|\^/| 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 > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > > > > > > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 3 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 2 > ; > if (glob_iter = 1) then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if ( not found ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > array_tmp3[1] := sinh(array_tmp2[1]); > array_tmp3_g[1] := cosh(array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sinh LINEAR $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / 1; > array_tmp3_g[2] := array_tmp3[1] * array_tmp2[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sinh LINEAR $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / 2; > array_tmp3_g[3] := array_tmp3[2] * array_tmp2[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sinh LINEAR $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / 3; > array_tmp3_g[4] := array_tmp3[3] * array_tmp2[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sinh LINEAR $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / 4; > array_tmp3_g[5] := array_tmp3[4] * array_tmp2[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sinh LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / (kkk - 1); > array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_tmp2[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sinh(array_tmp2[1]); array_tmp3_g[1] := cosh(array_tmp2[1]); array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]; array_tmp3_g[2] := array_tmp3[1]*array_tmp2[2]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 1/2*array_tmp3_g[2]*array_tmp2[2]; array_tmp3_g[3] := 1/2*array_tmp3[2]*array_tmp2[2]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 1/3*array_tmp3_g[3]*array_tmp2[2]; array_tmp3_g[4] := 1/3*array_tmp3[3]*array_tmp2[2]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 1/4*array_tmp3_g[4]*array_tmp2[2]; array_tmp3_g[5] := 1/4*array_tmp3[4]*array_tmp2[2]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_tmp2[2]/(kkk - 1); array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_tmp2[2]/(kkk - 1); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs >= 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > 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_minute, years_in_century; secs := secs_in; if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); 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_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs >= 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > > > > > > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats; > > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > > > > > > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > 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_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > > > > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # Begin Function number 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 (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 < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 17 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 18 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > > > > if (nnn <= glob_max_terms) then # if number 13 > if (array_fact_1[nnn] = 0) then # if number 14 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 18 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # Begin Function number 19 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > > > > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13 > if (array_fact_2[mmm,nnn] = 0) then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 19 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # Begin Function number 20 > convfp := proc(mmm) > (mmm); > > # End Function number 20 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 21 > convfloat := proc(mmm) > (mmm); > > # End Function number 21 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(cosh(2.0*x+3.0)/2.0); > end; exact_soln_y := proc(x) return cosh(2.0*x + 3.0)/2.0 end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_dump_analytic, > glob_optimal_done, > glob_not_yet_finished, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_max_trunc_err, > glob_not_yet_start_msg, > glob_optimal_start, > glob_disp_incr, > glob_display_flag, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_initial_pass, > glob_dump, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_hmin, > years_in_century, > glob_subiter_method, > glob_current_iter, > glob_warned2, > glob_almost_1, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_h, > glob_normmax, > glob_max_hours, > glob_last_good_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_smallish_float, > glob_no_eqs, > glob_abserr, > days_in_year, > glob_good_digits, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_clock_sec, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_orig_start_sec, > centuries_in_millinium, > min_in_hour, > sec_in_minute, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp3_g, > array_pole, > array_y, > array_x, > array_last_rel_error, > array_y_init, > array_m1, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_fact_1, > array_poles, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > INFO := 2; > glob_iolevel := 5; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_max_sec := 10000.0; > glob_dump_analytic := false; > glob_optimal_done := false; > glob_not_yet_finished := true; > djd_debug := true; > glob_percent_done := 0.0; > glob_log10abserr := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_not_yet_start_msg := true; > glob_optimal_start := 0.0; > glob_disp_incr := 0.1; > glob_display_flag := true; > glob_iter := 0; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_reached_optimal_h := false; > glob_initial_pass := true; > glob_dump := false; > glob_log10normmin := 0.1; > glob_curr_iter_when_opt := 0; > glob_start := 0; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > years_in_century := 100; > glob_subiter_method := 3; > glob_current_iter := 0; > glob_warned2 := false; > glob_almost_1 := 0.9990; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_hmax := 1.0; > glob_h := 0.1; > glob_normmax := 0.0; > glob_max_hours := 0.0; > glob_last_good_h := 0.1; > glob_clock_start_sec := 0.0; > hours_in_day := 24; > djd_debug2 := true; > glob_smallish_float := 0.1e-100; > glob_no_eqs := 0; > glob_abserr := 0.1e-10; > days_in_year := 365; > glob_good_digits := 0; > MAX_UNCHANGED := 10; > glob_optimal_clock_start_sec := 0.0; > glob_log10_relerr := 0.1e-10; > glob_clock_sec := 0.0; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_orig_start_sec := 0.0; > centuries_in_millinium := 10; > min_in_hour := 60; > sec_in_minute := 60; > glob_html_log := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/lin_sinhpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 1;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(cosh(2.0*x+3.0)/2.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp3_g:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3_g[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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[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_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[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_tmp3_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 1; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-08-21T17:54:51-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"lin_sinh") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_good_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," 123 ") > ; > logitem_str(html_log_file,"lin_sinh diffeq.mxt") > ; > logitem_str(html_log_file,"lin_sinh maple results") > ; > logitem_str(html_log_file,"c c++ Maple and Maxima") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if (glob_html_log) then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > > # End Function number 8 > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global glob_max_terms, INFO, glob_iolevel, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_max_sec, glob_dump_analytic, glob_optimal_done, glob_not_yet_finished, djd_debug, glob_percent_done, glob_log10abserr, glob_max_trunc_err, glob_not_yet_start_msg, glob_optimal_start, glob_disp_incr, glob_display_flag, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_log10_abserr, glob_look_poles, glob_reached_optimal_h, glob_initial_pass, glob_dump, glob_log10normmin, glob_curr_iter_when_opt, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_hmin, years_in_century, glob_subiter_method, glob_current_iter, glob_warned2, glob_almost_1, glob_large_float, glob_hmin_init, glob_hmax, glob_h, glob_normmax, glob_max_hours, glob_last_good_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_smallish_float, glob_no_eqs, glob_abserr, days_in_year, glob_good_digits, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_log10_relerr, glob_clock_sec, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_orig_start_sec, centuries_in_millinium, min_in_hour, sec_in_minute, glob_html_log, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp3_g, array_pole, array_y, array_x, array_last_rel_error, array_y_init, array_m1, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_fact_1, array_poles, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; INFO := 2; glob_iolevel := 5; DEBUGL := 3; DEBUGMASSIVE := 4; ALWAYS := 1; glob_max_sec := 10000.0; glob_dump_analytic := false; glob_optimal_done := false; glob_not_yet_finished := true; djd_debug := true; glob_percent_done := 0.; glob_log10abserr := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_not_yet_start_msg := true; glob_optimal_start := 0.; glob_disp_incr := 0.1; glob_display_flag := true; glob_iter := 0; glob_warned := false; glob_unchanged_h_cnt := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_reached_optimal_h := false; glob_initial_pass := true; glob_dump := false; glob_log10normmin := 0.1; glob_curr_iter_when_opt := 0; glob_start := 0; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); years_in_century := 100; glob_subiter_method := 3; glob_current_iter := 0; glob_warned2 := false; glob_almost_1 := 0.9990; glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_hmax := 1.0; glob_h := 0.1; glob_normmax := 0.; glob_max_hours := 0.; glob_last_good_h := 0.1; glob_clock_start_sec := 0.; hours_in_day := 24; djd_debug2 := true; glob_smallish_float := 0.1*10^(-100); glob_no_eqs := 0; glob_abserr := 0.1*10^(-10); days_in_year := 365; glob_good_digits := 0; MAX_UNCHANGED := 10; glob_optimal_clock_start_sec := 0.; glob_log10_relerr := 0.1*10^(-10); glob_clock_sec := 0.; glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_orig_start_sec := 0.; centuries_in_millinium := 10; min_in_hour := 60; sec_in_minute := 60; glob_html_log := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/lin_sinhpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 1;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(cosh(2.0*x+3.0)/2.