|\^/| 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_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > 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_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, 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_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre arccos $eq_no = 1 > array_tmp1[1] := arccos(array_x[1]); > array_tmp1_a1[1] := sin(array_tmp1[1]); > #emit pre add $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] * (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 arccos $eq_no = 1 > temp := att(1,array_tmp1_a1,array_tmp1,2); > array_tmp1[2] := -(array_x[2] + temp) / array_tmp1_a1[1]; > array_tmp1_a1[2] := att(1,array_x,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[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] * (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 arccos $eq_no = 1 > temp := att(2,array_tmp1_a1,array_tmp1,2); > array_tmp1[3] := -(array_x[3] + temp) / array_tmp1_a1[1]; > array_tmp1_a1[3] := att(2,array_x,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[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] * (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 arccos $eq_no = 1 > temp := att(3,array_tmp1_a1,array_tmp1,2); > array_tmp1[4] := -(array_x[4] + temp) / array_tmp1_a1[1]; > array_tmp1_a1[4] := att(3,array_x,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[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] * (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 arccos $eq_no = 1 > temp := att(4,array_tmp1_a1,array_tmp1,2); > array_tmp1[5] := -(array_x[5] + temp) / array_tmp1_a1[1]; > array_tmp1_a1[5] := att(4,array_x,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[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] * (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 arccos $eq_no = 1 > temp := att(kkk-1,array_tmp1_a1,array_tmp1,2); > array_tmp1[kkk] := - (array_x[kkk] + temp) / array_tmp1_a1[1]; > array_tmp1_a1[kkk] := att(kkk-1,array_x,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[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] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; Warning, `temp` is implicitly declared local to procedure `atomall` atomall := proc() local kkk, order_d, adj2, temporary, term, temp; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; array_tmp1[1] := arccos(array_x[1]); array_tmp1_a1[1] := sin(array_tmp1[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]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; temp := att(1, array_tmp1_a1, array_tmp1, 2); array_tmp1[2] := -(array_x[2] + temp)/array_tmp1_a1[1]; array_tmp1_a1[2] := att(1, array_x, array_tmp1, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; temp := att(2, array_tmp1_a1, array_tmp1, 2); array_tmp1[3] := -(array_x[3] + temp)/array_tmp1_a1[1]; array_tmp1_a1[3] := att(2, array_x, array_tmp1, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; temp := att(3, array_tmp1_a1, array_tmp1, 2); array_tmp1[4] := -(array_x[4] + temp)/array_tmp1_a1[1]; array_tmp1_a1[4] := att(3, array_x, array_tmp1, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; temp := att(4, array_tmp1_a1, array_tmp1, 2); array_tmp1[5] := -(array_x[5] + temp)/array_tmp1_a1[1]; array_tmp1_a1[5] := att(4, array_x, array_tmp1, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do temp := att(kkk - 1, array_tmp1_a1, array_tmp1, 2); array_tmp1[kkk] := -(array_x[kkk] + temp)/array_tmp1_a1[1]; array_tmp1_a1[kkk] := att(kkk - 1, array_x, array_tmp1, 1); array_tmp2[kkk] := array_const_0D0[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]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 + x * arccos(x) - sqrt(1.0-x*x) > end; exact_soln_y := proc(x) 2.0 + x*arccos(x) - sqrt(1.0 - x*x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_h, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > glob_dump, > glob_iter, > glob_abserr, > glob_optimal_expect_sec, > glob_log10normmin, > glob_percent_done, > glob_current_iter, > glob_orig_start_sec, > glob_max_hours, > glob_disp_incr, > glob_clock_sec, > glob_almost_1, > hours_in_day, > sec_in_min, > glob_warned2, > glob_initial_pass, > centuries_in_millinium, > days_in_year, > glob_max_opt_iter, > glob_log10relerr, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_max_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10_abserr, > glob_warned, > glob_small_float, > glob_hmin, > glob_reached_optimal_h, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_smallish_float, > glob_optimal_start, > glob_max_iter, > glob_not_yet_start_msg, > djd_debug2, > glob_display_flag, > glob_max_minutes, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_large_float, > glob_hmin_init, > glob_html_log, > glob_dump_analytic, > glob_last_good_h, > glob_hmax, > min_in_hour, > djd_debug, > glob_subiter_method, > glob_relerr, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_m1, > array_pole, > array_y, > array_x, > array_type_pole, > array_last_rel_error, > array_tmp1_a1, > array_complex_pole, > array_y_higher_work, > array_y_higher, > array_poles, > array_y_higher_work2, > array_real_pole, > array_y_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > INFO := 2; > glob_start := 0; > glob_unchanged_h_cnt := 0; > glob_h := 0.1; > glob_optimal_done := false; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > glob_dump := false; > glob_iter := 0; > glob_abserr := 0.1e-10; > glob_optimal_expect_sec := 0.1; > glob_log10normmin := 0.1; > glob_percent_done := 0.0; > glob_current_iter := 0; > glob_orig_start_sec := 0.0; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > hours_in_day := 24.0; > sec_in_min := 60.0; > glob_warned2 := false; > glob_initial_pass := true; > centuries_in_millinium := 10.0; > days_in_year := 365.0; > glob_max_opt_iter := 10; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > years_in_century := 100.0; > glob_normmax := 0.0; > MAX_UNCHANGED := 10; > glob_smallish_float := 0.1e-100; > glob_optimal_start := 0.0; > glob_max_iter := 1000; > glob_not_yet_start_msg := true; > djd_debug2 := true; > glob_display_flag := true; > glob_max_minutes := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_html_log := true; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > min_in_hour := 60.0; > djd_debug := true; > glob_subiter_method := 3; > glob_relerr := 0.1e-10; > glob_look_poles := false; > #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/arccospostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = arccos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -0.8;"); > omniout_str(ALWAYS,"x_end := 0.8 ;"); > 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 := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"2.0 + x * arccos(x) - sqrt(1.0-x*x)"); > 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 > max_terms := 30; > Digits := 32; > #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_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp1_a1:= Array(1..(max_terms + 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_a1[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_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 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #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_tmp1_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -0.8; > x_end := 0.8 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = arccos ( 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,"2012-06-13T01:26:23-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"arccos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = arccos ( 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_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"arccos diffeq.mxt") > ; > logitem_str(html_log_file,"arccos maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, glob_start, glob_unchanged_h_cnt, glob_h, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, glob_dump, glob_iter, glob_abserr, glob_optimal_expect_sec, glob_log10normmin, glob_percent_done, glob_current_iter, glob_orig_start_sec, glob_max_hours, glob_disp_incr, glob_clock_sec, glob_almost_1, hours_in_day, sec_in_min, glob_warned2, glob_initial_pass, centuries_in_millinium, days_in_year, glob_max_opt_iter, glob_log10relerr, glob_log10abserr, glob_curr_iter_when_opt, glob_max_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10_abserr, glob_warned, glob_small_float, glob_hmin, glob_reached_optimal_h, years_in_century, glob_normmax, MAX_UNCHANGED, glob_smallish_float, glob_optimal_start, glob_max_iter, glob_not_yet_start_msg, djd_debug2, glob_display_flag, glob_max_minutes, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_large_float, glob_hmin_init, glob_html_log, glob_dump_analytic, glob_last_good_h, glob_hmax, min_in_hour, djd_debug, glob_subiter_method, glob_relerr, glob_look_poles, array_const_0D0, array_const_1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_m1, array_pole, array_y, array_x, array_type_pole, array_last_rel_error, array_tmp1_a1, array_complex_pole, array_y_higher_work, array_y_higher, array_poles, array_y_higher_work2, array_real_pole, array_y_set_initial, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; INFO := 2; glob_start := 0; glob_unchanged_h_cnt := 0; glob_h := 0.1; glob_optimal_done := false; glob_not_yet_finished := true; glob_clock_start_sec := 0.; glob_dump := false; glob_iter := 0; glob_abserr := 0.1*10^(-10); glob_optimal_expect_sec := 0.1; glob_log10normmin := 0.1; glob_percent_done := 0.; glob_current_iter := 0; glob_orig_start_sec := 