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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> 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 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 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,"");
> est_tmp := 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 (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
max_estimated_step_error := 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, "");
est_tmp := 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_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> if (iter >= 0) then # if number 3
> 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 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> 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 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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)) + 3
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 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #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]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> 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) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #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 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> 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) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> 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) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> 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 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) 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 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. 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
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) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. 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_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
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_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre tan $eq_no = 1
> array_tmp1_a1[1] := sin(array_x[1]);
> array_tmp1_a2[1] := cos(array_x[1]);
> array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[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_tmp2[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 tan $eq_no = 1
> array_tmp1_a1[2] := array_tmp1_a2[1] * array_x[2] / 1;
> array_tmp1_a2[2] := -array_tmp1_a1[1] * array_x[2] / 1;
> array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[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_tmp2[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 tan $eq_no = 1
> array_tmp1_a1[3] := array_tmp1_a2[2] * array_x[2] / 2;
> array_tmp1_a2[3] := -array_tmp1_a1[2] * array_x[2] / 2;
> array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[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_tmp2[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 tan $eq_no = 1
> array_tmp1_a1[4] := array_tmp1_a2[3] * array_x[2] / 3;
> array_tmp1_a2[4] := -array_tmp1_a1[3] * array_x[2] / 3;
> array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[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_tmp2[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 tan $eq_no = 1
> array_tmp1_a1[5] := array_tmp1_a2[4] * array_x[2] / 4;
> array_tmp1_a2[5] := -array_tmp1_a1[4] * array_x[2] / 4;
> array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[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_tmp2[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
> array_tmp1_a1[kkk] := array_tmp1_a2[kkk-1] * array_x[2] / (kkk - 1);
> array_tmp1_a2[kkk] := -array_tmp1_a1[kkk-1] * array_x[2] / (kkk - 1);
> array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp2[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 1
> 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 1
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_tmp1_a1[1] := sin(array_x[1]);
array_tmp1_a2[1] := cos(array_x[1]);
array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[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_a1[2] := array_tmp1_a2[1]*array_x[2];
array_tmp1_a2[2] := -array_tmp1_a1[1]*array_x[2];
array_tmp1[2] := (
array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1_a1[3] := 1/2*array_tmp1_a2[2]*array_x[2];
array_tmp1_a2[3] := -1/2*array_tmp1_a1[2]*array_x[2];
array_tmp1[3] := (
array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1_a1[4] := 1/3*array_tmp1_a2[3]*array_x[2];
array_tmp1_a2[4] := -1/3*array_tmp1_a1[3]*array_x[2];
array_tmp1[4] := (
array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1_a1[5] := 1/4*array_tmp1_a2[4]*array_x[2];
array_tmp1_a2[5] := -1/4*array_tmp1_a1[4]*array_x[2];
array_tmp1[5] := (
array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1_a1[kkk] := array_tmp1_a2[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_a2[kkk] := -array_tmp1_a1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1[kkk] := (
array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[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 13
> #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
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", 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, " |
")
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 Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
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,m,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_int(ALWAYS,"m",4, m ,4," ");
> 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, m, 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_int(ALWAYS, "m", 4, m, 4, " ");
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
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> 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")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(-ln(cos(x)));
> end;
exact_soln_y := proc(x) return -ln(cos(x)) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1_a1,
> array_tmp1_a2,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> 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_min_h := 0.000001;
> glob_type_given_pole := 0;
> 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 := 0.0;
> glob_smallish_float := 0.0;
> 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/tanpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 1.5 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000;");
> omniout_str(ALWAYS,"glob_max_h := 0.001;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"## Not Given = 0");
> omniout_str(ALWAYS,"## No Pole = 3");
> omniout_str(ALWAYS,"## Pole = 4");
> omniout_str(ALWAYS,"glob_type_given_pole := 4;");
> omniout_str(ALWAYS,"## Real Part");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := 1.570796327;");
> omniout_str(ALWAYS,"## Imag Part");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 0.0;");
> omniout_str(ALWAYS,"## Order");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 0.0;");
> omniout_str(ALWAYS,"## Not Used");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := 0.0;");
> omniout_str(ALWAYS,"");
> 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:=0.01;");
> 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(-ln(cos(x)));");
> 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 := 0.0;
> glob_smallish_float := 0.0;
> 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..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1_a1:= Array(0..(max_terms + 1),[]);
> array_tmp1_a2:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= 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..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 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 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 1.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 10000;
> glob_max_h := 0.001;
> ## Not Given = 0
> ## No Pole = 3
> ## Pole = 4
> glob_type_given_pole := 4;
> ## Real Part
> array_given_rad_poles[1,1] := 1.570796327;
> ## Imag Part
> array_given_rad_poles[1,2] := 0.0;
> ## Order
> array_given_ord_poles[1,1] := 0.0;
> ## Not Used
> array_given_ord_poles[1,2] := 0.0;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> 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);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> 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,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> 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 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
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> 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 1
> 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 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> 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 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> 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 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> 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 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = tan ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T05:36:15-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tan")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( x ) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"tan diffeq.mxt")
