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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> reached_interval := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
>
>
> local ret;
>
> if ((((array_x[1] >= glob_next_display) and not glob_neg_h) or ((array_x[1] <= glob_next_display) and glob_neg_h)) or (glob_next_display = 0.0)) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1
> ;
> return(ret);
>
> # End Function number 3
> end;
reached_interval := proc()
local ret;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
if glob_next_display <= array_x[1] and not glob_neg_h or
array_x[1] <= glob_next_display and glob_neg_h or
glob_next_display = 0. then ret := true
else ret := false
end if;
return ret
end proc
> # Begin Function number 4
> display_alot := proc(iter)
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>
>
>
>
>
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 4
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3
> ;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2
> ;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
>
> # End Function number 4
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # Begin Function number 5
> adjust_for_pole := proc(h_param)
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 5
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # Begin Function number 6
> prog_report := proc(x_start,x_end)
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> 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 6
> 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 INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
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 7
> check_for_pole := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> 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 ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) 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 (omniabs(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 (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif ((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) 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 ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := 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 (reached_interval()) 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 (reached_interval()) 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
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
>
> # End Function number 7
> 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 INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float or
omniabs(array_y_higher[1, m - 2]) < glob_small_float) 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 < omniabs(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 < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) 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 omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(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 < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := 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 reached_interval() 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 reached_interval() 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;
if reached_interval() then display_pole() end if
end proc
> # Begin Function number 8
> get_norms := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2
> ;
>
> # End Function number 8
> end;
get_norms := proc()
local iii;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 9
> atomall := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre sin 1 $eq_no = 1
> array_tmp2[1] := sin(array_x[1]);
> array_tmp2_g[1] := cos(array_x[1]);
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp3[1] := (array_tmp1[1] * (array_tmp2[1]));
> #emit pre add CONST FULL $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] * expt(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 sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp2[2] := array_tmp2_g[1] * array_x[2] / 1;
> array_tmp2_g[2] := -array_tmp2[1] * array_x[2] / 1;
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp3[2] := ats(2,array_tmp1,array_tmp2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[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] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp2[3] := array_tmp2_g[2] * array_x[2] / 2;
> array_tmp2_g[3] := -array_tmp2[2] * array_x[2] / 2;
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp3[3] := ats(3,array_tmp1,array_tmp2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[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] * expt(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 sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp2[4] := array_tmp2_g[3] * array_x[2] / 3;
> array_tmp2_g[4] := -array_tmp2[3] * array_x[2] / 3;
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp3[4] := ats(4,array_tmp1,array_tmp2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[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] * expt(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 sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp2[5] := array_tmp2_g[4] * array_x[2] / 4;
> array_tmp2_g[5] := -array_tmp2[4] * array_x[2] / 4;
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp3[5] := ats(5,array_tmp1,array_tmp2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[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] * expt(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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit sin LINEAR $eq_no = 1
> array_tmp2[kkk] := array_tmp2_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp2_g[kkk] := -array_tmp2[kkk - 1] * array_x[2] / (kkk - 1);
> #emit mult FULL FULL $eq_no = 1
> array_tmp3[kkk] := ats(kkk,array_tmp1,array_tmp2,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[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] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 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
>
> #BOTTOM ATOMALL ???
