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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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 sqrt 1 $eq_no = 1
> array_tmp1[1] := sqrt(array_x[1]);
> #emit pre arctan $eq_no = 1
> array_tmp2[1] := Si(array_tmp1[1]);
> array_tmp2_a1[1] := sin(array_tmp1[1]);
> array_tmp2_a2[1] := cos(array_tmp1[1]);
> array_tmp2_a3[1] := array_tmp2_a1[1] / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[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_tmp3[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 sqrt 2 $eq_no = 1
> array_tmp1[2] := array_x[2] / array_tmp1[1]/2.0;
> #emit pre Si $eq_no = 1
> array_tmp2_a1[2] := att(1,array_tmp2_a2,array_tmp1,1);
> array_tmp2_a2[2] := -att(1,array_tmp2_a1,array_tmp1,1);
> array_tmp2_a3[2] := (array_tmp2_a1[2] - ats(2,array_tmp1,array_tmp2_a3,2))/array_tmp1[1];
> array_tmp2[2] := att(1,array_tmp2_a3,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[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_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := 0.0;
> array_tmp1[3] := -ats(3,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0;
> #emit pre Si $eq_no = 1
> array_tmp2_a1[3] := att(2,array_tmp2_a2,array_tmp1,1);
> array_tmp2_a2[3] := -att(2,array_tmp2_a1,array_tmp1,1);
> array_tmp2_a3[3] := (array_tmp2_a1[3] - ats(3,array_tmp1,array_tmp2_a3,2))/array_tmp1[1];
> array_tmp2[3] := att(2,array_tmp2_a3,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[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_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := 0.0;
> array_tmp1[4] := -ats(4,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0;
> #emit pre Si $eq_no = 1
> array_tmp2_a1[4] := att(3,array_tmp2_a2,array_tmp1,1);
> array_tmp2_a2[4] := -att(3,array_tmp2_a1,array_tmp1,1);
> array_tmp2_a3[4] := (array_tmp2_a1[4] - ats(4,array_tmp1,array_tmp2_a3,2))/array_tmp1[1];
> array_tmp2[4] := att(3,array_tmp2_a3,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[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_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := 0.0;
> array_tmp1[5] := -ats(5,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0;
> #emit pre Si $eq_no = 1
> array_tmp2_a1[5] := att(4,array_tmp2_a2,array_tmp1,1);
> array_tmp2_a2[5] := -att(4,array_tmp2_a1,array_tmp1,1);
> array_tmp2_a3[5] := (array_tmp2_a1[5] - ats(5,array_tmp1,array_tmp2_a3,2))/array_tmp1[1];
> array_tmp2[5] := att(4,array_tmp2_a3,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[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_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp1[kkk] := 0.0;
> array_tmp1[kkk] := -ats(kkk,array_tmp1,array_tmp1,2) /array_tmp1[1] / 2.0;
> #emit Si $eq_no = 1
> array_tmp2_a1[kkk] := att(kkk-1,array_tmp2_a3,array_tmp1,1);
> array_tmp2_a3[kkk] := -att(kkk-1,array_tmp2_a1,array_tmp1,1);
> array_tmp2_a3[kkk] := (array_tmp2_a1[kkk] - ats(kkk,array_tmp1,array_tmp2_a3,2)) / array_tmp1[1];
> array_tmp2[kkk] := att(kkk-1,array_tmp2_a3,array_tmp1,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[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_tmp3[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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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[1] := sqrt(array_x[1]);
array_tmp2[1] := Si(array_tmp1[1]);
array_tmp2_a1[1] := sin(array_tmp1[1]);
array_tmp2_a2[1] := cos(array_tmp1[1]);
array_tmp2_a3[1] := array_tmp2_a1[1]/array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_x[2]/(array_tmp1[1]*2.0);
array_tmp2_a1[2] := att(1, array_tmp2_a2, array_tmp1, 1);
array_tmp2_a2[2] := -att(1, array_tmp2_a1, array_tmp1, 1);
array_tmp2_a3[2] := (
array_tmp2_a1[2] - ats(2, array_tmp1, array_tmp2_a3, 2))/
array_tmp1[1];
array_tmp2[2] := att(1, array_tmp2_a3, array_tmp1, 1);
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 0.;
array_tmp1[3] := -ats(3, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0)
;
array_tmp2_a1[3] := att(2, array_tmp2_a2, array_tmp1, 1);
array_tmp2_a2[3] := -att(2, array_tmp2_a1, array_tmp1, 1);
array_tmp2_a3[3] := (
array_tmp2_a1[3] - ats(3, array_tmp1, array_tmp2_a3, 2))/
array_tmp1[1];
array_tmp2[3] := att(2, array_tmp2_a3, array_tmp1, 1);
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 0.;
array_tmp1[4] := -ats(4, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0)
;
array_tmp2_a1[4] := att(3, array_tmp2_a2, array_tmp1, 1);
array_tmp2_a2[4] := -att(3, array_tmp2_a1, array_tmp1, 1);
array_tmp2_a3[4] := (
array_tmp2_a1[4] - ats(4, array_tmp1, array_tmp2_a3, 2))/
array_tmp1[1];
array_tmp2[4] := att(3, array_tmp2_a3, array_tmp1, 1);
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 0.;
array_tmp1[5] := -ats(5, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0)
;
array_tmp2_a1[5] := att(4, array_tmp2_a2, array_tmp1, 1);
array_tmp2_a2[5] := -att(4, array_tmp2_a1, array_tmp1, 1);
array_tmp2_a3[5] := (
array_tmp2_a1[5] - ats(5, array_tmp1, array_tmp2_a3, 2))/
array_tmp1[1];
array_tmp2[5] := att(4, array_tmp2_a3, array_tmp1, 1);
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := 0.;
array_tmp1[kkk] :=
-ats(kkk, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0);
array_tmp2_a1[kkk] := att(kkk - 1, array_tmp2_a3, array_tmp1, 1);
array_tmp2_a3[kkk] := -att(kkk - 1, array_tmp2_a1, array_tmp1, 1);
array_tmp2_a3[kkk] := (
array_tmp2_a1[kkk] - ats(kkk, array_tmp1, array_tmp2_a3, 2))/
array_tmp1[1];
array_tmp2[kkk] := att(kkk - 1, array_tmp2_a3, array_tmp1, 1);
array_tmp3[kkk] := array_tmp2[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_tmp3[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
> ## Comment 5
> exact_soln_y := proc(x)
> ## Comment 6
> return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));
> ## Comment 7
> end;
exact_soln_y :=
proc(x) return x*Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(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,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2_a3,
> array_tmp2,
> array_tmp3,
> 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/Si_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = Si(sqrt(x));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"## Comment 1");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"## Comment 2");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"## Comment 3");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 1.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_max_h := 0.001;");
> omniout_str(ALWAYS,"## Comment 4");
> 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,"## Comment 5");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"## Comment 6");
> omniout_str(ALWAYS," ");
> omniout_str(ALWAYS,"return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"## Comment 7");
> 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
> ## Comment 1