0.; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_clock_sec := 0.; glob_almost_1 := 0.9990; hours_in_day := 24.0; sec_in_min := 60.0; glob_warned2 := false; glob_initial_pass := true; centuries_in_millinium := 10.0; days_in_year := 365.0; glob_max_opt_iter := 10; glob_log10relerr := 0.; glob_log10abserr := 0.; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_warned := false; glob_small_float := 0.1*10^(-50); glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; years_in_century := 100.0; glob_normmax := 0.; MAX_UNCHANGED := 10; glob_smallish_float := 0.1*10^(-100); glob_optimal_start := 0.; glob_max_iter := 1000; glob_not_yet_start_msg := true; djd_debug2 := true; glob_display_flag := true; glob_max_minutes := 0.; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_html_log := true; glob_dump_analytic := false; glob_last_good_h := 0.1; glob_hmax := 1.0; min_in_hour := 60.0; djd_debug := true; glob_subiter_method := 3; glob_relerr := 0.1*10^(-10); glob_look_poles := false; 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/arccospostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -0.8;"); omniout_str(ALWAYS, "x_end := 0.8 ;"); 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 := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "2.0 + x * arccos(x) - sqrt(1.0-x*x)"); 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; max_terms := 30; Digits := 32; glob_max_terms := max_terms; glob_html_log := true; array_1st_rel_error := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_tmp1_a1 := Array(1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); 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_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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 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; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_tmp1_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a1[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := -0.8; x_end := 0.8; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = arccos ( 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, "2012-06-13T01:26:23-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "arccos") ; logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos ( 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_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "arccos diffeq.mxt"); logitem_str(html_log_file, "arccos maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/arccospostode.ode################# diff ( y , x , 1 ) = arccos ( x ) ; ! #BEGIN FIRST INPUT BLOCK max_terms := 30; Digits := 32; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -0.8; x_end := 0.8 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0 + x * arccos(x) - sqrt(1.0-x*x) end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -0.8 y[1] (analytic) = -0.5984732358372070813278673236498 y[1] (numeric) = -0.5984732358372070813278673236498 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7999 y[1] (analytic) = -0.59822343501544360196562980764631 y[1] (numeric) = -0.59822343501544360196594277346525 absolute error = 3.1296581894e-22 relative error = 5.2315874073358651461601528262802e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7998 y[1] (analytic) = -0.59797365085664479504050349769644 y[1] (numeric) = -0.59797365085664479504112872519849 absolute error = 6.2522750205e-22 relative error = 1.0455770102149348828085730455738e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7997 y[1] (analytic) = -0.59772388335711135041499570195926 y[1] (numeric) = -0.59772388335711135041593248894317 absolute error = 9.3678698391e-22 relative error = 1.5672570730293450733723434672590e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7996 y[1] (analytic) = -0.59747413251314688272549020263662 y[1] (numeric) = -0.59747413251314688272673784882915 absolute error = 1.24764619253e-21 relative error = 2.0882011866891101999154227742899e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7995 y[1] (analytic) = -0.5972243983210579277288913435793 y[1] (numeric) = -0.59722439832105792773044915062897 absolute error = 1.55780704967e-21 relative error = 2.6084116021538503461281691232951e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7994 memory used=3.8MB, alloc=2.9MB, time=0.15 y[1] (analytic) = -0.59697468077715393865566576448373 y[1] (numeric) = -0.59697468077715393865753303595511 absolute error = 1.86727147138e-21 relative error = 3.1278905647206804950980978370066e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7993 y[1] (analytic) = -0.59672497987774728256926740783101 y[1] (numeric) = -0.59672497987774728257144344919789 absolute error = 2.17604136688e-21 relative error = 3.6466403121347654788156010902992e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7992 