> ;
> logitem_str(html_log_file,"tan maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #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, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
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_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
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.;
glob_smallish_float := 0.;
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/tanpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 1.5 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000;");
omniout_str(ALWAYS, "glob_max_h := 0.001;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "## Not Given = 0");
omniout_str(ALWAYS, "## No Pole = 3");
omniout_str(ALWAYS, "## Pole = 4");
omniout_str(ALWAYS, "glob_type_given_pole := 4;");
omniout_str(ALWAYS, "## Real Part");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := 1.570796327;");
omniout_str(ALWAYS, "## Imag Part");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := 0.0;");
omniout_str(ALWAYS, "## Order");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := 0.0;");
omniout_str(ALWAYS, "## Not Used");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := 0.0;");
omniout_str(ALWAYS, "");
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:=0.01;");
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(-ln(cos(x)));");
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.;
glob_smallish_float := 0.;
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 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1_a1 := Array(0 .. max_terms + 1, []);
array_tmp1_a2 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := 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 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 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 <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_a2[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_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 <= 2 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 <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp1_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_a1[term] := 0.; term := term + 1
end do;
array_tmp1_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_a2[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 1.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_h := 0.001;
glob_type_given_pole := 4;
array_given_rad_poles[1, 1] := 1.570796327;
array_given_rad_poles[1, 2] := 0.;
array_given_ord_poles[1, 1] := 0.;
array_given_ord_poles[1, 2] := 0.;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
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);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
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, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h 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();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if 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 ) = tan ( x ) ;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T05:36:15-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "tan");
logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( x ) ;")
;
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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, " 189 | ");
logitem_str(html_log_file,
"tan diffeq.mxt");
logitem_str(html_log_file,
"tan 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 13
> main();
##############ECHO OF PROBLEM#################
##############temp/tanpostode.ode#################
diff ( y , x , 1 ) = tan ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 1.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_h := 0.001;
## Not Given = 0
## No Pole = 3
## Pole = 4
glob_type_given_pole := 4;
## Real Part
array_given_rad_poles[1,1] := 1.570796327;
## Imag Part
array_given_rad_poles[1,2] := 0.0;
## Order
array_given_ord_poles[1,1] := 0.0;
## Not Used
array_given_ord_poles[1,2] := 0.0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
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(-ln(cos(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 1.4
estimated_steps = 1400000
step_error = 7.1428571428571428571428571428571e-17
est_needed_step_err = 7.1428571428571428571428571428571e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.7545349881333858732823046613652e-162
estimated_step_error = 1.7545349881333858732823046613652e-162
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1774488590573532239307284745361e-154
estimated_step_error = 1.1774488590573532239307284745361e-154
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.9017303673035447986682384028776e-147
estimated_step_error = 7.9017303673035447986682384028776e-147
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.3027679717378352124110150784201e-139
estimated_step_error = 5.3027679717378352124110150784201e-139
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.5586360516496029956506643574241e-131
estimated_step_error = 3.5586360516496029956506643574241e-131
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.3881719122569965421151336516878e-123
estimated_step_error = 2.3881719122569965421151336516878e-123
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6026907230790530667830817420081e-115
estimated_step_error = 1.6026907230790530667830817420081e-115
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0755685869512843352017551453386e-107
estimated_step_error = 1.0755685869512843352017551453386e-107
best_h = 0.000256
opt_iter = 9
bytes used=4000036, alloc=2883056, time=0.28
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.2183011397030182533279186888254e-100
estimated_step_error = 7.2183011397030182533279186888254e-100
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.8444991607453669861841049715834e-92
estimated_step_error = 4.8444991607453669861841049715834e-92
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.2515975312764918051583899910931e-84
estimated_step_error = 3.2515975312764918051583899910931e-84
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.0050083556232353090791329977212671
y[1] (numeric) = 0.0050083556232353090791329977212671
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.471
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.309
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=8001488, alloc=4062488, time=0.58
x[1] = 0.11
y[1] (analytic) = 0.0060622403465323032306356113409113
y[1] (numeric) = 0.0060622403465323032306356113409134
absolute error = 2.1e-33
relative error = 3.4640658897683477849595778723851e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.461
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.349
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.0072173466466277368000894604662206
y[1] (numeric) = 0.0072173466466277368000894604662168
absolute error = 3.8e-33
relative error = 5.2650928188069335365755048237809e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.451
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.379
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=12002528, alloc=4259060, time=0.90
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.008473908649082293939847075567037
y[1] (numeric) = 0.0084739086490822939398470755670326
absolute error = 4.4e-33
relative error = 5.1924090549129421234068325682876e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.441
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.401
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16003572, alloc=4324584, time=1.21
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.0098321816582955505386607580817523
y[1] (numeric) = 0.0098321816582955505386607580817521
absolute error = 2e-34
relative error = 2.0341365421300691197282114176828e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.431
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.416
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=20004552, alloc=4390108, time=1.53
x[1] = 0.15
y[1] (analytic) = 0.011292442366641786981368027419826
y[1] (numeric) = 0.011292442366641786981368027419827
absolute error = 1e-33
relative error = 8.8554802188234314590609468704173e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.421
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.425
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 5.301
Order of pole (three term test) = 2373
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.012854989082009649242948557584918
y[1] (numeric) = 0.01285498908200964924294855758492
absolute error = 2e-33
relative error = 1.5558161794154830346126250679557e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.431
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 2.964
Order of pole (three term test) = 1330
NO COMPLEX POLE (six term test) for Equation 1
bytes used=24008020, alloc=4390108, time=1.85
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.014520141974147117510638725229194
y[1] (numeric) = 0.01452014197414711751063872522919
absolute error = 4e-33
relative error = 2.7547940007211613759040100212574e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.401
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.432
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 2.241