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp3_g := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_tmp3_g[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp3_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*expt(glob_h, term_no - 1) /factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-08-21T17:54:51-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "lin_sinh"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_good_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, " 123 "); logitem_str(html_log_file, "lin_sinh diffeq.mxt"); logitem_str(html_log_file, "\ lin_sinh maple results"); logitem_str(html_log_file, "c c++ Maple and Maxima"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/lin_sinhpostode.ode################# diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(cosh(2.0*x+3.0)/2.0); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 5.033830997888882920976968017558 y[1] (numeric) = 5.033830997888882920976968017558 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 1e-05 y[1] (analytic) = 5.0339311776449298981905782945155 y[1] (numeric) = 5.0339311776449298981905782945312 absolute error = 1.57e-29 relative error = 3.1188348521175203497126834656077e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 2e-05 y[1] (analytic) = 5.034031359414549346529279613119 y[1] (numeric) = 5.0340313594145493465292796131501 absolute error = 3.11e-29 relative error = 6.1779511845585494243146736870795e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 3e-05 y[1] (analytic) = 5.03413154319778133870092108846 y[1] (numeric) = 5.0341315431977813387009210885072 absolute error = 4.72e-29 relative error = 9.3759965537208853284726057686488e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 4e-05 y[1] (analytic) = 5.034231728994665948218796853192 y[1] (numeric) = 5.0342317289946659482187968532548 absolute error = 6.28e-29 relative error = 1.2474594611587562884236814561842e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 5e-05 y[1] (analytic) = 5.0343319168052432494016620869325 y[1] (numeric) = 5.0343319168052432494016620870108 absolute error = 7.83e-29 relative error = 1.5553205726985261827895307910365e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 6e-05 y[1] (analytic) = 5.034432106629553317373749045992 y[1] (numeric) = 5.0344321066295533173737490460858 absolute error = 9.38e-29 relative error = 1.8631694303013877022030105544696e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 7e-05 y[1] (analytic) = 5.034532298467636228064783093423 y[1] (numeric) = 5.0345322984676362280647830935329 absolute error = 1.099e-28 relative error = 2.1829237252773277933906276084336e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 8e-05 y[1] (analytic) = 5.0346324923195320582099987293945 y[1] (numeric) = 5.0346324923195320582099987295197 absolute error = 1.252e-28 relative error = 2.4867753543281656381773540505665e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 9e-05 y[1] (analytic) = 5.0347326881852808853501556218815 y[1] (numeric) = 5.0347326881852808853501556220223 absolute error = 1.408e-28 relative error = 2.7965734969486523782925757896426e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0001 y[1] (analytic) = 5.034832886064922787831554637685 y[1] (numeric) = 5.0348328860649227878315546378417 absolute error = 1.567e-28 relative error = 3.1123177977506242204107715137285e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00011 y[1] (analytic) = 5.03493308595849784480605387377 y[1] (numeric) = 5.0349330859584978448060538739421 absolute error = 1.721e-28 relative error = 3.4181189116486024540471127378333e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00012 y[1] (analytic) = 5.035033287866046136231084688924 y[1] (numeric) = 5.035033287866046136231084689112 absolute error = 1.880e-28 relative error = 3.7338382737818678078740317217963e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00013 y[1] (analytic) = 5.035133491787607742869667735743 y[1] (numeric) = 5.0351334917876077428696677359467 absolute error = 2.037e-28 relative error = 4.0455729789932744004384509423248e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00014 y[1] (analytic) = 5.0352336977232227462904289929345 y[1] (numeric) = 5.035233697723222746290428993154 absolute error = 2.195e-28 relative error = 4.3592812802164698852644708742743e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00015 y[1] (analytic) = 5.0353339056729312288676157979465 