> Digits:=32;
> max_terms:=30;
> ## Comment 2
> #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:= Array(0..(max_terms + 1),[]);
> array_tmp2_a1:= Array(0..(max_terms + 1),[]);
> array_tmp2_a2:= Array(0..(max_terms + 1),[]);
> array_tmp2_a3:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= 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[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2_a3[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_tmp3[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 := 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_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2_a3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2_a3[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_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[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
> ## Comment 3
> x_start := 0.1;
> x_end := 1.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_max_h := 0.001;
> ## Comment 4
> #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 ) = Si(sqrt(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,"2013-05-26T05:47:09-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"Si_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = Si(sqrt(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,"Si_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"Si_sqrt maple results")
> ;
> logitem_str(html_log_file,"Maple - Si")
> ;
> 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, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2,
array_tmp3, 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/Si_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = Si(sqrt(x));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "## Comment 1");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "## Comment 2");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "## Comment 3");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 1.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_max_h := 0.001;");
omniout_str(ALWAYS, "## Comment 4");
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, "## Comment 5");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "## Comment 6");
omniout_str(ALWAYS, " ");
omniout_str(ALWAYS,
"return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "## Comment 7");
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 := Array(0 .. max_terms + 1, []);
array_tmp2_a1 := Array(0 .. max_terms + 1, []);
array_tmp2_a2 := Array(0 .. max_terms + 1, []);
array_tmp2_a3 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := 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[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_a3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_a1[term] := 0.; term := term + 1
end do;
array_tmp2_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_a2[term] := 0.; term := term + 1
end do;
array_tmp2_a3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_a3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_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 := 1.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_max_h := 0.001;
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 ) = Si(sqrt(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, "2013-05-26T05:47:09-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"Si_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = Si(sqrt(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,
"Si_sqrt diffeq.mxt");
logitem_str(html_log_file, "Si_sqrt maple results");
logitem_str(html_log_file, "Maple - Si");
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/Si_sqrtpostode.ode#################
diff ( y , x , 1 ) = Si(sqrt(x));
!
#BEGIN FIRST INPUT BLOCK
## Comment 1
Digits:=32;
max_terms:=30;
## Comment 2
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
## Comment 3
x_start := 0.1;
x_end := 1.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_max_h := 0.001;
## Comment 4
#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
## Comment 5
exact_soln_y := proc(x)
## Comment 6
return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));
## Comment 7
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 = 0.9
estimated_steps = 900000
step_error = 1.1111111111111111111111111111111e-16
est_needed_step_err = 1.1111111111111111111111111111111e-16
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7934972345263677994492432536923e-136
estimated_step_error = 2.7934972345263677994492432536923e-136
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 = 1.8746757545277430858295647309101e-128
estimated_step_error = 1.8746757545277430858295647309101e-128
best_h = 4.00e-06
opt_iter = 3
bytes used=4000260, alloc=3014104, time=0.11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2580621869022487523552569889240e-120
estimated_step_error = 1.2580621869022487523552569889240e-120
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 = 8.4425592064326376762845024137538e-113
estimated_step_error = 8.4425592064326376762845024137538e-113
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 = 5.6654999468467072467004477432864e-105
estimated_step_error = 5.6654999468467072467004477432864e-105
best_h = 3.200000e-05
opt_iter = 6
bytes used=8001408, alloc=4128012, time=0.23
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.8017766936847523362136045928833e-97
estimated_step_error = 3.8017766936847523362136045928833e-97
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 = 2.5509588439224448644899615291520e-89
estimated_step_error = 2.5509588439224448644899615291520e-89
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 = 1.7114227009495059828892151116974e-81
estimated_step_error = 1.7114227009495059828892151116974e-81
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1478501222293516470784396804835e-73
estimated_step_error = 1.1478501222293516470784396804835e-73
best_h = 0.000512
opt_iter = 10
bytes used=12002324, alloc=4259060, time=0.36
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.6941657096191853536892214747610e-66
estimated_step_error = 7.6941657096191853536892214747610e-66
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 = 5.1515288845800874120846536268485e-58
estimated_step_error = 5.1515288845800874120846536268485e-58
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.02101172861653694101443709332267
y[1] (numeric) = 0.02101172861653694101443709332267
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1122
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=0.49
bytes used=20004492, alloc=4455632, time=0.61
TOP MAIN SOLVE Loop
bytes used=24005448, alloc=4455632, time=0.74
x[1] = 0.11
y[1] (analytic) = 0.0242329446790716645869461308976
y[1] (numeric) = 0.024232944679071664582905527669564
absolute error = 4.040603228036e-21
relative error = 1.6674008386300623225066515790395e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1234
