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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> 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 := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
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 := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
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_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(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 < abs(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");
newline();
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
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> 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));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> 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_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, 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));
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))
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
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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 ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> 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;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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 abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_x[1] * (array_x[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre div $eq_no = 1 i = 1
> array_tmp3[1] := (array_const_1D0[1] / (array_tmp2[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2] + array_const_1D0[2];
> #emit pre div $eq_no = 1 i = 2
> array_tmp3[2] := ((array_const_1D0[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 2
> array_tmp4[2] := array_const_0D0[2] + array_tmp3[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_tmp4[2] * (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 $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3] + array_const_1D0[3];
> #emit pre div $eq_no = 1 i = 3
> array_tmp3[3] := ((array_const_1D0[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 3
> array_tmp4[3] := array_const_0D0[3] + array_tmp3[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_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4] + array_const_1D0[4];
> #emit pre div $eq_no = 1 i = 4
> array_tmp3[4] := ((array_const_1D0[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 4
> array_tmp4[4] := array_const_0D0[4] + array_tmp3[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_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5] + array_const_1D0[5];
> #emit pre div $eq_no = 1 i = 5
> array_tmp3[5] := ((array_const_1D0[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 5
> array_tmp4[5] := array_const_0D0[5] + array_tmp3[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_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> 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 $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_x,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk] + array_const_1D0[kkk];
> #emit div $eq_no = 1
> array_tmp3[kkk] := ((array_const_1D0[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit add $eq_no = 1
> array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp4[kkk] * (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 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
array_tmp1[1] := array_x[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := array_const_1D0[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_x, array_x, 1);
array_tmp2[2] := array_tmp1[2] + array_const_1D0[2];
array_tmp3[2] := (
array_const_1D0[2] - ats(2, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[2] := array_const_0D0[2] + array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*glob_h*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] := ats(3, array_x, array_x, 1);
array_tmp2[3] := array_tmp1[3] + array_const_1D0[3];
array_tmp3[3] := (
array_const_1D0[3] - ats(3, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[3] := array_const_0D0[3] + array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_x, array_x, 1);
array_tmp2[4] := array_tmp1[4] + array_const_1D0[4];
array_tmp3[4] := (
array_const_1D0[4] - ats(4, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[4] := array_const_0D0[4] + array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_x, array_x, 1);
array_tmp2[5] := array_tmp1[5] + array_const_1D0[5];
array_tmp3[5] := (
array_const_1D0[5] - ats(5, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[5] := array_const_0D0[5] + array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_x, array_x, 1);
array_tmp2[kkk] := array_tmp1[kkk] + array_const_1D0[kkk];
array_tmp3[kkk] := (
array_const_1D0[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*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 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> 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
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_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,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= 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)