Order of pole (three term test) = 1010
NO COMPLEX POLE (six term test) for Equation 1
bytes used=28009432, alloc=4455632, time=2.18
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.016288243340248848521775773334465
y[1] (numeric) = 0.016288243340248848521775773334461
absolute error = 4e-33
relative error = 2.4557589891328875496598955846129e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.391
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.431
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.9
Order of pole (three term test) = 860.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.018159657890259910149161840872723
y[1] (numeric) = 0.018159657890259910149161840872717
absolute error = 6e-33
relative error = 3.3040270010913322249437818052116e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.428
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.708
Order of pole (three term test) = 777.5
NO COMPLEX POLE (six term test) for Equation 1
bytes used=32010404, alloc=4455632, time=2.50
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0.020134773052408348925755928105682
y[1] (numeric) = 0.020134773052408348925755928105681
absolute error = 1e-33
relative error = 4.9665322643425006151950931220052e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.423
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 727.2
NO COMPLEX POLE (six term test) for Equation 1
bytes used=36011140, alloc=4455632, time=2.83
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.022213999299519054687682950444782
y[1] (numeric) = 0.022213999299519054687682950444785
absolute error = 3e-33
relative error = 1.3504997274691332376701629135856e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.361
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.417
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 694.9
NO COMPLEX POLE (six term test) for Equation 1
bytes used=40012376, alloc=4455632, time=3.15
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.024397770496703150585626911321445
y[1] (numeric) = 0.024397770496703150585626911321446
absolute error = 1e-33
relative error = 4.0987351698186075094151270232649e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.351
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.408
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.451
Order of pole (three term test) = 673.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.026686544271060789125605597428335
y[1] (numeric) = 0.026686544271060789125605597428335
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.341
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.41
Order of pole (three term test) = 658.9
NO COMPLEX POLE (six term test) for Equation 1
bytes used=44013460, alloc=4455632, time=3.48
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.029080802404080932719476939417643
y[1] (numeric) = 0.029080802404080932719476939417643
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.331
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.378
Order of pole (three term test) = 648.9
NO COMPLEX POLE (six term test) for Equation 1
bytes used=48015648, alloc=4455632, time=3.80
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.031581051247469607713948928307465
y[1] (numeric) = 0.031581051247469607713948928307466
absolute error = 1e-33
relative error = 3.1664557084056020807309863415846e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.321
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.381
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.354
Order of pole (three term test) = 641.9
NO COMPLEX POLE (six term test) for Equation 1
bytes used=52016640, alloc=4521156, time=4.12
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.034187822163188422429682548760632
y[1] (numeric) = 0.034187822163188422429682548760626
absolute error = 6e-33
relative error = 1.7550108840979265212372091952948e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.311
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.371
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.333
Order of pole (three term test) = 637
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.036901671988538022962828423907479
y[1] (numeric) = 0.036901671988538022962828423907476
absolute error = 3e-33
relative error = 8.1297129326059421630631290100100e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.301
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.361
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.316
Order of pole (three term test) = 633.5
NO COMPLEX POLE (six term test) for Equation 1
bytes used=56017588, alloc=4521156, time=4.44
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.039723183527176829264819318516813
y[1] (numeric) = 0.039723183527176829264819318516815
absolute error = 2e-33
relative error = 5.0348431883151793787126812218300e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.291
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 631
NO COMPLEX POLE (six term test) for Equation 1
bytes used=60018764, alloc=4521156, time=4.77
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.04265296606702406673056111562254
y[1] (numeric) = 0.042652966067024066730561115622538
absolute error = 2e-33
relative error = 4.6890056763162442361124474062756e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.281
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.287
Order of pole (three term test) = 629.3
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64020432, alloc=4521156, time=5.09
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.045691655926058019453301984654094
y[1] (numeric) = 0.045691655926058019453301984654094
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.271
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.329
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 628.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.048839917027085832016946896893199
y[1] (numeric) = 0.048839917027085832016946896893201
absolute error = 2e-33
relative error = 4.0950110519041876860802642675505e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.261
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.318
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 627.2
NO COMPLEX POLE (six term test) for Equation 1
bytes used=68021208, alloc=4521156, time=5.42
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0.052098441502630347658225662533815
y[1] (numeric) = 0.052098441502630347658225662533814
absolute error = 1e-33
relative error = 1.9194432139577763959996581380792e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.308
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 626.6
NO COMPLEX POLE (six term test) for Equation 1
bytes used=72022952, alloc=4521156, time=5.74
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.055467950331152682936048083594259
y[1] (numeric) = 0.055467950331152682936048083594266
absolute error = 7e-33
relative error = 1.2619900245473037588847466038327e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.241
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.297
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 626.1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=76023952, alloc=4521156, time=6.07
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.05894919400590681631636664753468
y[1] (numeric) = 0.058949194005906816316366647534685
absolute error = 5e-33
relative error = 8.4818801754931389186751276571028e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.231
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.287
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.231
Order of pole (three term test) = 625.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 0.062542953237804748550628956240186
y[1] (numeric) = 0.062542953237804748550628956240192
absolute error = 6e-33
relative error = 9.5934069137835925515673590119066e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.221
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.276
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 625.6
NO COMPLEX POLE (six term test) for Equation 1
bytes used=80024952, alloc=4521156, time=6.40
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.066250039693758141520080425462836
y[1] (numeric) = 0.066250039693758141520080425462837
absolute error = 1e-33
relative error = 1.5094330578857248221729736638924e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.266
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.21
Order of pole (three term test) = 625.4
NO COMPLEX POLE (six term test) for Equation 1
bytes used=84025908, alloc=4521156, time=6.73
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.070071296772055153862035972018276
y[1] (numeric) = 0.07007129677205515386203597201828
absolute error = 4e-33
relative error = 5.7084714915611831164887372594294e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.201
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.255
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 625.3
NO COMPLEX POLE (six term test) for Equation 1
bytes used=88027368, alloc=4521156, time=7.05
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0.074007600416429892867616152336733
y[1] (numeric) = 0.074007600416429892867616152336735
absolute error = 2e-33
relative error = 2.7024251411291460336078626552939e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.191
