|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > > > > > > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := 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 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 3 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 2 > ; > if (glob_iter = 1) then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := 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 proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > 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 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, 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 5 > prog_report := proc(x_start,x_end) > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > 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) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, 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)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > 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 7 > end; get_norms := proc() local iii; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, 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 8 > atomall := proc() > global > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_x[1] * array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp1[3] := array_x[2] * array_x[2]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 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 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, array_y_higher, glob_last; array_tmp1[1] := array_x[1]*array_x[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := 2*array_x[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_x[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp2[kkk] := array_tmp1[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_tmp2[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 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 > 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 15 > 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 16 > 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 16 > 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 17 > 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 17 > 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 18 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 18 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 19 > 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 19 > 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 20 > 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 20 > 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 21 > convfp := proc(mmm) > (mmm); > > # End Function number 21 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 22 > convfloat := proc(mmm) > (mmm); > > # End Function number 22 > 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(1.0 + x * x * x / 3.0); > end; exact_soln_y := proc(x) return 1.0 + x*x*x/3.0 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 > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > glob_clock_sec, > years_in_century, > glob_orig_start_sec, > glob_disp_incr, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_dump, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_h, > djd_debug, > glob_max_opt_iter, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned, > glob_small_float, > glob_max_hours, > djd_debug2, > glob_good_digits, > glob_optimal_expect_sec, > glob_normmax, > glob_smallish_float, > glob_hmin_init, > glob_display_flag, > glob_log10normmin, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_optimal_start, > glob_no_eqs, > days_in_year, > glob_max_minutes, > glob_start, > glob_max_iter, > sec_in_minute, > glob_subiter_method, > glob_percent_done, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmin, > glob_reached_optimal_h, > glob_initial_pass, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_optimal_done, > glob_not_yet_finished, > hours_in_day, > glob_log10abserr, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_fact_1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_m1, > array_type_pole, > array_y_init, > array_real_pole, > array_fact_2, > array_y_set_initial, > array_y_higher_work2, > array_poles, > array_complex_pole, > array_y_higher_work, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > INFO := 2; > glob_log10relerr := 0.0; > glob_max_sec := 10000.0; > glob_unchanged_h_cnt := 0; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > glob_clock_sec := 0.0; > years_in_century := 100; > glob_orig_start_sec := 0.0; > glob_disp_incr := 0.1; > glob_clock_start_sec := 0.0; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10; > glob_dump := false; > glob_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_h := 0.1; > djd_debug := true; > glob_max_opt_iter := 10; > glob_html_log := true; > glob_curr_iter_when_opt := 0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_max_hours := 0.0; > djd_debug2 := true; > glob_good_digits := 0; > glob_optimal_expect_sec := 0.1; > glob_normmax := 0.0; > glob_smallish_float := 0.1e-100; > glob_hmin_init := 0.001; > glob_display_flag := true; > glob_log10normmin := 0.1; > glob_iter := 0; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > days_in_year := 365; > glob_max_minutes := 0.0; > glob_start := 0; > glob_max_iter := 1000; > sec_in_minute := 60; > glob_subiter_method := 3; > glob_percent_done := 0.0; > glob_warned2 := false; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > glob_initial_pass := true; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_large_float := 9.0e100; > glob_optimal_done := false; > glob_not_yet_finished := true; > hours_in_day := 24; > glob_log10abserr := 0.0; > glob_relerr := 0.1e-10; > glob_look_poles := false; > glob_not_yet_start_msg := true; > min_in_hour := 60; > #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/multpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = x * 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 := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 1;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + x * x * x / 3.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_fact_1:= 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_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 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_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > 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_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 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_m1[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_y_init[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 <=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 <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_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_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_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #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 := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 1; > #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)); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * 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 (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / 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 ) = x * 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,"2012-09-02T22:15:24-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mult") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = x * 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," 126 ") > ; > logitem_str(html_log_file,"mult diffeq.mxt") > ; > logitem_str(html_log_file,"mult 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 8 > 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 ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, INFO, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_dump_analytic, glob_last_good_h, glob_hmax, glob_clock_sec, years_in_century, glob_orig_start_sec, glob_disp_incr, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_dump, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_h, djd_debug, glob_max_opt_iter, glob_html_log, glob_curr_iter_when_opt, glob_warned, glob_small_float, glob_max_hours, djd_debug2, glob_good_digits, glob_optimal_expect_sec, glob_normmax, glob_smallish_float, glob_hmin_init, glob_display_flag, glob_log10normmin, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_optimal_start, glob_no_eqs, days_in_year, glob_max_minutes, glob_start, glob_max_iter, sec_in_minute, glob_subiter_method, glob_percent_done, glob_warned2, glob_max_rel_trunc_err, glob_hmin, glob_reached_optimal_h, glob_initial_pass, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_optimal_done, glob_not_yet_finished, hours_in_day, glob_log10abserr, glob_relerr, glob_look_poles, glob_not_yet_start_msg, min_in_hour, array_const_1, array_const_0D0, array_fact_1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_pole, array_1st_rel_error, array_last_rel_error, array_m1, array_type_pole, array_y_init, array_real_pole, array_fact_2, array_y_set_initial, array_y_higher_work2, array_poles, array_complex_pole, array_y_higher_work, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; glob_iolevel := 5; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; INFO := 2; glob_log10relerr := 0.; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_dump_analytic := false; glob_last_good_h := 0.1; glob_hmax := 1.0; glob_clock_sec := 0.; years_in_century := 100; glob_orig_start_sec := 0.; glob_disp_incr := 0.1; glob_clock_start_sec := 0.; glob_almost_1 := 0.9990; centuries_in_millinium := 10; glob_dump := false; glob_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_h := 0.1; djd_debug := true; glob_max_opt_iter := 10; glob_html_log := true; glob_curr_iter_when_opt := 0; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_max_hours := 0.; djd_debug2 := true; glob_good_digits := 0; glob_optimal_expect_sec := 0.1; glob_normmax := 0.; glob_smallish_float := 0.1*10^(-100); glob_hmin_init := 0.001; glob_display_flag := true; glob_log10normmin := 0.1; glob_iter := 0; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_optimal_start := 0.; glob_no_eqs := 0; days_in_year := 365; glob_max_minutes := 0.; glob_start := 0; glob_max_iter := 1000; sec_in_minute := 60; glob_subiter_method := 3; glob_percent_done := 0.; glob_warned2 := false; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; glob_initial_pass := true; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_optimal_done := false; glob_not_yet_finished := true; hours_in_day := 24; glob_log10abserr := 0.; glob_relerr := 0.1*10^(-10); glob_look_poles := false; glob_not_yet_start_msg := true; min_in_hour := 60; 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/multpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * 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 := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 1;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(1.0 + x * x * x / 3.