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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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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 mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[1] := array_m1[1] * array_const_2D0[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp1[1] / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp8[1] := array_const_0D0[1] + array_tmp7[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_tmp8[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp1[2] := array_m1[2] * array_const_2D0[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp1[2] - array_tmp3[1] * array_tmp2[2]) / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp8[2] := array_tmp7[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_tmp8[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp1[3] := array_m1[3] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp1[3] - array_tmp3[2] * array_tmp2[2]) / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp8[3] := array_tmp7[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_tmp8[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp1[4] := array_m1[4] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp1[4] - array_tmp3[3] * array_tmp2[2]) / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp8[4] := array_tmp7[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_tmp8[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp1[5] := array_m1[5] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp1[5] - array_tmp3[4] * array_tmp2[2]) / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp8[5] := array_tmp7[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_tmp8[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := -ats(kkk,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := -ats(kkk,array_tmp4,array_tmp5,2) / array_tmp4[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp7[kkk] := -ats(kkk,array_tmp6,array_tmp7,2) / array_tmp6[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp8[kkk] := array_tmp7[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_tmp8[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_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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] := array_m1[1]*array_const_2D0[1];
array_tmp2[1] := array_x[1] - array_const_6D0[1];
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_x[1] - array_const_6D0[1];
array_tmp5[1] := array_tmp3[1]/array_tmp4[1];
array_tmp6[1] := array_x[1] - array_const_6D0[1];
array_tmp7[1] := array_tmp5[1]/array_tmp6[1];
array_tmp8[1] := array_const_0D0[1] + array_tmp7[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp8[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_m1[2]*array_const_2D0[1];
array_tmp2[2] := array_x[2];
array_tmp3[2] :=
(array_tmp1[2] - array_tmp3[1]*array_tmp2[2])/array_tmp2[1];
array_tmp4[2] := array_x[2];
array_tmp5[2] :=
(array_tmp3[2] - array_tmp5[1]*array_tmp4[2])/array_tmp4[1];
array_tmp6[2] := array_x[2];
array_tmp7[2] :=
(array_tmp5[2] - array_tmp7[1]*array_tmp6[2])/array_tmp6[1];
array_tmp8[2] := array_tmp7[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp8[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_m1[3]*array_const_2D0[1];
array_tmp3[3] :=
(array_tmp1[3] - array_tmp3[2]*array_tmp2[2])/array_tmp2[1];
array_tmp5[3] :=
(array_tmp3[3] - array_tmp5[2]*array_tmp4[2])/array_tmp4[1];
array_tmp7[3] :=
(array_tmp5[3] - array_tmp7[2]*array_tmp6[2])/array_tmp6[1];
array_tmp8[3] := array_tmp7[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp8[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_m1[4]*array_const_2D0[1];
array_tmp3[4] :=
(array_tmp1[4] - array_tmp3[3]*array_tmp2[2])/array_tmp2[1];
array_tmp5[4] :=
(array_tmp3[4] - array_tmp5[3]*array_tmp4[2])/array_tmp4[1];
array_tmp7[4] :=
(array_tmp5[4] - array_tmp7[3]*array_tmp6[2])/array_tmp6[1];
array_tmp8[4] := array_tmp7[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp8[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_m1[5]*array_const_2D0[1];
array_tmp3[5] :=
(array_tmp1[5] - array_tmp3[4]*array_tmp2[2])/array_tmp2[1];
array_tmp5[5] :=
(array_tmp3[5] - array_tmp5[4]*array_tmp4[2])/array_tmp4[1];
array_tmp7[5] :=
(array_tmp5[5] - array_tmp7[4]*array_tmp6[2])/array_tmp6[1];
array_tmp8[5] := array_tmp7[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp8[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_m1[kkk]*array_const_2D0[1];
array_tmp3[kkk] :=
-ats(kkk, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp5[kkk] :=
-ats(kkk, array_tmp4, array_tmp5, 2)/array_tmp4[1];
array_tmp7[kkk] :=
-ats(kkk, array_tmp6, array_tmp7, 2)/array_tmp6[1];
array_tmp8[kkk] := array_tmp7[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_tmp8[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(1.0/ ( x - 6.0 ) / ( x - 6.0 ));
> end;
exact_soln_y := proc(x) return 1.0/((x - 6.0)*(x - 6.0)) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,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,
> array_const_2D0,
> array_const_6D0,
> #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,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> 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/sing6postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 2.0;");
> omniout_str(ALWAYS,"x_end := 3.0;");
> 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 := 100;");
> omniout_str(ALWAYS,"## Not Given = 0");
> omniout_str(ALWAYS,"## No Pole = 3");
> omniout_str(ALWAYS,"## Pole = 4");
> omniout_str(ALWAYS,"glob_type_given_pole := 4;");
> omniout_str(ALWAYS,"## Real Part");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := 6.0;");
> omniout_str(ALWAYS,"## Imag Part");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 0.0;");
> omniout_str(ALWAYS,"## Order");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 3.0;");
> omniout_str(ALWAYS,"## Not Used");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := 0.0;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0/ ( x - 6.0 ) / ( x - 6.0 ));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=40;
> #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:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= 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[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_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp8[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_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_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 := 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_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp8[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_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2D0[1] := 2.0;