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.245
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 625.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.078059859970586954708407708121751
y[1] (numeric) = 0.078059859970586954708407708121749
absolute error = 2e-33
relative error = 2.5621362897058773963001112408045e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.181
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.234
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 625.2
NO COMPLEX POLE (six term test) for Equation 1
bytes used=92029948, alloc=4521156, time=7.38
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0.082229019075055429399409173994342
y[1] (numeric) = 0.082229019075055429399409173994339
absolute error = 3e-33
relative error = 3.6483470601317978122022328021689e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.171
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.224
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.169
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=96030872, alloc=4521156, time=7.70
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.086516056608366045624893433143116
y[1] (numeric) = 0.086516056608366045624893433143118
absolute error = 2e-33
relative error = 2.3117096160004607963261615715471e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.161
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.214
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=100031716, alloc=4521156, time=8.04
x[1] = 0.42
y[1] (analytic) = 0.090921987674672412487058343650493
y[1] (numeric) = 0.090921987674672412487058343650495
absolute error = 2e-33
relative error = 2.1996879425427782290544313905053e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.151
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.203
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.149
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.095447864640073219965858582901525
y[1] (numeric) = 0.095447864640073219965858582901526
absolute error = 1e-33
relative error = 1.0476923750687618106997094118368e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.141
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.193
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.139
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=104032644, alloc=4521156, time=8.36
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.1000947782200374826708000675464
y[1] (numeric) = 0.1000947782200374826708000675464
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.131
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.182
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.129
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=108033624, alloc=4521156, time=8.69
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0.1048638586204902087536765449528
y[1] (numeric) = 0.10486385862049020875367654495281
absolute error = 1e-32
relative error = 9.5361739798176929228709214477871e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.121
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.172
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.119
Order of pole (three term test) = 625.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112034812, alloc=4521156, time=9.02
x[1] = 0.46
y[1] (analytic) = 0.10975627673528207129354998536697
y[1] (numeric) = 0.10975627673528207129354998536699
absolute error = 2e-32
relative error = 1.8222192474911854457753939988704e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.111
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.161
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.11477324540294465066547177211419
y[1] (numeric) = 0.11477324540294465066547177211421
absolute error = 2e-32
relative error = 1.7425663907807276373990099461198e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.151
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.099
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=116035740, alloc=4521156, time=9.34
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.11991602072582358236478155761168
y[1] (numeric) = 0.11991602072582358236478155761168
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.091
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.089
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=120036548, alloc=4521156, time=9.67
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0.12518590345488655415521215776159
y[1] (numeric) = 0.1251859034548865541552121577616
absolute error = 1e-32
relative error = 7.9881198473785957229312899573591e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.081
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.079
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0.13058424044372271678761259182601
y[1] (numeric) = 0.130584240443722716787612591826
absolute error = 1e-32
relative error = 7.6578919217358801615068075265730e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.071
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.119
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.069
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=124039520, alloc=4521156, time=10.00
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0.13611242617548598054384463663251
y[1] (numeric) = 0.1361124261754859805438446366325
absolute error = 1e-32
relative error = 7.3468677922964043087651262237556e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.061
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.109
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=128040772, alloc=4521156, time=10.32
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0.14177190436678826263712043626926
y[1] (numeric) = 0.14177190436678826263712043626925
absolute error = 1e-32
relative error = 7.0535837440176318233430622044113e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.051
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.099
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.049
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=132041556, alloc=4521156, time=10.65
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0.14756416965282155837629888639352
y[1] (numeric) = 0.14756416965282155837629888639349
absolute error = 3e-32
relative error = 2.0330138454735900908122135190440e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.041
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.088
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.039
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0.15349076935828140966659957147956
y[1] (numeric) = 0.15349076935828140966659957147954
absolute error = 2e-32
relative error = 1.3030099519089369968591266716306e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.031
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.078
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=136042212, alloc=4521156, time=10.98
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0.15955330535898077874467619601204
y[1] (numeric) = 0.15955330535898077874467619601202
absolute error = 2e-32
relative error = 1.2534995721337000661899541168466e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.021
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.067
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=140043248, alloc=4521156, time=11.30
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0.16575343603938452477904084553625
y[1] (numeric) = 0.16575343603938452477904084553624
absolute error = 1e-32
relative error = 6.0330574369655353622983370220351e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 1.011
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.057
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=144044136, alloc=4521156, time=11.63
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0.17209287835166284853206403837245
y[1] (numeric) = 0.17209287835166284853206403837243
absolute error = 2e-32
relative error = 1.1621631407158546065857100512740e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 1.001
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.046
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9994
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0.17857340998225966096732308406808
y[1] (numeric) = 0.17857340998225966096732308406807
absolute error = 1e-32
relative error = 5.5999378636457958453221053068043e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.036
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9894
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=148045208, alloc=4521156, time=11.96
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0.18519687163240153853967239844412
y[1] (numeric) = 0.18519687163240153853967239844411
absolute error = 1e-32
relative error = 5.3996592447031526038026899738309e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.025
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9794
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=152046432, alloc=4586680, time=12.29
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0.19196516941943771967052566250649
y[1] (numeric) = 0.1919651694194377196705256625065
absolute error = 1e-32
relative error = 5.2092783447346751220031869080219e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.015
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9694
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=156047724, alloc=4586680, time=12.62