> # End Function number 9
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := sin(array_x[1]);
array_tmp2_g[1] := cos(array_x[1]);
array_tmp3[1] := array_tmp1[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]*expt(glob_h, 1)*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] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := array_tmp2_g[1]*array_x[2];
array_tmp2_g[2] := -array_tmp2[1]*array_x[2];
array_tmp3[2] := ats(2, array_tmp1, array_tmp2, 1);
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := 1/2*array_tmp2_g[2]*array_x[2];
array_tmp2_g[3] := -1/2*array_tmp2[2]*array_x[2];
array_tmp3[3] := ats(3, array_tmp1, array_tmp2, 1);
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*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] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := 1/3*array_tmp2_g[3]*array_x[2];
array_tmp2_g[4] := -1/3*array_tmp2[3]*array_x[2];
array_tmp3[4] := ats(4, array_tmp1, array_tmp2, 1);
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*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] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := 1/4*array_tmp2_g[4]*array_x[2];
array_tmp2_g[5] := -1/4*array_tmp2[4]*array_x[2];
array_tmp3[5] := ats(5, array_tmp1, array_tmp2, 1);
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*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] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := array_tmp2_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2_g[kkk] := -array_tmp2[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3[kkk] := ats(kkk, array_tmp1, array_tmp2, 1);
array_tmp4[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]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 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_minute, 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);
> fprintf(fd,"
");
> if (secs >= 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_minute * 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_minute;
> sec_int := floor(seconds);
> 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_minute, years_in_century;
secs := secs_in;
fprintf(fd, "");
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
sec_int := floor(seconds);
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_minute, 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_minute * 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_minute;
> 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_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
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
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
>
> local good_digits;
>
>
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 11
> if (rel_error <> 0.0) then # if number 12
> good_digits := -trunc(log10(rel_error/100.0));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 12
> ;
> else
> fprintf(file,"Unknown");
> fi;# end if 11
> ;
> fprintf(file," | ");
>
> # End Function number 9
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if rel_error <> 0. then
good_digits := -trunc(log10(rel_error/100.0));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 10
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 10
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 11
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 12
> 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 12
> 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 13
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 13
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 14
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 14
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 15
> not_reached_end := proc(x,x_end)
> global neg_h;
> local ret;
>
>
>
> if ((glob_neg_h and (x > x_end)) or (( not glob_neg_h) and (x < x_end))) then # if number 13
> ret := true;
> else
> ret := false;
> fi;# end if 13
> ;
>
>
> ret;
>
> # End Function number 15
> end;
not_reached_end := proc(x, x_end)
local ret;
global neg_h;
if glob_neg_h and x_end < x or not glob_neg_h and x < x_end then
ret := true
else ret := false
end if;
ret
end proc
> # Begin Function number 16
> 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 16
> 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 17
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (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 17
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # Begin Function number 18
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
>
>
>
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr;
>
> # End Function number 18
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 19
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 19
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 20
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 20
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 21
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 21
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 22
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 22
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 23
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 23
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(-(sin(x) * cos(x))/2.0 + x/2.0);
> end;
exact_soln_y := proc(x) return -sin(x)*cos(x)/2.0 + x/2.0 end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_next_display,
> glob_last_good_h,
> sec_in_minute,