> array_const_6D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_6D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_6D0[1] := 6.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 2.0;
> x_end := 3.0;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 100;
> ## Not Given = 0
> ## No Pole = 3
> ## Pole = 4
> glob_type_given_pole := 4;
> ## Real Part
> array_given_rad_poles[1,1] := 6.0;
> ## Imag Part
> array_given_rad_poles[1,2] := 0.0;
> ## Order
> array_given_ord_poles[1,1] := 3.0;
> ## Not Used
> array_given_ord_poles[1,2] := 0.0;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := 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 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;");
> 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,"2013-05-26T04:50:56-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing6")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_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,"sing6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing6 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_6D0, 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, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, 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/sing6postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( \
x - 6.0 ) / ( x - 6.0) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 2.0;");
omniout_str(ALWAYS, "x_end := 3.0;");
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 := 100;");
omniout_str(ALWAYS, "## Not Given = 0");
omniout_str(ALWAYS, "## No Pole = 3");
omniout_str(ALWAYS, "## Pole = 4");
omniout_str(ALWAYS, "glob_type_given_pole := 4;");
omniout_str(ALWAYS, "## Real Part");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := 6.0;");
omniout_str(ALWAYS, "## Imag Part");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := 0.0;");
omniout_str(ALWAYS, "## Order");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := 3.0;");
omniout_str(ALWAYS, "## Not Used");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := 0.0;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0/ ( x - 6.0 ) / ( x - 6.0 ));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 64;
max_terms := 40;
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 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := 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[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_6D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_6D0[term] := 0.; term := term + 1
end do;
array_const_6D0[1] := 6.0;
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 := 2.0;
x_end := 3.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
glob_type_given_pole := 4;
array_given_rad_poles[1, 1] := 6.0;
array_given_rad_poles[1, 2] := 0.;
array_given_ord_poles[1, 1] := 3.0;
array_given_ord_poles[1, 2] := 0.;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := 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 ) = m1 * 2.0 / ( x - 6.0 ) / \
( x - 6.0 ) / ( x - 6.0) ;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T04:50:56-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sing6")
;
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / (\
x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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,
"sing6 diffeq.mxt");
logitem_str(html_log_file,
"sing6 maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/sing6postode.ode#################
diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.0;
x_end := 3.0;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
## Not Given = 0
## No Pole = 3
## Pole = 4
glob_type_given_pole := 4;
## Real Part
array_given_rad_poles[1,1] := 6.0;
## Imag Part
array_given_rad_poles[1,2] := 0.0;
## Order
array_given_ord_poles[1,1] := 3.0;
## Not Used
array_given_ord_poles[1,2] := 0.0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0/ ( x - 6.0 ) / ( x - 6.0 ));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 1
estimated_steps = 1000000
step_error = 1.0000000000000000000000000000000e-16
est_needed_step_err = 1.0000000000000000000000000000000e-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 = 1.1029076175414498559823914499286e-239
estimated_step_error = 1.1029076175414498559823914499286e-239
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 = 7.5791243583451921780697302340811e-229
estimated_step_error = 7.5791243583451921780697302340811e-229
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.2083358671183506697486960644855e-218
estimated_step_error = 5.2083358671183506697486960644855e-218
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 = 3.5791428957426397726637458511143e-207
estimated_step_error = 3.5791428957426397726637458511143e-207
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 = 2.4595706626861734939643381571370e-196
estimated_step_error = 2.4595706626861734939643381571370e-196
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6902073784087161279921419836162e-185
estimated_step_error = 1.6902073784087161279921419836162e-185
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1615061866698747474670763476401e-174
estimated_step_error = 1.1615061866698747474670763476401e-174
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 = 7.9818718670074936540500120068101e-164
estimated_step_error = 7.9818718670074936540500120068101e-164
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 = 5.4851859730809211674392574905467e-153
estimated_step_error = 5.4851859730809211674392574905467e-153
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.7695084665146557018575829028652e-142
estimated_step_error = 3.7695084665146557018575829028652e-142
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 = 2.5905478178842016360715878548256e-131
estimated_step_error = 2.5905478178842016360715878548256e-131
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.7804326687478811950140685416922e-120
estimated_step_error = 1.7804326687478811950140685416922e-120
best_h = 0.004096
opt_iter = 13
bytes used=4000404, alloc=3276200, time=0.20
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2238089172282182010308698446705e-109
estimated_step_error = 1.2238089172282182010308698446705e-109
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 8.4141445365476183566450963907145e-99
estimated_step_error = 8.4141445365476183566450963907145e-99
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.7879284749683902014936694349973e-88
estimated_step_error = 5.7879284749683902014936694349973e-88
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.9853913168419842636520277294002e-77
estimated_step_error = 3.9853913168419842636520277294002e-77
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7497413242850662766782068721399e-66
estimated_step_error = 2.7497413242850662766782068721399e-66
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9049066404130780601063301975142e-55
