|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found_sing := 0;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float
and array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> 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 CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_g[1] := sin(array_tmp3[1]);
> array_tmp4[1] := cos(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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 CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[2] := (att(1,array_tmp4,array_tmp3,1));
> array_tmp4[2] := (-att(1,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[3] := (att(2,array_tmp4,array_tmp3,1));
> array_tmp4[3] := (-att(2,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[4] := (att(3,array_tmp4,array_tmp3,1));
> array_tmp4[4] := (-att(3,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[5] := (att(4,array_tmp4,array_tmp3,1));
> array_tmp4[5] := (-att(4,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit cos FULL $eq_no = 1
> array_tmp4[kkk] := -att(kkk-1,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
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_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := sin(array_tmp3[1]);
array_tmp4[1] := cos(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[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_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp4[2] := -att(1, array_tmp4_g, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[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_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp4[3] := -att(2, array_tmp4_g, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[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_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp4[4] := -att(3, array_tmp4_g, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[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_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp4[5] := -att(4, array_tmp4_g, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[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_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4[kkk] := -att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 16
> # Begin Function number 17
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 26
> # Begin Function number 27
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 27
> # Begin Function number 28
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));
> end;
exact_soln_y := proc(x)
return
cos(sqrt(2.0*x + 3.0)) + sqrt(2.0*x + 3.0)*sin(sqrt(2.0*x + 3.0))
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/cos_sqrt_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4_g:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= 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_g[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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4_g[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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_2D0[1] := 2.0;
> array_const_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 := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T12:29:59-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/cos_sqrt_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(\
sqrt(2.0*x+3.0)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4_g := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := 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_g[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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_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 := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-01-28T12:29:59-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"cos_sqrt_lin");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 165 | ");
logitem_str(html_log_file, "cos_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "cos_sqrt_lin maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/cos_sqrt_linpostode.ode#################
diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));
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 = 6
estimated_steps = 6000
step_error = 1.6666666666666666666666666666667e-14
est_needed_step_err = 1.6666666666666666666666666666667e-14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 4.6145358669108669108669108669109e-107
max_value3 = 4.6145358669108669108669108669109e-107
value3 = 4.6145358669108669108669108669109e-107
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 1.3817732906760362240534389290733
y[1] (numeric) = 1.3817732906760362240534389290733
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -0.999
y[1] (analytic) = 1.3823131722966041549270989688663
y[1] (numeric) = 1.3823131722966041549270989688663
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.01692
Order of pole = 31.45
memory used=3.8MB, alloc=2.8MB, time=0.32
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.67
x[1] = -0.99798484344400505092512079121076
y[1] (analytic) = 1.382860376274414257584439340003
y[1] (numeric) = 1.3828603762744142575844393400029
absolute error = 1e-31
relative error = 7.2313880501379005575877615656127e-30 %
Correct digits = 31
h = 0.00016919275933249151247986813153578
Real estimate of pole used for equation 1
Radius of convergence = 0.01886
Order of pole = 60.08
memory used=11.4MB, alloc=4.0MB, time=1.01
TOP MAIN SOLVE Loop
x[1] = -0.99695637802596259142109001040574
y[1] (analytic) = 1.3834138705219039838786402252302
y[1] (numeric) = 1.3834138705219039838786402252301
absolute error = 1e-31
relative error = 7.2284948221803065736632920533088e-30 %
Correct digits = 31
h = 8.6814523340830827765196068396046e-05
NO POLE for equation 1
memory used=15.2MB, alloc=4.1MB, time=1.37
memory used=19.0MB, alloc=4.1MB, time=1.72
TOP MAIN SOLVE Loop
x[1] = -0.99591460374587262148790765758494
y[1] (analytic) = 1.3839736208444646977153657998573
y[1] (numeric) = 1.3839736208444646977153657998571
absolute error = 2e-31
relative error = 1.4451142492005389758691347388120e-29 %
Correct digits = 30
h = 8.6814523340830827765196068396046e-05
NO POLE for equation 1
memory used=22.8MB, alloc=4.2MB, time=2.08
memory used=26.7MB, alloc=4.2MB, time=2.44
TOP MAIN SOLVE Loop
x[1] = -0.99495964398912348238249050083254
y[1] (analytic) = 1.3844859242123584729996461929723
y[1] (numeric) = 1.3844859242123584729996461929721
absolute error = 2e-31
relative error = 1.4445795114441562938007479858339e-29 %
Correct digits = 30
h = 8.6814523340830827765196068396046e-05
NO POLE for equation 1
memory used=30.5MB, alloc=4.2MB, time=2.80
memory used=34.3MB, alloc=4.3MB, time=3.16
memory used=38.1MB, alloc=4.3MB, time=3.52
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=3.88
x[1] = -0.99396514846458449893766672778486
y[1] (analytic) = 1.3850186229567694642811358865996
y[1] (numeric) = 1.3850186229567694642811358865995
absolute error = 1e-31
relative error = 7.2201195234846525489314459664664e-30 %
Correct digits = 31
h = 4.8010234591472722961432913004860e-05
NO POLE for equation 1
memory used=45.7MB, alloc=4.3MB, time=4.24
memory used=49.5MB, alloc=4.3MB, time=4.60
memory used=53.4MB, alloc=4.3MB, time=4.97