> fi;
> # End Function number 1
> 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
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> 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 5
> 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 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 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
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> 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 10
> 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 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> 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 + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_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 + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_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 11
> 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 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_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
+ array_aa[iii_att]*array_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
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> 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 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> 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
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> 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 (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> 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 < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> arctan(x);
> end;
exact_soln_y := proc(x) arctan(x) end proc
>
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_smallish_float,
> years_in_century,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> days_in_year,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_not_yet_finished,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_dump,
> glob_html_log,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_relerr,
> glob_dump_analytic,
> glob_max_hours,
> glob_log10_relerr,
> djd_debug2,
> glob_log10abserr,
> glob_warned2,
> glob_clock_sec,
> glob_max_opt_iter,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_max_minutes,
> glob_max_sec,
> glob_warned,
> glob_almost_1,
> glob_current_iter,
> glob_start,
> glob_max_iter,
> glob_look_poles,
> glob_large_float,
> min_in_hour,
> sec_in_min,
> glob_display_flag,
> djd_debug,
> glob_log10normmin,
> glob_percent_done,
> glob_normmax,
> glob_max_trunc_err,
> glob_disp_incr,
> glob_initial_pass,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_1D0,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_type_pole,
> array_last_rel_error,
> array_y,
> array_x,
> array_y_higher_work,
> array_complex_pole,
> array_poles,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_iolevel := 5;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> glob_curr_iter_when_opt := 0;
> glob_orig_start_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> years_in_century := 100.0;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_iter := 0;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> days_in_year := 365.0;
> glob_no_eqs := 0;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_not_yet_finished := true;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> hours_in_day := 24.0;
> glob_dump := false;
> glob_html_log := true;
> glob_subiter_method := 3;
> MAX_UNCHANGED := 10;
> glob_unchanged_h_cnt := 0;
> glob_optimal_start := 0.0;
> glob_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_max_hours := 0.0;
> glob_log10_relerr := 0.1e-10;
> djd_debug2 := true;
> glob_log10abserr := 0.0;
> glob_warned2 := false;
> glob_clock_sec := 0.0;
> glob_max_opt_iter := 10;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> glob_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_max_minutes := 0.0;
> glob_max_sec := 10000.0;
> glob_warned := false;
> glob_almost_1 := 0.9990;
> glob_current_iter := 0;
> glob_start := 0;
> glob_max_iter := 1000;
> glob_look_poles := false;
> glob_large_float := 9.0e100;
> min_in_hour := 60.0;
> sec_in_min := 60.0;
> glob_display_flag := true;
> djd_debug := true;
> glob_log10normmin := 0.1;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> #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/sing2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.0;");
> omniout_str(ALWAYS,"x_end := 1.0;");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_adjust_h := false;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> 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,"arctan(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -2.0;
> x_end := 1.0;
> glob_h := 0.00001;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_adjust_h := false;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> 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;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> 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] * 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]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T04:03:44-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;")