> glob_log10relerr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10normmin,
> glob_max_minutes,
> glob_iter,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_hmin,
> glob_clock_sec,
> glob_dump,
> glob_subiter_method,
> glob_log10abserr,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_disp_incr,
> glob_no_eqs,
> glob_hmax,
> glob_clock_start_sec,
> glob_orig_start_sec,
> glob_log10_relerr,
> glob_neg_h,
> glob_look_poles,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_html_log,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_not_yet_finished,
> hours_in_day,
> glob_display_flag,
> glob_good_digits,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_large_float,
> djd_debug2,
> djd_debug,
> glob_optimal_expect_sec,
> glob_start,
> glob_max_sec,
> glob_warned,
> glob_display_interval,
> glob_initial_pass,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_m1,
> array_fact_1,
> array_pole,
> array_tmp2_g,
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_real_pole,
> array_poles,
> array_y_higher_work2,
> array_fact_2,
> array_complex_pole,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> DEBUGL := 3;
> ALWAYS := 1;
> glob_optimal_start := 0.0;
> glob_next_display := 0.0;
> glob_last_good_h := 0.1;
> sec_in_minute := 60;
> glob_log10relerr := 0.0;
> glob_current_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_max_hours := 0.0;
> glob_not_yet_start_msg := true;
> glob_max_opt_iter := 10;
> glob_warned2 := false;
> glob_dump_analytic := false;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10;
> glob_log10normmin := 0.1;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> MAX_UNCHANGED := 10;
> glob_smallish_float := 0.1e-100;
> glob_hmin := 0.00000000001;
> glob_clock_sec := 0.0;
> glob_dump := false;
> glob_subiter_method := 3;
> glob_log10abserr := 0.0;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_no_eqs := 0;
> glob_hmax := 1.0;
> glob_clock_start_sec := 0.0;
> glob_orig_start_sec := 0.0;
> glob_log10_relerr := 0.1e-10;
> glob_neg_h := false;
> glob_look_poles := false;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> days_in_year := 365;
> min_in_hour := 60;
> glob_html_log := true;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_not_yet_finished := true;
> hours_in_day := 24;
> glob_display_flag := true;
> glob_good_digits := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> djd_debug2 := true;
> djd_debug := true;
> glob_optimal_expect_sec := 0.1;
> glob_start := 0;
> glob_max_sec := 10000.0;
> glob_warned := false;
> glob_display_interval := 0.0;
> glob_initial_pass := true;
> years_in_century := 100;
> #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/mult_sin_sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x) * sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.005 ;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(-(sin(x) * cos(x))/2.0 + x/2.0);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> 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_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_tmp2_g:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> 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_g[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_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_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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2_g[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_norms[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 <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_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 <=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 <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> 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 <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_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[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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1_g[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_tmp2_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2_g[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_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.005 ;
> glob_display_interval := 0.1;
> glob_look_poles := true;
> glob_max_iter := 10000;
> glob_max_minutes := 10;
> #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 := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1
> ;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> 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;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(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 not_reached_end(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
> if (reached_interval()) then # if number 2
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 2
> ;
> 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
> if (reached_interval()) then # if number 2
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 2
> ;
> 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] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> 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 ) = sin(x) * sin(x);");
> 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,"2012-09-21T03:26:32-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mult_sin_sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x) * sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_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," 130 | ")