estimated_step_error = 1.9049066404130780601063301975142e-55
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0.0625
y[1] (numeric) = 0.0625
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.125
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.997
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 0.062813675793493759461309916394998
y[1] (numeric) = 0.062813675793493728801540762559105
absolute error = 3.0659769153835892681676214849607e-17
relative error = 4.8810659090598279508155350802723e-14 %
Correct digits = 16
h = 0.01
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.115
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.987
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 8.258
Order of pole (six term test) = -1.732e-58
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 0.063129718946491250220954016312719
y[1] (numeric) = 0.063129718946491188280899124490258
absolute error = 6.1940054891822460929858583540040e-17
relative error = 9.8115524550842451011333190670765e-14 %
Correct digits = 16
h = 0.01
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.104
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.977
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0.063448153341496995729939280117252
y[1] (numeric) = 0.063448153341496901874917967496079
absolute error = 9.3855021312621172804694524023586e-17
relative error = 1.4792396054060910424575099236833e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.97
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.094
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.967
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0.063769003162942556881950821344761
y[1] (numeric) = 0.063769003162942430462758156566007
absolute error = 1.2641919266477875394416215931622e-16
relative error = 1.9824552116919945078507733175333e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.084
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.957
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0.064092292901778561128024355071303
y[1] (numeric) = 0.064092292901778401480560909436575
absolute error = 1.5964746344563472803670666029300e-16
relative error = 2.4908995484105158441927156672216e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.073
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.947
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 24.96
Order of pole (six term test) = -6.018e-57
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 0.064418047360148419181117781957793
y[1] (numeric) = 0.064418047360148225626008972014738
absolute error = 1.9355510880994305552697438378228e-16
relative error = 3.0046720871220320167785395440826e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.063
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.937
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 5.61
Order of pole (six term test) = 1.243e-58
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 0.064746291656145394272543040097378
y[1] (numeric) = 0.064746291656145166114747741573317
absolute error = 2.2815779529852406185815691459532e-16
relative error = 3.5238743326061742829930477302332e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.053
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 7.453
Order of pole (six term test) = -4.263e-58
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0.065077051228654727197001249479384
y[1] (numeric) = 0.065077051228654463725409351845536
absolute error = 2.6347159189763384752727890188415e-16
relative error = 4.0486098697358007546431785179126e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.92
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.042
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.917
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0.065410351842282559637888292201124
y[1] (numeric) = 0.065410351842282260124906852077418
absolute error = 2.9951298144012370528682698793435e-16
relative error = 4.5789844115547552187955396742391e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.91
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.032
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.907
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 10.48
Order of pole (six term test) = 7.767e-58
bytes used=8001456, alloc=4324584, time=0.42
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 0.065746219592373438527284681130835
y[1] (numeric) = 0.065746219592373102228412321268508
absolute error = 3.3629887235986232706143113500268e-16
relative error = 5.1151058485935059946043675633908e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.022
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.897
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 0.066084680910118225494148201505409
y[1] (numeric) = 0.066084680910117851647537390196026
absolute error = 3.7384661081130938271274385793158e-16
relative error = 5.6570842994578147101475113326064e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.012
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.887
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 0.066425762567754277819109363375492
y[1] (numeric) = 0.066425762567753865645116196814451
absolute error = 4.1217399316656104010425741194765e-16
relative error = 6.2050321627266765221455327824247e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 4.001
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.877
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0.066769491683859810775260567941296
y[1] (numeric) = 0.066769491683859359475981665304451
absolute error = 4.5129927890263684496725949736531e-16
relative error = 6.7590641701969017633901487660905e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.991
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.867
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0.067115895728744395822706649842949
y[1] (numeric) = 0.067115895728743904581502757599155
absolute error = 4.9124120389224379371864596295744e-16
relative error = 7.3192974415128756288903373896807e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.981
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.857
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 3.301
Order of pole (six term test) = 2.256e-58
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 0.067465002529937594872659807724743
y[1] (numeric) = 0.067465002529937062853665695986595
absolute error = 5.3201899411173814780002014441243e-16
relative error = 7.8858515402212386957657985905533e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.97
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.847
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 1.008
Order of pole (six term test) = 1.840e-58
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0.067816840277777777777777777777778
y[1] (numeric) = 0.067816840277777204125397997268456
absolute error = 5.7365237978050932224208526439183e-16