> ;
> 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_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"sing2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing2 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `glob_adjust_h` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp,
glob_adjust_h;
global glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_smallish_float,
years_in_century, glob_optimal_expect_sec, glob_log10relerr, glob_iter,
glob_small_float, glob_max_rel_trunc_err, glob_last_good_h, days_in_year,
glob_no_eqs, glob_hmax, glob_h, glob_not_yet_finished,
glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_optimal_start, glob_relerr, glob_dump_analytic, glob_max_hours,
glob_log10_relerr, djd_debug2, glob_log10abserr, glob_warned2,
glob_clock_sec, glob_max_opt_iter, glob_hmin_init, glob_optimal_done,
glob_clock_start_sec, centuries_in_millinium, glob_max_minutes,
glob_max_sec, glob_warned, glob_almost_1, glob_current_iter, glob_start,
glob_max_iter, glob_look_poles, glob_large_float, min_in_hour, sec_in_min,
glob_display_flag, djd_debug, glob_log10normmin, glob_percent_done,
glob_normmax, glob_max_trunc_err, glob_disp_incr, glob_initial_pass,
array_const_1, array_const_1D0, array_const_0D0, array_pole,
array_1st_rel_error, array_y_init, array_m1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_norms, array_type_pole,
array_last_rel_error, array_y, array_x, array_y_higher_work,
array_complex_pole, array_poles, array_real_pole, array_y_set_initial,
array_y_higher_work2, array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_iolevel := 5;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
glob_curr_iter_when_opt := 0;
glob_orig_start_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
years_in_century := 100.0;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_iter := 0;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
days_in_year := 365.0;
glob_no_eqs := 0;
glob_hmax := 1.0;
glob_h := 0.1;
glob_not_yet_finished := true;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
hours_in_day := 24.0;
glob_dump := false;
glob_html_log := true;
glob_subiter_method := 3;
MAX_UNCHANGED := 10;
glob_unchanged_h_cnt := 0;
glob_optimal_start := 0.;
glob_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_max_hours := 0.;
glob_log10_relerr := 0.1*10^(-10);
djd_debug2 := true;
glob_log10abserr := 0.;
glob_warned2 := false;
glob_clock_sec := 0.;
glob_max_opt_iter := 10;
glob_hmin_init := 0.001;
glob_optimal_done := false;
glob_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_max_minutes := 0.;
glob_max_sec := 10000.0;
glob_warned := false;
glob_almost_1 := 0.9990;
glob_current_iter := 0;
glob_start := 0;
glob_max_iter := 1000;
glob_look_poles := false;
glob_large_float := 0.90*10^101;
min_in_hour := 60.0;
sec_in_min := 60.0;
glob_display_flag := true;
djd_debug := true;
glob_log10normmin := 0.1;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_initial_pass := true;
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/sing2postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.0;");
omniout_str(ALWAYS, "x_end := 1.0;");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_adjust_h := false;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
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, "arctan(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[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
;
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 <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[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_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[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_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 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_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_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := -2.0;
x_end := 1.0;
glob_h := 0.00001;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_adjust_h := false;
glob_max_iter := 100;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
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;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*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]*
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();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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;
display_alot(current_iter)
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 ) = 1.0/ (x * x + 1.0) ;");
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, "2012-06-13T04:03:44-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sing2");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
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_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"sing2 diffeq.mxt");
logitem_str(html_log_file,
"sing2 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/sing2postode.ode#################
diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.0;