y[1] (numeric) = 5.0353339056729312288676157981814 absolute error = 2.349e-28 relative error = 4.6650332311697516820467290529836e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00016 y[1] (analytic) = 5.035434115636773273781112879915 y[1] (numeric) = 5.0354341156367732737811128801657 absolute error = 2.507e-28 relative error = 4.9787167152379048172709952385353e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00017 y[1] (analytic) = 5.035534327614788965016458392939 y[1] (numeric) = 5.0355343276147889650164583932051 absolute error = 2.661e-28 relative error = 5.2844441659490214494031666645436e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=2.9MB, time=0.38 x[1] = 0.00018 y[1] (analytic) = 5.0356345416070183873648599496715 y[1] (numeric) = 5.0356345416070183873648599499536 absolute error = 2.821e-28 relative error = 5.6020745284262354800336072005528e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00019 y[1] (analytic) = 5.0357347576135016264232106552395 y[1] (numeric) = 5.035734757613501626423210655537 absolute error = 2.975e-28 relative error = 5.9077774013059617857375770389370e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 5.0358349756342787685941051414785 y[1] (numeric) = 5.0358349756342787685941051417921 absolute error = 3.136e-28 relative error = 6.2273684804474976642061265045226e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00021 y[1] (analytic) = 5.0359351956693899010858556014985 y[1] (numeric) = 5.0359351956693899010858556018275 absolute error = 3.290e-28 relative error = 6.5330467374346036418046835126078e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00022 y[1] (analytic) = 5.0360354177188751119125078245625 y[1] (numeric) = 5.0360354177188751119125078249071 absolute error = 3.446e-28 relative error = 6.8426842032832678602233887697127e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00023 y[1] (analytic) = 5.036135641782774489893857231295 y[1] (numeric) = 5.0361356417827744898938572316555 absolute error = 3.605e-28 relative error = 7.1582662907066628302848959080777e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00024 y[1] (analytic) = 5.03623586786112812465546490921 y[1] (numeric) = 5.0362358678611281246554649095861 absolute error = 3.761e-28 relative error = 7.4678789847809166112437068878864e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00025 y[1] (analytic) = 5.0363360959539761066286736485595 y[1] (numeric) = 5.0363360959539761066286736489513 absolute error = 3.918e-28 relative error = 7.7794649232158872313894242406682e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00026 y[1] (analytic) = 5.0364363260613585270506239785075 y[1] (numeric) = 5.0364363260613585270506239789149 absolute error = 4.074e-28 relative error = 8.0890529260120477550588933473639e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00027 y[1] (analytic) = 5.036536558183315477964270203624 y[1] (numeric) = 5.0365365581833154779642702040471 absolute error = 4.231e-28 relative error = 8.4006140948694444901923856276174e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00028 y[1] (analytic) = 5.036636792319887052218396440703 y[1] (numeric) = 5.0366367923198870522183964411417 absolute error = 4.387e-28 relative error = 8.7101774078478611535950266487482e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00029 y[1] (analytic) = 5.036737028471113343467632655901 y[1] (numeric) = 5.0367370284711133434676326563555 absolute error = 4.545e-28 relative error = 9.0236992209609587919043548283321e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 5.0368372666370344461724707022 y[1] (numeric) = 5.0368372666370344461724707026702 absolute error = 4.702e-28 relative error = 9.3352231789283186407227847023581e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00031 y[1] (analytic) = 5.0369375068176904555992803571905 y[1] (numeric) = 5.0369375068176904555992803576766 absolute error = 4.861e-28 relative error = 9.6507054006932740181693811296962e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00032 y[1] (analytic) = 5.0370377490131214678203253611795 y[1] (numeric) = 5.0370377490131214678203253616812 absolute error = 5.017e-28 relative error = 9.9602191803763087709472921046221e-27 % Correct digits = 28 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00033 y[1] (analytic) = 5.0371379932233675797137794556175 y[1] (numeric) = 5.037137993223367579713779456135 absolute error = 5.175e-28 relative error = 1.0273691145571359866076005494477e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00034 y[1] (analytic) = 5.037238239448468888963742421852 y[1] (numeric) = 5.0372382394484688889637424223848 absolute error = 5.328e-28 relative error = 1.0577224555857748830830008611336e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00035 y[1] (analytic) = 5.0373384876884654940602561201985 y[1] (numeric) = 5.037338487688465494060256120747 absolute error = 5.485e-28 relative error = 1.0888686582022717071512222276567e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00036 y[1] (analytic) = 5.037438737943397494299320529339 y[1] (numeric) = 5.0374387379433974942993205299034 absolute error = 5.644e-28 relative error = 1.1204106478730576772888859152253e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00037 