relative error = 8.4588485312914782620528924746162e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.837
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 2.761
Order of pole (six term test) = 3.771e-59
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 0.068171437531103218373565843382939
y[1] (numeric) = 0.068171437531102602211955896849103
absolute error = 6.1616160994653383628440185298270e-16
relative error = 9.0384130401447101910722623412179e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.827
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0.068528823223047613826375373482087
y[1] (numeric) = 0.068528823223046954258907840090408
absolute error = 6.5956746753339167823183886791092e-16
relative error = 9.6246723132342647254302854961033e-13 %
Correct digits = 15
h = 0.01
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.939
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.817
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0.06888902666694222277333443555776
y[1] (numeric) = 0.068889026666941518882049570954374
absolute error = 7.0389128486460338620822865828328e-16
relative error = 1.0217756280223069214537268026506e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.929
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.807
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 0.069252077562326869806094182825485
y[1] (numeric) = 0.069252077562326120651134501090888
absolute error = 7.4915495968173459644371901177637e-16
relative error = 1.0817797617804247572647302530051e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.919
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.797
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0.069618006001072117292416510606303
y[1] (numeric) = 0.069618006001071321911444837279585
absolute error = 7.9538097167332671792797251611668e-16
relative error = 1.1424931815212832308989190018752e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.908
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.787
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0.069986842473614960387447159933932
y[1] (numeric) = 0.069986842473614117795047627585176
absolute error = 8.4259239953234875673698945845348e-16
relative error = 1.2039297241478011975760800178167e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.78
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.898
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.777
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 0.070358617875310457401374807393284
y[1] (numeric) = 0.070358617875309566588436246866103
absolute error = 8.9081293856052718057875323370040e-16
relative error = 1.2661035214466916764847761835260e-12 %
Correct digits = 14
h = 0.01
bytes used=12004540, alloc=4455632, time=0.64
Radius of convergence (given) for eq 1 = 3.77
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.888
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.767
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 0.070733363512901765504753282028067
y[1] (numeric) = 0.07073336351290082543783444342889
absolute error = 9.4006691883859917719566346425467e-16
relative error = 1.3290290071772579727521411792247e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.878
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.757
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0.071111111111111111111111111111111
y[1] (numeric) = 0.071111111111110120731787128860249
absolute error = 9.9037932398225086221705877423791e-16
relative error = 1.3927209243500402749927389012721e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.867
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.747
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0.071491892819354285224055592095856
y[1] (numeric) = 0.071491892819353243448245087848728
absolute error = 1.0417758105042471282137027979881e-15
relative error = 1.4571943327009207130601989257138e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.74
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.857
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.737
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0.071875741218581316619827641972558
y[1] (numeric) = 0.071875741218580222337099837937411
absolute error = 1.0942827278040351472859302869886e-15
relative error = 1.5224646163664760600674419489844e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.73
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.847
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.727
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 0.072262689328246040004624812117008
y[1] (numeric) = 0.072262689328244892077486005206655
absolute error = 1.1479271388069103522883911515481e-15
relative error = 1.5885474917665548219107672111583e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.836
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0.072652770613407342288998190946012
y[1] (numeric) = 0.072652770613406139552156915272617
absolute error = 1.2027368412756733948920904700055e-15
relative error = 1.6554590157002496174634222438202e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.71
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.826
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.707
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0.073046018991964937910883856829803
y[1] (numeric) = 0.073046018991963679170494038249259
absolute error = 1.2587403898185805435670281736925e-15
relative error = 1.7232155936616367641432615697851e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.7
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.816
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 3.67
Order of pole (six term test) = -1.069e-58
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0.073442468842032593767672094065114
y[1] (numeric) = 0.073442468842031277800553475765375
absolute error = 1.3159671186182997391294809625422e-15
relative error = 1.7918339883818631077960925734071e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.805
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.687
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 7.5
Order of pole (six term test) = -3.904e-58
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0.073842155009451795841209829867675
y[1] (numeric) = 0.073842155009450421394044922336038
absolute error = 1.3744471649075316373386755619192e-15
relative error = 1.8613313286043756445495279929735e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.795
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 0.074245112815448923074638611913371
y[1] (numeric) = 0.074245112815447488863145393972293
absolute error = 1.4342114932179410779029776495048e-15
relative error = 1.9317251181003126584167415663415e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.67
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.785