x_end := 1.0;
glob_h := 0.00001;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_adjust_h := false;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
arctan(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -2
y[1] (analytic) = -1.1071487177940905030170654601785
y[1] (numeric) = -1.1071487177940905030170654601785
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.244
Order of pole = 2.182
x[1] = -1.9999
y[1] (analytic) = -1.1071287169940611687237058863759
y[1] (numeric) = -1.1071287169940611687237058699494
absolute error = 1.64265e-26
relative error = 1.4837028204452323502640984565306e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.244
Order of pole = 2.182
x[1] = -1.9998
y[1] (analytic) = -1.1071087145938558209895590834752
y[1] (numeric) = -1.1071087145938558209895590506236
absolute error = 3.28516e-26
relative error = 2.9673327982113887913711516968491e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.244
Order of pole = 2.182
x[1] = -1.9997
y[1] (analytic) = -1.1070887105932984252506887980461
y[1] (numeric) = -1.1070887105932984252506887487707
absolute error = 4.92754e-26
relative error = 4.4508989684840058129113467346939e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.244
Order of pole = 2.182
x[1] = -1.9996
y[1] (analytic) = -1.1070687049922129238968604445428
y[1] (numeric) = -1.1070687049922129238968603788449
absolute error = 6.56979e-26
relative error = 5.9344013342389726704597722305454e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9995
y[1] (analytic) = -1.1070486977904232362683914605932
y[1] (numeric) = -1.1070486977904232362683913784741
absolute error = 8.21191e-26
relative error = 7.4178398984527841247657004325086e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9994
y[1] (analytic) = -1.1070286889877532586530013244488
y[1] (numeric) = -1.1070286889877532586530012259098
absolute error = 9.85390e-26
relative error = 8.9012146641025405924826718843224e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9993
y[1] (analytic) = -1.1070086785840268642826612346212
y[1] (numeric) = -1.1070086785840268642826611196636
absolute error = 1.149576e-25
relative error = 1.0384525634165948296942932477934e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9992
y[1] (analytic) = -1.1069886665790679033304434517335
y[1] (numeric) = -1.1069886665790679033304433203586
absolute error = 1.313749e-25
relative error = 1.1867772811621319418976237938916e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9991
y[1] (analytic) = -1.1069686529727002029073703026122
y[1] (numeric) = -1.1069686529727002029073701548214
absolute error = 1.477908e-25
relative error = 1.3350947165768097092284950724347e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.999
y[1] (analytic) = -1.106948637764747567059262846648
y[1] (numeric) = -1.1069486377647475670592626824426
absolute error = 1.642054e-25
relative error = 1.4834057732938597438390958839044e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9989
y[1] (analytic) = -1.1069286209550337767635892044509
y[1] (numeric) = -1.1069286209550337767635890238321
absolute error = 1.806188e-25
relative error = 1.6317113550119072194871468295259e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9988
y[1] (analytic) = -1.1069086025433825899263125488282
y[1] (numeric) = -1.1069086025433825899263123517974
absolute error = 1.970308e-25
relative error = 1.7800096552441226248954617305999e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9987
y[1] (analytic) = -1.1068885825296177413787387581121
y[1] (numeric) = -1.1068885825296177413787385446707
absolute error = 2.134414e-25
relative error = 1.9283006742396207608636376351260e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9986
y[1] (analytic) = -1.1068685609135629428743637318635
y[1] (numeric) = -1.1068685609135629428743635020127
absolute error = 2.298508e-25
relative error = 2.0765862191468405087807932485533e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.243
Order of pole = 2.182
x[1] = -1.9985
y[1] (analytic) = -1.1068485376950418830857203689796
y[1] (numeric) = -1.1068485376950418830857201227209
absolute error = 2.462587e-25
relative error = 2.2248635799151141018375506851299e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
memory used=3.8MB, alloc=2.9MB, time=0.46
x[1] = -1.9984
y[1] (analytic) = -1.1068285128738782276012252082334
y[1] (numeric) = -1.106828512873878227601224945568
absolute error = 2.626654e-25
relative error = 2.3731354671916588502853345625555e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9983
y[1] (analytic) = -1.1068084864498956189220247312703
y[1] (numeric) = -1.1068084864498956189220244521996
absolute error = 2.790707e-25
relative error = 2.5214000743265291092200995526670e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9982
y[1] (analytic) = -1.1067884584229176764588413280921
y[1] (numeric) = -1.1067884584229176764588410326174
absolute error = 2.954747e-25
relative error = 2.6696583050841268464644329778032e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9981
y[1] (analytic) = -1.1067684287927679965288189250528
y[1] (numeric) = -1.1067684287927679965288186131754
absolute error = 3.118774e-25