> ;
> logitem_str(html_log_file,"mult_sin_sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"mult_sin_sin maple results")
> ;
> logitem_str(html_log_file,"c c++ Maple and Maxima")
> ;
> 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 9
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global INFO, glob_max_terms, DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS,
glob_optimal_start, glob_next_display, glob_last_good_h, sec_in_minute,
glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_max_hours,
glob_not_yet_start_msg, glob_max_opt_iter, glob_warned2, glob_dump_analytic,
glob_h, glob_almost_1, centuries_in_millinium, glob_log10normmin,
glob_max_minutes, glob_iter, MAX_UNCHANGED, glob_smallish_float, glob_hmin,
glob_clock_sec, glob_dump, glob_subiter_method, glob_log10abserr,
glob_small_float, glob_max_rel_trunc_err, glob_max_iter, glob_relerr,
glob_log10_abserr, glob_disp_incr, glob_no_eqs, glob_hmax,
glob_clock_start_sec, glob_orig_start_sec, glob_log10_relerr, glob_neg_h,
glob_look_poles, glob_optimal_done, glob_reached_optimal_h, days_in_year,
min_in_hour, glob_html_log, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmin_init,
glob_not_yet_finished, hours_in_day, glob_display_flag, glob_good_digits,
glob_optimal_clock_start_sec, glob_abserr, glob_large_float, djd_debug2,
djd_debug, glob_optimal_expect_sec, glob_start, glob_max_sec, glob_warned,
glob_display_interval, glob_initial_pass, years_in_century, array_const_0D0,
array_const_1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_last_rel_error, array_y_init, array_m1,
array_fact_1, array_pole, array_tmp2_g, array_1st_rel_error, array_norms,
array_y, array_x, array_real_pole, array_poles, array_y_higher_work2,
array_fact_2, array_complex_pole, array_y_higher_work, array_y_set_initial,
array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
DEBUGL := 3;
ALWAYS := 1;
glob_optimal_start := 0.;
glob_next_display := 0.;
glob_last_good_h := 0.1;
sec_in_minute := 60;
glob_log10relerr := 0.;
glob_current_iter := 0;
glob_unchanged_h_cnt := 0;
glob_max_hours := 0.;
glob_not_yet_start_msg := true;
glob_max_opt_iter := 10;
glob_warned2 := false;
glob_dump_analytic := false;
glob_h := 0.1;
glob_almost_1 := 0.9990;
centuries_in_millinium := 10;
glob_log10normmin := 0.1;
glob_max_minutes := 0.;
glob_iter := 0;
MAX_UNCHANGED := 10;
glob_smallish_float := 0.1*10^(-100);
glob_hmin := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_dump := false;
glob_subiter_method := 3;
glob_log10abserr := 0.;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_no_eqs := 0;
glob_hmax := 1.0;
glob_clock_start_sec := 0.;
glob_orig_start_sec := 0.;
glob_log10_relerr := 0.1*10^(-10);
glob_neg_h := false;
glob_look_poles := false;
glob_optimal_done := false;
glob_reached_optimal_h := false;
days_in_year := 365;
min_in_hour := 60;
glob_html_log := true;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_curr_iter_when_opt := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_not_yet_finished := true;
hours_in_day := 24;
glob_display_flag := true;
glob_good_digits := 0;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
djd_debug2 := true;
djd_debug := true;
glob_optimal_expect_sec := 0.1;
glob_start := 0;
glob_max_sec := 10000.0;
glob_warned := false;
glob_display_interval := 0.;
glob_initial_pass := true;
years_in_century := 100;
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/mult_sin_sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) * sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.005 ;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(-(sin(x) * cos(x))/2.0 + x/2.0);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
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_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_tmp2_g := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[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_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_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_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_g[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_norms[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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[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 <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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 <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_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[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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp2_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_g[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_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_h := 0.005;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
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 := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
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;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*expt(glob_h, term_no - 1)
/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(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
not_reached_end(array_x[1], x_end) and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
if reached_interval() then
glob_next_display := glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