y[1] (analytic) = 5.0375389902133049897829097860395 y[1] (numeric) = 5.0375389902133049897829097866196 absolute error = 5.801e-28 relative error = 1.1515543624118664555470312365248e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00038 y[1] (analytic) = 5.0376392444982280814189882251905 y[1] (numeric) = 5.0376392444982280814189882257861 absolute error = 5.956e-28 relative error = 1.1822998255591136224382006109125e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00039 y[1] (analytic) = 5.0377395007982068709215264201695 y[1] (numeric) = 5.037739500798206870921526420781 absolute error = 6.115e-28 relative error = 1.2138380714268981377859882097916e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 5.037839759113281460810517223529 y[1] (numeric) = 5.0378397591132814608105172241561 absolute error = 6.271e-28 relative error = 1.2447795681980502532548772992119e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00041 y[1] (analytic) = 5.037940019443491954411991808002 y[1] (numeric) = 5.0379400194434919544119918086445 absolute error = 6.425e-28 relative error = 1.2753228452905891134699145316360e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00042 y[1] (analytic) = 5.038040281788878455858035707833 y[1] (numeric) = 5.0380402817888784558580357084911 absolute error = 6.581e-28 relative error = 1.3062618859536502662715964962734e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00043 y[1] (analytic) = 5.0381405461494810700868048604315 y[1] (numeric) = 5.0381405461494810700868048611057 absolute error = 6.742e-28 relative error = 1.3381921243052129830911474092348e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00044 y[1] (analytic) = 5.038240812525339902842541648348 y[1] (numeric) = 5.0382408125253399028425416490379 absolute error = 6.899e-28 relative error = 1.3693271633322313298460479452001e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00045 y[1] (analytic) = 5.0383410809164950606755909415695 y[1] (numeric) = 5.038341080916495060675590942275 absolute error = 7.055e-28 relative error = 1.4002624845550683419106570125839e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00046 y[1] (analytic) = 5.038441351322986650942416140141 y[1] (numeric) = 5.0384413513229866509424161408622 absolute error = 7.212e-28 relative error = 1.4313950480154509408451245771402e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00047 y[1] (analytic) = 5.038541623744854781805615217108 y[1] (numeric) = 5.0385416237448547818056152178449 absolute error = 7.369e-28 relative error = 1.4625263717724437737503787830764e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00048 y[1] (analytic) = 5.0386418981821395622339367617815 y[1] (numeric) = 5.038641898182139562233936762534 absolute error = 7.525e-28 relative error = 1.4934579896846605024487613808989e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE memory used=7.6MB, alloc=4.1MB, time=0.82 x[1] = 0.00049 y[1] (analytic) = 5.038742174634881102002296023325 y[1] (numeric) = 5.0387421746348811020022960240933 absolute error = 7.683e-28 relative error = 1.5247853003228385918628537345786e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 5.0388424531031195116917909546655 y[1] (numeric) = 5.0388424531031195116917909554495 absolute error = 7.840e-28 relative error = 1.5559129051895274688362835564597e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00051 y[1] (analytic) = 5.0389427335868949026897182567255 y[1] (numeric) = 5.0389427335868949026897182575247 absolute error = 7.992e-28 relative error = 1.5860469988534710146201958126879e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00052 y[1] (analytic) = 5.039043016086247387189589422976 y[1] (numeric) = 5.0390430160862473871895894237912 absolute error = 8.152e-28 relative error = 1.6177674955296455799158675572039e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00053 y[1] (analytic) = 5.039143300601217078191146784318 y[1] (numeric) = 5.0391433006012170781911467851489 absolute error = 8.309e-28 relative error = 1.6488913897345722111949547084259e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00054 y[1] (analytic) = 5.039243587131844089500379554279 y[1] (numeric) = 5.0392435871318440895003795551253 absolute error = 8.463e-28 relative error = 1.6794187170493249998872769688639e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00055 y[1] (analytic) = 5.039343875678168535729539874536 y[1] (numeric) = 5.0393438756781685357295398753979 absolute error = 8.619e-28 relative error = 1.7103417057126509489967457125662e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00056 y[1] (analytic) = 5.039444166240230532297158860761 y[1] (numeric) = 5.0394441662402305322971588616389 absolute error = 8.779e-28 relative error = 1.7420572012309312826815024960449e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00057 y[1] (analytic) = 5.0395444588180701954280626487895 y[1] (numeric) = 5.0395444588180701954280626496828 absolute error = 8.933e-28 relative error = 1.7725808499157612625822323475844e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00058 y[1] (analytic) = 5.0396447534117276421533884411075 y[1] (numeric) = 5.0396447534117276421533884420164 