relative error = 2.8179101597629337220726493080723e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.998
y[1] (analytic) = -1.1067483975592701523523682753958
y[1] (numeric) = -1.1067483975592701523523679471171
absolute error = 3.282787e-25
relative error = 2.9661547351137642437373473833400e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9979
y[1] (analytic) = -1.1067283647222476940500119123591
y[1] (numeric) = -1.1067283647222476940500115676805
absolute error = 3.446786e-25
relative error = 3.1143920313861564109724183479283e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9978
y[1] (analytic) = -1.1067083302815241486392287648764
y[1] (numeric) = -1.1067083302815241486392284037991
absolute error = 3.610773e-25
relative error = 3.2626238559905775685380582038885e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9977
y[1] (analytic) = -1.1066882942369230200312984359004
y[1] (numeric) = -1.1066882942369230200312980584258
absolute error = 3.774746e-25
relative error = 3.4108484020812200763280042737610e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9976
y[1] (analytic) = -1.1066682565882677890281451433787
y[1] (numeric) = -1.1066682565882677890281447495081
absolute error = 3.938706e-25
relative error = 3.5590665735209411986520913968132e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9975
y[1] (analytic) = -1.1066482173353819133191813239063
y[1] (numeric) = -1.1066482173353819133191809136411
absolute error = 4.102652e-25
relative error = 3.7072774669790537329528602115067e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.242
Order of pole = 2.182
x[1] = -1.9974
y[1] (analytic) = -1.1066281764780888274781508990862
y[1] (numeric) = -1.1066281764780888274781504724277
absolute error = 4.266585e-25
relative error = 3.8554819863512467965411719562702e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9973
y[1] (analytic) = -1.1066081340162119429599722046223
y[1] (numeric) = -1.1066081340162119429599717615719
absolute error = 4.430504e-25
relative error = 4.0036792282742181440726630697132e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9972
y[1] (analytic) = -1.1065880899495746480975805821754
y[1] (numeric) = -1.1065880899495746480975801227345
absolute error = 4.594409e-25
relative error = 4.1518691929978746338303098406688e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9971
y[1] (analytic) = -1.1065680442780003080987706340082
y[1] (numeric) = -1.106568044278000308098770158178
absolute error = 4.758302e-25
relative error = 4.3000536881621567501633595344104e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.997
y[1] (analytic) = -1.1065479970013122650430381404474
y[1] (numeric) = -1.1065479970013122650430376482294
absolute error = 4.922180e-25
relative error = 4.4482300029812107131433308390986e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9969
y[1] (analytic) = -1.1065279481193338378784216401926
y[1] (numeric) = -1.1065279481193338378784211315881
absolute error = 5.086045e-25
relative error = 4.5963999451114577307772466471466e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9968
y[1] (analytic) = -1.106507897631888322418343673497
y[1] (numeric) = -1.1065078976318883224183431485074
absolute error = 5.249896e-25
relative error = 4.7445626111080220253124462335571e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9967
y[1] (analytic) = -1.1064878455387989913384516882505
y[1] (numeric) = -1.1064878455387989913384511468771
absolute error = 5.413734e-25
relative error = 4.8927189049815617171044122040887e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9966
y[1] (analytic) = -1.106467791839889094173458608992
y[1] (numeric) = -1.1064677918398890941734580512363
absolute error = 5.577557e-25
relative error = 5.0408670194776874125584221226905e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9965
y[1] (analytic) = -1.1064477365349818573139830688798
y[1] (numeric) = -1.106447736534981857313982494743
absolute error = 5.741368e-25
relative error = 5.1890096661772860920457107029806e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9964
y[1] (analytic) = -1.1064276796239004840033893046463
y[1] (numeric) = -1.1064276796239004840033887141299
absolute error = 5.905164e-25
relative error = 5.3371441340000616448800097998255e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.241
Order of pole = 2.182
x[1] = -1.9963
y[1] (analytic) = -1.1064076211064681543346267145685
y[1] (numeric) = -1.1064076211064681543346261076739
absolute error = 6.068946e-25
relative error = 5.4852713269732559857272609162264e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9962
y[1] (analytic) = -1.1063875609825080252470690794795
y[1] (numeric) = -1.1063875609825080252470684562079
absolute error = 6.232716e-25
relative error = 5.6333930530321093957571835858601e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9961
y[1] (analytic) = -1.1063674992518432305233534468502
y[1] (numeric) = -1.1063674992518432305233528072032
absolute error = 6.396470e-25
relative error = 5.7815056970902278176517769258969e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.996
y[1] (analytic) = -1.1063474359142968807862186779712
y[1] (numeric) = -1.10634743591429688078621802195