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.667
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 0.074651378064439069545223804831437
y[1] (numeric) = 0.074651378064437574253303374760192
absolute error = 1.4952919204300712446977848466113e-15
relative error = 2.0030332449313062365473646691267e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.66
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.774
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.657
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0.075060987051979733533495965471946
y[1] (numeric) = 0.075060987051978175812354312489825
absolute error = 1.5577211416529821211299344385274e-15
relative error = 2.0752739909671854308753551557282e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.65
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.764
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.647
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0.075473976572877671778770679869581
y[1] (numeric) = 0.075473976572876050246013716401001
absolute error = 1.6215327569634685801374644123509e-15
relative error = 2.1484660416663173299389348477885e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.754
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.637
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 0.075890383929452299099181142757401
y[1] (numeric) = 0.075890383929450612337882106883849
absolute error = 1.6867612990358735518536885276025e-15
relative error = 2.2226284961265802205420868359365e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.743
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.627
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16005396, alloc=4521156, time=0.86
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 0.076310246939959097707640181923629
y[1] (numeric) = 0.07631024693995734426537848720338
absolute error = 1.7534422616947202483396751370660e-15
relative error = 2.2977808774152292022342438866167e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.733
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.617
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 8.26
Order of pole (six term test) = -1.959e-58
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 0.076733603947176587042763637479762
y[1] (numeric) = 0.076733603947174765430634213833205
absolute error = 1.8216121294236465568188718794040e-15
relative error = 2.3739431431861904293119220219581e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.723
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.607
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0.07716049382716049382716049382716
y[1] (numeric) = 0.077160493827158602518752628390454
absolute error = 1.8913084078654367062575009908457e-15
relative error = 2.4511356965936059713097212841360e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.6
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.713
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.597
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 9.969
Order of pole (six term test) = 9.818e-59
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0.077590955998168853438443215058853
y[1] (numeric) = 0.077590955998166890868787865746312
absolute error = 1.9625696553493125407551416699447e-15
relative error = 2.5293793975107474956506341356414e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.59
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.702
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.587
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 0.078025030429761867607128366780063
y[1] (numeric) = 0.078025030429759832171612883708379
absolute error = 2.0354355154830716844540599213212e-15
relative error = 2.6086955740637239936637013575621e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.58
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.692
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.577
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 0.078462757652080440019144912867108
y[1] (numeric) = 0.078462757652078330072394063721944
absolute error = 2.1099467508491451633080467947616e-15
relative error = 2.6891060344897270191844725594557e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.57
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.682
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.567
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 0.078904178765307410680469637672011
y[1] (numeric) = 0.07890417876530522453519179247662
absolute error = 2.1861452778451953912695750800454e-15
relative error = 2.7706330793298868310794086734463e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.56
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.671
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.557
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 0.079349335449315611981749652846657
y[1] (numeric) = 0.079349335449313347907546941356961
absolute error = 2.2640742027114896962976372828110e-15
relative error = 2.8532995139671548897590973856625e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.55
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.661
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.547
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 0.07979826997350697436879568450956
y[1] (numeric) = 0.079798269973504630590936895541802
absolute error = 2.3437778587889677576945950550926e-15
relative error = 2.9371286615199828352325587392398e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.54
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.651
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.537
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 0.080251025206847017470648187530596
y[1] (numeric) = 0.080251025206844592168803133853997
absolute error = 2.4253018450536765990047204145397e-15
relative error = 3.0221443761029358732537920613537e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.53
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.527
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 6.301
Order of pole (six term test) = 7.506e-58
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 0.080707644628099173553719008264463
y[1] (numeric) = 0.080707644628096664860653033187031
absolute error = 2.5086930659750774316340564270564e-15
relative error = 3.1083710564657599408918612753800e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.517
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 2.72
Order of pole (six term test) = 1.729e-58
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 0.081168172336263504354672445840537
y[1] (numeric) = 0.081168172336260910354899698202401
absolute error = 2.5939997727476381362120509514873e-15
relative error = 3.1958336600228176601946088927419e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 0.081632653061224489795918367346939
y[1] (numeric) = 0.081632653061221808524312420229805