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=28006192, alloc=4455632, time=0.87
bytes used=32007180, alloc=4455632, time=0.99
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.0276022462635188132778091477758
y[1] (numeric) = 0.02760224626351881327109036890219
absolute error = 6.718778873610e-21
relative error = 2.4341420656368967769423524272921e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1346
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5261
Order of pole (six term test) = -0.75
bytes used=36008356, alloc=4455632, time=1.12
bytes used=40009172, alloc=4521156, time=1.25
bytes used=44010268, alloc=4521156, time=1.38
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.03111307913423200057866560545161
y[1] (numeric) = 0.031113079134232000570109075485143
absolute error = 8.556529966467e-21
relative error = 2.7501392355129271695423578741170e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1459
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1715
Order of pole (six term test) = -0.75
bytes used=48011116, alloc=4521156, time=1.50
bytes used=52012160, alloc=4521156, time=1.63
TOP MAIN SOLVE Loop
bytes used=56013948, alloc=4521156, time=1.76
x[1] = 0.14
y[1] (analytic) = 0.03475965364933978756736821344522
y[1] (numeric) = 0.034759653649339787557513176497292
absolute error = 9.855036947928e-21
relative error = 2.8351942304566613677945378051034e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1571
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=60014880, alloc=4521156, time=1.89
bytes used=64016096, alloc=4521156, time=2.01
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0.03853680550514419831820980956466
y[1] (numeric) = 0.03853680550514419830741401738675
absolute error = 1.0795792177910e-20
relative error = 2.8014237393052447149951991779228e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1683
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=68017100, alloc=4521156, time=2.14
bytes used=72017996, alloc=4521156, time=2.27
bytes used=76018812, alloc=4521156, time=2.40
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.04243988965272320273635241812664
y[1] (numeric) = 0.042439889652723202724860127541383
absolute error = 1.1492290585257e-20
relative error = 2.7078983190804748920386492408582e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1795
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=80020136, alloc=4521156, time=2.52
bytes used=84021128, alloc=4586680, time=2.65
TOP MAIN SOLVE Loop
bytes used=88022212, alloc=4586680, time=2.79
x[1] = 0.17
y[1] (analytic) = 0.04646469786246896746347503888234
y[1] (numeric) = 0.04646469786246896745145722913717
absolute error = 1.2017809745170e-20
relative error = 2.5864388015050823953171096147814e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.1907
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=92023048, alloc=4586680, time=2.91
bytes used=96023696, alloc=4586680, time=3.04
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.05060739355700686104977308733273
y[1] (numeric) = 0.050607393557006861037352090060139
absolute error = 1.2420997272591e-20
relative error = 2.4543839149904702599500640280461e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.202
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=100024628, alloc=4586680, time=3.17
bytes used=104025380, alloc=4586680, time=3.30
bytes used=108026200, alloc=4586680, time=3.42
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.05486445951916478534735693006468
y[1] (numeric) = 0.054864459519164785334621979688214
absolute error = 1.2734950376466e-20
relative error = 2.3211657397294756333550617736473e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2132
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=112027392, alloc=4586680, time=3.55
bytes used=116028384, alloc=4586680, time=3.68
TOP MAIN SOLVE Loop
bytes used=120029292, alloc=4586680, time=3.81
x[1] = 0.2
y[1] (analytic) = 0.0592326553757257311850347617666
y[1] (numeric) = 0.059232655375725731172052080747057
absolute error = 1.2982681019543e-20
relative error = 2.1918114150363520504991871668470e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2244
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=124030236, alloc=4586680, time=3.94
bytes used=128031096, alloc=4586680, time=4.07
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.0637089826239078639394934553792
y[1] (numeric) = 0.063708982623907863926312953062056
absolute error = 1.3180502317144e-20
relative error = 2.0688609006601520438858679735921e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2356
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3674
Order of pole (six term test) = -0.75
bytes used=132032004, alloc=4586680, time=4.20
bytes used=136033132, alloc=4586680, time=4.32
bytes used=140034296, alloc=4586680, time=4.45
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.0682906555612834706531438647202
y[1] (numeric) = 0.068290655561283470639803682935907
absolute error = 1.3340181784293e-20
relative error = 1.9534417519717073109719372772849e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2468
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=144035356, alloc=4586680, time=4.58
bytes used=148036500, alloc=4586680, time=4.71
TOP MAIN SOLVE Loop
bytes used=152037320, alloc=4586680, time=4.84
x[1] = 0.23
y[1] (analytic) = 0.07297507689552925974513803766118
y[1] (numeric) = 0.072975076895529259731667695094419
absolute error = 1.3470342566761e-20
relative error = 1.8458826136004039168936200868426e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.258
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=156038328, alloc=4586680, time=4.97
bytes used=160039284, alloc=4586680, time=5.09
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.07775981710693572198563031071952
y[1] (numeric) = 0.077759817106935721972052916174535
absolute error = 1.3577394544985e-20
relative error = 1.7460682200825258404261761245590e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2693
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=164039972, alloc=4586680, time=5.22
bytes used=168041148, alloc=4586680, time=5.35
bytes used=172042184, alloc=4586680, time=5.48
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.08264259685175003007525953297954
y[1] (numeric) = 0.082642596851750030061593368107921
absolute error = 1.3666164871619e-20
relative error = 1.6536465929470132414951124338802e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2805
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=176043328, alloc=4652204, time=5.61
bytes used=180044256, alloc=4652204, time=5.74
TOP MAIN SOLVE Loop
bytes used=184045180, alloc=4652204, time=5.87
x[1] = 0.26
y[1] (analytic) = 0.08762127185292661212609148179727
y[1] (numeric) = 0.087621271852926612112351149400529
absolute error = 1.3740332396741e-20