memory used=57.2MB, alloc=4.3MB, time=5.33
memory used=61.0MB, alloc=4.3MB, time=5.69
TOP MAIN SOLVE Loop
x[1] = -0.99299632520006582871336674829627
y[1] (analytic) = 1.3855367718672399787274706537696
y[1] (numeric) = 1.3855367718672399787274706537697
absolute error = 1e-31
relative error = 7.2174194168252538845720992919155e-30 %
Correct digits = 31
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=64.8MB, alloc=4.3MB, time=6.06
memory used=68.6MB, alloc=4.3MB, time=6.42
memory used=72.4MB, alloc=4.3MB, time=6.78
memory used=76.2MB, alloc=4.3MB, time=7.15
memory used=80.1MB, alloc=4.3MB, time=7.52
memory used=83.9MB, alloc=4.3MB, time=7.88
memory used=87.7MB, alloc=4.3MB, time=8.24
TOP MAIN SOLVE Loop
x[1] = -0.99199953877270291380916502222046
y[1] (analytic) = 1.3860690538422602866958943604489
y[1] (numeric) = 1.3860690538422602866958943604488
absolute error = 1e-31
relative error = 7.2146477639620085406491400121116e-30 %
Correct digits = 31
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=91.5MB, alloc=4.3MB, time=8.61
memory used=95.3MB, alloc=4.3MB, time=8.97
memory used=99.1MB, alloc=4.3MB, time=9.34
memory used=103.0MB, alloc=4.3MB, time=9.70
memory used=106.8MB, alloc=4.3MB, time=10.06
memory used=110.6MB, alloc=4.4MB, time=10.43
memory used=114.4MB, alloc=4.4MB, time=10.79
TOP MAIN SOLVE Loop
x[1] = -0.99097719371899736006126581598886
y[1] (analytic) = 1.3866141180576783557528004172563
y[1] (numeric) = 1.3866141180576783557528004172561
absolute error = 2e-31
relative error = 1.4423623515398297070875777174520e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=118.2MB, alloc=4.4MB, time=11.15
memory used=122.0MB, alloc=4.4MB, time=11.52
memory used=125.8MB, alloc=4.4MB, time=11.89
memory used=129.7MB, alloc=4.4MB, time=12.26
memory used=133.5MB, alloc=4.4MB, time=12.62
memory used=137.3MB, alloc=4.4MB, time=12.98
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=13.34
x[1] = -0.98998040729163444515706408991305
y[1] (analytic) = 1.3871447116068700250807160695411
y[1] (numeric) = 1.387144711606870025080716069541
absolute error = 1e-31
relative error = 7.2090531840877571665011717498011e-30 %
Correct digits = 31
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=144.9MB, alloc=4.4MB, time=13.71
memory used=148.7MB, alloc=4.4MB, time=14.08
memory used=152.5MB, alloc=4.4MB, time=14.44
memory used=156.4MB, alloc=4.4MB, time=14.80
memory used=160.2MB, alloc=4.4MB, time=15.16
memory used=164.0MB, alloc=4.4MB, time=15.53
TOP MAIN SOLVE Loop
x[1] = -0.98898362086427153025286236383724
y[1] (analytic) = 1.3876744720797698931182440748829
y[1] (numeric) = 1.3876744720797698931182440748832
absolute error = 3e-31
relative error = 2.1618903138743812250002055770888e-29 %
Correct digits = 30
memory used=167.8MB, alloc=4.4MB, time=15.89
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=171.6MB, alloc=4.4MB, time=16.26
memory used=175.4MB, alloc=4.4MB, time=16.62
memory used=179.2MB, alloc=4.4MB, time=16.98
memory used=183.1MB, alloc=4.4MB, time=17.35
memory used=186.9MB, alloc=4.4MB, time=17.72
memory used=190.7MB, alloc=4.4MB, time=18.08
TOP MAIN SOLVE Loop
x[1] = -0.98798683443690861534866063776143
y[1] (analytic) = 1.3882033997740067578147624804092
y[1] (numeric) = 1.3882033997740067578147624804095
absolute error = 3e-31
relative error = 2.1610665990937541626158114737705e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=194.5MB, alloc=4.4MB, time=18.45
memory used=198.3MB, alloc=4.4MB, time=18.81
memory used=202.1MB, alloc=4.4MB, time=19.18
memory used=206.0MB, alloc=4.4MB, time=19.54
memory used=209.8MB, alloc=4.4MB, time=19.91
memory used=213.6MB, alloc=4.4MB, time=20.27
memory used=217.4MB, alloc=4.4MB, time=20.63
TOP MAIN SOLVE Loop
x[1] = -0.98699004800954570044445891168562
y[1] (analytic) = 1.3887314949871482735385516260997
y[1] (numeric) = 1.3887314949871482735385516261001
absolute error = 4e-31
relative error = 2.8803264089844935554860117773536e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=221.2MB, alloc=4.4MB, time=21.00
memory used=225.0MB, alloc=4.4MB, time=21.37
memory used=228.8MB, alloc=4.4MB, time=21.73
memory used=232.7MB, alloc=4.4MB, time=22.09
memory used=236.5MB, alloc=4.4MB, time=22.46
memory used=240.3MB, alloc=4.4MB, time=22.82
memory used=244.1MB, alloc=4.4MB, time=23.19
TOP MAIN SOLVE Loop
x[1] = -0.98599326158218278554025718560981
y[1] (analytic) = 1.3892587580167009599281361746794
y[1] (numeric) = 1.38925875801670095992813617468
absolute error = 6e-31
relative error = 4.3188498653523486093892338177926e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=247.9MB, alloc=4.4MB, time=23.56
memory used=251.7MB, alloc=4.4MB, time=23.92
memory used=255.5MB, alloc=4.4MB, time=24.29
memory used=259.4MB, alloc=4.4MB, time=24.65
memory used=263.2MB, alloc=4.4MB, time=25.02
memory used=267.0MB, alloc=4.4MB, time=25.38
memory used=270.8MB, alloc=4.4MB, time=25.74
TOP MAIN SOLVE Loop
x[1] = -0.984996475154819870636055459534
y[1] (analytic) = 1.3897851891601102107426365537719
y[1] (numeric) = 1.3897851891601102107426365537726
absolute error = 7e-31
relative error = 5.0367496031745125753947272475879e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=274.6MB, alloc=4.4MB, time=26.11
memory used=278.4MB, alloc=4.4MB, time=26.47
memory used=282.2MB, alloc=4.4MB, time=26.83
memory used=286.1MB, alloc=4.4MB, time=27.20
memory used=289.9MB, alloc=4.4MB, time=27.56
memory used=293.7MB, alloc=4.4MB, time=27.93
memory used=297.5MB, alloc=4.4MB, time=28.29
TOP MAIN SOLVE Loop
x[1] = -0.98399968872745695573185373345819
y[1] (analytic) = 1.3903107887147603027111299007248
y[1] (numeric) = 1.3903107887147603027111299007256
absolute error = 8e-31
relative error = 5.7541091279277272053286419695413e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=301.3MB, alloc=4.4MB, time=28.66
memory used=305.1MB, alloc=4.4MB, time=29.02
memory used=309.0MB, alloc=4.4MB, time=29.39
memory used=312.8MB, alloc=4.4MB, time=29.75
memory used=316.6MB, alloc=4.4MB, time=30.12
memory used=320.4MB, alloc=4.4MB, time=30.48
memory used=324.2MB, alloc=4.4MB, time=30.84
TOP MAIN SOLVE Loop
x[1] = -0.98297734367375140198395452722659
y[1] (analytic) = 1.3908490016462526025487115641828
y[1] (numeric) = 1.3908490016462526025487115641835
absolute error = 7e-31
relative error = 5.0328971669207656191266286957451e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=328.0MB, alloc=4.4MB, time=31.21
memory used=331.8MB, alloc=4.4MB, time=31.57
memory used=335.7MB, alloc=4.4MB, time=31.93
memory used=339.5MB, alloc=4.4MB, time=32.30
memory used=343.3MB, alloc=4.4MB, time=32.66
memory used=347.1MB, alloc=4.4MB, time=33.02
memory used=350.9MB, alloc=4.4MB, time=33.39
TOP MAIN SOLVE Loop
x[1] = -0.98198055724638848707975280115078
y[1] (analytic) = 1.3913729176116580911213906947204
y[1] (numeric) = 1.3913729176116580911213906947208
absolute error = 4e-31
relative error = 2.8748583139494655345840759905297e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=354.7MB, alloc=4.4MB, time=33.75
memory used=358.5MB, alloc=4.4MB, time=34.12
memory used=362.4MB, alloc=4.4MB, time=34.49
memory used=366.2MB, alloc=4.4MB, time=34.85
memory used=370.0MB, alloc=4.4MB, time=35.22
memory used=373.8MB, alloc=4.4MB, time=35.59