y[1] (analytic) = -0.59647529561915323673193146414769 y[1] (numeric) = -0.59647529561915323673441558278706 absolute error = 2.48411863937e-21 relative error = 4.1646630759308067849473620263874e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7991 y[1] (analytic) = -0.59622562799768998497682296047918 y[1] (numeric) = -0.59622562799768998497961446566536 absolute error = 2.79150518618e-21 relative error = 4.6819610816709398483565186385088e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.799 y[1] (analytic) = -0.59597597700967861408652573614255 y[1] (numeric) = -0.59597597700967861408962393904059 absolute error = 3.09820289804e-21 relative error = 5.1985365477066626310342831578792e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7989 y[1] (analytic) = -0.59572634265144311017785758887372 y[1] (numeric) = -0.59572634265144311018126180253381 absolute error = 3.40421366009e-21 relative error = 5.7143916868584584207263941826693e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7988 y[1] (analytic) = -0.59547672491931035509299741341553 y[1] (numeric) = -0.59547672491931035509670695276642 absolute error = 3.70953935089e-21 relative error = 6.2295287047409929567331627987435e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7987 y[1] (analytic) = -0.5952271238096101227969101933846 y[1] (numeric) = -0.59522712380961012280092437522794 absolute error = 4.01418184334e-21 relative error = 6.7439498012929595166297704946418e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7986 y[1] (analytic) = -0.59497753931867507578105574593601 y[1] (numeric) = -0.59497753931867507578537388893992 absolute error = 4.31814300391e-21 relative error = 7.2576571694703344953096096795406e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7985 y[1] (analytic) = -0.59472797144284076147336715728721 y[1] (numeric) = -0.59472797144284076147798858198048 absolute error = 4.62142469327e-21 relative error = 7.7706529962903629934995499915256e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.32 NO POLE x[1] = -0.7984 y[1] (analytic) = -0.59447842017844560865448488559191 y[1] (numeric) = -0.59447842017844560865940891435808 absolute error = 4.92402876617e-21 relative error = 8.2829394626165670170922852695089e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7983 y[1] (analytic) = -0.59422888552183092388023254595242 y[1] (numeric) = -0.59422888552183092388545850302363 absolute error = 5.22595707121e-21 relative error = 8.7945187427581009620300079924463e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7982 y[1] (analytic) = -0.59397936746934088791032043053582 y[1] (numeric) = -0.59397936746934088791584764198697 absolute error = 5.52721145115e-21 relative error = 9.3053930049772226931402913862648e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7981 y[1] (analytic) = -0.5937298660173225521432628548146 y[1] (numeric) = -0.5937298660173225521490906485573 absolute error = 5.82779374270e-21 relative error = 9.8155644111222280566104788923984e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.798 y[1] (analytic) = -0.59348038116212583505749545888194 y[1] (numeric) = -0.59348038116212583506362316465864 absolute error = 6.12770577670e-21 relative error = 1.0325035116916602942721253140344e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7979 y[1] (analytic) = -0.59323091290010351865867863060196 y[1] (numeric) = -0.59323091290010351866510557998013 absolute error = 6.42694937817e-21 relative error = 1.0833807272029768998241319875471e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7978 y[1] (analytic) = -0.59298146122761124493317325504239 y[1] (numeric) = -0.59298146122761124493989878140852 absolute error = 6.72552636613e-21 relative error = 1.1341883019760140335965707333735e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7977 y[1] (analytic) = -0.59273202614100751230767503220214 y[1] (numeric) = -0.59273202614100751231469847075609 absolute error = 7.02343855395e-21 relative error = 1.1849264497611547465997970073369e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7976 y[1] (analytic) = -0.59248260763665367211499364249366 y[1] (numeric) = -0.59248260763665367212231433024273 absolute error = 7.32068774907e-21 relative error = 1.2355953836807797831798580737027e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7975 y[1] (analytic) = -0.59223320571091392506596307676258 y[1] (numeric) = -0.59223320571091392507358035251567 absolute error = 7.61727575309e-21 relative error = 1.2861953162430766429723857332377e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7974 memory used=11.4MB, alloc=4.1MB, time=0.50 y[1] (analytic) = -0.59198382036015531772746948483363 y[1] (numeric) = -0.59198382036015531773538268919542 absolute error = 7.91320436179e-21 relative error = 