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0.19888027740640474945477660860593
y[1] (numeric) = 0.19888027740640474945477660860592
absolute error = 1e-32
relative error = 5.0281506695434444056176029093369e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 1.004
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9594
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0.2059442402677545113221722854327
y[1] (numeric) = 0.20594424026775451132217228543269
absolute error = 1e-32
relative error = 4.8556832601866840341514871911572e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.994
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9494
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=160048748, alloc=4586680, time=12.94
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0.21315917609977549587585267775296
y[1] (numeric) = 0.21315917609977549587585267775295
absolute error = 1e-32
relative error = 4.6913298235489531097560011142313e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9836
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9395
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=164050128, alloc=4586680, time=13.27
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0.22052727938487867644382399752528
y[1] (numeric) = 0.22052727938487867644382399752526
absolute error = 2e-32
relative error = 9.0691727825176167118275975948168e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9731
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9295
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=168051128, alloc=4586680, time=13.60
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0.22805082411961619408242495471385
y[1] (numeric) = 0.22805082411961619408242495471384
absolute error = 1e-32
relative error = 4.3849874424285548340639618231153e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9627
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9195
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0.23573216711705864347290962598666
y[1] (numeric) = 0.23573216711705864347290962598665
absolute error = 1e-32
relative error = 4.2421024344268860157420143879628e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9522
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9095
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=172052904, alloc=4586680, time=13.94
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0.24357375149498113754754544323105
y[1] (numeric) = 0.24357375149498113754754544323104
absolute error = 1e-32
relative error = 4.1055326933313054624520373142816e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.9008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9417
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8995
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=176053860, alloc=4586680, time=14.26
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0.25157811036220622931999672046961
y[1] (numeric) = 0.25157811036220622931999672046959
absolute error = 2e-32
relative error = 7.9498172441176486786750190360357e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.8908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9313
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8895
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=180055080, alloc=4586680, time=14.59
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0.25974787071643065894544560756899
y[1] (numeric) = 0.25974787071643065894544560756896
absolute error = 3e-32
relative error = 1.1549661568833917104472994049817e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9208
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8795
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0.26808575756793110052941329261424
y[1] (numeric) = 0.26808575756793110052941329261419
absolute error = 5e-32
relative error = 1.8650748347692563037572436643028e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.9104
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8696
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=184056216, alloc=4586680, time=14.92
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0.27659459830471089647622620475432
y[1] (numeric) = 0.27659459830471089647622620475427
absolute error = 5e-32
relative error = 1.8076997998680154028977902519084e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8999
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8596
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=188057012, alloc=4586680, time=15.24
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0.28527732731592556251069378115938
y[1] (numeric) = 0.28527732731592556251069378115934
absolute error = 4e-32
relative error = 1.4021443756623068379972593372306e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8895
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8496
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=192058260, alloc=4586680, time=15.57
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0.29413699089182122586533133649918
y[1] (numeric) = 0.29413699089182122586533133649913
absolute error = 5e-32
relative error = 1.6998881999982512285977634552204e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.879
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8396
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0.30317675241995011257089763534277
y[1] (numeric) = 0.30317675241995011257089763534272
absolute error = 5e-32
relative error = 1.6492029682652482134406878673694e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8686
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8296
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=196059356, alloc=4586680, time=15.89
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0.31239989789910529045450249364086
y[1] (numeric) = 0.3123998978991052904545024936408
absolute error = 6e-32
relative error = 1.9206152243807067927165326175636e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8581
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8196
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=200060028, alloc=4586680, time=16.22
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0.32180984179425945068151423381541
y[1] (numeric) = 0.32180984179425945068151423381537
absolute error = 4e-32
relative error = 1.2429700650849868786083279752077e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.8108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8477
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8096
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=204061140, alloc=4586680, time=16.55
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0.33141013325781794977317349320871
y[1] (numeric) = 0.33141013325781794977317349320868
absolute error = 3e-32
relative error = 9.0522277351917094352483658436037e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.8008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8372
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7997
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0.34120446274472532274703956801391
y[1] (numeric) = 0.34120446274472532274703956801388
absolute error = 3e-32
relative error = 8.7923820687083817390578760451850e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8267
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7897
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=208062696, alloc=4586680, time=16.87
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0.35119666905142033592219992599373
y[1] (numeric) = 0.3511966690514203359221999259937
absolute error = 3e-32
relative error = 8.5422222485850401458553333666287e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8163
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7797
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=212063440, alloc=4586680, time=17.20
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0.36139074681134370073955187701716
y[1] (numeric) = 0.36139074681134370073955187701713
absolute error = 3e-32
relative error = 8.3012640098560291785317531038220e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.8058
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7697
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=216064784, alloc=4586680, time=17.52
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0.37179085448269458146368508643973
y[1] (numeric) = 0.3717908544826945814636850864397
absolute error = 3e-32
relative error = 8.0690527048444069090164142013195e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7954
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7597
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0.38240132286744070218141983186178
y[1] (numeric) = 0.38240132286744070218141983186177
absolute error = 1e-32
relative error = 2.6150537150381398764755980197267e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7849
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7497
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=220066656, alloc=4586680, time=17.85
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0.39322666420425041395821766021091
y[1] (numeric) = 0.39322666420425041395821766021089
absolute error = 2e-32
relative error = 5.0861250827109650082452479904619e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7745
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7397