absolute error = 2.6812716059471171337405123563648e-15
relative error = 3.2845577172852184888321276365468e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.609
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.497
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 0.082101132174612687908966264644789
y[1] (numeric) = 0.082101132174609917349326599622142
absolute error = 2.7705596396650226473045847916716e-15
relative error = 3.3745693467083942346434573221040e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.49
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.599
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.487
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 1.028
Order of pole (six term test) = -6.315e-59
bytes used=20006072, alloc=4521156, time=1.07
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 0.082573655700885189589113489232395
y[1] (numeric) = 0.08257365570088232767268631233251
absolute error = 2.8619164271768998856978864919839e-15
relative error = 3.4658952699683128375755684572522e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.589
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.477
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 3.251
Order of pole (six term test) = 2.756e-58
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 0.083050270328629919690388592214868
y[1] (numeric) = 0.083050270328626964294340389853179
absolute error = 2.9553960482023616882964114968185e-15
relative error = 3.5585628276799816852608261192042e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.578
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 0.083531023422098967556550502856761
y[1] (numeric) = 0.083531023422095916502392685716702
absolute error = 3.0510541578171400592232831935252e-15
relative error = 3.6525999955723673932997457079606e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.46
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.568
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.457
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 0.084015963032976265490443184204999
y[1] (numeric) = 0.084015963032973116542406104303589
absolute error = 3.1489480370799014102876725504144e-15
relative error = 3.7480354011343526535949022531308e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.45
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.558
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.447
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 0.084505137912385073012439156300703
y[1] (numeric) = 0.084505137912381823875793717158624
absolute error = 3.2491366454391420785871346382429e-15
relative error = 3.8448983407468631701168716455112e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.44
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.548
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.437
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 0.084998597523140868175675101360828
y[1] (numeric) = 0.084998597523137516495000113192947
absolute error = 3.3516806749881678806640732810372e-15
relative error = 3.9432187973168296299224755744075e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.43
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.537
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.427
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 0.085496392052255394822338497315413
y[1] (numeric) = 0.085496392052251938179731858347953
absolute error = 3.4566426066389674605940923896570e-15
relative error = 4.0430274584292019006092742226384e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.42
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.527
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.417
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 4.921
Order of pole (six term test) = 6.092e-58
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 0.085998572423697766617074156569001
y[1] (numeric) = 0.085998572423694202530305867849398
absolute error = 3.5640867682887196030876739412620e-15
relative error = 4.1443557350338060416663781356389e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.41
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.517
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.407
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 0.086505190311418685121107266435986
y[1] (numeric) = 0.08650519031141501104171221070057
absolute error = 3.6740793950557354165256767735023e-15
relative error = 4.2472357806844301415036823501687e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.4
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.506
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.397
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 0.087016298152643990219368087642815
y[1] (numeric) = 0.08701629815264020353067642280927
absolute error = 3.7866886916648335450873028232665e-15
relative error = 4.3517005113481433583497792775261e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.39
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.496
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.387
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 0.087531949161443927033367179020342
y[1] (numeric) = 0.087531949161440025048470113533484
absolute error = 3.9019848970654868583913207243686e-15
relative error = 4.4577836258034948065005804483477e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.38
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.486
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.377
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 0.08805219734258468420079423082003
y[1] (numeric) = 0.088052197342580664160442861250793
absolute error = 4.0200403513695692372699928782255e-15
relative error = 4.5655196266469060870751582118720e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.37
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.475
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.367
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 0.088577097505668934240362811791383
y[1] (numeric) = 0.088577097505664793310797612613063
absolute error = 4.1409295651991783205218378351614e-15
relative error = 4.6749438419272643567363340423838e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.36
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.465
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.357
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 0.08910670527957228781465805301849
y[1] (numeric) = 0.089106705279568023085366514196527
absolute error = 4.2647292915388219629289275214635e-15
relative error = 4.7860924474294429478969889109624e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.35
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.455
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.347
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
bytes used=24007044, alloc=4586680, time=1.29
