333393292608
y[1] (numeric) = -2.7357844366010846065541460300785
absolute error = 1.78461791932991823e-14
relative error = 6.5232402650374777469920125000002e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.715
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.714
y[1] (analytic) = -2.747295435997214286384625800669
y[1] (numeric) = -2.7472954359971962246045107139836
absolute error = 1.80617801150866854e-14
relative error = 6.5743858044632225553073776000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.714
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -0.713
y[1] (analytic) = -2.7588711038232526799529061806125
y[1] (numeric) = -2.7588711038232343998380791911026
absolute error = 1.82801148269895099e-14
relative error = 6.6259401541655449029057603000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.712
y[1] (analytic) = -2.7705118948492770604097485137645
y[1] (numeric) = -2.770511894849258559187849567124
absolute error = 1.85012218989466405e-14
relative error = 6.6779074052497992738019839999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.712
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -0.711
y[1] (analytic) = -2.7822182676884652605452394936406
y[1] (numeric) = -2.7822182676884465354047391672084
absolute error = 1.87251405003264322e-14
relative error = 6.7302916948653835341772782000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.711
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = -2.7939906848350567599207624241782
y[1] (numeric) = -2.7939906848350378080103523203475
absolute error = 1.89519104101038307e-14
relative error = 6.7830972067906721496676999999997e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.709
y[1] (analytic) = -2.805829612702724661731917576432
y[1] (numeric) = -2.8058296127027054801598903513876
absolute error = 1.91815720272250444e-14
relative error = 6.8363281720262163937218075999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.709
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -0.708
y[1] (analytic) = -2.8177355216633818633049323626257
y[1] (numeric) = -2.8177355216633624491385511992281
absolute error = 1.94141663811633976e-14
relative error = 6.8899888693963424488730112000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.707
y[1] (analytic) = -2.8297088860864269552544896847392
y[1] (numeric) = -2.8297088860864073055193470145753
absolute error = 1.96497351426701639e-14
relative error = 6.9440836261592768999625276999998e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.707
Order of pole = 3.8e-29
TOP MAIN SOLVE Loop
x[1] = -0.706
y[1] (analytic) = -2.8417501843784354628416497000919
y[1] (numeric) = -2.8417501843784155745210149758278
absolute error = 1.98883206347242641e-14
relative error = 6.9986168186259328504690056000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used
Radius of convergence = 0.706
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -0.705
y[1] (analytic) = -2.8538598990233021228080126397455
y[1] (numeric) = -2.8538598990232819928421689549461
absolute error = 2.01299658436847994e-14
relative error = 7.0535928727874933823584250000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.704
y[1] (analytic) = -2.8660385166228399699474079639368
y[1] (numeric) = -2.86603851662281959523297731347
absolute error = 2.03747144306504668e-14
relative error = 7.1090162649519282744983552000002e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.703
y[1] (analytic) = -2.8782865279378420899305255604119
y[1] (numeric) = -2.878286527937821467319782530412
absolute error = 2.06226107430299999e-14
relative error = 7.1648915223895855940671073000001e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.579
Order of pole = 1.575e-27
TOP MAIN SOLVE Loop
x[1] = -0.702
y[1] (analytic) = -2.890604427929611978442750920247
y[1] (numeric) = -2.8906044279295911047429245923868
absolute error = 2.08736998263278602e-14
relative error = 7.2212232239879997222365616000001e-13 %
Correct digits = 14
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -0.701
y[1] (analytic) = -2.9029927158019685315531547212295
y[1] (numeric) = -2.9029927158019474035257185717304
absolute error = 2.11280274361494991e-14
relative error = 7.2780160009160613050746091000000e-13 %
Correct digits = 14
h = 0.001
NO POLE
Finished!
diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;
Iterations = 300
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Time to Timeout = 2 Minutes 56 Seconds
Percent Done = 100.3 %
> quit
memory used=57.0MB, alloc=4.4MB, time=3.63