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=224067576, alloc=4586680, time=18.18
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0.40427158188207693854781095755977
y[1] (numeric) = 0.40427158188207693854781095755976
absolute error = 1e-32
relative error = 2.4735847010183680947066511350799e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.764
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7298
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=228068612, alloc=4586680, time=18.50
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0.41554098082563456072414008672357
y[1] (numeric) = 0.41554098082563456072414008672356
absolute error = 1e-32
relative error = 2.4065015152370993074744156440428e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7536
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7198
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0.42703997860902009961970846262481
y[1] (numeric) = 0.4270399786090200996197084626248
absolute error = 1e-32
relative error = 2.3417011289136422379392072638076e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7431
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7098
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=232070988, alloc=4586680, time=18.83
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0.43877391735931483133143230370915
y[1] (numeric) = 0.43877391735931483133143230370915
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.7008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7327
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6998
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=236072696, alloc=4586680, time=19.16
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0.45074837651822568140685167564968
y[1] (numeric) = 0.45074837651822568140685167564969
absolute error = 1e-32
relative error = 2.2185326716524862077584661218965e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7222
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6898
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=240073612, alloc=4586680, time=19.49
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0.46296918653677419992400132049904
y[1] (numeric) = 0.46296918653677419992400132049905
absolute error = 1e-32
relative error = 2.1599709636843591446046130781641e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7117
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6798
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0.47544244358581428500971793610522
y[1] (numeric) = 0.47544244358581428500971793610523
absolute error = 1e-32
relative error = 2.1033040139579092287837196962823e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.7013
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6698
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=244074524, alloc=4586680, time=19.82
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0.48817452537386607244011633638259
y[1] (numeric) = 0.4881745253738660724401163363826
absolute error = 1e-32
relative error = 2.0484477333882895493558612541152e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6908
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6599
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=248075352, alloc=4586680, time=20.15
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0.50117210817352206486580922236454
y[1] (numeric) = 0.50117210817352206486580922236455
absolute error = 1e-32
relative error = 1.9953225323021518071425780477080e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6804
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6499
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=252076712, alloc=4586680, time=20.47
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0.51444218516866049589961060443574
y[1] (numeric) = 0.51444218516866049589961060443575
absolute error = 1e-32
relative error = 1.9438530292226108637170845310439e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6699
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6399
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0.52799208624706146590424159189259
y[1] (numeric) = 0.52799208624706146590424159189264
absolute error = 5e-32
relative error = 9.4698389052376207741018584733058e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6595
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6299
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=256077628, alloc=4586680, time=20.80
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0.54182949937696228955735782951295
y[1] (numeric) = 0.541829499376962289557357829513
absolute error = 5e-32
relative error = 9.2279951640680121311163537073748e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.649
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6199
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=260079596, alloc=4586680, time=21.13
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0.55596249372184078297003425326856
y[1] (numeric) = 0.5559624937218407829700342532686
absolute error = 4e-32
relative error = 7.1947299416231492178750215311288e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6386
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6099
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=264080940, alloc=4586680, time=21.46
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0.57039954466554805723971068073415
y[1] (numeric) = 0.57039954466554805723971068073416
absolute error = 1e-32
relative error = 1.7531570797209292852374561767918e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.6008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6281
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.5999
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0.58514956094014013115956949852153
y[1] (numeric) = 0.58514956094014013115956949852154
absolute error = 1e-32
relative error = 1.7089647959289820069389438382598e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6177
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.59
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=268081852, alloc=4586680, time=21.79
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0.60022191407174835977683955432996
y[1] (numeric) = 0.60022191407174835977683955432998
absolute error = 2e-32
relative error = 3.3321009331907318922592495494910e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.6072
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.58
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=272082996, alloc=4586680, time=22.12
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0.61562647038601426214703751640889
y[1] (numeric) = 0.61562647038601426214703751640891
absolute error = 2e-32
relative error = 3.2487232050726254656885231606205e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5967
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.57
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=276084340, alloc=4586680, time=22.44
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0.63137362584450315188279089363379
y[1] (numeric) = 0.6313736258445031518827908936338
absolute error = 1e-32
relative error = 1.5838482303761662159127203336818e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5863
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.56
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0.64747434401770284367387505983639
y[1] (numeric) = 0.64747434401770284367387505983641
bytes used=280086088, alloc=4586680, time=22.77
absolute error = 2e-32
relative error = 3.0889254817258322672268823959777e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5758
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.55
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0.66394019753941837193284368197813
y[1] (numeric) = 0.66394019753941837193284368197815
absolute error = 2e-32
relative error = 3.0123194941533258645616326942854e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5654
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.54
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=284087284, alloc=4586680, time=23.10
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 0.68078341343243336216822163902211
y[1] (numeric) = 0.68078341343243336216822163902212
absolute error = 1e-32
relative error = 1.4688959517361219623537727973747e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5549
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.53
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=288088120, alloc=4586680, time=23.43
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0.6980169227472259234768425271063
y[1] (numeric) = 0.69801692274722592347684252710631
absolute error = 1e-32
relative error = 1.4326300228714250399781130143757e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5445
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.5201
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=292089048, alloc=4586680, time=23.76
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0.7156544150154985808589391935345
y[1] (numeric) = 0.71565441501549858085893919353452
absolute error = 2e-32
relative error = 2.7946449543760405211816886542539e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.534
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.5101
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0.73371039808974145199588183609803
y[1] (numeric) = 0.73371039808974145199588183609807