absolute error = 9.089e-28 relative error = 1.8035001363631729661386067671028e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00059 y[1] (analytic) = 5.0397450500212429903106005536665 y[1] (numeric) = 5.0397450500212429903106005545911 absolute error = 9.246e-28 relative error = 1.8346166141799231008801346209442e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 5.0398453486466563585435064630175 y[1] (numeric) = 5.0398453486466563585435064639579 absolute error = 9.404e-28 relative error = 1.8659302715559009897816342499422e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00061 y[1] (analytic) = 5.039945649288007866302272853769 y[1] (numeric) = 5.039945649288007866302272854725 absolute error = 9.560e-28 relative error = 1.8968458521671834547620957904241e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00062 y[1] (analytic) = 5.040045951945337633843441666366 y[1] (numeric) = 5.0400459519453376338434416673377 absolute error = 9.717e-28 relative error = 1.9279586124109581887411922403437e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00063 y[1] (analytic) = 5.0401462566186857822299461451935 y[1] (numeric) = 5.0401462566186857822299461461813 absolute error = 9.878e-28 relative error = 1.9598637613002356008963878137626e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00064 y[1] (analytic) = 5.040246563308092433331126887003 y[1] (numeric) = 5.040246563308092433331126888006 absolute error = 1.0030e-27 relative error = 1.9899820125896689390701293191629e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00065 y[1] (analytic) = 5.040346872013597709822747889656 y[1] (numeric) = 5.0403468720135977098227478906748 absolute error = 1.0188e-27 relative error = 2.0212894585824281127916818804165e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00066 y[1] (analytic) = 5.040447182735241735187012601199 y[1] (numeric) = 5.0404471827352417351870126022338 absolute error = 1.0348e-27 relative error = 2.0529924478614552954378148091545e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00067 y[1] (analytic) = 5.0405474954730646337125799692545 y[1] (numeric) = 5.040547495473064633712579970305 absolute error = 1.0505e-27 relative error = 2.0840990010379986449176797906364e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00068 y[1] (analytic) = 5.040647810227106530494580490736 y[1] (numeric) = 5.0406478102271065304945804918017 absolute error = 1.0657e-27 relative error = 2.1142123792854015249702201241352e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00069 y[1] (analytic) = 5.0407481269974075514346322618855 y[1] (numeric) = 5.0407481269974075514346322629669 absolute error = 1.0814e-27 relative error = 2.1453164743705436926339489150019e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 5.040848445784007823240857028636 y[1] (numeric) = 5.0408484457840078232408570297334 absolute error = 1.0974e-27 relative error = 2.1770144685024752069064681246811e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00071 y[1] (analytic) = 5.0409487665869474734278962372945 y[1] (numeric) = 5.0409487665869474734278962384076 absolute error = 1.1131e-27 relative error = 2.2081160740573080939137911479214e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00072 y[1] (analytic) = 5.0410490894062666303169270855465 y[1] (numeric) = 5.0410490894062666303169270866751 absolute error = 1.1286e-27 relative error = 2.2388196980103722741990870045981e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00073 y[1] (analytic) = 5.0411494142420054230356785737845 y[1] (numeric) = 5.041149414242005423035678574929 absolute error = 1.1445e-27 relative error = 2.2703155688395494401702924009118e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00074 y[1] (analytic) = 5.041249741094203981518447556761 y[1] (numeric) = 5.0412497410942039815184475579213 absolute error = 1.1603e-27 relative error = 2.3016118216515032601497338460685e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00075 y[1] (analytic) = 5.0413500699629024365061147955605 y[1] (numeric) = 5.0413500699629024365061147967364 absolute error = 1.1759e-27 relative error = 2.3325101087626970609997637474507e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00076 y[1] (analytic) = 5.0414504008481409195461610098965 y[1] (numeric) = 5.0414504008481409195461610110877 absolute error = 1.1912e-27 relative error = 2.3628120982794955940160463437750e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00077 y[1] (analytic) = 5.0415507337499595629926829307295 y[1] (numeric) = 5.0415507337499595629926829319363 absolute error = 1.2068e-27 relative error = 2.3937079357770723126733850740658e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00078 y[1] (analytic) = 5.04165106866839850000640935321 y[1] (numeric) = 5.0416510686683985000064093544329 absolute error = 1.2229e-27 relative error = 2.4255942812063598410094382202725e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00079 y[1] (analytic) = 5.0417514056034978645547171899435 y[1] (numeric) = 5.0417514056034978645547171911819 absolute error = 1.2384e-27 relative error = 2.4562892938823179950923040260059e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0008 y[1] (analytic) = 