1.3367264593440591962804406366281e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7973 y[1] (analytic) = -0.59173445158074773900658293365685 y[1] (numeric) = -0.59173445158074773901479140902212 absolute error = 8.20847536527e-21 relative error = 1.3871890242898720638608025629340e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7972 y[1] (analytic) = -0.59148509936906391664077950309489 y[1] (numeric) = -0.59148509936906391664928259364291 absolute error = 8.50309054802e-21 relative error = 1.4375832218073170862123799608712e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7971 y[1] (analytic) = -0.59123576372147941369424018424053 y[1] (numeric) = -0.59123576372147941370303723592906 absolute error = 8.79705168853e-21 relative error = 1.4879092619766035669240976524522e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.797 y[1] (analytic) = -0.59098644463437262506021308188167 y[1] (numeric) = -0.5909864446343726250693034424413 absolute error = 9.09036055963e-21 relative error = 1.5381673542874508601736167681398e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7969 y[1] (analytic) = -0.59073714210412477396942545934504 y[1] (numeric) = -0.59073714210412477397880847827395 absolute error = 9.38301892891e-21 relative error = 1.5883577077088757231083644387578e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7968 y[1] (analytic) = -0.59048785612711990850453220044563 y[1] (numeric) = -0.59048785612711990851420722900341 absolute error = 9.67502855778e-21 relative error = 1.6384805305288386910919242457486e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7967 y[1] (analytic) = -0.59023858669974489812058729964229 y[1] (numeric) = -0.59023858669974489813055369084443 absolute error = 9.96639120214e-21 relative error = 1.6885360304662554328300881356641e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7966 y[1] (analytic) = -0.58998933381838943017152502776684 y[1] (numeric) = -0.58998933381838943018178213637937 absolute error = 1.025710861253e-20 relative error = 1.7385244146951551663364528849142e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7965 y[1] (analytic) = -0.58974009747944600644263745683767 y[1] (numeric) = -0.58974009747944600645318463937121 absolute error = 1.054718253354e-20 relative error = 1.7884458897434216015733571665617e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7964 y[1] (analytic) = -0.58949087767930993968903506349661 y[1] (numeric) = -0.58949087767930993969987167820118 absolute error = 1.083661470457e-20 relative error = 1.8383006616202884653368581111124e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.2MB, time=0.68 NO POLE x[1] = -0.7963 y[1] (analytic) = -0.58924167441437935018007716652794 y[1] (numeric) = -0.58924167441437935019120257338697 absolute error = 1.112540685903e-20 relative error = 1.8880889356794117955597482503991e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7962 y[1] (analytic) = -0.58899248768105516224975898971241 y[1] (numeric) = -0.58899248768105516226117255043761 absolute error = 1.141356072520e-20 relative error = 1.9378109167634321143290347757443e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7961 y[1] (analytic) = -0.58874331747574110085304217696153 y[1] (numeric) = -0.58874331747574110086474325498727 absolute error = 1.170107802574e-20 relative error = 1.9874668091196020358742475244110e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.796 y[1] (analytic) = -0.58849416379484368812811562224478 y[1] (numeric) = -0.58849416379484368814010358272235 absolute error = 1.198796047757e-20 relative error = 2.0370568163780721256593594246621e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7959 y[1] (analytic) = -0.58824502663477223996457351228248 y[1] (numeric) = -0.58824502663477223997684772207491 absolute error = 1.227420979243e-20 relative error = 2.0865811416457199501245069635878e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7958 y[1] (analytic) = -0.58799590599193886257749751532474 y[1] (numeric) = -0.58799590599193886259005734300131 absolute error = 1.255982767657e-20 relative error = 2.1360399874522577235066890627854e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7957 y[1] (analytic) = -0.58774680186275844908743008456725 y[1] (numeric) = -0.58774680186275844910027490039794 absolute error = 1.284481583069e-20 relative error = 2.1854335557387384825038261620824e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7956 y[1] (analytic) = -0.58749771424364867610622587987679 y[1] (numeric) = -0.5874977142436486761193550558269 absolute error = 1.312917595011e-20 relative error = 2.2347620478851823849315218731916e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7955 y[1] (analytic) = -0.58724864313103000032876834650881 y[1] (numeric) = -0.58724864313103000034218125623371 absolute error = 1.341290972490e-20 relative error = 