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.4MB, time=35.95
x[1] = -0.98098377081902557217555107507497
y[1] (analytic) = 1.3918960028877103720346292895062
y[1] (numeric) = 1.3918960028877103720346292895065
absolute error = 3e-31
relative error = 2.1553334399811632982444935493443e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=381.4MB, alloc=4.4MB, time=36.31
memory used=385.3MB, alloc=4.4MB, time=36.68
memory used=389.1MB, alloc=4.4MB, time=37.05
memory used=392.9MB, alloc=4.4MB, time=37.41
memory used=396.7MB, alloc=4.4MB, time=37.78
memory used=400.5MB, alloc=4.4MB, time=38.14
TOP MAIN SOLVE Loop
x[1] = -0.97998698439166265727134934899916
y[1] (analytic) = 1.3924182577715477762914739133713
y[1] (numeric) = 1.3924182577715477762914739133716
absolute error = 3e-31
relative error = 2.1545250381887810867888836076931e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=404.3MB, alloc=4.4MB, time=38.51
memory used=408.1MB, alloc=4.4MB, time=38.87
memory used=412.0MB, alloc=4.4MB, time=39.23
memory used=415.8MB, alloc=4.4MB, time=39.60
memory used=419.6MB, alloc=4.4MB, time=39.96
memory used=423.4MB, alloc=4.4MB, time=40.33
memory used=427.2MB, alloc=4.4MB, time=40.70
TOP MAIN SOLVE Loop
x[1] = -0.97899019796429974236714762292335
y[1] (analytic) = 1.3929396825602475623236449902813
y[1] (numeric) = 1.3929396825602475623236449902819
absolute error = 6e-31
relative error = 4.3074370520996966555645857068176e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=431.0MB, alloc=4.4MB, time=41.07
memory used=434.8MB, alloc=4.4MB, time=41.43
memory used=438.7MB, alloc=4.4MB, time=41.79
memory used=442.5MB, alloc=4.4MB, time=42.16
memory used=446.3MB, alloc=4.4MB, time=42.52
memory used=450.1MB, alloc=4.4MB, time=42.89
memory used=453.9MB, alloc=4.4MB, time=43.25
TOP MAIN SOLVE Loop
x[1] = -0.97799341153693682746294589684754
y[1] (analytic) = 1.3934602775508259248349312801736
y[1] (numeric) = 1.3934602775508259248349312801742
absolute error = 6e-31
relative error = 4.3058277990856846078495505646990e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=457.7MB, alloc=4.4MB, time=43.62
memory used=461.5MB, alloc=4.4MB, time=43.98
memory used=465.4MB, alloc=4.4MB, time=44.35
memory used=469.2MB, alloc=4.4MB, time=44.71
memory used=473.0MB, alloc=4.4MB, time=45.08
memory used=476.8MB, alloc=4.4MB, time=45.44
memory used=480.6MB, alloc=4.4MB, time=45.81
TOP MAIN SOLVE Loop
x[1] = -0.97699662510957391255874417077173
y[1] (analytic) = 1.393980043040238003643594493471
y[1] (numeric) = 1.3939800430402380036435944934719
absolute error = 9e-31
relative error = 6.4563334639793046381167880770040e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=484.4MB, alloc=4.4MB, time=46.17
memory used=488.2MB, alloc=4.4MB, time=46.56
memory used=492.1MB, alloc=4.4MB, time=46.92
memory used=495.9MB, alloc=4.4MB, time=47.29
memory used=499.7MB, alloc=4.4MB, time=47.65
memory used=503.5MB, alloc=4.4MB, time=48.02
memory used=507.3MB, alloc=4.4MB, time=48.38
TOP MAIN SOLVE Loop
x[1] = -0.97599983868221099765454244469592
y[1] (analytic) = 1.3944989793253778925237841336237
y[1] (numeric) = 1.3944989793253778925237841336247
absolute error = 1.0e-30
relative error = 7.1710342913536862295999929625626e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
Real estimate of pole used for equation 1
Radius of convergence = 0.01272
Order of pole = 11.29
memory used=511.1MB, alloc=4.4MB, time=48.75
memory used=515.0MB, alloc=4.4MB, time=49.11
memory used=518.8MB, alloc=4.4MB, time=49.48
memory used=522.6MB, alloc=4.4MB, time=49.84
memory used=526.4MB, alloc=4.4MB, time=50.21
memory used=530.2MB, alloc=4.4MB, time=50.57
memory used=534.0MB, alloc=4.4MB, time=50.93
TOP MAIN SOLVE Loop
x[1] = -0.97497749362850544390664323846432
y[1] (analytic) = 1.3950303606107640117349062458489
y[1] (numeric) = 1.3950303606107640117349062458497
absolute error = 8e-31
relative error = 5.7346422170320987950836556999095e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=537.8MB, alloc=4.4MB, time=51.30
memory used=541.7MB, alloc=4.4MB, time=51.66
memory used=545.5MB, alloc=4.4MB, time=52.02
memory used=549.3MB, alloc=4.4MB, time=52.39
memory used=553.1MB, alloc=4.4MB, time=52.75
memory used=556.9MB, alloc=4.4MB, time=53.12
memory used=560.7MB, alloc=4.4MB, time=53.49
TOP MAIN SOLVE Loop
x[1] = -0.97398070720114252900244151238851
y[1] (analytic) = 1.3955476181352720864378068682413
y[1] (numeric) = 1.3955476181352720864378068682423
absolute error = 1.0e-30
relative error = 7.1656458511691488086778667933487e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=564.5MB, alloc=4.4MB, time=53.85
memory used=568.4MB, alloc=4.4MB, time=54.21
memory used=572.2MB, alloc=4.4MB, time=54.58
memory used=576.0MB, alloc=4.4MB, time=54.94
memory used=579.8MB, alloc=4.4MB, time=55.31
memory used=583.6MB, alloc=4.4MB, time=55.67
memory used=587.4MB, alloc=4.4MB, time=56.04
TOP MAIN SOLVE Loop
x[1] = -0.9729839207737796140982397863127
y[1] (analytic) = 1.3960640473534312369686991194824
y[1] (numeric) = 1.3960640473534312369686991194834
absolute error = 1.0e-30
relative error = 7.1629951497980047643230360557701e-29 %
Correct digits = 30
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=591.3MB, alloc=4.4MB, time=56.40
memory used=595.1MB, alloc=4.4MB, time=56.77
memory used=598.9MB, alloc=4.4MB, time=57.13
memory used=602.7MB, alloc=4.4MB, time=57.50
memory used=606.5MB, alloc=4.4MB, time=57.86
memory used=610.3MB, alloc=4.4MB, time=58.23
TOP MAIN SOLVE Loop
memory used=614.1MB, alloc=4.4MB, time=58.60
x[1] = -0.97198713434641669919403806023689
y[1] (analytic) = 1.3965796485618898970592125855944
y[1] (numeric) = 1.3965796485618898970592125855958
absolute error = 1.4e-30
relative error = 1.0024490915656920579248281571697e-28 %
Correct digits = 29
h = 2.5558626342638843697480155793169e-05
NO POLE for equation 1
memory used=618.0MB, alloc=4.4MB, time=58.96
memory used=621.8MB, alloc=4.4MB, time=59.32
memory used=625.6MB, alloc=4.4MB, time=59.69
memory used=629.4MB, alloc=4.4MB, time=60.05
memory used=633.2MB, alloc=4.4MB, time=60.42
memory used=637.0MB, alloc=4.4MB, time=60.78
memory used=640.8MB, alloc=4.4MB, time=61.15
memory used=644.7MB, alloc=4.4MB, time=61.51
memory used=648.5MB, alloc=4.4MB, time=61.88
TOP MAIN SOLVE Loop
x[1] = -0.97098790786991216118153636304323
y[1] (analytic) = 1.3970956811640318584991610317997
y[1] (numeric) = 1.3970956811640318584991610318008
absolute error = 1.1e-30
relative error = 7.8734764900532957974888383630245e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=652.3MB, alloc=4.4MB, time=62.24
memory used=656.1MB, alloc=4.4MB, time=62.61
memory used=659.9MB, alloc=4.4MB, time=62.97
memory used=663.7MB, alloc=4.4MB, time=63.34
memory used=667.5MB, alloc=4.4MB, time=63.71
memory used=671.4MB, alloc=4.4MB, time=64.08
memory used=675.2MB, alloc=4.4MB, time=64.44
memory used=679.0MB, alloc=4.4MB, time=64.81
memory used=682.8MB, alloc=4.4MB, time=65.17
memory used=686.6MB, alloc=4.4MB, time=65.54
memory used=690.4MB, alloc=4.4MB, time=65.90
memory used=694.3MB, alloc=4.4MB, time=66.27
TOP MAIN SOLVE Loop
memory used=698.1MB, alloc=4.4MB, time=66.63
x[1] = -0.96999284217430768594109158763514
y[1] (analytic) = 1.3976087387195088412626214414685