absolute error = 6.560212e-25
relative error = 5.9296128748005579678503496800972e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=1.02
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9959
y[1] (analytic) = -1.10632737096969206349534365826
y[1] (numeric) = -1.1063273709696920634953429858661
absolute error = 6.723939e-25
relative error = 6.0777118748372744595109217140018e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9958
y[1] (analytic) = -1.1063073044178518429441851707255
y[1] (numeric) = -1.1063073044178518429441844819603
absolute error = 6.887652e-25
relative error = 6.2258036013098007092106794269138e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9957
y[1] (analytic) = -1.1062872362585992602568154326151
y[1] (numeric) = -1.1062872362585992602568147274799
absolute error = 7.051352e-25
relative error = 6.3738889583931862614389218113146e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9956
y[1] (analytic) = -1.106267166491757333384759295275
y[1] (numeric) = -1.1062671664917573333847585737712
absolute error = 7.215038e-25
relative error = 6.5219670424465755849642442992804e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9955
y[1] (analytic) = -1.1062470951171490571038311072518
y[1] (numeric) = -1.1062470951171490571038303693808
absolute error = 7.378710e-25
relative error = 6.6700378537207470403253380991948e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9954
y[1] (analytic) = -1.1062270221345974030109712406631
y[1] (numeric) = -1.1062270221345974030109704864263
absolute error = 7.542368e-25
relative error = 6.8181013924665286824900200672097e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9953
y[1] (analytic) = -1.1062069475439253195210822808668
y[1] (numeric) = -1.1062069475439253195210815102657
absolute error = 7.706011e-25
relative error = 6.9661567549448150059689471645851e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.24
Order of pole = 2.182
x[1] = -1.9952
y[1] (analytic) = -1.1061868713449557318638648794575
y[1] (numeric) = -1.1061868713449557318638640924934
absolute error = 7.869641e-25
relative error = 7.1142057493700934994155468649160e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9951
y[1] (analytic) = -1.1061667935375115420806532706179
y[1] (numeric) = -1.1061667935375115420806524672923
absolute error = 8.033256e-25
relative error = 7.2622465679969644941836721956898e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.995
y[1] (analytic) = -1.1061467141214156290212504508558
y[1] (numeric) = -1.10614671412141562902124963117
absolute error = 8.196858e-25
relative error = 7.4102810191056410522782204473151e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9949
y[1] (analytic) = -1.1061266330964908483407630221531
y[1] (numeric) = -1.1061266330964908483407621861085
absolute error = 8.360446e-25
relative error = 7.5583081989408100888420219319365e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9948
y[1] (analytic) = -1.106106550462560032496435698558
y[1] (numeric) = -1.106106550462560032496434846156
absolute error = 8.524020e-25
relative error = 7.7063281077535980779150976435992e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9947
y[1] (analytic) = -1.1060864662194459907444854762476
y[1] (numeric) = -1.1060864662194459907444846074897
absolute error = 8.687579e-25
relative error = 7.8543398417067301967989014021957e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9946
y[1] (analytic) = -1.1060663803669715091369354670908
y[1] (numeric) = -1.1060663803669715091369345819783
absolute error = 8.851125e-25
relative error = 8.0023452092119166500122509528926e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9945
y[1] (analytic) = -1.10604629290495935051844839574
y[1] (numeric) = -1.1060462929049593505184474942743
absolute error = 9.014657e-25
relative error = 8.1503433064483982871976160158024e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9944
y[1] (analytic) = -1.1060262038332322545231597602807
y[1] (numeric) = -1.1060262038332322545231588424634
absolute error = 9.178173e-25
relative error = 8.2983323253920792035079324982618e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9943
y[1] (analytic) = -1.1060061131516129375715106564691
y[1] (numeric) = -1.1060061131516129375715097223014
absolute error = 9.341677e-25
relative error = 8.4463158828123305656176922127015e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9942
y[1] (analytic) = -1.1059860208599240928670802655841
y[1] (numeric) = -1.1059860208599240928670793150676
absolute error = 9.505165e-25
relative error = 8.5942903623768794620901007382102e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.9941
y[1] (analytic) = -1.1059659269579883903934180059269
y[1] (numeric) = -1.105965926957988390393417039063
absolute error = 9.668639e-25
relative error = 8.7422575726126111588795684114886e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.239
Order of pole = 2.182
x[1] = -1.994
y[1] (analytic) = -1.1059458314456284769108753479934
y[1] (numeric) = -1.1059458314456284769108743647835
absolute error = 9.832099e-25
relative error = 8.8902175137710392164151327312698e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9939