2.2840256647314621660169952426937e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7954 y[1] (analytic) = -0.58699958852132565513053852439698 y[1] (numeric) = -0.5869995885213256551442345432367 absolute error = 1.369601883972e-20 relative error = 2.3332246065488382479481977313990e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=0.86 NO POLE x[1] = -0.7953 y[1] (analytic) = -0.58675055041096164717102319638129 y[1] (numeric) = -0.58675055041096164718500170135486 absolute error = 1.397850497357e-20 relative error = 2.3823590729960829030474669039907e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7952 y[1] (analytic) = -0.58650152879636675300294951841638 y[1] (numeric) = -0.58650152879636675301720988821695 absolute error = 1.426036980057e-20 relative error = 2.4314292632511105281696032335782e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7951 y[1] (analytic) = -0.58625252367397251568733330937175 y[1] (numeric) = -0.58625252367397251570187492436095 absolute error = 1.454161498920e-20 relative error = 2.4804353758802582240113040337860e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.795 y[1] (analytic) = -0.58600353504021324141432821248641 y[1] (numeric) = -0.58600353504021324142915045468923 absolute error = 1.482224220282e-20 relative error = 2.5293776089256620740082670261094e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7949 y[1] (analytic) = -0.58575456289152599612986297489242 y[1] (numeric) = -0.58575456289152599614496522799199 absolute error = 1.510225309957e-20 relative error = 2.5782561598870101651530594482884e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7948 y[1] (analytic) = -0.58550560722435060216805412585748 y[1] (numeric) = -0.58550560722435060218343577518951 absolute error = 1.538164933203e-20 relative error = 2.6270712256622590952989868889431e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7947 y[1] (analytic) = -0.5852566680351296348893813685254 y[1] (numeric) = -0.58525666803512963490504180107338 absolute error = 1.566043254798e-20 relative error = 2.6758230026761511667003829248696e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7946 y[1] (analytic) = -0.58500774532030841932461303395871 y[1] (numeric) = -0.58500774532030841934055163834833 absolute error = 1.593860438962e-20 relative error = 2.7245116867458155928978556478476e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7945 y[1] (analytic) = -0.5847588390763350268244689801958 y[1] (numeric) = -0.58475883907633502684068514668987 absolute error = 1.621616649407e-20 relative error = 2.7731374731649203452194686341743e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7944 y[1] (analytic) = -0.58450994929966027171500835284605 y[1] (numeric) = -0.5845099492996602717315014733394 absolute error = 1.649312049335e-20 relative error = 2.8217005566990758689056370405835e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7943 y[1] (analytic) = -0.58426107598673770795872965744334 y[1] (numeric) = -0.58426107598673770797549912545764 absolute error = 1.676946801430e-20 relative error = 2.8702011315709579215988686649774e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=1.04 NO POLE x[1] = -0.7942 y[1] (analytic) = -0.58401221913402362582137062737167 y[1] (numeric) = -0.58401221913402362583841583805022 absolute error = 1.704521067855e-20 relative error = 2.9186393914539540931972561755868e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7941 y[1] (analytic) = -0.5837633787379770485443954046629 y[1] (numeric) = -0.58376337873797704856171575476562 absolute error = 1.732035010272e-20 relative error = 2.9670155295051938605000509544372e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.794 y[1] (analytic) = -0.58351455479505972902315658434862 y[1] (numeric) = -0.58351455479505972904075147224668 absolute error = 1.759488789806e-20 relative error = 3.0153297383026932269963485187556e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7939 y[1] (analytic) = -0.58326574730173614649071970632108 y[1] (numeric) = -0.58326574730173614650858853199216 absolute error = 1.786882567108e-20 relative error = 3.0635822099520726861945119170484e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7938 y[1] (analytic) = -0.58301695625447350320733781183201 y[1] (numeric) = -0.58301695625447350322547997685518 absolute error = 1.814216502317e-20 relative error = 3.1117731360203118841888837324619e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7937 y[1] (analytic) = -0.58276818164974172115556371482077 y[1] (numeric) = -0.58276818164974172117397862237116 absolute error = 1.841490755039e-20 relative error = 3.1599027074985059559142178553926e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7936 y[1] (analytic) = -0.58251942348401343874098767122519 y[1] (numeric) = -0.58251942348401343875967472606922 absolute error = 