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 ) = sin(x) * sin(x);");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-09-21T03:26:32-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mult_sin_sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) * sin(x);")
;
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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, " 130 | ");
logitem_str(html_log_file, "mult_sin_sin diffeq.mxt");
logitem_str(html_log_file, "mult_sin_sin maple results");
logitem_str(html_log_file, "c c++ Maple and Maxima");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> main();
##############ECHO OF PROBLEM#################
##############temp/mult_sin_sinpostode.ode#################
diff ( y , x , 1 ) = sin(x) * sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.005 ;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(-(sin(x) * cos(x))/2.0 + x/2.0);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 0.000332667301234696135146843220402
y[1] (numeric) = 0.000332667301234696135146843220402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.35
x[1] = 0.2
y[1] (analytic) = 0.002645414422837377083422060801075
y[1] (numeric) = 0.0026454144229083802306426167409798
absolute error = 7.10031472205559399048e-14
relative error = 2.6840084717010236381658669327767e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=4.0MB, time=0.72
memory used=11.4MB, alloc=4.1MB, time=1.11
x[1] = 0.3
y[1] (analytic) = 0.00883938165124116069976363858534
y[1] (numeric) = 0.0088393816514278490385134170100191
absolute error = 1.866883387497784246791e-13
relative error = 2.1120067682965700060552864884176e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.2MB, time=1.48
x[1] = 0.4
y[1] (analytic) = 0.02066097727511930959320634735465
y[1] (numeric) = 0.020660977275461753164273477190123
absolute error = 3.42443571067129835473e-13
relative error = 1.6574413035123593832816188653905e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=19.0MB, alloc=4.3MB, time=1.88
memory used=22.8MB, alloc=4.3MB, time=2.28
x[1] = 0.5
y[1] (analytic) = 0.03963225379802587333687441959242
y[1] (numeric) = 0.03963225379855793271144859526425
absolute error = 5.32059374574175671830e-13
relative error = 1.3424908340708045761843822944488e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.3MB, time=2.68
x[1] = 0.6
y[1] (analytic) = 0.06699022850819341258246639112629
y[1] (numeric) = 0.066990228508941388948018750819428
absolute error = 7.47976365552359693138e-13
relative error = 1.1165454756746747260984667078494e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=3.08
x[1] = 0.7
y[1] (analytic) = 0.10363756750288495483513135529848
y[1] (numeric) = 0.10363756750386654145006820326949
absolute error = 9.8158661493684797101e-13
relative error = 9.4713397717437123709058114467226e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.3MB, time=3.48
memory used=38.1MB, alloc=4.3MB, time=3.89
x[1] = 0.8
y[1] (analytic) = 0.15010659923962370891447154361344
y[1] (numeric) = 0.15010659924084728573375599646443
absolute error = 1.22357681928445285099e-12
relative error = 8.1513859182912239884660994866493e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=41.9MB, alloc=4.3MB, time=4.29
x[1] = 0.9
y[1] (analytic) = 0.20653809228045120336690670528916
y[1] (numeric) = 0.20653809228191550295969878959642
absolute error = 1.46429959279208430726e-12
relative error = 7.0897313741223125651770056638738e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.3MB, time=4.70
x[1] = 1
memory used=49.5MB, alloc=4.3MB, time=5.10
y[1] (analytic) = 0.27267564329357957615099503352206
y[1] (numeric) = 0.2726756432952737342291196662761
absolute error = 1.69415807812463275404e-12
relative error = 6.2130891401275495578202553717166e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.3MB, time=5.51
x[1] = 1.1
y[1] (analytic) = 0.34787589904510245392399077239597
y[1] (numeric) = 0.34787589904700644246682305767381
absolute error = 1.90398854283228527784e-12
relative error = 5.4731832474126966829800723274914e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.3MB, time=5.91
x[1] = 1.2
y[1] (analytic) = 0.43113420486221226835855711866468
y[1] (numeric) = 0.43113420486429769406700258836994
absolute error = 2.08542570844546970526e-12
relative error = 4.8370685622402852732253623448187e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.3MB, time=6.31
memory used=64.8MB, alloc=4.4MB, time=6.72
x[1] = 1.3
y[1] (analytic) = 0.52112465704463394118556826619766
y[1] (numeric) = 0.52112465704686517743329753990913
absolute error = 2.23123624772927371147e-12
relative error = 4.2815787308604934773128432363318e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.4MB, time=7.13
x[1] = 1.4
y[1] (analytic) = 0.6162529624610237701140365618219
y[1] (numeric) = 0.61625296246335937726865077854558
absolute error = 2.33560715461421672368e-12
relative error = 3.7900136743958243737030256193583e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.4MB, time=7.55
memory used=76.2MB, alloc=4.4MB, time=7.96
x[1] = 1.5
y[1] (analytic) = 0.71471999798503319447481379929797
y[1] (numeric) = 0.71471999798742757196521803798092
absolute error = 2.39437749040423868295e-12
relative error = 3.3500916402990851433009832328639e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.4MB, time=8.37
x[1] = 1.6
y[1] (analytic) = 0.81459353585689497728430435365477
y[1] (numeric) = 0.81459353585930018155157626425659