y[1] (numeric) = 1.3976087387195088412626214414689
absolute error = 4e-31
relative error = 2.8620313319340045172949164312908e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=701.9MB, alloc=4.4MB, time=67.00
memory used=705.7MB, alloc=4.4MB, time=67.36
memory used=709.5MB, alloc=4.4MB, time=67.73
memory used=713.3MB, alloc=4.4MB, time=68.09
memory used=717.1MB, alloc=4.4MB, time=68.46
memory used=721.0MB, alloc=4.4MB, time=68.82
memory used=724.8MB, alloc=4.4MB, time=69.19
memory used=728.6MB, alloc=4.4MB, time=69.55
memory used=732.4MB, alloc=4.4MB, time=69.92
memory used=736.2MB, alloc=4.4MB, time=70.31
memory used=740.0MB, alloc=4.4MB, time=70.67
memory used=743.8MB, alloc=4.4MB, time=71.03
TOP MAIN SOLVE Loop
x[1] = -0.96899777647870321070064681222705
y[1] (analytic) = 1.3981209720082936652663266219498
y[1] (numeric) = 1.3981209720082936652663266219508
absolute error = 1.0e-30
relative error = 7.1524569048097219420006537112229e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=747.7MB, alloc=4.4MB, time=71.40
memory used=751.5MB, alloc=4.4MB, time=71.76
memory used=755.3MB, alloc=4.4MB, time=72.13
memory used=759.1MB, alloc=4.4MB, time=72.49
memory used=762.9MB, alloc=4.4MB, time=72.85
memory used=766.7MB, alloc=4.4MB, time=73.22
memory used=770.5MB, alloc=4.4MB, time=73.58
memory used=774.4MB, alloc=4.4MB, time=73.95
memory used=778.2MB, alloc=4.4MB, time=74.31
memory used=782.0MB, alloc=4.4MB, time=74.67
memory used=785.8MB, alloc=4.4MB, time=75.04
memory used=789.6MB, alloc=4.4MB, time=75.40
memory used=793.4MB, alloc=4.4MB, time=75.77
TOP MAIN SOLVE Loop
x[1] = -0.96798869577330148933005492730617
y[1] (analytic) = 1.3986395783904527718701525402176
y[1] (numeric) = 1.3986395783904527718701525402184
absolute error = 8e-31
relative error = 5.7198438565612155954171133702940e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=797.3MB, alloc=4.4MB, time=76.13
memory used=801.1MB, alloc=4.4MB, time=76.50
memory used=804.9MB, alloc=4.4MB, time=76.86
memory used=808.7MB, alloc=4.4MB, time=77.22
memory used=812.5MB, alloc=4.4MB, time=77.59
memory used=816.3MB, alloc=4.4MB, time=77.95
memory used=820.1MB, alloc=4.4MB, time=78.32
memory used=824.0MB, alloc=4.4MB, time=78.69
memory used=827.8MB, alloc=4.4MB, time=79.05
memory used=831.6MB, alloc=4.4MB, time=79.42
memory used=835.4MB, alloc=4.4MB, time=79.78
memory used=839.2MB, alloc=4.4MB, time=80.15
TOP MAIN SOLVE Loop
x[1] = -0.96699363007769701408961015189808
y[1] (analytic) = 1.3991501524314295134957849055857
y[1] (numeric) = 1.3991501524314295134957849055867
absolute error = 1.0e-30
relative error = 7.1471957335115872694640899145873e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=843.0MB, alloc=4.4MB, time=80.51
memory used=846.8MB, alloc=4.4MB, time=80.88
memory used=850.7MB, alloc=4.4MB, time=81.25
memory used=854.5MB, alloc=4.4MB, time=81.62
memory used=858.3MB, alloc=4.4MB, time=81.98
memory used=862.1MB, alloc=4.4MB, time=82.35
memory used=865.9MB, alloc=4.4MB, time=82.71
memory used=869.7MB, alloc=4.4MB, time=83.08
memory used=873.5MB, alloc=4.4MB, time=83.44
memory used=877.4MB, alloc=4.4MB, time=83.81
memory used=881.2MB, alloc=4.4MB, time=84.18
memory used=885.0MB, alloc=4.4MB, time=84.54
TOP MAIN SOLVE Loop
memory used=888.8MB, alloc=4.4MB, time=84.91
x[1] = -0.96599856438209253884916537648999
y[1] (analytic) = 1.3996599030942997757953704022443
y[1] (numeric) = 1.3996599030942997757953704022453
absolute error = 1.0e-30
relative error = 7.1445927527769340587189107191457e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=892.6MB, alloc=4.4MB, time=85.27
memory used=896.4MB, alloc=4.4MB, time=85.64
memory used=900.3MB, alloc=4.4MB, time=86.01
memory used=904.1MB, alloc=4.4MB, time=86.37
memory used=907.9MB, alloc=4.4MB, time=86.73
memory used=911.7MB, alloc=4.4MB, time=87.11
memory used=915.5MB, alloc=4.4MB, time=87.47
memory used=919.3MB, alloc=4.4MB, time=87.84
memory used=923.1MB, alloc=4.4MB, time=88.21
memory used=927.0MB, alloc=4.4MB, time=88.57
memory used=930.8MB, alloc=4.4MB, time=88.94
memory used=934.6MB, alloc=4.4MB, time=89.30
TOP MAIN SOLVE Loop
x[1] = -0.96498948367669081747857349156911
y[1] (analytic) = 1.4001759927912416827978700399529
y[1] (numeric) = 1.4001759927912416827978700399545
absolute error = 1.6e-30
relative error = 1.1427134933305137348629326233474e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=938.4MB, alloc=4.4MB, time=89.67
memory used=942.2MB, alloc=4.4MB, time=90.03
memory used=946.0MB, alloc=4.4MB, time=90.40
memory used=949.8MB, alloc=4.4MB, time=90.77
memory used=953.7MB, alloc=4.4MB, time=91.13
memory used=957.5MB, alloc=4.4MB, time=91.50
memory used=961.3MB, alloc=4.4MB, time=91.86
memory used=965.1MB, alloc=4.4MB, time=92.22
memory used=968.9MB, alloc=4.4MB, time=92.59
memory used=972.7MB, alloc=4.4MB, time=92.96
memory used=976.5MB, alloc=4.4MB, time=93.32
memory used=980.4MB, alloc=4.4MB, time=93.68
memory used=984.2MB, alloc=4.4MB, time=94.05
TOP MAIN SOLVE Loop
x[1] = -0.96399441798108634223812871616102
y[1] (analytic) = 1.4006840859954367007391417818421
y[1] (numeric) = 1.400684085995436700739141781844
absolute error = 1.9e-30
relative error = 1.3564800364314198571879943719680e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=988.0MB, alloc=4.4MB, time=94.41
memory used=991.8MB, alloc=4.4MB, time=94.78
memory used=995.6MB, alloc=4.4MB, time=95.15
memory used=999.4MB, alloc=4.4MB, time=95.51
memory used=1003.3MB, alloc=4.4MB, time=95.88
memory used=1007.1MB, alloc=4.4MB, time=96.24
memory used=1010.9MB, alloc=4.4MB, time=96.61
memory used=1014.7MB, alloc=4.4MB, time=96.97
memory used=1018.5MB, alloc=4.4MB, time=97.34
memory used=1022.3MB, alloc=4.4MB, time=97.70
memory used=1026.1MB, alloc=4.4MB, time=98.07
memory used=1030.0MB, alloc=4.4MB, time=98.43
TOP MAIN SOLVE Loop
x[1] = -0.96299935228548186699768394075293
y[1] (analytic) = 1.4011913567095610326980652739436
y[1] (numeric) = 1.4011913567095610326980652739454
absolute error = 1.8e-30
relative error = 1.2846211128699561550294462705587e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1033.8MB, alloc=4.4MB, time=98.80
memory used=1037.6MB, alloc=4.4MB, time=99.16
memory used=1041.4MB, alloc=4.4MB, time=99.53
memory used=1045.2MB, alloc=4.4MB, time=99.89
memory used=1049.0MB, alloc=4.4MB, time=100.26
memory used=1052.8MB, alloc=4.4MB, time=100.62
memory used=1056.7MB, alloc=4.4MB, time=100.99
memory used=1060.5MB, alloc=4.4MB, time=101.35
memory used=1064.3MB, alloc=4.4MB, time=101.71
memory used=1068.1MB, alloc=4.4MB, time=102.07
memory used=1071.9MB, alloc=4.4MB, time=102.44
memory used=1075.7MB, alloc=4.4MB, time=102.80
memory used=1079.5MB, alloc=4.4MB, time=103.17
TOP MAIN SOLVE Loop
x[1] = -0.96199027158008014562709205583205
y[1] (analytic) = 1.4017049324355994955540351067403
y[1] (numeric) = 1.4017049324355994955540351067422
absolute error = 1.9e-30
relative error = 1.3554921267905964058793438059317e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1083.4MB, alloc=4.4MB, time=103.53
memory used=1087.2MB, alloc=4.4MB, time=103.90
memory used=1091.0MB, alloc=4.4MB, time=104.26
memory used=1094.8MB, alloc=4.4MB, time=104.63
memory used=1098.6MB, alloc=4.4MB, time=105.00
memory used=1102.4MB, alloc=4.4MB, time=105.36