y[1] (analytic) = -1.1059257343226669759534372933514
y[1] (numeric) = -1.1059257343226669759534362937969
absolute error = 9.995545e-25
relative error = 9.0381701861037270680757979645949e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9938
y[1] (analytic) = -1.1059056355889264878255535172509
y[1] (numeric) = -1.1059056355889264878255525013532
absolute error = 1.0158977e-24
relative error = 9.1861155898622880322902413462040e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9937
y[1] (analytic) = -1.1058855352442295895989691749966
y[1] (numeric) = -1.1058855352442295895989681427572
absolute error = 1.0322394e-24
relative error = 9.3340528210456682664005691795853e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9936
y[1] (analytic) = -1.1058654332883988351095553721126
y[1] (numeric) = -1.1058654332883988351095543235329
absolute error = 1.0485797e-24
relative error = 9.4819827841254237038163839213318e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9935
y[1] (analytic) = -1.1058453297212567549541392983283
y[1] (numeric) = -1.1058453297212567549541382334097
absolute error = 1.0649186e-24
relative error = 9.6299054793533116451283985724972e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
memory used=11.4MB, alloc=4.1MB, time=1.60
x[1] = -1.9934
y[1] (analytic) = -1.1058252245426258564873340254153
y[1] (numeric) = -1.1058252245426258564873329441593
absolute error = 1.0812560e-24
relative error = 9.7778200026791051444376022806238e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9933
y[1] (analytic) = -1.1058051177523286238183679689045
y[1] (numeric) = -1.1058051177523286238183668713126
absolute error = 1.0975919e-24
relative error = 9.9257263543053327645867299447367e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9932
y[1] (analytic) = -1.1057850093501875178079140137136
y[1] (numeric) = -1.1057850093501875178079128997871
absolute error = 1.1139265e-24
relative error = 1.0073626343104405203221428713195e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9931
y[1] (analytic) = -1.1057648993360249760649183037131
y[1] (numeric) = -1.1057648993360249760649171734535
absolute error = 1.1302596e-24
relative error = 1.0221518160674871091845083678313e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.993
y[1] (analytic) = -1.105744787709663412943428695263
y[1] (numeric) = -1.1057447877096634129434275486717
absolute error = 1.1465913e-24
relative error = 1.0369402711587203061813016233345e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.238
Order of pole = 2.182
x[1] = -1.9929
y[1] (analytic) = -1.1057246744709252195394228747471
y[1] (numeric) = -1.1057246744709252195394217118256
absolute error = 1.1629215e-24
relative error = 1.0517279091709178983899090308742e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9928
y[1] (analytic) = -1.1057045596196327636876361401371
y[1] (numeric) = -1.1057045596196327636876349608868
absolute error = 1.1792503e-24
relative error = 1.0665148205644257221696429087906e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9927
y[1] (analytic) = -1.1056844431556083899583888466142
y[1] (numeric) = -1.1056844431556083899583876510366
absolute error = 1.1955776e-24
relative error = 1.0813009149227403080757097931777e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9926
y[1] (analytic) = -1.1056643250786744196544135162799
y[1] (numeric) = -1.1056643250786744196544123043765
absolute error = 1.2119034e-24
relative error = 1.0960861922661437547351862216401e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9925
y[1] (analytic) = -1.1056442053886531508076816119845
y[1] (numeric) = -1.1056442053886531508076803837567
absolute error = 1.2282278e-24
relative error = 1.1108707430599309165371941130414e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9924
y[1] (analytic) = -1.105624084085366858176229975304
y[1] (numeric) = -1.1056240840853668581762287307533
absolute error = 1.2445507e-24
relative error = 1.1256544768826747210370268704884e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9923
y[1] (analytic) = -1.105603961168637793240986928695
y[1] (numeric) = -1.1056039611686377932409856678229
absolute error = 1.2608721e-24
relative error = 1.1404373937546694033485920764396e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9922
y[1] (analytic) = -1.105583836638288184202598041858
y[1] (numeric) = -1.1055838366382881842025967646659
absolute error = 1.2771921e-24
relative error = 1.1552195841461605714720911970702e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9921
y[1] (analytic) = -1.1055637104941402359782515623386
y[1] (numeric) = -1.1055637104941402359782502688279
absolute error = 1.2935107e-24
relative error = 1.1700010480823899384376194685645e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.992
y[1] (analytic) = -1.1055435827360161301985035103973
y[1] (numeric) = -1.1055435827360161301985022005696
absolute error = 1.3098277e-24
relative error = 1.1847816046821224531259510710819e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9919
y[1] (analytic) = -1.1055234533637380252041024381781
y[1] (numeric) = -1.1055234533637380252041011120348
absolute error = 1.3261433e-24