relative error = 1.5681503025662898125231386961176e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.2917
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=188046396, alloc=4652204, time=6.00
bytes used=192048596, alloc=4652204, time=6.13
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.09269381984325844644578324423321
y[1] (numeric) = 0.092693819843258446431980512497045
absolute error = 1.3802731736165e-20
relative error = 1.4890670984867026773012015680421e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3029
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=196049740, alloc=4652204, time=6.26
bytes used=200050580, alloc=4652204, time=6.39
bytes used=204051512, alloc=4652204, time=6.52
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.09785832921543259067893378612129
y[1] (numeric) = 0.0978583292154325906650782169168
absolute error = 1.3855569204490e-20
relative error = 1.4158804176992764052150736215316e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3141
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=208052484, alloc=4652204, time=6.64
bytes used=212053368, alloc=4652204, time=6.77
TOP MAIN SOLVE Loop
bytes used=216054204, alloc=4652204, time=6.90
x[1] = 0.29
y[1] (analytic) = 0.10311298910210522186354368864912
y[1] (numeric) = 0.10311298910210522184964311042855
absolute error = 1.390057822057e-20
relative error = 1.3480918690859866414553848371397e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3254
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=220055232, alloc=4652204, time=7.03
bytes used=224056092, alloc=4652204, time=7.16
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.10845608066211933050373087816212
y[1] (numeric) = 0.10845608066211933048979174562147
absolute error = 1.393913254065e-20
relative error = 1.2852329215247539691520827170561e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3366
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3929
Order of pole (six term test) = -0.75
bytes used=228057000, alloc=4652204, time=7.29
bytes used=232057896, alloc=4652204, time=7.42
bytes used=236058680, alloc=4652204, time=7.54
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.1138859693904133281896463623123
y[1] (numeric) = 0.11388596939041332817567403259883
absolute error = 1.397232971347e-20
relative error = 1.2268701568997805057812088158364e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3478
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=240059724, alloc=4652204, time=7.67
bytes used=244060920, alloc=4652204, time=7.80
TOP MAIN SOLVE Loop
bytes used=248062140, alloc=4652204, time=7.93
x[1] = 0.32
y[1] (analytic) = 0.11940109830182609816376755995711
y[1] (numeric) = 0.11940109830182609814976650671044
absolute error = 1.400105324667e-20
relative error = 1.1726067386145534725604320237705e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.359
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=252063112, alloc=4652204, time=8.06
bytes used=256064012, alloc=4652204, time=8.19
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.12499998186496788596664318429292
y[1] (numeric) = 0.12499998186496788595261716491613
absolute error = 1.402601937679e-20
relative error = 1.1220817129351031891812368528977e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3702
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=260065308, alloc=4652204, time=8.32
bytes used=264066380, alloc=4652204, time=8.45
bytes used=268067564, alloc=4652204, time=8.57
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.13068120058313194952274967679503
y[1] (numeric) = 0.13068120058313194950870186421088
absolute error = 1.404781258415e-20
relative error = 1.0749681301874465383618249765943e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3815
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=272068424, alloc=4652204, time=8.71
bytes used=276069472, alloc=4652204, time=8.84
TOP MAIN SOLVE Loop
bytes used=280070308, alloc=4652204, time=8.97
x[1] = 0.35
y[1] (analytic) = 0.13644339613601686663871970248489
y[1] (numeric) = 0.13644339613601686662465278968872
absolute error = 1.406691279617e-20
relative error = 1.0309705852049491014115159526205e-17 %
Correct digits = 19
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.3927
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=284071388, alloc=4652204, time=9.10
bytes used=288073996, alloc=4652204, time=9.23
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.14228526700968044522749929915703
y[1] (numeric) = 0.14228526700968044521341558276183
absolute error = 1.408371639520e-20
relative error = 9.8982253687880472647108520202513e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4039
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=292074916, alloc=4652204, time=9.36
bytes used=296076056, alloc=4652204, time=9.49
bytes used=300077076, alloc=4652204, time=9.62
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.1482055645533135708706721697601
y[1] (numeric) = 0.14820556455331357085657361719358
absolute error = 1.409855256652e-20
relative error = 9.5128361806201732331272354687505e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4151
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=304077884, alloc=4652204, time=9.75
bytes used=308078740, alloc=4652204, time=9.88
TOP MAIN SOLVE Loop
bytes used=312079976, alloc=4652204, time=10.00
x[1] = 0.38
y[1] (analytic) = 0.15420308941061341619435798007207
y[1] (numeric) = 0.1542030894106134161802462839594
absolute error = 1.411169611267e-20
relative error = 9.1513705507502802054502564909581e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4263
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=316081060, alloc=4652204, time=10.13
bytes used=320081952, alloc=4652204, time=10.26
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.16027668828114320969946369125599
y[1] (numeric) = 0.16027668828114320968534031368962
absolute error = 1.412337756637e-20
relative error = 8.8118725922237790186896886111371e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4376
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=324082952, alloc=4652204, time=10.39
bytes used=328085340, alloc=4652204, time=10.52
bytes used=332086592, alloc=4652204, time=10.65
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0.16642525097339690401226591334186
y[1] (numeric) = 0.16642525097339690399813212211841
absolute error = 1.413379122345e-20
relative error = 8.4925761810683933973944053034988e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4488
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5979
Order of pole (six term test) = -0.75
bytes used=336087528, alloc=4652204, time=10.77
bytes used=340088580, alloc=4652204, time=10.90
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.17264770771658263461500700740523
y[1] (numeric) = 0.17264770771658263460086390584286
absolute error = 1.414310156237e-20