memory used=1106.3MB, alloc=4.4MB, time=105.73
memory used=1110.1MB, alloc=4.4MB, time=106.09
memory used=1113.9MB, alloc=4.4MB, time=106.46
memory used=1117.7MB, alloc=4.4MB, time=106.82
memory used=1121.5MB, alloc=4.4MB, time=107.19
memory used=1125.3MB, alloc=4.4MB, time=107.55
TOP MAIN SOLVE Loop
x[1] = -0.96099520588447567038664728042396
y[1] (analytic) = 1.4022105474790741454893756872591
y[1] (numeric) = 1.4022105474790741454893756872606
absolute error = 1.5e-30
relative error = 1.0697394929005019576011318898352e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1129.1MB, alloc=4.4MB, time=107.92
memory used=1133.0MB, alloc=4.4MB, time=108.28
memory used=1136.8MB, alloc=4.4MB, time=108.65
memory used=1140.6MB, alloc=4.4MB, time=109.01
memory used=1144.4MB, alloc=4.4MB, time=109.38
memory used=1148.2MB, alloc=4.4MB, time=109.74
memory used=1152.0MB, alloc=4.4MB, time=110.11
memory used=1155.8MB, alloc=4.4MB, time=110.37
memory used=1159.7MB, alloc=4.4MB, time=110.53
memory used=1163.5MB, alloc=4.4MB, time=110.68
memory used=1167.3MB, alloc=4.4MB, time=110.83
memory used=1171.1MB, alloc=4.4MB, time=110.99
memory used=1174.9MB, alloc=4.4MB, time=111.14
TOP MAIN SOLVE Loop
x[1] = -0.95998612517907394901605539550308
y[1] (analytic) = 1.4027224448207228476175173581791
y[1] (numeric) = 1.4027224448207228476175173581806
absolute error = 1.5e-30
relative error = 1.0693491114642496959589526697066e-28 %
Correct digits = 29
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1178.7MB, alloc=4.4MB, time=111.30
memory used=1182.5MB, alloc=4.4MB, time=111.45
memory used=1186.4MB, alloc=4.4MB, time=111.60
memory used=1190.2MB, alloc=4.4MB, time=111.76
memory used=1194.0MB, alloc=4.4MB, time=111.91
memory used=1197.8MB, alloc=4.4MB, time=112.06
memory used=1201.6MB, alloc=4.4MB, time=112.22
memory used=1205.4MB, alloc=4.4MB, time=112.37
memory used=1209.3MB, alloc=4.4MB, time=112.53
memory used=1213.1MB, alloc=4.4MB, time=112.68
memory used=1216.9MB, alloc=4.4MB, time=112.83
memory used=1220.7MB, alloc=4.4MB, time=112.99
TOP MAIN SOLVE Loop
memory used=1224.5MB, alloc=4.4MB, time=113.14
x[1] = -0.95899105948346947377561062009499
y[1] (analytic) = 1.4032264053877330162047450877207
y[1] (numeric) = 1.4032264053877330162047450877218
absolute error = 1.1e-30
relative error = 7.8390771138321980096948460832811e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1228.3MB, alloc=4.4MB, time=113.30
memory used=1232.1MB, alloc=4.4MB, time=113.45
memory used=1236.0MB, alloc=4.4MB, time=113.61
memory used=1239.8MB, alloc=4.4MB, time=113.76
memory used=1243.6MB, alloc=4.4MB, time=113.92
memory used=1247.4MB, alloc=4.4MB, time=114.07
memory used=1251.2MB, alloc=4.4MB, time=114.23
memory used=1255.0MB, alloc=4.4MB, time=114.38
memory used=1258.8MB, alloc=4.4MB, time=114.53
memory used=1262.7MB, alloc=4.4MB, time=114.69
memory used=1266.5MB, alloc=4.4MB, time=114.84
memory used=1270.3MB, alloc=4.4MB, time=115.00
TOP MAIN SOLVE Loop
x[1] = -0.9579959937878649985351658446869
y[1] (analytic) = 1.4037295449448922143228151078631
y[1] (numeric) = 1.4037295449448922143228151078636
absolute error = 5e-31
relative error = 3.5619397041303213503355228697525e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1274.1MB, alloc=4.4MB, time=115.15
memory used=1277.9MB, alloc=4.4MB, time=115.31
memory used=1281.7MB, alloc=4.4MB, time=115.46
memory used=1285.5MB, alloc=4.4MB, time=115.62
memory used=1289.4MB, alloc=4.4MB, time=115.77
memory used=1293.2MB, alloc=4.4MB, time=115.93
memory used=1297.0MB, alloc=4.4MB, time=116.08
memory used=1300.8MB, alloc=4.4MB, time=116.24
memory used=1304.6MB, alloc=4.4MB, time=116.39
memory used=1308.4MB, alloc=4.4MB, time=116.55
memory used=1312.3MB, alloc=4.4MB, time=116.70
memory used=1316.1MB, alloc=4.4MB, time=116.86
memory used=1319.9MB, alloc=4.4MB, time=117.01
TOP MAIN SOLVE Loop
x[1] = -0.95698691308246327716457395976602
y[1] (analytic) = 1.4042389328399829604519096225398
y[1] (numeric) = 1.4042389328399829604519096225401
absolute error = 3e-31
relative error = 2.1363885659634097138722865906170e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1323.7MB, alloc=4.4MB, time=117.17
memory used=1327.5MB, alloc=4.4MB, time=117.32
memory used=1331.3MB, alloc=4.4MB, time=117.48
memory used=1335.1MB, alloc=4.4MB, time=117.63
memory used=1339.0MB, alloc=4.4MB, time=117.78
memory used=1342.8MB, alloc=4.4MB, time=117.94
memory used=1346.6MB, alloc=4.4MB, time=118.09
memory used=1350.4MB, alloc=4.4MB, time=118.25
memory used=1354.2MB, alloc=4.4MB, time=118.40
memory used=1358.0MB, alloc=4.4MB, time=118.55
memory used=1361.8MB, alloc=4.4MB, time=118.71
memory used=1365.7MB, alloc=4.4MB, time=118.86
TOP MAIN SOLVE Loop
x[1] = -0.95599184738685880192412918435793
y[1] (analytic) = 1.4047404197068571293942661740247
y[1] (numeric) = 1.4047404197068571293942661740247
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1369.5MB, alloc=4.4MB, time=119.02
memory used=1373.3MB, alloc=4.4MB, time=119.17
memory used=1377.1MB, alloc=4.4MB, time=119.33
memory used=1380.9MB, alloc=4.4MB, time=119.48
memory used=1384.7MB, alloc=4.4MB, time=119.63
memory used=1388.5MB, alloc=4.4MB, time=119.79
memory used=1392.4MB, alloc=4.4MB, time=119.94
memory used=1396.2MB, alloc=4.4MB, time=120.10
memory used=1400.0MB, alloc=4.4MB, time=120.25
memory used=1403.8MB, alloc=4.4MB, time=120.41
memory used=1407.6MB, alloc=4.4MB, time=120.56
memory used=1411.4MB, alloc=4.4MB, time=120.72
memory used=1415.3MB, alloc=4.4MB, time=120.87
TOP MAIN SOLVE Loop
x[1] = -0.95499678169125432668368440894984
y[1] (analytic) = 1.4052410864504500744359087390719
y[1] (numeric) = 1.4052410864504500744359087390718
absolute error = 1e-31
relative error = 7.1162166381424031930466216367511e-30 %
Correct digits = 31
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1419.1MB, alloc=4.4MB, time=121.03
memory used=1422.9MB, alloc=4.4MB, time=121.18
memory used=1426.7MB, alloc=4.4MB, time=121.34
memory used=1430.5MB, alloc=4.4MB, time=121.49
memory used=1434.3MB, alloc=4.4MB, time=121.64
memory used=1438.1MB, alloc=4.4MB, time=121.80
memory used=1442.0MB, alloc=4.4MB, time=121.95
memory used=1445.8MB, alloc=4.4MB, time=122.11
memory used=1449.6MB, alloc=4.4MB, time=122.26
memory used=1453.4MB, alloc=4.4MB, time=122.42
memory used=1457.2MB, alloc=4.4MB, time=122.57
memory used=1461.0MB, alloc=4.4MB, time=122.73
TOP MAIN SOLVE Loop
x[1] = -0.95398770098585260531309252402896
y[1] (analytic) = 1.405747967608815594661378298962
y[1] (numeric) = 1.405747967608815594661378298962
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1464.8MB, alloc=4.4MB, time=122.88
memory used=1468.7MB, alloc=4.4MB, time=123.03
memory used=1472.5MB, alloc=4.4MB, time=123.19
memory used=1476.3MB, alloc=4.4MB, time=123.34
memory used=1480.1MB, alloc=4.4MB, time=123.50
memory used=1483.9MB, alloc=4.4MB, time=123.65
memory used=1487.7MB, alloc=4.4MB, time=123.81
memory used=1491.5MB, alloc=4.4MB, time=123.96
memory used=1495.4MB, alloc=4.4MB, time=124.12
memory used=1499.2MB, alloc=4.4MB, time=124.27
memory used=1503.0MB, alloc=4.4MB, time=124.43
memory used=1506.8MB, alloc=4.4MB, time=124.58
memory used=1510.6MB, alloc=4.4MB, time=124.73
TOP MAIN SOLVE Loop
x[1] = -0.95299263529024813007264774862087