1.868705484403e-20 relative error = 3.2079711148967111252822256324564e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7935 y[1] (analytic) = -0.58227068175376400749858816228842 y[1] (numeric) = -0.58227068175376400751754677077869 absolute error = 1.895860849027e-20 relative error = 3.2559785481844663945754151315034e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7934 y[1] (analytic) = -0.58202195645547148880468354062582 y[1] (numeric) = -0.58202195645547148882391311069626 absolute error = 1.922957007044e-20 relative error = 3.3039251968342518537197524443014e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7933 y[1] (analytic) = -0.58177324758561665059447232046971 y[1] (numeric) = -0.58177324758561665061397226163039 absolute error = 1.949994116068e-20 relative error = 3.3518112497619257533331516898746e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=1.24 NO POLE x[1] = -0.7932 y[1] (analytic) = -0.58152455514068296408514992605526 y[1] (numeric) = -0.5815245551406829641049196493876 absolute error = 1.976972333234e-20 relative error = 3.3996368953942607027878618564706e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7931 y[1] (analytic) = -0.58127587911715660050458974455939 y[1] (numeric) = -0.58127587911715660052462866271112 absolute error = 2.003891815173e-20 relative error = 3.4474023216248305108610992697138e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.793 y[1] (analytic) = -0.58102721951152642782557636234575 y[1] (numeric) = -0.58102721951152642784588388952615 absolute error = 2.030752718040e-20 relative error = 3.4951077158610017463571052322389e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7929 y[1] (analytic) = -0.58077857632028400750557889551329 y[1] (numeric) = -0.58077857632028400752615444748801 absolute error = 2.057555197472e-20 relative error = 3.5427532649505183998009148798470e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7928 y[1] (analytic) = -0.58052994953992359123205235788404 y[1] (numeric) = -0.58052994953992359125289535197033 absolute error = 2.084299408629e-20 relative error = 3.5903391552508709409510526202065e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7927 y[1] (analytic) = -0.58028133916694211767325504160815 y[1] (numeric) = -0.58028133916694211769436489667038 absolute error = 2.110985506223e-20 relative error = 3.6378655726781643369139577800957e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7926 y[1] (analytic) = -0.58003274519783920923456991750383 y[1] (numeric) = -0.58003274519783920925594605394799 absolute error = 2.137613644416e-20 relative error = 3.6853327025302626533009138132400e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7925 y[1] (analytic) = -0.57978416762911716882031809408441 y[1] (numeric) = -0.57978416762911716884195993385371 absolute error = 2.164183976930e-20 relative error = 3.7327407296751322293464638381021e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7924 y[1] (analytic) = -0.57953560645728097660105240597137 y[1] (numeric) = -0.57953560645728097662295937254126 absolute error = 2.190696656989e-20 relative error = 3.7800898384497825437044311980357e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7923 y[1] (analytic) = -0.57928706167883828678631923402578 y[1] (numeric) = -0.57928706167883828680849075239918 absolute error = 2.217151837340e-20 relative error = 3.8273802126953216611445249010282e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7922 y[1] (analytic) = -0.57903853329029942440287669107487 y[1] (numeric) = -0.57903853329029942442531218777756 absolute error = 2.243549670269e-20 relative error = 3.8746120357834672053294961034910e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=1.42 NO POLE x[1] = -0.7921 y[1] (analytic) = -0.57879002128817738207835733855195 y[1] (numeric) = -0.57879002128817738210105624162757 absolute error = 2.269890307562e-20 relative error = 3.9217854905481000410353690456756e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.792 y[1] (analytic) = -0.57854152566898781683036363071016 y[1] (numeric) = -0.57854152566898781685332536971551 absolute error = 2.296173900535e-20 relative error = 3.9689007593359072121841193323017e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7919 y[1] (analytic) = -0.57829304642924904686098431431806 y[1] (numeric) = -0.5782930464292490468842083203185 absolute error = 2.322400600044e-20 relative error = 4.0159580240225711549617862491508e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7918 y[1] (analytic) = -0.57804458356548204835672004289248 y[1] (numeric) = -0.57804458356548204838020574845711 absolute error = 2.348570556463e-20 relative error = 4.0629574659736418458141598629566e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7917 y[1] (analytic) = -0.57779613707421045229380649557397 y[1] (numeric) = -0.57779613707421045231755333477083 