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_fact_1 := 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_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work := 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_fact_1[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 ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[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 <= 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 <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_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_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; 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); chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*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 array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( 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 ) = x * 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, "2012-09-02T22:15:24-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mult"); logitem_str(html_log_file, "diff ( y , x , 1 ) = x * 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, " 126 "); logitem_str(html_log_file, "mult diffeq.mxt"); logitem_str(html_log_file, "mult 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/multpostode.ode################# diff ( y , x , 1 ) = x * x ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(1.0 + x * x * x / 3.0); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.0003333333333333333333333333333 y[1] (numeric) = 1.0003333333333333333333333333333 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10001 y[1] (analytic) = 1.0003334333433336666666666666667 y[1] (numeric) = 1.0003334333433336666666666666666 absolute error = 1e-31 relative error = 9.9966667779740275267529967258480e-30 % Correct digits = 31 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 1.000333533373336 y[1] (numeric) = 1.0003335333733359999999999999999 absolute error = 1e-31 relative error = 9.9966657783408374304466559525669e-30 % Correct digits = 31 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 1.0003336334233423333333333333333 y[1] (numeric) = 1.0003336334233423333333333333332 absolute error = 1e-31 relative error = 9.9966647785079406673466296879216e-30 % Correct digits = 31 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10004 y[1] (analytic) = 1.0003337334933546666666666666667 y[1] (numeric) = 1.0003337334933546666666666666665 absolute error = 2e-31 relative error = 1.9993327556950634741398987272482e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 1.000333833583375 y[1] (numeric) = 1.0003338335833749999999999999998 absolute error = 2e-31 relative error = 1.9993325556485895347583470968740e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 1.0003339336934053333333333333333 y[1] (numeric) = 1.0003339336934053333333333333331 absolute error = 2e-31 relative error = 1.9993323555621623419899525697003e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 1.0003340338234476666666666666667 y[1] (numeric) = 1.0003340338234476666666666666664 absolute error = 3e-31 relative error = 2.9989982331536668837619733665393e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 1.000334133973504 y[1] (numeric) = 1.0003341339735039999999999999997 absolute error = 3e-31 relative error = 2.9989979329041484544905355768358e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 1.0003342341435763333333333333333 y[1] (numeric) = 1.000334234143576333333333333333 absolute error = 3e-31 relative error = 2.9989976325946822652044800133576e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 1.0003343343336666666666666666667 y[1] (numeric) = 1.0003343343336666666666666666663 absolute error = 4e-31 relative error = 3.9986631096336831412662089618237e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 1.000334434543777 y[1] (numeric) = 1.0003344345437769999999999999996 absolute error = 4e-31 relative error = 3.9986627090611770223785381982583e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 1.0003345347739093333333333333333 y[1] (numeric) = 1.0003345347739093333333333333329 absolute error = 4e-31 relative error = 3.9986623084087167170360653749024e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 1.0003346350240656666666666666667 y[1] (numeric) = 1.0003346350240656666666666666662 absolute error = 5e-31 relative error = 