relative error = 8.1918849369186091156129435084555e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.46
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=344089444, alloc=4652204, time=11.03
bytes used=348090452, alloc=4652204, time=11.16
bytes used=352091604, alloc=4652204, time=11.29
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0.17894302670258953540380865243176
y[1] (numeric) = 0.17894302670258953538965720402723
absolute error = 1.415144840453e-20
relative error = 7.9083542205029721717574366658619e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4712
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=356092828, alloc=4652204, time=11.42
bytes used=360094212, alloc=4652204, time=11.55
bytes used=364095260, alloc=4652204, time=11.67
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.1853102118333601316561250900761
y[1] (numeric) = 0.18531021183336013164196613899127
absolute error = 1.415895108483e-20
relative error = 7.6406750306682563245294362063467e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4824
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=368096176, alloc=4652204, time=11.81
bytes used=372097100, alloc=4652204, time=11.93
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.19174830065207680268522342109599
y[1] (numeric) = 0.19174830065207680267105770925556
absolute error = 1.416571184043e-20
relative error = 7.3876596518752891935862310084123e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.4937
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=376098000, alloc=4652204, time=12.06
bytes used=380099064, alloc=4652204, time=12.19
bytes used=384100032, alloc=4652204, time=12.32
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0.1982563624392836852608743680207
y[1] (numeric) = 0.19825636243928368524670254944311
absolute error = 1.417181857759e-20
relative error = 7.1482288907273486123640172361545e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5049
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=388100940, alloc=4652204, time=12.45
bytes used=392102140, alloc=4652204, time=12.58
TOP MAIN SOLVE Loop
bytes used=396103332, alloc=4717728, time=12.71
x[1] = 0.46
y[1] (analytic) = 0.20483349645738424032739463660336
y[1] (numeric) = 0.20483349645738424031321728946168
absolute error = 1.417734714168e-20
relative error = 6.9214007410304630062180620139244e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5161
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=400104148, alloc=4717728, time=12.84
bytes used=404105228, alloc=4717728, time=12.97
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.21147883032894414147392841058774
y[1] (numeric) = 0.21147883032894414145974604739959
absolute error = 1.418236318815e-20
relative error = 6.7062803241771688271589307229717e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5273
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=408106552, alloc=4717728, time=13.10
bytes used=412107940, alloc=4717728, time=13.23
bytes used=416108756, alloc=4717728, time=13.36
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.21819151853594202238755819189924
y[1] (numeric) = 0.2181915185359420223733712681684
absolute error = 1.418692373084e-20
relative error = 6.5020509623993617274559544961488e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5385
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7307
Order of pole (six term test) = -0.75
bytes used=420109692, alloc=4717728, time=13.49
bytes used=424110592, alloc=4717728, time=13.61
TOP MAIN SOLVE Loop
bytes used=428111532, alloc=4717728, time=13.74
x[1] = 0.49
y[1] (analytic) = 0.22497074102859038704234597934801
y[1] (numeric) = 0.22497074102859038702815490091879
absolute error = 1.419107842922e-20
relative error = 6.3079662556725667863638470280180e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5498
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=432112584, alloc=4717728, time=13.87
bytes used=436113648, alloc=4717728, time=14.00
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0.23181570193363150761099449299946
y[1] (numeric) = 0.23181570193363150759679962233728
absolute error = 1.419487066218e-20
relative error = 6.1233430452627279160528528885217e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.561
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4776
Order of pole (six term test) = -0.75
bytes used=440115724, alloc=4717728, time=14.13
bytes used=444116624, alloc=4717728, time=14.26
bytes used=448118804, alloc=4717728, time=14.39
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0.23872562835312814792158035069624
y[1] (numeric) = 0.23872562835312814790738201226857
absolute error = 1.419833842767e-20
relative error = 5.9475551601303185665585194557049e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5722
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2733
Order of pole (six term test) = -0.75
bytes used=452119460, alloc=4717728, time=14.52
bytes used=456120260, alloc=4717728, time=14.65
TOP MAIN SOLVE Loop
bytes used=460121252, alloc=4717728, time=14.78
x[1] = 0.52
y[1] (analytic) = 0.24569976924574120962724244197333
y[1] (numeric) = 0.24569976924574120961304092687451
absolute error = 1.420151509882e-20
relative error = 5.7800278536753893470638791796894e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5834
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=464122336, alloc=4717728, time=14.90
bytes used=468123080, alloc=4717728, time=15.03
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0.252737394383336592027233416646
y[1] (numeric) = 0.25273739438333659201302898658395
absolute error = 1.420443006205e-20
relative error = 5.6202328494791676655538703119356e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5946
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=472124188, alloc=4717728, time=15.16
bytes used=476125160, alloc=4717728, time=15.29
bytes used=480126544, alloc=4717728, time=15.42
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0.25983779337650903834691957291989
y[1] (numeric) = 0.25983779337650903833271246366303
absolute error = 1.420710925686e-20
relative error = 5.4676839239754764380987551681262e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6059
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=484127344, alloc=4717728, time=15.55
bytes used=488128260, alloc=4717728, time=15.67
TOP MAIN SOLVE Loop
bytes used=492129380, alloc=4717728, time=15.80
x[1] = 0.55
y[1] (analytic) = 0.26700027476326612021203093917204
y[1] (numeric) = 0.26700027476326612019782136353751
absolute error = 1.420957563453e-20
relative error = 5.3219329632259061843885802857052e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6171
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=496130440, alloc=4717728, time=15.93
bytes used=500132240, alloc=4717728, time=16.06
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0.27422416515569312869459758597341