absolute error = 4e-32
relative error = 5.4517422819878760007801684848994e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.5008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5236
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.5001
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=296089988, alloc=4586680, time=24.09
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0.75220026402071845962429762508506
y[1] (numeric) = 0.75220026402071845962429762508511
absolute error = 5e-32
relative error = 6.6471659731593512976606625454245e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5131
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4901
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=300091148, alloc=4586680, time=24.42
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0.77114036171872549545405346664079
y[1] (numeric) = 0.77114036171872549545405346664083
absolute error = 4e-32
relative error = 5.1871231212496247031462113180340e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.5027
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=304092436, alloc=4586680, time=24.75
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0.79054807725423157832360761284218
y[1] (numeric) = 0.79054807725423157832360761284223
absolute error = 5e-32
relative error = 6.3247260272471131690939094290130e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4922
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4701
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0.8104419227821336686144201585331
y[1] (numeric) = 0.81044192278213366861442015853312
absolute error = 2e-32
relative error = 2.4677894168335714623164795292032e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4817
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4601
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=308093348, alloc=4586680, time=25.08
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0.8308416352250578146554749380697
y[1] (numeric) = 0.83084163522505781465547493806973
absolute error = 3e-32
relative error = 3.6107964175234935705964526984736e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4713
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4502
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=312094532, alloc=4586680, time=25.41
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0.85176828602948452590182842787181
y[1] (numeric) = 0.85176828602948452590182842787183
absolute error = 2e-32
relative error = 2.3480564289649646211425483134459e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4608
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4402
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=316095472, alloc=4586680, time=25.75
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0.87324440351957250437741676966729
y[1] (numeric) = 0.87324440351957250437741676966732
absolute error = 3e-32
relative error = 3.4354643303852096881547049181364e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4504
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4302
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=320096580, alloc=4586680, time=26.08
x[1] = 1.15
y[1] (analytic) = 0.89529410962432754843323878013503
y[1] (numeric) = 0.89529410962432754843323878013507
absolute error = 4e-32
relative error = 4.4678055590898855209791356180875e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4399
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4202
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0.9179432730528043730621826802488
y[1] (numeric) = 0.91794327305280437306218268024884
absolute error = 4e-32
relative error = 4.3575677467488792927370114281950e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4295
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4102
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=324097636, alloc=4586680, time=26.41
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 0.94121968135004839415224478118841
y[1] (numeric) = 0.94121968135004839415224478118844
absolute error = 3e-32
relative error = 3.1873536640212604822423854789607e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.4008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.419
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4002
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=328098880, alloc=4586680, time=26.73
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0.9651532346968997068056452965941
y[1] (numeric) = 0.96515323469689970680564529659414
absolute error = 4e-32
relative error = 4.1444196177368403072870306854722e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.3908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.4086
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3902
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=332100040, alloc=4586680, time=27.06
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0.98977616483648983560036133331333
y[1] (numeric) = 0.9897761648364898356003613333134
absolute error = 7e-32
relative error = 7.0723060917075063448710753500221e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.3808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3981
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3803
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 1.0151232831406596166642531887589
y[1] (numeric) = 1.015123283140659616664253188759
absolute error = 1e-31
relative error = 9.8510202318099714696838520120862e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.3708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3877
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3703
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=336100932, alloc=4586680, time=27.39
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 1.0412322625978628317573860361734
y[1] (numeric) = 1.0412322625978628317573860361736
absolute error = 2e-31
relative error = 1.9208010276304946632342586423945e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3772
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3603
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=340102312, alloc=4586680, time=27.72
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 1.0681439594453074953144590293971
y[1] (numeric) = 1.0681439594453074953144590293972
absolute error = 1e-31
relative error = 9.3620339389393261696122831330832e-30 %
Correct digits = 32
h = 0.001
Radius of convergence (given) for eq 1 = 0.3508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3667
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3503
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=344103180, alloc=4586680, time=28.05
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 1.0959027813271406152089727445301
y[1] (numeric) = 1.0959027813271406152089727445303
absolute error = 2e-31
relative error = 1.8249793997036814859923563484792e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3563
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3403
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 1.1245571102958336035990707821674
y[1] (numeric) = 1.1245571102958336035990707821677
absolute error = 3e-31
relative error = 2.6677168927514936953581750871937e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3458
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3303
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=348104232, alloc=4586680, time=28.38
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 1.1541597907619533834757535760123
y[1] (numeric) = 1.1541597907619533834757535760125
absolute error = 2e-31
relative error = 1.7328623090219073569901017154433e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3354
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3203
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=352105292, alloc=4586680, time=28.71
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 1.1847686947387932103640751409307
y[1] (numeric) = 1.1847686947387932103640751409309
absolute error = 2e-31
relative error = 1.6880932192768153875077449544539e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3249
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3104
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=356106712, alloc=4586680, time=29.04
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 1.2164473795563924951328697040191
y[1] (numeric) = 1.2164473795563924951328697040195
absolute error = 4e-31
relative error = 3.2882638963460125520618266235853e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.3008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.3145
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3004
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 1.2492658568129765948943342669988
y[1] (numeric) = 1.2492658568129765948943342669993
absolute error = 5e-31
relative error = 4.0023506387628211989853966864742e-29 %
Correct digits = 31
h = 0.001
bytes used=360108588, alloc=4586680, time=29.37
Radius of convergence (given) for eq 1 = 0.2908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.304
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2904
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 1.2833014959320560732328761350587
y[1] (numeric) = 1.2833014959320560732328761350592
absolute error = 5e-31
relative error = 3.8962005544679293081279135251741e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2936