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 0.089641077127182760228046900211553
y[1] (numeric) = 0.089641077127178368709446709970922
absolute error = 4.3915186001902406307541292697193e-15
relative error = 4.8990024896282248380440764481280e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.34
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.444
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.337
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 0.090180270360450540630720810900991
y[1] (numeric) = 0.090180270360446019251765878597603
absolute error = 4.5213789549323033878727094416859e-15
relative error = 5.0137119093348819037781687727910e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.434
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.328
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 0.090724343155755552329801132239803
y[1] (numeric) = 0.090724343155750897935507639469507
absolute error = 4.6543942934927702957718316644334e-15
relative error = 5.1302595660594711308115437338051e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.424
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.318
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 3.493
Order of pole (six term test) = -1.952e-58
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 0.091273354569600496527048858626701
y[1] (numeric) = 0.09127335456959570587593841535849
absolute error = 4.7906511104432682112775675166169e-15
relative error = 5.2486852631127490849578157468807e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.413
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.308
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 5.147
Order of pole (six term test) = -6.018e-58
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 0.091827364554637281910009182736455
y[1] (numeric) = 0.091827364554632351671466049146611
absolute error = 4.9302385431335898447631120676800e-15
relative error = 5.3690297734724793409470290417035e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.403
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.298
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 0.092386433976034959026616531628496
y[1] (numeric) = 0.092386433976029885778155745220722
absolute error = 5.0732484607864077732851883796270e-15
relative error = 5.4913348664398156378816207539921e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.29
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.393
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.288
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 0.09295062462819750148720999405116
y[1] (numeric) = 0.092950624628192281711653115344503
absolute error = 5.2197755568787066569731753011580e-15
relative error = 5.6156433351123877698380209159978e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.28
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.382
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 0.09351999925184000598527995211776
y[1] (numeric) = 0.093519999251834636067835010428243
absolute error = 5.3699174449416895169827675041640e-15
relative error = 5.7419990247016991836145034645275e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.372
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.268
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 1.6
Order of pole (six term test) = 7.686e-59
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 0.094094621551432120140012796868531
y[1] (numeric) = 0.094094621551426596365254880249002
absolute error = 5.5237747579166195293201178859543e-15
relative error = 5.8704468617234665709802484844768e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.362
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.258
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 0.094674556213017751479289940828402
y[1] (numeric) = 0.094674556213012070028038730798472
absolute error = 5.6814512512100299299963923381797e-15
relative error = 6.0010328840905941135586894072023e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.25
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.352
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.248
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 0.095259868922420362749580856576741
y[1] (numeric) = 0.095259868922414519695671258592204
absolute error = 5.8430539095979845369476798354561e-15
relative error = 6.1338042721395802475061963840684e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.341
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.238
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 0.095850626383843418416739353391674
y[1] (numeric) = 0.095850626383837409723681217777676
absolute error = 6.0086930581356139984641923760400e-15
relative error = 6.2688093806223047284577072639987e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.23
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.331
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.228
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 0.096446896338875814976274063500637
y[1] (numeric) = 0.096446896338869636493796828497793
absolute error = 6.1784824772350028434460029468084e-15
relative error = 6.4060977716963403481985536953688e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.321
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.218
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 0.09704874758591240380042895546433
y[1] (numeric) = 0.097048747585906051260906873789144
absolute error = 6.3525395220816751859153335062783e-15
relative error = 6.5457202489481789283190187982043e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28008404, alloc=4586680, time=1.50
x[1] = 2.8
y[1] (analytic) = 0.09765625
y[1] (numeric) = 0.097656249999993469014753432561197
absolute error = 6.5309852465674388029255216033205e-15
relative error = 6.6877288924850573341957341218002e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.198
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 0.09826947455311956446968878057409
y[1] (numeric) = 0.098269474553112850525156855358676
absolute error = 6.7139445319252154142622797294004e-15
relative error = 6.8321770951324184577074384754352e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.19
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.188
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 0.09888849333491554922669198212096
y[1] (numeric) = 0.098888493334908647680471722393538
absolute error = 6.9015462202597274219178523009799e-15
relative error = 6.9791195997754467581402089608429e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.279
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.178
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 2.594
Order of pole (six term test) = -1.645e-58
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 0.099513379573883708664629959498055
y[1] (numeric) = 0.099513379573876614741376782950882
absolute error = 7.0939232531765471728187349454858e-15