absolute error = 2.40520426727191060182e-12
relative error = 2.9526434490322897795068137752678e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=83.9MB, alloc=4.4MB, time=8.77
x[1] = 1.7
y[1] (analytic) = 0.91388527550670782981247560734094
y[1] (numeric) = 0.91388527550907548566826499585328
absolute error = 2.36765585578938851234e-12
relative error = 2.5907582923651231829367129693534e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.4MB, time=9.18
memory used=91.5MB, alloc=4.4MB, time=9.59
x[1] = 1.8
y[1] (analytic) = 1.0106301108237130960666818368732
y[1] (numeric) = 1.0106301108259963252593134530537
absolute error = 2.2832291926316161805e-12
relative error = 2.2592135027232391003036588562459e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.4MB, time=9.99
x[1] = 1.9
y[1] (analytic) = 1.1029644727356797689333965215297
y[1] (numeric) = 1.1029644727378350590358314734716
absolute error = 2.1552901024349519419e-12
relative error = 1.9540884187223109626498867696774e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=99.1MB, alloc=4.4MB, time=10.39
memory used=103.0MB, alloc=4.4MB, time=10.79
x[1] = 2
y[1] (analytic) = 1.189200623826982062843159773628
y[1] (numeric) = 1.1892006238289710019561501645697
absolute error = 1.9889391129903909417e-12
relative error = 1.6725008994611523153873895082399e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.4MB, time=11.20
x[1] = 2.1
y[1] (analytic) = 1.2678939431033970150046442744772
y[1] (numeric) = 1.2678939431051878231179404588407
absolute error = 1.7908081132961843635e-12
relative error = 1.4124273745742971729443549176952e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.4MB, time=11.61
x[1] = 2.2
y[1] (analytic) = 1.3379005184723789885088480833451
y[1] (numeric) = 1.3379005184739477844699196984421
absolute error = 1.5687959610716150970e-12
relative error = 1.1725804268787290663159401378917e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=12.03
NO POLE
memory used=118.2MB, alloc=4.4MB, time=12.44
x[1] = 2.3
y[1] (analytic) = 1.3984227509083661140345261649772
y[1] (numeric) = 1.3984227509096978676147521818501
absolute error = 1.3317535802260168729e-12
relative error = 9.5232545334446017954822621239670e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=122.0MB, alloc=4.4MB, time=12.86
x[1] = 2.4
y[1] (analytic) = 1.4490411522089601679453991166259
y[1] (numeric) = 1.4490411522100492990478523312926
absolute error = 1.0891311024532146667e-12
relative error = 7.5162192653597985787197105911224e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.4MB, time=13.29
memory used=129.7MB, alloc=4.4MB, time=13.71
x[1] = 2.5
y[1] (analytic) = 1.489731068665784617223288601539
y[1] (numeric) = 1.4897310686666352183435911084883
absolute error = 8.506011203025069493e-13
relative error = 5.7097629108608998808614130728862e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.4MB, time=14.12
x[1] = 2.6
y[1] (analytic) = 1.5208636639300383161682711101054
y[1] (numeric) = 1.520863663930663989239708466137
absolute error = 6.256730714373560316e-13
relative error = 4.1139326704707030023412351295077e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=137.3MB, alloc=4.4MB, time=14.52
x[1] = 2.7
y[1] (analytic) = 1.5431911218889968405896174456836
y[1] (numeric) = 1.5431911218894201547169819573655
absolute error = 4.233141273645116819e-13
relative error = 2.7431088823679809710242289212378e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=14.93
NO POLE
memory used=144.9MB, alloc=4.4MB, time=15.34
x[1] = 2.8
y[1] (analytic) = 1.5578166594680803278659172884292
y[1] (numeric) = 1.5578166594683319195665208714925
absolute error = 2.515917006035830633e-13
relative error = 1.6150276675657683750917491416710e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.4MB, time=15.75
x[1] = 2.9
y[1] (analytic) = 1.5661505448534393028545566316756
y[1] (numeric) = 1.5661505448535566546769647059625
absolute error = 1.173518224080742869e-13
relative error = 7.4930103490821244840670780717863e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=152.5MB, alloc=4.4MB, time=16.15
memory used=156.4MB, alloc=4.4MB, time=16.56
x[1] = 3
y[1] (analytic) = 1.569853874549731468202888861653
y[1] (numeric) = 1.5698538745497574144159920697633
absolute error = 2.59462131032081103e-14
relative error = 1.6527788683930887162708993103251e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.4MB, time=16.96
x[1] = 3.1
y[1] (analytic) = 1.5707723507043741445001448222746
y[1] (numeric) = 1.5707723507043551634260297116674
absolute error = 1.89810741151106072e-14
relative error = 1.2083911527089850006521090282414e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=164.0MB, alloc=4.4MB, time=17.37
memory used=167.8MB, alloc=4.4MB, time=17.77
x[1] = 3.2
y[1] (analytic) = 1.5708626987873766776298948778003
y[1] (numeric) = 1.5708626987873610386998131370067
absolute error = 1.56389300817407936e-14
relative error = 9.9556314462194719376855473079476e-13 %
Correct digits = 14
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=171.6MB, alloc=4.4MB, time=18.18
x[1] = 3.3
y[1] (analytic) = 1.5721146591216554564112537236019
y[1] (numeric) = 1.5721146591216912958157211760814
absolute error = 3.58394044674524795e-14
relative error = 2.2796940579051688168932235704300e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=175.4MB, alloc=4.4MB, time=18.59
x[1] = 3.4
y[1] (analytic) = 1.5764716622153479194444801555949
y[1] (numeric) = 1.5764716622154813210952634270756