4.9983273845953678483515229639303e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10014 y[1] (analytic) = 1.000334735294248 y[1] (numeric) = 1.0003347352942479999999999999995 absolute error = 5e-31 relative error = 4.9983268835798772009655230989958e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10015 y[1] (analytic) = 1.0003348355844583333333333333333 y[1] (numeric) = 1.0003348355844583333333333333328 absolute error = 5e-31 relative error = 4.9983263824644140209801044820373e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10016 y[1] (analytic) = 1.0003349358946986666666666666667 y[1] (numeric) = 1.0003349358946986666666666666661 absolute error = 6e-31 relative error = 5.9979910574987620503099470298285e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10017 y[1] (analytic) = 1.000335036224971 y[1] (numeric) = 1.0003350362249709999999999999994 absolute error = 6e-31 relative error = 5.9979904559202363968197236046535e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10018 y[1] (analytic) = 1.0003351365752773333333333333333 y[1] (numeric) = 1.0003351365752773333333333333327 absolute error = 6e-31 relative error = 5.9979898542217079449890952458704e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10019 y[1] (analytic) = 1.0003352369456196666666666666667 y[1] (numeric) = 1.000335236945619666666666666666 absolute error = 7e-31 relative error = 6.9976541278036922376466687621513e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002 y[1] (analytic) = 1.000335337336 y[1] (numeric) = 1.0003353373359999999999999999993 absolute error = 7e-31 relative error = 6.9976534255420274621548021678214e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10021 y[1] (analytic) = 1.0003354377464203333333333333333 y[1] (numeric) = 1.0003354377464203333333333333326 absolute error = 7e-31 relative error = 6.9976527231403177030933238313521e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10022 y[1] (analytic) = 1.0003355381768826666666666666667 y[1] (numeric) = 1.0003355381768826666666666666659 absolute error = 8e-31 relative error = 7.9973165949697703477012334583719e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10023 y[1] (analytic) = 1.000335638627389 y[1] (numeric) = 1.0003356386273889999999999999992 absolute error = 8e-31 relative error = 7.9973157919048086964513744303310e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10024 y[1] (analytic) = 1.0003357390979413333333333333333 y[1] (numeric) = 1.0003357390979413333333333333325 absolute error = 8e-31 relative error = 7.9973149886797479570227110641022e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10025 y[1] (analytic) = 1.0003358395885416666666666666667 y[1] (numeric) = 1.0003358395885416666666666666658 absolute error = 9e-31 relative error = 8.9969784584563937662699062664257e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10026 y[1] (analytic) = 1.000335940099192 y[1] (numeric) = 1.0003359400991919999999999999991 absolute error = 9e-31 relative error = 8.9969775544679238480796938053243e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10027 y[1] (analytic) = 1.0003360406298943333333333333333 y[1] (numeric) = 1.0003360406298943333333333333324 absolute error = 9e-31 relative error = 8.9969766502992888178298194704178e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10028 y[1] (analytic) = 1.0003361411806506666666666666667 y[1] (numeric) = 1.0003361411806506666666666666657 absolute error = 1.0e-30 relative error = 9.9966397177227453292291951435594e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10029 y[1] (analytic) = 1.000336241751463 y[1] (numeric) = 1.000336241751462999999999999999 absolute error = 1.0e-30 relative error = 9.9966387126905021159234969759151e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003 y[1] (analytic) = 1.0003363423423333333333333333333 y[1] (numeric) = 1.0003363423423333333333333333323 absolute error = 1.0e-30 relative error = 9.9966377074580158475140213472334e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10031 y[1] (analytic) = 1.0003364429532636666666666666667 y[1] (numeric) = 1.0003364429532636666666666666656 absolute error = 1.1e-30 relative error = 1.0996300372227793324160535015180e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10032 y[1] (analytic) = 1.000336543584256 y[1] (numeric) = 1.0003365435842559999999999999989 absolute error = 1.1e-30 relative error = 1.0996299266031458151005010707208e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10033 y[1] (analytic) = 1.0003366442353123333333333333333 y[1] (numeric) = 1.0003366442353123333333333333322 absolute error = 1.1e-30 relative error = 1.0996298159614790060646828258800e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10034 y[1] (analytic) = 1.0003367449064346666666666666667 y[1] (numeric) = 1.0003367449064346666666666666655 absolute error = 1.2e-30 relative error = 1.1995960421430291491976133530458e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10035 y[1] (analytic) = 1.000336845597625 y[1] (numeric) = 1.0003368455976249999999999999988 absolute error = 1.2e-30 relative error = 1.1995959213949492058111120368431e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10036 