relative error = 1.1995614348705037310223426155766e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.237
Order of pole = 2.182
x[1] = -1.9918
y[1] (analytic) = -1.1055033223771280560428138532052
y[1] (numeric) = -1.1055033223771280560428125107477
absolute error = 1.3424575e-24
relative error = 1.2143405386727893643329527049289e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9917
y[1] (analytic) = -1.1054831897760083344662443062389
y[1] (numeric) = -1.1054831897760083344662429474688
absolute error = 1.3587701e-24
relative error = 1.2291187351978751957645916739646e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9916
y[1] (analytic) = -1.1054630555602009489266651435213
y[1] (numeric) = -1.10546305556020094892666376844
absolute error = 1.3750813e-24
relative error = 1.2438962053808014103007694755253e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9915
y[1] (analytic) = -1.1054429197295279645738359234408
y[1] (numeric) = -1.1054429197295279645738345320498
absolute error = 1.3913910e-24
relative error = 1.2586728587853598176297922778645e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9914
y[1] (analytic) = -1.1054227822838114232518274976473
y[1] (numeric) = -1.1054227822838114232518260899481
absolute error = 1.4076992e-24
relative error = 1.2734486954318811147057532082921e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9913
y[1] (analytic) = -1.1054026432228733434958447566473
y[1] (numeric) = -1.1054026432228733434958433326414
absolute error = 1.4240059e-24
relative error = 1.2882237153406998624223290038415e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9912
y[1] (analytic) = -1.1053825025465357205290490399104
y[1] (numeric) = -1.1053825025465357205290475995993
absolute error = 1.4403111e-24
relative error = 1.3029979185321544865083976214056e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9911
y[1] (analytic) = -1.105362360254620526259380210517
y[1] (numeric) = -1.1053623602546205262593787539021
absolute error = 1.4566149e-24
relative error = 1.3177713954946578367202519628474e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.991
y[1] (analytic) = -1.1053422163469497092763783943778
y[1] (numeric) = -1.1053422163469497092763769214606
absolute error = 1.4729172e-24
relative error = 1.3325440557837829178215793064104e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9909
y[1] (analytic) = -1.1053220708233451948480053840565
y[1] (numeric) = -1.1053220708233451948480038948385
absolute error = 1.4892180e-24
relative error = 1.3473158994198803324992171769887e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=2.16
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9908
y[1] (analytic) = -1.1053019236836288849174657072253
y[1] (numeric) = -1.1053019236836288849174642017081
absolute error = 1.5055172e-24
relative error = 1.3620868359502873091251701777198e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.236
Order of pole = 2.182
x[1] = -1.9907
y[1] (analytic) = -1.1052817749276226581000273597847
y[1] (numeric) = -1.1052817749276226581000258379697
absolute error = 1.5218150e-24
relative error = 1.3768570463397473944509022327953e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9906
y[1] (analytic) = -1.1052616245551483696798422036778
y[1] (numeric) = -1.1052616245551483696798406655665
absolute error = 1.5381113e-24
relative error = 1.3916264401372546438420814677396e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9905
y[1] (analytic) = -1.1052414725660278516067660294304
y[1] (numeric) = -1.1052414725660278516067644750243
absolute error = 1.5544061e-24
relative error = 1.4063950173631751395331839020399e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9904
y[1] (analytic) = -1.1052213189600829124931782834471
y[1] (numeric) = -1.1052213189600829124931767127478
absolute error = 1.5706993e-24
relative error = 1.4211626875582633195303873135873e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9903
y[1] (analytic) = -1.1052011637371353376108014600956
y[1] (numeric) = -1.1052011637371353376107998731045
absolute error = 1.5869911e-24
relative error = 1.4359296317004739942995493423265e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9902
y[1] (analytic) = -1.1051810068970068888875201586078
y[1] (numeric) = -1.1051810068970068888875185553265
absolute error = 1.6032813e-24
relative error = 1.4506956688493033976037099648081e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.9901
y[1] (analytic) = -1.1051608484395193049041998048316
y[1] (numeric) = -1.1051608484395193049041981852615
absolute error = 1.6195701e-24
relative error = 1.4654609799893142873179933034563e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.235
Order of pole = 2.182
x[1] = -1.99
y[1] (analytic) = -1.1051406883644943008915050378617
y[1] (numeric) = -1.1051406883644943008915034020044
absolute error = 1.6358573e-24
relative error = 1.4802253841734096785276026082305e-22 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;
Iterations = 100
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 11 Minutes 9 Seconds
Optimized Time Remaining = 11 Minutes 3 Seconds
Time to Timeout = 14 Minutes 57 Seconds
Percent Done = 0.3367 %
> quit
memory used=16.6MB, alloc=4.1MB, time=2.36