absolute error = 2.374683919686e-20 relative error = 4.1098992660468453713194005852293e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7916 y[1] (analytic) = -0.57754770695196054124892332170417 y[1] (numeric) = -0.57754770695196054127293073009597 absolute error = 2.400740839180e-20 relative error = 4.1567836046827030940221645461600e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7915 y[1] (analytic) = -0.57729929319526124621527726302375 y[1] (numeric) = -0.57729929319526124623954467766272 absolute error = 2.426741463897e-20 relative error = 4.2036106617511442952393243705333e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7914 y[1] (analytic) = -0.57705089580064414342404783616522 y[1] (numeric) = -0.57705089580064414344857469558877 absolute error = 2.452685942355e-20 relative error = 4.2503806166905913072426398771346e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7913 y[1] (analytic) = -0.5768025147646434511711839887859 y[1] (numeric) = -0.57680251476464345119596973301198 absolute error = 2.478574422608e-20 relative error = 4.2970936484549640548890219227783e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7912 y[1] (analytic) = -0.5765541500837960266495401732515 y[1] (numeric) = -0.57655415008379602667458424377365 absolute error = 2.504407052215e-20 relative error = 4.3437499354588133909873944459867e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=1.61 NO POLE x[1] = -0.7911 y[1] (analytic) = -0.57630580175464136278634031225485 y[1] (numeric) = -0.57630580175464136281164215203818 absolute error = 2.530183978333e-20 relative error = 4.3903496557374763484043618273361e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.791 y[1] (analytic) = -0.57605746977372158508595816113769 y[1] (numeric) = -0.57605746977372158511151721461384 absolute error = 2.555905347615e-20 relative error = 4.4368929867691380031741439894306e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7909 y[1] (analytic) = -0.57580915413758144847800260196147 y[1] (numeric) = -0.57580915413758144850381831502426 absolute error = 2.581571306279e-20 relative error = 4.4833801055934065108575868123966e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7908 y[1] (analytic) = -0.57556085484276833417069643456954 y[1] (numeric) = -0.57556085484276833419676825457035 absolute error = 2.607182000081e-20 relative error = 4.5298111887634014983550044907382e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7907 y[1] (analytic) = -0.57531257188583224650953725997567 y[1] (numeric) = -0.57531257188583224653586463571897 absolute error = 2.632737574330e-20 relative error = 4.5761864123707224014112900460471e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7906 y[1] (analytic) = -0.57506430526332580984122908141885 y[1] (numeric) = -0.57506430526332580986781146315765 absolute error = 2.658238173880e-20 relative error = 4.6225059520304861848200969400094e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7905 y[1] (analytic) = -0.57481605497180426538287327833314 y[1] (numeric) = -0.57481605497180426540971011776436 absolute error = 2.683683943122e-20 relative error = 4.6687699828663265145322118981242e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7904 y[1] (analytic) = -0.57456782100782546809640763829779 y[1] (numeric) = -0.57456782100782546812349838855814 absolute error = 2.709075026035e-20 relative error = 4.7149786795980401498460585122469e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7903 y[1] (analytic) = -0.57431960336794988356828216175978 y[1] (numeric) = -0.57431960336794988359562627742091 absolute error = 2.734411566113e-20 relative error = 4.7611322164135531959500882883294e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7902 y[1] (analytic) = -0.57407140204874058489436038394829 y[1] (numeric) = -0.57407140204874058492195732101262 absolute error = 2.759693706433e-20 relative error = 4.8072307670861694669299261963230e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7901 y[1] (analytic) = -0.57382321704676324957003498794628 y[1] (numeric) = -0.57382321704676324959788420384239 absolute error = 2.784921589611e-20 relative error = 4.8532745048969413050005893026056e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=1.80 NO POLE x[1] = -0.79 y[1] (analytic) = -0.57357504835858615638554651232857 y[1] (numeric) = -0.57357504835858615641364746590684 absolute error = 2.810095357827e-20 relative error = 4.8992636026771371958223679020203e-18 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = arccos ( x ) ; Iterations = 100 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Expected Time Remaining = 4 Minutes 39 Seconds Optimized Time Remaining = 4 Minutes 37 Seconds Time to Timeout = 14 Minutes 58 Seconds Percent Done = 0.6312 % > quit memory used=38.5MB, alloc=4.3MB, time=1.82