y[1] (numeric) = 0.2742241651556931286803857364249
absolute error = 1.421184954851e-20
relative error = 5.1825664380967666237039974234973e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6283
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=504133464, alloc=4717728, time=16.19
bytes used=508134256, alloc=4717728, time=16.32
bytes used=512135216, alloc=4717728, time=16.45
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0.28150880843992995365617709626816
y[1] (numeric) = 0.28150880843992995364196314717991
absolute error = 1.421394908825e-20
relative error = 5.0492022494859368250494906996184e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6395
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=516136840, alloc=4717728, time=16.58
bytes used=520137696, alloc=4717728, time=16.71
TOP MAIN SOLVE Loop
bytes used=524138768, alloc=4717728, time=16.83
x[1] = 0.58
y[1] (analytic) = 0.28885356502524293556735739340893
y[1] (numeric) = 0.28885356502524293555314150304387
absolute error = 1.421589036506e-20
relative error = 4.9214869007476754641017949602048e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6507
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=528139928, alloc=4717728, time=16.96
bytes used=532140780, alloc=4717728, time=17.09
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0.29625781113837574911119902618758
y[1] (numeric) = 0.29625781113837574909698133842984
absolute error = 1.421768775774e-20
relative error = 4.7990929599824860537032119018224e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.662
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=536141640, alloc=4717728, time=17.22
bytes used=540142880, alloc=4717728, time=17.35
bytes used=544143760, alloc=4717728, time=17.48
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0.3037209381597201121017272675031
y[1] (numeric) = 0.30372093815972011208750791337886
absolute error = 1.421935412424e-20
relative error = 4.6817167793556454483647708409475e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6732
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=548144632, alloc=4717728, time=17.61
bytes used=552145624, alloc=4717728, time=17.73
TOP MAIN SOLVE Loop
bytes used=556146712, alloc=4717728, time=17.86
x[1] = 0.61
y[1] (analytic) = 0.31124235199816507030331787757062
y[1] (numeric) = 0.31124235199816507028909697658619
absolute error = 1.422090098443e-20
relative error = 4.5690764425639089568725249333864e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6844
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1652
Order of pole (six term test) = -0.75
bytes used=560147840, alloc=4717728, time=17.99
bytes used=564148936, alloc=4717728, time=18.12
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0.31882147250176757398043480450662
y[1] (numeric) = 0.31882147250176757396621246582828
absolute error = 1.422233867834e-20
relative error = 4.4609099151128066247325388992131e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6956
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=568149964, alloc=4717728, time=18.25
bytes used=572151196, alloc=4717728, time=18.38
bytes used=576152144, alloc=4717728, time=18.51
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0.32645773290164116217850611633425
y[1] (numeric) = 0.3264577329016411621642824398307
absolute error = 1.422367650355e-20
relative error = 4.3569733751215715193248293714335e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7068
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=580153168, alloc=4717728, time=18.64
bytes used=584154192, alloc=4717728, time=18.77
TOP MAIN SOLVE Loop
bytes used=588155604, alloc=4717728, time=18.90
x[1] = 0.64
y[1] (analytic) = 0.33415057928668737367191479071961
y[1] (numeric) = 0.33415057928668737365768986788487
absolute error = 1.422492283474e-20
relative error = 4.2570397050054504539850715512049e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.718
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=592156748, alloc=4717728, time=19.03
bytes used=596157844, alloc=4717728, time=19.16
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0.34189947010699910143662624273517
y[1] (numeric) = 0.34189947010699910142240015750733
absolute error = 1.422608522784e-20
relative error = 4.1608971266869403052138612559668e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7293
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=600158828, alloc=4717728, time=19.28
bytes used=604160068, alloc=4717728, time=19.41
bytes used=608160928, alloc=4717728, time=19.54
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0.34970387570394918680215167774942
y[1] (numeric) = 0.34970387570394918678792450723831
absolute error = 1.422717051111e-20
relative error = 4.0683479651093078632117364521278e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7405
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=612162044, alloc=4717728, time=19.67
bytes used=616163256, alloc=4717728, time=19.80
TOP MAIN SOLVE Loop
bytes used=620164040, alloc=4717728, time=19.93
x[1] = 0.67
y[1] (analytic) = 0.35756327786514344930166323559463
y[1] (numeric) = 0.35756327786514344928743505072971
absolute error = 1.422818486492e-20
relative error = 3.9792075265307926882267901114680e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7517
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=624164856, alloc=4717728, time=20.06
bytes used=628165980, alloc=4717728, time=20.19
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0.36547716940256711007416462988609
y[1] (numeric) = 0.3654771694025671100599354959944
absolute error = 1.422913389169e-20
relative error = 3.8933030796287147298960911460827e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7629
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=632167476, alloc=4717728, time=20.32
bytes used=636169200, alloc=4717728, time=20.45
bytes used=640170072, alloc=4717728, time=20.58
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0.37344505375238897584772666954199
y[1] (numeric) = 0.37344505375238897583349664686455
absolute error = 1.423002267744e-20
relative error = 3.8104729288703207846530823144751e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7741
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=644171016, alloc=4717728, time=20.71
bytes used=648171836, alloc=4717728, time=20.84
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0.3814664445950103717571801853617
y[1] (numeric) = 0.38146644459501037174294932951572
absolute error = 1.423085584598e-20
relative error = 3.7305655707380510587993295822671e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7854
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5233
Order of pole (six term test) = -0.75
bytes used=652172560, alloc=4717728, time=20.97
bytes used=656173796, alloc=4717728, time=21.10
bytes used=660174776, alloc=4717728, time=21.22