y[1] (analytic) = 1.0003369463088853333333333333333 y[1] (numeric) = 1.0003369463088853333333333333321 absolute error = 1.2e-30 relative error = 1.1995958006228257925998382356834e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10037 y[1] (analytic) = 1.0003370470402176666666666666667 y[1] (numeric) = 1.0003370470402176666666666666654 absolute error = 1.3e-30 relative error = 1.2995619864788779028545978811435e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10038 y[1] (analytic) = 1.000337147791624 y[1] (numeric) = 1.0003371477916239999999999999987 absolute error = 1.3e-30 relative error = 1.2995618555903089397420700561924e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10039 y[1] (analytic) = 1.0003372485631063333333333333333 y[1] (numeric) = 1.000337248563106333333333333332 absolute error = 1.3e-30 relative error = 1.2995617246756851368165109920871e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004 y[1] (analytic) = 1.0003373493546666666666666666667 y[1] (numeric) = 1.0003373493546666666666666666653 absolute error = 1.4e-30 relative error = 1.3995278701761580586326009592373e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10041 y[1] (analytic) = 1.000337450166307 y[1] (numeric) = 1.0003374501663069999999999999986 absolute error = 1.4e-30 relative error = 1.3995277291350521186133108255717e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10042 y[1] (analytic) = 1.0003375509980293333333333333333 y[1] (numeric) = 1.0003375509980293333333333333319 absolute error = 1.4e-30 relative error = 1.3995275880658787769198537515561e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10043 y[1] (analytic) = 1.0003376518498356666666666666667 y[1] (numeric) = 1.0003376518498356666666666666652 absolute error = 1.5e-30 relative error = 1.4994936931806806275987448146054e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=2.8MB, time=0.50 x[1] = 0.10044 y[1] (analytic) = 1.000337752721728 y[1] (numeric) = 1.0003377527217279999999999999985 absolute error = 1.5e-30 relative error = 1.4994935419749843900097838816414e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10045 y[1] (analytic) = 1.0003378536137083333333333333333 y[1] (numeric) = 1.0003378536137083333333333333318 absolute error = 1.5e-30 relative error = 1.4994933907392069970235271161616e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10046 y[1] (analytic) = 1.0003379545257786666666666666667 y[1] (numeric) = 1.0003379545257786666666666666651 absolute error = 1.6e-30 relative error = 1.5994594554382351668047296393770e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10047 y[1] (analytic) = 1.000338055457941 y[1] (numeric) = 1.0003380554579409999999999999984 absolute error = 1.6e-30 relative error = 1.5994592940558899475445345339096e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10048 y[1] (analytic) = 1.0003381564101973333333333333333 y[1] (numeric) = 1.0003381564101973333333333333317 absolute error = 1.6e-30 relative error = 1.5994591326414486273128138917116e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10049 y[1] (analytic) = 1.0003382573825496666666666666667 y[1] (numeric) = 1.000338257382549666666666666665 absolute error = 1.7e-30 relative error = 1.6994251568945897794499995595669e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005 y[1] (analytic) = 1.000338358375 y[1] (numeric) = 1.0003383583749999999999999999983 absolute error = 1.7e-30 relative error = 1.6994249853235315310219021670933e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10051 y[1] (analytic) = 1.0003384593875503333333333333333 y[1] (numeric) = 1.0003384593875503333333333333316 absolute error = 1.7e-30 relative error = 1.6994248137183610442078497265863e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10052 y[1] (analytic) = 1.0003385604202026666666666666667 y[1] (numeric) = 1.0003385604202026666666666666649 absolute error = 1.8e-30 relative error = 1.7993907974954911150450250018171e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10053 y[1] (analytic) = 1.000338661472959 y[1] (numeric) = 1.0003386614729589999999999999982 absolute error = 1.8e-30 relative error = 1.7993906157236504266008349525194e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10054 y[1] (analytic) = 1.0003387625458213333333333333333 y[1] (numeric) = 1.0003387625458213333333333333315 absolute error = 1.8e-30 relative error = 1.7993904339156801705269701709471e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10055 y[1] (analytic) = 1.0003388636387916666666666666667 y[1] (numeric) = 1.0003388636387916666666666666648 absolute error = 1.9e-30 relative error = 1.8993563771866643695747014975118e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10056 y[1] (analytic) = 1.000338964751872 y[1] (numeric) = 1.0003389647518719999999999999981 absolute error = 1.9e-30 relative error = 1.8993561852019664669583210082329e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10057 y[1] (analytic) = 1.0003390658850643333333333333333 y[1] (numeric) = 1.0003390658850643333333333333314 absolute error = 1.9e-30 relative error = 1.8993559931791204756501741959853e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10058 