y[1] (analytic) = 1.406246983447196974395513579665
y[1] (numeric) = 1.4062469834471969743955135796654
absolute error = 4e-31
relative error = 2.8444505460873015945678244839448e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1514.4MB, alloc=4.4MB, time=124.89
memory used=1518.2MB, alloc=4.4MB, time=125.04
memory used=1522.1MB, alloc=4.4MB, time=125.20
memory used=1525.9MB, alloc=4.4MB, time=125.35
memory used=1529.7MB, alloc=4.4MB, time=125.50
memory used=1533.5MB, alloc=4.4MB, time=125.66
memory used=1537.3MB, alloc=4.4MB, time=125.81
memory used=1541.1MB, alloc=4.4MB, time=125.96
memory used=1545.0MB, alloc=4.4MB, time=126.12
memory used=1548.8MB, alloc=4.4MB, time=126.27
memory used=1552.6MB, alloc=4.4MB, time=126.43
memory used=1556.4MB, alloc=4.4MB, time=126.58
TOP MAIN SOLVE Loop
x[1] = -0.95199756959464365483220297321278
y[1] (analytic) = 1.4067451800483178694524547714405
y[1] (numeric) = 1.4067451800483178694524547714408
absolute error = 3e-31
relative error = 2.1325823912877797544123472582983e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1560.2MB, alloc=4.4MB, time=126.74
memory used=1564.0MB, alloc=4.4MB, time=126.89
memory used=1567.8MB, alloc=4.4MB, time=127.04
memory used=1571.7MB, alloc=4.4MB, time=127.20
memory used=1575.5MB, alloc=4.4MB, time=127.35
memory used=1579.3MB, alloc=4.4MB, time=127.51
memory used=1583.1MB, alloc=4.4MB, time=127.66
memory used=1586.9MB, alloc=4.4MB, time=127.82
memory used=1590.7MB, alloc=4.4MB, time=127.98
memory used=1594.5MB, alloc=4.4MB, time=128.13
memory used=1598.4MB, alloc=4.4MB, time=128.28
memory used=1602.2MB, alloc=4.4MB, time=128.44
memory used=1606.0MB, alloc=4.4MB, time=128.59
TOP MAIN SOLVE Loop
x[1] = -0.9509884888892419334616110882919
y[1] (analytic) = 1.4072495571781128329260912841479
y[1] (numeric) = 1.4072495571781128329260912841482
absolute error = 3e-31
relative error = 2.1318180451346170498017157485848e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1609.8MB, alloc=4.4MB, time=128.75
memory used=1613.6MB, alloc=4.4MB, time=128.90
memory used=1617.4MB, alloc=4.4MB, time=129.06
memory used=1621.2MB, alloc=4.4MB, time=129.21
memory used=1625.1MB, alloc=4.4MB, time=129.37
memory used=1628.9MB, alloc=4.4MB, time=129.53
memory used=1632.7MB, alloc=4.4MB, time=129.68
memory used=1636.5MB, alloc=4.4MB, time=129.83
memory used=1640.3MB, alloc=4.4MB, time=129.99
memory used=1644.1MB, alloc=4.4MB, time=130.15
memory used=1648.0MB, alloc=4.4MB, time=130.30
memory used=1651.8MB, alloc=4.4MB, time=130.45
TOP MAIN SOLVE Loop
memory used=1655.6MB, alloc=4.4MB, time=130.60
x[1] = -0.94999342319363745822116631288381
y[1] (analytic) = 1.4077461046579901204274202696734
y[1] (numeric) = 1.407746104657990120427420269674
absolute error = 6e-31
relative error = 4.2621321985172115393189356420369e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1659.4MB, alloc=4.4MB, time=130.76
memory used=1663.2MB, alloc=4.4MB, time=130.91
memory used=1667.0MB, alloc=4.4MB, time=131.07
memory used=1670.8MB, alloc=4.4MB, time=131.22
memory used=1674.7MB, alloc=4.4MB, time=131.38
memory used=1678.5MB, alloc=4.4MB, time=131.53
memory used=1682.3MB, alloc=4.4MB, time=131.69
memory used=1686.1MB, alloc=4.4MB, time=131.84
memory used=1689.9MB, alloc=4.4MB, time=132.00
memory used=1693.7MB, alloc=4.4MB, time=132.15
memory used=1697.5MB, alloc=4.4MB, time=132.31
memory used=1701.4MB, alloc=4.4MB, time=132.46
TOP MAIN SOLVE Loop
x[1] = -0.94899835749803298298072153747572
y[1] (analytic) = 1.4082418337860788944977855491984
y[1] (numeric) = 1.4082418337860788944977855491992
absolute error = 8e-31
relative error = 5.6808424576422944830104773790552e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1705.2MB, alloc=4.4MB, time=132.62
memory used=1709.0MB, alloc=4.4MB, time=132.77
memory used=1712.8MB, alloc=4.4MB, time=132.92
memory used=1716.6MB, alloc=4.4MB, time=133.08
memory used=1720.4MB, alloc=4.4MB, time=133.23
memory used=1724.3MB, alloc=4.4MB, time=133.39
memory used=1728.1MB, alloc=4.4MB, time=133.54
memory used=1731.9MB, alloc=4.4MB, time=133.70
memory used=1735.7MB, alloc=4.4MB, time=133.85
memory used=1739.5MB, alloc=4.4MB, time=134.01
memory used=1743.3MB, alloc=4.4MB, time=134.17
memory used=1747.1MB, alloc=4.4MB, time=134.32
memory used=1751.0MB, alloc=4.4MB, time=134.47
TOP MAIN SOLVE Loop
x[1] = -0.94798927679263126161012965255484
y[1] (analytic) = 1.4087437095937806410636407631779
y[1] (numeric) = 1.408743709593780641063640763179
absolute error = 1.1e-30
relative error = 7.8083755938629272233437774487435e-29 %
Correct digits = 30
h = 1.4015009797246130147109512788374e-05
NO POLE for equation 1
memory used=1754.8MB, alloc=4.4MB, time=134.63
memory used=1758.6MB, alloc=4.4MB, time=134.78
memory used=1762.4MB, alloc=4.4MB, time=134.94
memory used=1766.2MB, alloc=4.4MB, time=135.09
memory used=1770.0MB, alloc=4.4MB, time=135.25
memory used=1773.8MB, alloc=4.4MB, time=135.40
memory used=1777.7MB, alloc=4.4MB, time=135.56
memory used=1781.5MB, alloc=4.4MB, time=135.71
memory used=1785.3MB, alloc=4.4MB, time=135.86
memory used=1789.1MB, alloc=4.4MB, time=136.02
memory used=1792.9MB, alloc=4.4MB, time=136.17
memory used=1796.7MB, alloc=4.4MB, time=136.32
memory used=1800.5MB, alloc=4.4MB, time=136.48
memory used=1804.4MB, alloc=4.4MB, time=136.63
memory used=1808.2MB, alloc=4.4MB, time=136.79
memory used=1812.0MB, alloc=4.4MB, time=136.95
memory used=1815.8MB, alloc=4.4MB, time=137.10
TOP MAIN SOLVE Loop
x[1] = -0.94699797305726917272652302454624
y[1] (analytic) = 1.4092359249900959759821456629274
y[1] (numeric) = 1.4092359249900959759821456629285
absolute error = 1.1e-30
relative error = 7.8056482984403816757812765655095e-29 %
Correct digits = 30
h = 1.0075141500668481994428025733770e-05
NO POLE for equation 1
memory used=1819.6MB, alloc=4.4MB, time=137.25
memory used=1823.4MB, alloc=4.4MB, time=137.41
memory used=1827.3MB, alloc=4.4MB, time=137.57
memory used=1831.1MB, alloc=4.4MB, time=137.72
memory used=1834.9MB, alloc=4.4MB, time=137.88
memory used=1838.7MB, alloc=4.4MB, time=138.03
memory used=1842.5MB, alloc=4.4MB, time=138.19
memory used=1846.3MB, alloc=4.4MB, time=138.34
memory used=1850.1MB, alloc=4.4MB, time=138.50
memory used=1854.0MB, alloc=4.4MB, time=138.65
memory used=1857.8MB, alloc=4.4MB, time=138.80
memory used=1861.6MB, alloc=4.5MB, time=138.96
memory used=1865.4MB, alloc=4.5MB, time=139.12
memory used=1869.2MB, alloc=4.5MB, time=139.27
memory used=1873.0MB, alloc=4.5MB, time=139.43
memory used=1876.8MB, alloc=4.5MB, time=139.59
memory used=1880.7MB, alloc=4.5MB, time=139.74
TOP MAIN SOLVE Loop
memory used=1884.5MB, alloc=4.5MB, time=139.89
x[1] = -0.94599045890720232452708022197324
y[1] (analytic) = 1.4097353580927114676356540788892
y[1] (numeric) = 1.4097353580927114676356540788906
absolute error = 1.4e-30
relative error = 9.9309419456862965319842288950629e-29 %
Correct digits = 30
h = 1.0075141500668481994428025733770e-05
NO POLE for equation 1
memory used=1888.3MB, alloc=4.5MB, time=140.05
memory used=1892.1MB, alloc=4.5MB, time=140.21
memory used=1895.9MB, alloc=4.5MB, time=140.36
memory used=1899.7MB, alloc=4.5MB, time=140.51
memory used=1903.5MB, alloc=4.5MB, time=140.67
memory used=1907.4MB, alloc=4.5MB, time=140.82