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0.38954086549405701862250238081336
y[1] (numeric) = 0.3895408654940570186082707432066
absolute error = 1.423163760676e-20
relative error = 3.6534389244912542288636375543186e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.7966
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=664175656, alloc=4717728, time=21.36
bytes used=668176804, alloc=4717728, time=21.48
bytes used=672177828, alloc=4717728, time=21.61
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0.39766784955311305291452998148413
y[1] (numeric) = 0.39766784955311305290029760968691
absolute error = 1.423237179722e-20
relative error = 3.5789596300565669133628035835997e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8078
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=676178836, alloc=4717728, time=21.74
bytes used=680179896, alloc=4717728, time=21.87
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0.40584693908908825136674503319275
y[1] (numeric) = 0.40584693908908825135251197127255
absolute error = 1.423306192020e-20
relative error = 3.5070024064110713622355810138461e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.819
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=684181072, alloc=4717728, time=22.00
bytes used=688181872, alloc=4717728, time=22.13
bytes used=692182868, alloc=4717728, time=22.25
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0.41407768532119318847729432173213
y[1] (numeric) = 0.414077685321193188463060610555
absolute error = 1.423371117713e-20
relative error = 3.4374494646069001429848639768622e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8302
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=696183696, alloc=4717728, time=22.38
bytes used=700184524, alloc=4717728, time=22.51
TOP MAIN SOLVE Loop
bytes used=704185720, alloc=4717728, time=22.64
x[1] = 0.75
y[1] (analytic) = 0.42235964807457335695436084521896
y[1] (numeric) = 0.4223596480745733569401265227212
absolute error = 1.423432249776e-20
relative error = 3.3701899702423125903000877308984e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8415
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=708186856, alloc=4717728, time=22.77
bytes used=712187708, alloc=4717728, time=22.90
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0.4306923954977229567889229319278
y[1] (numeric) = 0.43069239549772295677468803336145
absolute error = 1.423489856635e-20
relative error = 3.3051195505552544635870867904582e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8527
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=716188536, alloc=4717728, time=23.03
bytes used=720189652, alloc=4717728, time=23.16
bytes used=724190500, alloc=4717728, time=23.29
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0.43907550379286276358809156616832
y[1] (numeric) = 0.43907550379286276357385612432323
absolute error = 1.423544184509e-20
relative error = 3.2421398420362979004639259114104e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8639
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=728191552, alloc=4717728, time=23.42
bytes used=732192348, alloc=4717728, time=23.55
TOP MAIN SOLVE Loop
bytes used=736193292, alloc=4717728, time=23.68
x[1] = 0.78
y[1] (analytic) = 0.44750855695852480400976127263357
y[1] (numeric) = 0.44750855695852480399552531803849
absolute error = 1.423595459508e-20
relative error = 3.1811580747939511570680639132344e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8751
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.186
Order of pole (six term test) = -0.75
bytes used=740195936, alloc=4717728, time=23.80
bytes used=744196840, alloc=4717728, time=23.93
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0.45599114654364001485177203774162
y[1] (numeric) = 0.45599114654364001483753559884646
absolute error = 1.423643889516e-20
relative error = 3.1220866902944399392347211608231e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8863
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=748197900, alloc=4717728, time=24.07
bytes used=752199068, alloc=4717728, time=24.19
bytes used=756200264, alloc=4717728, time=24.32
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0.46452287141247410580008615162259
y[1] (numeric) = 0.46452287141247410578584925496404
absolute error = 1.423689665855e-20
relative error = 3.0648429893795942472291938557979e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.8976
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=760201436, alloc=4717728, time=24.45
bytes used=764202628, alloc=4717728, time=24.58
TOP MAIN SOLVE Loop
bytes used=768203752, alloc=4717728, time=24.71
x[1] = 0.81
y[1] (analytic) = 0.47310333751980189792187140402686
y[1] (numeric) = 0.47310333751980189790763407437894
absolute error = 1.423732964792e-20
relative error = 3.0093488079280547922452634670378e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9088
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.367
Order of pole (six term test) = -0.75
bytes used=772205312, alloc=4717728, time=24.84
bytes used=776206424, alloc=4717728, time=24.97
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0.48173215769575184105218496698933
y[1] (numeric) = 0.48173215769575184103794722750028
absolute error = 1.423773948905e-20
relative error = 2.9555302176945692453610449447154e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.92
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=780207592, alloc=4717728, time=25.10
bytes used=784208376, alloc=4717728, time=25.23
bytes used=788209332, alloc=4717728, time=25.36
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0.49040895143979055513623865085879
y[1] (numeric) = 0.49040895143979055512200052317607
absolute error = 1.423812768272e-20
relative error = 2.9033172500049830756121144192884e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9312
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=792210404, alloc=4717728, time=25.49
bytes used=796211472, alloc=4717728, time=25.62
TOP MAIN SOLVE Loop
bytes used=800212696, alloc=4717728, time=25.75
x[1] = 0.84
y[1] (analytic) = 0.49913334472335239115583054753454
y[1] (numeric) = 0.49913334472335239114159205191859
absolute error = 1.423849561595e-20
relative error = 2.8526436405168984292835143164688e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9424
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=804213628, alloc=4717728, time=25.88
bytes used=808214500, alloc=4717728, time=26.01
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0.50790496980065143408757155422775
y[1] (numeric) = 0.5079049698006514340733327096561
absolute error = 1.423884457165e-20
relative error = 2.8034465930188929986851669414658e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9537
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=812215320, alloc=4717728, time=26.14