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2804
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=364109456, alloc=4586680, time=29.64
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 1.3186400916291685666027959482477
y[1] (numeric) = 1.3186400916291685666027959482483
absolute error = 6e-31
relative error = 4.5501422549552935741970886524303e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2831
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2704
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=368110444, alloc=4586680, time=29.78
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 1.3553771323162041613521307414069
y[1] (numeric) = 1.3553771323162041613521307414074
absolute error = 5e-31
relative error = 3.6890101513336729654060881921967e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2727
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2604
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=372111340, alloc=4586680, time=29.92
x[1] = 1.32
y[1] (analytic) = 1.3936193166132841894311591204205
y[1] (numeric) = 1.3936193166132841894311591204211
absolute error = 6e-31
relative error = 4.3053364204085165271785848502106e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2622
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2504
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 1.4334863785846989858939593092082
y[1] (numeric) = 1.4334863785846989858939593092089
absolute error = 7e-31
relative error = 4.8831995229080566756789880993088e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2517
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2405
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=376113320, alloc=4586680, time=30.05
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 1.4751133003293379102707928607389
y[1] (numeric) = 1.4751133003293379102707928607397
absolute error = 8e-31
relative error = 5.4233122284328245728256241380044e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2413
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2305
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=380114572, alloc=4586680, time=30.19
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 1.5186530149603870751898958988672
y[1] (numeric) = 1.518653014960387075189895898868
absolute error = 8e-31
relative error = 5.2678261072090085038270403325028e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2308
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2205
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=384115588, alloc=4586680, time=30.33
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 1.5642797364730061261017717087599
y[1] (numeric) = 1.5642797364730061261017717087608
absolute error = 9e-31
relative error = 5.7534466439438581918796116009730e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2204
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2105
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 1.6121930994906972389671884851212
y[1] (numeric) = 1.6121930994906972389671884851221
absolute error = 9e-31
relative error = 5.5824578351334968427682401344631e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.2008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.2099
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2005
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=388116888, alloc=4586680, time=30.47
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 1.6626233574003796274966328950026
y[1] (numeric) = 1.6626233574003796274966328950035
absolute error = 9e-31
relative error = 5.4131321805030387011338955865748e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1995
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1905
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=392117940, alloc=4586680, time=30.61
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 1.7158379811678190697045444588912
y[1] (numeric) = 1.7158379811678190697045444588921
absolute error = 9e-31
relative error = 5.2452504833087425073870157145904e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.189
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1805
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=396119660, alloc=4586680, time=30.75
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 1.7721501376696990272141106868693
y[1] (numeric) = 1.7721501376696990272141106868704
absolute error = 1.1e-30
relative error = 6.2071490254570221754740733219416e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1708
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1786
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1706
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 1.8319297289558808289320648371267
y[1] (numeric) = 1.8319297289558808289320648371278
absolute error = 1.1e-30
relative error = 6.0045971339029008400052528782541e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1608
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1681
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1606
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=400122088, alloc=4586680, time=30.89
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 1.8956179807145446725622651027797
y[1] (numeric) = 1.8956179807145446725622651027807
absolute error = 1.0e-30
relative error = 5.2753245125004274192185554763821e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1508
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1577
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1506
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=404122988, alloc=4586680, time=31.03
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 1.9637470439243689010155627224162
y[1] (numeric) = 1.9637470439243689010155627224171
absolute error = 9e-31
relative error = 4.5830750084870009355542948859559e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1408
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1472
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1406
Order of pole (three term test) = 625
Radius of convergence (six term test) for eq 1 = 2.469
Order of pole (six term test) = -4.473e-24
bytes used=408123684, alloc=4586680, time=31.17
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 2.0369668305394392250598441967529
y[1] (numeric) = 2.0369668305394392250598441967538
absolute error = 9e-31
relative error = 4.4183340961013966433334485953978e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1308
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1367
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1306
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 2.1160825440137191518804053682086
y[1] (numeric) = 2.1160825440137191518804053682096
absolute error = 1.0e-30
relative error = 4.7257135730784456666013892843209e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1208
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1263
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1206
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=412124876, alloc=4586680, time=31.31
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 2.2021084657468975855988513433722
y[1] (numeric) = 2.2021084657468975855988513433732
absolute error = 1.0e-30
relative error = 4.5411023823516620443418311533001e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1108
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1158
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1106
Order of pole (three term test) = 625
Radius of convergence (six term test) for eq 1 = 0.1606
Order of pole (six term test) = 5.539e-27
bytes used=416125924, alloc=4586680, time=31.45
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 2.2963472549526355919112295036683
y[1] (numeric) = 2.2963472549526355919112295036695
absolute error = 1.2e-30
relative error = 5.2256904847988732160056597219459e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.1008
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.1054
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1007
Order of pole (three term test) = 625
Radius of convergence (six term test) for eq 1 = 0.03162
Order of pole (six term test) = 0
bytes used=420127048, alloc=4586680, time=31.59
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 2.4005108212575825445957134843943
y[1] (numeric) = 2.4005108212575825445957134843953
absolute error = 1.0e-30
relative error = 4.1657800129229110373776367044288e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.0908
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.09492
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.09067
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 2.5169120195352477327155332172207
y[1] (numeric) = 2.5169120195352477327155332172217
absolute error = 1.0e-30
relative error = 3.9731225892617882334872187302527e-29 %
Correct digits = 31
h = 0.001
Radius of convergence (given) for eq 1 = 0.0808
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 0.08447
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.08068
Order of pole (three term test) = 625
NO COMPLEX POLE (six term test) for Equation 1
bytes used=424128900, alloc=4586680, time=31.73
Finished!
diff ( y , x , 1 ) = tan ( x ) ;
Iterations = 1400
Total Elapsed Time = 31 Seconds
Elapsed Time(since restart) = 31 Seconds
Time to Timeout = 2 Minutes 28 Seconds
Percent Done = 100.1 %
> quit
bytes used=426569192, alloc=4586680, time=31.81