absolute error = 1.334016507832714807e-13
relative error = 8.4620392475566525748187794015689e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=179.2MB, alloc=4.4MB, time=18.98
memory used=183.1MB, alloc=4.4MB, time=19.39
x[1] = 3.5
y[1] (analytic) = 1.5857533503203027274007502271016
y[1] (numeric) = 1.585753350320575885710730803334
absolute error = 2.731583099805762324e-13
relative error = 1.7225775365721384355749136445983e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=186.9MB, alloc=4.4MB, time=19.79
x[1] = 3.6
y[1] (analytic) = 1.6015830340377117368838885630891
y[1] (numeric) = 1.6015830340381612746089733746321
absolute error = 4.495377250848115430e-13
relative error = 2.8068337109659122772745512210418e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=190.7MB, alloc=4.4MB, time=20.21
memory used=194.5MB, alloc=4.4MB, time=20.61
x[1] = 3.7
y[1] (analytic) = 1.6253229760470933101826252758664
y[1] (numeric) = 1.6253229760477488183880384780691
absolute error = 6.555082054132022027e-13
relative error = 4.0330950529441664834224855370932e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=198.3MB, alloc=4.4MB, time=21.00
x[1] = 3.8
y[1] (analytic) = 1.6580200819921283935241342454928
y[1] (numeric) = 1.6580200819930112518820267376104
absolute error = 8.828583578924921176e-13
relative error = 5.3247748171525679433436591165990e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=202.1MB, alloc=4.4MB, time=21.40
x[1] = 3.9
y[1] (analytic) = 1.700364163656348759140306669851
y[1] (numeric) = 1.7003641636574712835896948955957
absolute error = 1.1225244493882257447e-12
relative error = 6.6016708266447150425382016821431e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=206.0MB, alloc=4.4MB, time=21.81
memory used=209.8MB, alloc=4.4MB, time=22.21
x[1] = 4
y[1] (analytic) = 1.7526604383441545555479691004387
y[1] (numeric) = 1.7526604383455195072971116553878
absolute error = 1.3649517491425549491e-12
relative error = 7.7878847452739236633761709011308e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=213.6MB, alloc=4.4MB, time=22.62
x[1] = 4.1
y[1] (analytic) = 1.8148173608300567747115878125136
y[1] (numeric) = 1.8148173608316572501573256704383
absolute error = 1.6004754457378579247e-12
relative error = 8.8189339615190607205272724481927e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=217.4MB, alloc=4.4MB, time=23.04
memory used=221.2MB, alloc=4.4MB, time=23.47
x[1] = 4.2
y[1] (analytic) = 1.8863502729779298342916901796444
y[1] (numeric) = 1.8863502729797495402443190633253
absolute error = 1.8197059526288836809e-12
relative error = 9.6467023049550782594283818206971e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=225.0MB, alloc=4.4MB, time=23.88
x[1] = 4.3
y[1] (analytic) = 1.9664007255314717140707089531091
y[1] (numeric) = 1.9664007255334856173120367105229
absolute error = 2.0139032413277574138e-12
relative error = 1.0241570882168215690867076757807e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=228.8MB, alloc=4.4MB, time=24.30
x[1] = 4.4
y[1] (analytic) = 2.0537707017770594366172671720469
y[1] (numeric) = 2.053770701779234761896026209318
absolute error = 2.1753252787590372711e-12
relative error = 1.0591860507488984551602057403168e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=232.7MB, alloc=4.4MB, time=24.70
memory used=236.5MB, alloc=4.4MB, time=25.12
x[1] = 4.5
y[1] (analytic) = 2.1469703786895608575609318584119
y[1] (numeric) = 2.1469703786918583942386188924718
absolute error = 2.2975366776870340599e-12
relative error = 1.0701296582812539088670144612520e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=240.3MB, alloc=4.4MB, time=25.52
x[1] = 4.6
y[1] (analytic) = 2.2442775214749382606179827355604
y[1] (numeric) = 2.2442775214773139258732795949603
absolute error = 2.3756652552968593999e-12
relative error = 1.0585434432973214359222733228829e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=244.1MB, alloc=4.4MB, time=25.92
memory used=247.9MB, alloc=4.4MB, time=26.30
x[1] = 4.7
y[1] (analytic) = 2.3438061436366604697300567306581
y[1] (numeric) = 2.3438061436390670660018049240184
absolute error = 2.4065962717481933603e-12
relative error = 1.0267898129211776179270667539350e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=251.7MB, alloc=4.4MB, time=26.73
x[1] = 4.8
y[1] (analytic) = 2.4435816953057449962810254316301
y[1] (numeric) = 2.4435816953081340928860490196915
absolute error = 2.3890966050235880614e-12
relative error = 9.7770277523897572412475087057235e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=255.5MB, alloc=4.4MB, time=27.15
memory used=259.4MB, alloc=4.4MB, time=27.57
x[1] = 4.9
y[1] (analytic) = 2.5416197823129819370423132371822
y[1] (numeric) = 2.5416197823153058009539251989528
absolute error = 2.3238639116119617706e-12
relative error = 9.1432397866259402629796916053202e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
memory used=263.2MB, alloc=4.4MB, time=27.97
x[1] = 5
y[1] (analytic) = 2.6360052777223424533511869154628
y[1] (numeric) = 2.6360052777245559521643328835557
absolute error = 2.2134988131459680929e-12
relative error = 8.3971714011838253000046827318536e-11 %
Correct digits = 12
h = 0.005
Finished!
diff ( y , x , 1 ) = sin(x) * sin(x);
Iterations = 980
Total Elapsed Time = 28 Seconds
Elapsed Time(since restart) = 28 Seconds
Time to Timeout = 9 Minutes 31 Seconds
Percent Done = 100.1 %
> quit
memory used=264.9MB, alloc=4.4MB, time=28.14