y[1] (analytic) = 1.0003391670383706666666666666667 y[1] (numeric) = 1.0003391670383706666666666666647 absolute error = 2.0e-30 relative error = 1.9993218959138132856618649639327e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10059 y[1] (analytic) = 1.000339268211793 y[1] (numeric) = 1.000339268211792999999999999998 absolute error = 2.0e-30 relative error = 1.9993216937041780314529360474775e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006 y[1] (analytic) = 1.0003393694053333333333333333333 y[1] (numeric) = 1.0003393694053333333333333333313 absolute error = 2.0e-30 relative error = 1.9993214914543749756827042128773e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10061 y[1] (analytic) = 1.0003394706189936666666666666667 y[1] (numeric) = 1.0003394706189936666666666666646 absolute error = 2.1e-30 relative error = 2.0992873536226201527309235021192e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10062 y[1] (analytic) = 1.000339571852776 y[1] (numeric) = 1.0003395718527759999999999999979 absolute error = 2.1e-30 relative error = 2.0992871411759620462885075552152e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10063 y[1] (analytic) = 1.0003396731066823333333333333333 y[1] (numeric) = 1.0003396731066823333333333333312 absolute error = 2.1e-30 relative error = 2.0992869286871152336187426311097e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10064 y[1] (analytic) = 1.0003397743807146666666666666667 y[1] (numeric) = 1.0003397743807146666666666666645 absolute error = 2.2e-30 relative error = 2.1992527502587458071716057510987e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10065 y[1] (analytic) = 1.000339875674875 y[1] (numeric) = 1.0003398756748749999999999999978 absolute error = 2.2e-30 relative error = 2.1992525275629739846778955323464e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10066 y[1] (analytic) = 1.0003399769891653333333333333333 y[1] (numeric) = 1.0003399769891653333333333333311 absolute error = 2.2e-30 relative error = 2.1992523048229913595052249958381e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10067 y[1] (analytic) = 1.0003400783235876666666666666667 y[1] (numeric) = 1.0003400783235876666666666666644 absolute error = 2.3e-30 relative error = 2.2992180857678296325028258381488e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10068 y[1] (analytic) = 1.000340179678144 y[1] (numeric) = 1.0003401796781439999999999999977 absolute error = 2.3e-30 relative error = 2.2992178528108478670068898472951e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10069 y[1] (analytic) = 1.0003402810528363333333333333333 y[1] (numeric) = 1.000340281052836333333333333331 absolute error = 2.3e-30 relative error = 2.2992176198076320106057697439428e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007 y[1] (analytic) = 1.0003403824476666666666666666667 y[1] (numeric) = 1.0003403824476666666666666666643 absolute error = 2.4e-30 relative error = 2.3991833600954895595366649647533e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10071 y[1] (analytic) = 1.000340483862637 y[1] (numeric) = 1.0003404838626369999999999999976 absolute error = 2.4e-30 relative error = 2.3991831168651962609982242346192e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10072 y[1] (analytic) = 1.0003405852977493333333333333333 y[1] (numeric) = 1.0003405852977493333333333333309 absolute error = 2.4e-30 relative error = 2.3991828735866443915647246184404e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10073 y[1] (analytic) = 1.0003406867530056666666666666667 y[1] (numeric) = 1.0003406867530056666666666666642 absolute error = 2.5e-30 relative error = 2.4991485731873220665424696679138e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10074 y[1] (analytic) = 1.000340788228408 y[1] (numeric) = 1.0003407882284079999999999999975 absolute error = 2.5e-30 relative error = 2.4991483196716102818757069803069e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10075 y[1] (analytic) = 1.0003408897239583333333333333333 y[1] (numeric) = 1.0003408897239583333333333333308 absolute error = 2.5e-30 relative error = 2.4991480661056142545713297809134e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10076 y[1] (analytic) = 1.0003409912396586666666666666667 y[1] (numeric) = 1.0003409912396586666666666666641 absolute error = 2.6e-30 relative error = 2.5991137249889021794110667964738e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10077 y[1] (analytic) = 1.000341092775511 y[1] (numeric) = 1.0003410927755109999999999999974 absolute error = 2.6e-30 relative error = 2.5991134611756595925284683334179e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10078 y[1] (analytic) = 1.0003411943315173333333333333333 y[1] (numeric) = 1.0003411943315173333333333333307 absolute error = 2.6e-30 relative error = 2.5991131973101058995239976616141e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10079 y[1] (analytic) = 1.0003412959076796666666666666667 y[1] (numeric) = 1.000341295907679666666666666664 absolute error = 2.7e-30 relative error = 2.6990788154457834718190952421163e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008 y[1] (analytic) = 