bytes used=816216484, alloc=4717728, time=26.27
bytes used=820217576, alloc=4717728, time=26.39
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0.51672346502724331419153257735065
y[1] (numeric) = 0.51672346502724331417729340161303
absolute error = 1.423917573762e-20
relative error = 2.7556665608110645992759863416237e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9649
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=824218428, alloc=4717728, time=26.52
bytes used=828219164, alloc=4717728, time=26.65
TOP MAIN SOLVE Loop
bytes used=832219896, alloc=4717728, time=26.78
x[1] = 0.87
y[1] (analytic) = 0.52558847468593187074164261123563
y[1] (numeric) = 0.525588474685931870727403121021
absolute error = 1.423949021463e-20
relative error = 2.7092470441135303639286819156728e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9761
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=836220820, alloc=4717728, time=26.91
bytes used=840221712, alloc=4717728, time=27.04
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0.53449964881964131977406275271287
y[1] (numeric) = 0.53449964881964131975982296368922
absolute error = 1.423978902365e-20
relative error = 2.6641344021640316637865950920141e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9873
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.859
Order of pole (six term test) = -0.75
bytes used=844222624, alloc=4717728, time=27.17
bytes used=848223724, alloc=4717728, time=27.30
bytes used=852224516, alloc=4717728, time=27.43
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0.54345664307089829129628488942734
y[1] (numeric) = 0.54345664307089829128204481631486
absolute error = 1.424007311248e-20
relative error = 2.6202776788252946056075554173532e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9985
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.183
Order of pole (six term test) = -0.75
bytes used=856225420, alloc=4717728, time=27.56
bytes used=860226404, alloc=4717728, time=27.68
TOP MAIN SOLVE Loop
bytes used=864227204, alloc=4717728, time=27.81
x[1] = 0.9
y[1] (analytic) = 0.55245911852759008150266303407261
y[1] (numeric) = 0.55245911852759008148842269071085
absolute error = 1.424034336176e-20
relative error = 2.5776284405827632678321687283029e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.53
Order of pole (six term test) = -0.75
bytes used=868228324, alloc=4717728, time=27.94
bytes used=872229288, alloc=4717728, time=28.07
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0.56150674157468585659107857799664
y[1] (numeric) = 0.56150674157468585657683797740624
absolute error = 1.424060059040e-20
relative error = 2.5361406259279723445976386310696e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.021
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2575
Order of pole (six term test) = -0.75
bytes used=876230580, alloc=4717728, time=28.20
bytes used=880231820, alloc=4717728, time=28.32
bytes used=884233084, alloc=4717728, time=28.45
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0.57059918375162647793731703614644
y[1] (numeric) = 0.57059918375162647792307619058594
absolute error = 1.424084556050e-20
relative error = 2.4957704052200034092658318938440e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.032
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=888234036, alloc=4717728, time=28.58
bytes used=892234756, alloc=4717728, time=28.71
TOP MAIN SOLVE Loop
bytes used=896236056, alloc=4717728, time=28.84
x[1] = 0.93
y[1] (analytic) = 0.57973612161510621268402163268504
y[1] (numeric) = 0.57973612161510621266978055370315
absolute error = 1.424107898189e-20
relative error = 2.4564760502097579671190976435508e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.043
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=900237008, alloc=4717728, time=28.96
bytes used=904237992, alloc=4717728, time=29.09
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0.58891723660698595736683624368667
y[1] (numeric) = 0.58891723660698595735259494217047
absolute error = 1.424130151620e-20
relative error = 2.4182178124468677394770655596279e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.055
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=908238836, alloc=4717728, time=29.22
bytes used=912239944, alloc=4717728, time=29.35
bytes used=916240896, alloc=4717728, time=29.48
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0.59814221492709283336382336582135
y[1] (numeric) = 0.59814221492709283334958185204069
absolute error = 1.424151378066e-20
relative error = 2.3809578099074463216086969538405e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.066
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=920241724, alloc=4717728, time=29.61
bytes used=924242596, alloc=4717728, time=29.73
TOP MAIN SOLVE Loop
bytes used=928243460, alloc=4717728, time=29.86
x[1] = 0.96
y[1] (analytic) = 0.60741074741067520123436905096897
y[1] (numeric) = 0.60741074741067520122012733461755
absolute error = 1.424171635142e-20
relative error = 2.3446599211704535663198664244588e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.077
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=932244432, alloc=4717728, time=29.99
bytes used=936245528, alloc=4717728, time=30.12
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0.61672252941029536799001774696194
y[1] (numeric) = 0.61672252941029536797577583719517
absolute error = 1.424190976677e-20
relative error = 2.3092896866258458643567661961682e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.088
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=940246588, alloc=4717728, time=30.25
bytes used=944248172, alloc=4717728, time=30.38
bytes used=948249400, alloc=4717728, time=30.51
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0.62607726068195460143106106972141
y[1] (numeric) = 0.62607726068195460141681897519155
absolute error = 1.424209452986e-20
relative error = 2.2748142161155637211918527806110e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.1
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=952250236, alloc=4717728, time=30.64
bytes used=956251628, alloc=4717728, time=30.77
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0.63547464527525658684329825001407
y[1] (numeric) = 0.63547464527525658682905597890259
absolute error = 1.424227111148e-20
relative error = 2.2412021026127554763554562219621e-18 %
Correct digits = 20
h = 0.001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.111
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=960252436, alloc=4717728, time=30.90
bytes used=964253372, alloc=4717728, time=31.03
bytes used=968254548, alloc=4717728, time=31.16
Finished!
diff ( y , x , 1 ) = Si(sqrt(x));
Iterations = 900
Total Elapsed Time = 31 Seconds
Elapsed Time(since restart) = 30 Seconds
Time to Timeout = 2 Minutes 28 Seconds
Percent Done = 100.1 %
> quit
bytes used=969710424, alloc=4717728, time=31.20