relative error = 7.1286125378845804884938185593692e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.269
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.168
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 0.10014420765902900176253805479891
y[1] (numeric) = 0.10014420765902171054972233373483
absolute error = 7.2912128157210640792670859673483e-15
relative error = 7.2807134692664257469929413635553e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.259
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.158
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 0.10078105316200554295792391030486
y[1] (numeric) = 0.10078105316199804940143806189601
absolute error = 7.4935564858484088511530232159714e-15
relative error = 7.4354814230830836825565872860476e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.248
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.148
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 0.10142399285975090267353645178303
y[1] (numeric) = 0.10142399285974320157314679646803
absolute error = 7.7011003896553150021541064730662e-15
relative error = 7.5929769401845543795238628181844e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.238
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.138
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 0.10207310475762741275301370841797
y[1] (numeric) = 0.10207310475761949875765109309872
absolute error = 7.9139953626153192527142981963864e-15
relative error = 7.7532621168006021186916708000178e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.13
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.228
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.128
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 0.10272846811308349769888231426693
y[1] (numeric) = 0.10272846811307536530176524463761
absolute error = 8.1323971170696293245790565324676e-15
relative error = 7.9164006496402599697182367909653e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.217
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.118
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 0.10339016345984843002036786220159
y[1] (numeric) = 0.10339016345984007355395162475546
absolute error = 8.3564664162374461347998132437640e-15
relative error = 8.0824578824490202760397273675010e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.207
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.108
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 0.10405827263267429760665972944849
y[1] (numeric) = 0.10405827263266571123740470790326
absolute error = 8.5863692550215452321971083906434e-15
relative error = 8.2515008540757049681414211634083e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.197
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.098
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 0.10473287879263937327845330484599
y[1] (numeric) = 0.1047328787926305510014054073173
absolute error = 8.8222770478975286933889592748978e-15
relative error = 8.4235983481030393717347122052652e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.09
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.187
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.088
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 0.10541406645302749198853094956991
y[1] (numeric) = 0.10541406645301842762170676118546
absolute error = 9.0643668241883844526442548533857e-15
relative error = 8.5988209440980690271564459241158e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.176
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.078
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 0.10610192150579847001029188638606
y[1] (numeric) = 0.10610192150578915718886084651832
absolute error = 9.3128214310398677471310152952148e-15
relative error = 8.7772410705407649529935106055870e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.07
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.166
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.068
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 10.93
Order of pole (six term test) = 3.650e-57
TOP MAIN SOLVE Loop
bytes used=32009128, alloc=4586680, time=1.72
x[1] = 2.94
y[1] (analytic) = 0.10679653124866504335939168695801
y[1] (numeric) = 0.1067965312486554755296472601746
absolute error = 9.5678297444267834091054209334674e-15
relative error = 8.9589330594914629129499519452616e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.06
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.156
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.058
Order of pole (three term test) = 1225
Radius of convergence (six term test) for eq 1 = 1.075
Order of pole (six term test) = 3.065e-59
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 0.10749798441279226014512227895727
y[1] (numeric) = 0.10749798441278243055823374342281
absolute error = 9.8295868885355344558162087615867e-15
relative error = 9.1439732030601809275230282004660e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.145
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.048
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 0.10820637119113573407202216066482
y[1] (numeric) = 0.10820637119112563577755827631463
absolute error = 1.0098294463884350192587432635538e-14
relative error = 9.3324398117433610739816017444591e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.135
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.038
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 0.10892178326743565445653476238713
y[1] (numeric) = 0.10892178326742528029575020293073
absolute error = 1.0374160784559456403371561879671e-14
relative error = 9.5244132746961913293713972461069e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.125
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.028
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 0.10964431384588395245822551642472
y[1] (numeric) = 0.10964431384587329505710055328071
absolute error = 1.0657401124963144007841264215317e-14
relative error = 9.7199761220113858609115466149375e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.114
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.018
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 0.11037405768148254434277767353561
y[1] (numeric) = 0.1103740576814715961048011852595
absolute error = 1.0948237976488276108718530502662e-14
relative error = 9.9192130890781430372600758207166e-12 %
Correct digits = 14
h = 0.01
Radius of convergence (given) for eq 1 = 3.01
Order of pole (given) = 3
Radius of convergence (ratio test) for eq 1 = 3.104
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.008
Order of pole (three term test) = 1225
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ;
Iterations = 100
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Time to Timeout = 2 Minutes 58 Seconds
Percent Done = 101 %
> quit
bytes used=33655896, alloc=4586680, time=1.81