memory used=1911.2MB, alloc=4.5MB, time=140.97
memory used=1915.0MB, alloc=4.5MB, time=141.13
memory used=1918.8MB, alloc=4.5MB, time=141.28
memory used=1922.6MB, alloc=4.5MB, time=141.44
memory used=1926.4MB, alloc=4.5MB, time=141.59
memory used=1930.3MB, alloc=4.5MB, time=141.75
memory used=1934.1MB, alloc=4.5MB, time=141.90
memory used=1937.9MB, alloc=4.5MB, time=142.05
memory used=1941.7MB, alloc=4.5MB, time=142.21
memory used=1945.5MB, alloc=4.5MB, time=142.36
memory used=1949.3MB, alloc=4.5MB, time=142.52
memory used=1953.1MB, alloc=4.5MB, time=142.67
memory used=1957.0MB, alloc=4.5MB, time=142.83
memory used=1960.8MB, alloc=4.5MB, time=142.98
memory used=1964.6MB, alloc=4.5MB, time=143.14
memory used=1968.4MB, alloc=4.5MB, time=143.29
memory used=1972.2MB, alloc=4.5MB, time=143.44
memory used=1976.0MB, alloc=4.5MB, time=143.60
memory used=1979.8MB, alloc=4.5MB, time=143.75
memory used=1983.7MB, alloc=4.5MB, time=143.90
memory used=1987.5MB, alloc=4.5MB, time=144.06
memory used=1991.3MB, alloc=4.5MB, time=144.21
memory used=1995.1MB, alloc=4.5MB, time=144.37
memory used=1998.9MB, alloc=4.5MB, time=144.52
memory used=2002.7MB, alloc=4.5MB, time=144.68
memory used=2006.5MB, alloc=4.5MB, time=144.83
memory used=2010.4MB, alloc=4.5MB, time=144.98
TOP MAIN SOLVE Loop
x[1] = -0.94499747051076572609875655316894
y[1] (analytic) = 1.4102267709430733148756863961263
y[1] (numeric) = 1.4102267709430733148756863961279
absolute error = 1.6e-30
relative error = 1.1345692997517115417735029366039e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2014.2MB, alloc=4.5MB, time=145.14
memory used=2018.0MB, alloc=4.5MB, time=145.29
memory used=2021.8MB, alloc=4.5MB, time=145.45
memory used=2025.6MB, alloc=4.5MB, time=145.61
memory used=2029.4MB, alloc=4.5MB, time=145.76
memory used=2033.3MB, alloc=4.5MB, time=145.92
memory used=2037.1MB, alloc=4.5MB, time=146.07
memory used=2040.9MB, alloc=4.5MB, time=146.22
memory used=2044.7MB, alloc=4.5MB, time=146.38
memory used=2048.5MB, alloc=4.5MB, time=146.53
memory used=2052.3MB, alloc=4.5MB, time=146.69
memory used=2056.1MB, alloc=4.5MB, time=146.84
memory used=2060.0MB, alloc=4.5MB, time=147.00
memory used=2063.8MB, alloc=4.5MB, time=147.15
memory used=2067.6MB, alloc=4.5MB, time=147.30
memory used=2071.4MB, alloc=4.5MB, time=147.46
memory used=2075.2MB, alloc=4.5MB, time=147.61
memory used=2079.0MB, alloc=4.5MB, time=147.77
memory used=2082.8MB, alloc=4.5MB, time=147.92
memory used=2086.7MB, alloc=4.5MB, time=148.07
memory used=2090.5MB, alloc=4.5MB, time=148.23
memory used=2094.3MB, alloc=4.5MB, time=148.38
memory used=2098.1MB, alloc=4.5MB, time=148.54
memory used=2101.9MB, alloc=4.5MB, time=148.69
memory used=2105.7MB, alloc=4.5MB, time=148.85
memory used=2109.5MB, alloc=4.5MB, time=149.00
memory used=2113.4MB, alloc=4.5MB, time=149.15
memory used=2117.2MB, alloc=4.5MB, time=149.31
memory used=2121.0MB, alloc=4.5MB, time=149.46
memory used=2124.8MB, alloc=4.5MB, time=149.62
memory used=2128.6MB, alloc=4.5MB, time=149.77
memory used=2132.4MB, alloc=4.5MB, time=149.93
memory used=2136.3MB, alloc=4.5MB, time=150.08
memory used=2140.1MB, alloc=4.5MB, time=150.23
memory used=2143.9MB, alloc=4.5MB, time=150.39
TOP MAIN SOLVE Loop
x[1] = -0.94399618234271660082713079491064
y[1] (analytic) = 1.4107214675099226849563143749122
y[1] (numeric) = 1.4107214675099226849563143749141
absolute error = 1.9e-30
relative error = 1.3468285864776037685456321496974e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2147.7MB, alloc=4.5MB, time=150.55
memory used=2151.5MB, alloc=4.5MB, time=150.70
memory used=2155.3MB, alloc=4.5MB, time=150.85
memory used=2159.1MB, alloc=4.5MB, time=151.01
memory used=2163.0MB, alloc=4.5MB, time=151.16
memory used=2166.8MB, alloc=4.5MB, time=151.32
memory used=2170.6MB, alloc=4.5MB, time=151.47
memory used=2174.4MB, alloc=4.5MB, time=151.63
memory used=2178.2MB, alloc=4.5MB, time=151.78
memory used=2182.0MB, alloc=4.5MB, time=151.94
memory used=2185.8MB, alloc=4.5MB, time=152.09
memory used=2189.7MB, alloc=4.5MB, time=152.25
memory used=2193.5MB, alloc=4.5MB, time=152.40
memory used=2197.3MB, alloc=4.5MB, time=152.55
memory used=2201.1MB, alloc=4.5MB, time=152.71
memory used=2204.9MB, alloc=4.5MB, time=152.87
memory used=2208.7MB, alloc=4.5MB, time=153.02
memory used=2212.5MB, alloc=4.5MB, time=153.17
memory used=2216.4MB, alloc=4.5MB, time=153.33
memory used=2220.2MB, alloc=4.5MB, time=153.48
memory used=2224.0MB, alloc=4.5MB, time=153.64
memory used=2227.8MB, alloc=4.5MB, time=153.79
memory used=2231.6MB, alloc=4.5MB, time=153.95
memory used=2235.4MB, alloc=4.5MB, time=154.10
memory used=2239.3MB, alloc=4.5MB, time=154.26
memory used=2243.1MB, alloc=4.5MB, time=154.41
memory used=2246.9MB, alloc=4.5MB, time=154.56
memory used=2250.7MB, alloc=4.5MB, time=154.72
memory used=2254.5MB, alloc=4.5MB, time=154.87
memory used=2258.3MB, alloc=4.5MB, time=155.03
memory used=2262.1MB, alloc=4.5MB, time=155.18
memory used=2266.0MB, alloc=4.5MB, time=155.33
memory used=2269.8MB, alloc=4.5MB, time=155.49
memory used=2273.6MB, alloc=4.5MB, time=155.64
memory used=2277.4MB, alloc=4.5MB, time=155.80
memory used=2281.2MB, alloc=4.5MB, time=155.95
TOP MAIN SOLVE Loop
x[1] = -0.94299985104678653063110714436649
y[1] (analytic) = 1.411212894385562128202843049952
y[1] (numeric) = 1.4112128943855621282028430499544
absolute error = 2.4e-30
relative error = 1.7006647328324992517036781691999e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2285.0MB, alloc=4.5MB, time=156.11
memory used=2288.8MB, alloc=4.5MB, time=156.26
memory used=2292.7MB, alloc=4.5MB, time=156.42
memory used=2296.5MB, alloc=4.5MB, time=156.57
memory used=2300.3MB, alloc=4.5MB, time=156.72
memory used=2304.1MB, alloc=4.5MB, time=156.88
memory used=2307.9MB, alloc=4.5MB, time=157.03
memory used=2311.7MB, alloc=4.5MB, time=157.19
memory used=2315.5MB, alloc=4.5MB, time=157.35
memory used=2319.4MB, alloc=4.5MB, time=157.50
memory used=2323.2MB, alloc=4.5MB, time=157.66
memory used=2327.0MB, alloc=4.5MB, time=157.81
memory used=2330.8MB, alloc=4.5MB, time=157.96
memory used=2334.6MB, alloc=4.5MB, time=158.12
memory used=2338.4MB, alloc=4.5MB, time=158.27
memory used=2342.3MB, alloc=4.5MB, time=158.42
memory used=2346.1MB, alloc=4.5MB, time=158.58
memory used=2349.9MB, alloc=4.5MB, time=158.73
memory used=2353.7MB, alloc=4.5MB, time=158.88
memory used=2357.5MB, alloc=4.5MB, time=159.04
memory used=2361.3MB, alloc=4.5MB, time=159.19
memory used=2365.1MB, alloc=4.5MB, time=159.35
memory used=2369.0MB, alloc=4.5MB, time=159.50
memory used=2372.8MB, alloc=4.5MB, time=159.66
memory used=2376.6MB, alloc=4.5MB, time=159.81
memory used=2380.4MB, alloc=4.5MB, time=159.96
memory used=2384.2MB, alloc=4.5MB, time=160.12
memory used=2388.0MB, alloc=4.5MB, time=160.27
memory used=2391.8MB, alloc=4.5MB, time=160.43
memory used=2395.7MB, alloc=4.5MB, time=160.58
memory used=2399.5MB, alloc=4.5MB, time=160.74
memory used=2403.3MB, alloc=4.5MB, time=160.89
memory used=2407.1MB, alloc=4.5MB, time=161.04
memory used=2410.9MB, alloc=4.5MB, time=161.20
memory used=2414.7MB, alloc=4.5MB, time=161.35
TOP MAIN SOLVE Loop
x[1] = -0.94199856287873740535948138610819
y[1] (analytic) = 1.4117059416872479559345016986607
y[1] (numeric) = 1.4117059416872479559345016986632