1.000341397504 y[1] (numeric) = 1.0003413975039999999999999999973 absolute error = 2.7e-30 relative error = 2.6990785413228924036753246837266e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10081 y[1] (analytic) = 1.0003414991204803333333333333333 y[1] (numeric) = 1.0003414991204803333333333333306 absolute error = 2.7e-30 relative error = 2.6990782671456621741947095869032e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10082 y[1] (analytic) = 1.0003416007571226666666666666667 y[1] (numeric) = 1.0003416007571226666666666666639 absolute error = 2.8e-30 relative error = 2.7990438445034980653934544646892e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10083 y[1] (analytic) = 1.000341702413929 y[1] (numeric) = 1.0003417024139289999999999999972 absolute error = 2.8e-30 relative error = 2.7990435600588354740292595450255e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10084 y[1] (analytic) = 1.0003418040909013333333333333333 y[1] (numeric) = 1.0003418040909013333333333333305 absolute error = 2.8e-30 relative error = 2.7990432755578044743935292236757e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10085 y[1] (analytic) = 1.0003419057880416666666666666667 y[1] (numeric) = 1.0003419057880416666666666666638 absolute error = 2.9e-30 relative error = 2.8990088121075566298758698515166e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10086 y[1] (analytic) = 1.000342007505352 y[1] (numeric) = 1.0003420075053519999999999999971 absolute error = 2.9e-30 relative error = 2.8990085173289941104620213837424e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10087 y[1] (analytic) = 1.0003421092428343333333333333333 y[1] (numeric) = 1.0003421092428343333333333333304 absolute error = 2.9e-30 relative error = 2.8990082224920327441332328804328e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10088 y[1] (analytic) = 1.0003422110004906666666666666667 y[1] (numeric) = 1.0003422110004906666666666666637 absolute error = 3.0e-30 relative error = 2.9989737182034483832875749503485e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10089 y[1] (analytic) = 1.000342312778323 y[1] (numeric) = 1.000342312778322999999999999997 absolute error = 3.0e-30 relative error = 2.9989734130788521681688383325270e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009 y[1] (analytic) = 1.0003424145763333333333333333333 y[1] (numeric) = 1.0003424145763333333333333333303 absolute error = 3.0e-30 relative error = 2.9989731078938254757940567046517e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10091 y[1] (analytic) = 1.0003425163945236666666666666667 y[1] (numeric) = 1.0003425163945236666666666666636 absolute error = 3.1e-30 relative error = 3.0989385627366410920941106156046e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10092 y[1] (analytic) = 1.000342618232896 y[1] (numeric) = 1.0003426182328959999999999999969 absolute error = 3.1e-30 relative error = 3.0989382472538720508332498284594e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10093 y[1] (analytic) = 1.0003427200914523333333333333333 y[1] (numeric) = 1.0003427200914523333333333333302 absolute error = 3.1e-30 relative error = 3.0989379317086397102885608161053e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10094 y[1] (analytic) = 1.0003428219701946666666666666667 y[1] (numeric) = 1.0003428219701946666666666666635 absolute error = 3.2e-30 relative error = 3.1989033456525810713702411075621e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10095 y[1] (analytic) = 1.000342923869125 y[1] (numeric) = 1.0003429238691249999999999999968 absolute error = 3.2e-30 relative error = 3.1989030197994947107920552155322e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10096 y[1] (analytic) = 1.0003430257882453333333333333333 y[1] (numeric) = 1.0003430257882453333333333333301 absolute error = 3.2e-30 relative error = 3.1989026938819110372266104157865e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10097 y[1] (analytic) = 1.0003431277275576666666666666667 y[1] (numeric) = 1.0003431277275576666666666666634 absolute error = 3.3e-30 relative error = 3.2988680668966931849649871841400e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10098 y[1] (analytic) = 1.000343229687064 y[1] (numeric) = 1.0003432296870639999999999999967 absolute error = 3.3e-30 relative error = 3.2988677306611396492003793510575e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10099 y[1] (analytic) = 1.0003433316667663333333333333333 y[1] (numeric) = 1.00034333166676633333333333333 absolute error = 3.3e-30 relative error = 3.2988673943590535950804739100835e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 1.0003434336666666666666666666667 y[1] (numeric) = 1.0003434336666666666666666666633 absolute error = 3.4e-30 relative error = 3.3988327264143808456667762249294e-28 % Correct digits = 29 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = x * x ; Iterations = 100 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Expected Time Remaining = 2 Hours 13 Minutes 17 Seconds Optimized Time Remaining = 2 Hours 8 Minutes 52 Seconds Time to Timeout = 59 Seconds Percent Done = 0.0102 % > quit memory used=7.0MB, alloc=3.1MB, time=0.91