absolute error = 2.5e-30
relative error = 1.7709070466984368609429080261344e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
Real estimate of pole used for equation 1
Radius of convergence = 0.0528
Order of pole = 31.16
memory used=2418.5MB, alloc=4.5MB, time=161.50
memory used=2422.4MB, alloc=4.5MB, time=161.66
memory used=2426.2MB, alloc=4.5MB, time=161.81
memory used=2430.0MB, alloc=4.5MB, time=161.97
memory used=2433.8MB, alloc=4.5MB, time=162.12
memory used=2437.6MB, alloc=4.5MB, time=162.27
memory used=2441.4MB, alloc=4.5MB, time=162.43
memory used=2445.3MB, alloc=4.5MB, time=162.58
memory used=2449.1MB, alloc=4.5MB, time=162.74
memory used=2452.9MB, alloc=4.5MB, time=162.89
memory used=2456.7MB, alloc=4.5MB, time=163.05
memory used=2460.5MB, alloc=4.5MB, time=163.20
memory used=2464.3MB, alloc=4.5MB, time=163.36
memory used=2468.1MB, alloc=4.5MB, time=163.51
memory used=2472.0MB, alloc=4.5MB, time=163.67
memory used=2475.8MB, alloc=4.5MB, time=163.82
memory used=2479.6MB, alloc=4.5MB, time=163.97
memory used=2483.4MB, alloc=4.5MB, time=164.13
memory used=2487.2MB, alloc=4.5MB, time=164.28
memory used=2491.0MB, alloc=4.5MB, time=164.44
memory used=2494.8MB, alloc=4.5MB, time=164.59
memory used=2498.7MB, alloc=4.5MB, time=164.74
memory used=2502.5MB, alloc=4.5MB, time=164.90
memory used=2506.3MB, alloc=4.5MB, time=165.05
memory used=2510.1MB, alloc=4.5MB, time=165.21
memory used=2513.9MB, alloc=4.5MB, time=165.36
memory used=2517.7MB, alloc=4.5MB, time=165.51
memory used=2521.6MB, alloc=4.5MB, time=165.67
memory used=2525.4MB, alloc=4.5MB, time=165.82
memory used=2529.2MB, alloc=4.5MB, time=165.98
memory used=2533.0MB, alloc=4.5MB, time=166.13
memory used=2536.8MB, alloc=4.5MB, time=166.29
memory used=2540.6MB, alloc=4.5MB, time=166.44
memory used=2544.4MB, alloc=4.5MB, time=166.59
memory used=2548.3MB, alloc=4.5MB, time=166.75
memory used=2552.1MB, alloc=4.5MB, time=166.90
TOP MAIN SOLVE Loop
x[1] = -0.94099727471068828008785562784989
y[1] (analytic) = 1.4121981627575606525526446666893
y[1] (numeric) = 1.4121981627575606525526446666921
absolute error = 2.8e-30
relative error = 1.9827245735347203194000992964894e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2555.9MB, alloc=4.5MB, time=167.06
memory used=2559.7MB, alloc=4.5MB, time=167.21
memory used=2563.5MB, alloc=4.5MB, time=167.37
memory used=2567.3MB, alloc=4.5MB, time=167.52
memory used=2571.1MB, alloc=4.5MB, time=167.68
memory used=2575.0MB, alloc=4.5MB, time=167.83
memory used=2578.8MB, alloc=4.5MB, time=167.99
memory used=2582.6MB, alloc=4.5MB, time=168.14
memory used=2586.4MB, alloc=4.5MB, time=168.29
memory used=2590.2MB, alloc=4.5MB, time=168.45
memory used=2594.0MB, alloc=4.5MB, time=168.60
memory used=2597.8MB, alloc=4.5MB, time=168.76
memory used=2601.7MB, alloc=4.5MB, time=168.91
memory used=2605.5MB, alloc=4.5MB, time=169.07
memory used=2609.3MB, alloc=4.5MB, time=169.22
memory used=2613.1MB, alloc=4.5MB, time=169.38
memory used=2616.9MB, alloc=4.5MB, time=169.53
memory used=2620.7MB, alloc=4.5MB, time=169.69
memory used=2624.5MB, alloc=4.5MB, time=169.84
memory used=2628.4MB, alloc=4.5MB, time=170.00
memory used=2632.2MB, alloc=4.5MB, time=170.15
memory used=2636.0MB, alloc=4.5MB, time=170.31
memory used=2639.8MB, alloc=4.5MB, time=170.46
memory used=2643.6MB, alloc=4.5MB, time=170.61
memory used=2647.4MB, alloc=4.5MB, time=170.77
memory used=2651.3MB, alloc=4.5MB, time=170.92
memory used=2655.1MB, alloc=4.5MB, time=171.07
memory used=2658.9MB, alloc=4.5MB, time=171.23
memory used=2662.7MB, alloc=4.5MB, time=171.38
memory used=2666.5MB, alloc=4.5MB, time=171.54
memory used=2670.3MB, alloc=4.5MB, time=171.69
memory used=2674.1MB, alloc=4.5MB, time=171.85
memory used=2678.0MB, alloc=4.5MB, time=172.00
memory used=2681.8MB, alloc=4.5MB, time=172.16
memory used=2685.6MB, alloc=4.5MB, time=172.31
TOP MAIN SOLVE Loop
x[1] = -0.93999598654263915481622986959159
y[1] (analytic) = 1.4126895578952064812256215975066
y[1] (numeric) = 1.4126895578952064812256215975095
absolute error = 2.9e-30
relative error = 2.0528218558653226951176183386040e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2689.4MB, alloc=4.5MB, time=172.47
memory used=2693.2MB, alloc=4.5MB, time=172.62
memory used=2697.0MB, alloc=4.5MB, time=172.78
memory used=2700.8MB, alloc=4.5MB, time=172.93
memory used=2704.7MB, alloc=4.5MB, time=173.08
memory used=2708.5MB, alloc=4.5MB, time=173.24
memory used=2712.3MB, alloc=4.5MB, time=173.40
memory used=2716.1MB, alloc=4.5MB, time=173.55
memory used=2719.9MB, alloc=4.5MB, time=173.70
memory used=2723.7MB, alloc=4.5MB, time=173.86
memory used=2727.6MB, alloc=4.5MB, time=174.01
memory used=2731.4MB, alloc=4.5MB, time=174.17
memory used=2735.2MB, alloc=4.5MB, time=174.32
memory used=2739.0MB, alloc=4.5MB, time=174.48
memory used=2742.8MB, alloc=4.5MB, time=174.63
memory used=2746.6MB, alloc=4.5MB, time=174.78
memory used=2750.4MB, alloc=4.5MB, time=174.94
memory used=2754.3MB, alloc=4.5MB, time=175.10
memory used=2758.1MB, alloc=4.5MB, time=175.25
memory used=2761.9MB, alloc=4.5MB, time=175.41
memory used=2765.7MB, alloc=4.5MB, time=175.56
memory used=2769.5MB, alloc=4.5MB, time=175.72
memory used=2773.3MB, alloc=4.5MB, time=175.87
memory used=2777.1MB, alloc=4.5MB, time=176.03
memory used=2781.0MB, alloc=4.5MB, time=176.18
memory used=2784.8MB, alloc=4.5MB, time=176.34
memory used=2788.6MB, alloc=4.5MB, time=176.49
memory used=2792.4MB, alloc=4.5MB, time=176.65
memory used=2796.2MB, alloc=4.5MB, time=176.80
memory used=2800.0MB, alloc=4.5MB, time=176.96
memory used=2803.8MB, alloc=4.5MB, time=177.11
memory used=2807.7MB, alloc=4.5MB, time=177.26
memory used=2811.5MB, alloc=4.5MB, time=177.42
memory used=2815.3MB, alloc=4.5MB, time=177.57
memory used=2819.1MB, alloc=4.5MB, time=177.72
TOP MAIN SOLVE Loop
x[1] = -0.93899965524670908462020621904744
y[1] (analytic) = 1.4131777008699731713486971936896
y[1] (numeric) = 1.4131777008699731713486971936931
absolute error = 3.5e-30
relative error = 2.4766878205376068716101344738792e-28 %
Correct digits = 29
h = 4.9568721190550756021077141548653e-06
NO POLE for equation 1
memory used=2822.9MB, alloc=4.5MB, time=177.88
memory used=2826.7MB, alloc=4.5MB, time=178.03
memory used=2830.6MB, alloc=4.5MB, time=178.19
memory used=2834.4MB, alloc=4.5MB, time=178.34
memory used=2838.2MB, alloc=4.5MB, time=178.50
memory used=2842.0MB, alloc=4.5MB, time=178.65
memory used=2845.8MB, alloc=4.5MB, time=178.80
memory used=2849.6MB, alloc=4.5MB, time=178.96
memory used=2853.4MB, alloc=4.5MB, time=179.12
memory used=2857.3MB, alloc=4.5MB, time=179.27
memory used=2861.1MB, alloc=4.5MB, time=179.42
memory used=2864.9MB, alloc=4.5MB, time=179.58
memory used=2868.7MB, alloc=4.5MB, time=179.73
memory used=2872.5MB, alloc=4.5MB, time=179.88
memory used=2876.3MB, alloc=4.5MB, time=180.04
Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));
Iterations = 4287
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 2 Minutes 59 Seconds
Expected Time Remaining = 4 Hours 50 Minutes 6 Seconds
Optimized Time Remaining = 4 Hours 49 Minutes 56 Seconds
Expected Total Time = 4 Hours 52 Minutes 56 Seconds
Time to Timeout Unknown
Percent Done = 1.024 %
> quit
memory used=2878.7MB, alloc=4.5MB, time=180.13