5.0418517445552977914116475245745 y[1] (numeric) = 5.0418517445552977914116475258284 absolute error = 1.2539e-27 relative error = 2.4869830838522537457338442703912e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=1.28 NO POLE x[1] = 0.00081 y[1] (analytic) = 5.041952085523838416157921665698 y[1] (numeric) = 5.0419520855238384161579216669678 absolute error = 1.2698e-27 relative error = 2.5184689946692996370848297769242e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00082 y[1] (analytic) = 5.042052428509159875180957201093 y[1] (numeric) = 5.0420524285091598751809572023783 absolute error = 1.2853e-27 relative error = 2.5491603235471294960216734723549e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00083 y[1] (analytic) = 5.0421527735113023056748840522745 y[1] (numeric) = 5.0421527735113023056748840535755 absolute error = 1.3010e-27 relative error = 2.5802470857978332255940685870637e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00084 y[1] (analytic) = 5.0422531205303058456405605293735 y[1] (numeric) = 5.0422531205303058456405605306904 absolute error = 1.3169e-27 relative error = 2.6117292577757351275873761146540e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00085 y[1] (analytic) = 5.042353469566210633885589386337 y[1] (numeric) = 5.0423534695662106338855893876695 absolute error = 1.3325e-27 relative error = 2.6426152153800392694731105219854e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00086 y[1] (analytic) = 5.04245382061905681002433387645 y[1] (numeric) = 5.0424538206190568100243338777979 absolute error = 1.3479e-27 relative error = 2.6731033103135483334682889972825e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00087 y[1] (analytic) = 5.0425541736888845144779338081815 y[1] (numeric) = 5.0425541736888845144779338095452 absolute error = 1.3637e-27 relative error = 2.7043834394790134319757431275693e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00088 y[1] (analytic) = 5.0426545287757338884743216013545 y[1] (numeric) = 5.0426545287757338884743216027338 absolute error = 1.3793e-27 relative error = 2.7352657060464328715239204882171e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00089 y[1] (analytic) = 5.042754885879645074048238343635 y[1] (numeric) = 5.04275488587964507404823834503 absolute error = 1.3950e-27 relative error = 2.7663450466453909759289515219511e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 5.0428552450006582140412498473475 y[1] (numeric) = 5.0428552450006582140412498487581 absolute error = 1.4106e-27 relative error = 2.7972248487569186268260641329504e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00091 y[1] (analytic) = 5.0429556061388134521017627066105 y[1] (numeric) = 5.042955606138813452101762708037 absolute error = 1.4265e-27 relative error = 2.8286983099028571187957355622371e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00092 y[1] (analytic) = 5.043055969294150932685040354797 y[1] (numeric) = 5.0430559692941509326850403562393 absolute error = 1.4423e-27 relative error = 2.8599722247418778355102699015292e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00093 y[1] (analytic) = 5.043156334466710801053219122316 y[1] (numeric) = 5.0431563344667108010532191237738 absolute error = 1.4578e-27 relative error = 2.8906500281121172972575320051485e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00094 y[1] (analytic) = 5.0432567016565332032753242947165 y[1] (numeric) = 5.04325670165653320327532429619 absolute error = 1.4735e-27 relative error = 2.9217231784295391000327930385441e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00095 y[1] (analytic) = 5.043357070863658286227286171117 y[1] (numeric) = 5.043357070863658286227286172606 absolute error = 1.4890e-27 relative error = 2.9523985295473311679894979655263e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00096 y[1] (analytic) = 5.043457442088126197591956122954 y[1] (numeric) = 5.0434574420881261975919561244587 absolute error = 1.5047e-27 relative error = 2.9834692119004259464756568973994e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00097 y[1] (analytic) = 5.0435578153299770858591226530565 y[1] (numeric) = 5.0435578153299770858591226545769 absolute error = 1.5204e-27 relative error = 3.0145386563800639844470646533251e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00098 y[1] (analytic) = 5.043658190589251100325527455041 y[1] (numeric) = 5.0436581905892511003255274565774 absolute error = 1.5364e-27 relative error = 3.0462016693889048644073815009805e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.00099 y[1] (analytic) = 5.0437585678659883910948814730315 y[1] (numeric) = 5.0437585678659883910948814745835 absolute error = 1.5520e-27 relative error = 3.0770703615511286998354441307004e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 5.043858947160229109077880961699 y[1] (numeric) = 5.0438589471602291090778809632667 absolute error = 1.5677e-27 relative error = 3.1081360847385302831406740699627e-26 % Correct digits = 27 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ; Iterations = 100 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Expected Time Remaining = 4 Hours 1 Minutes 23 Seconds Optimized Time Remaining = 3 Hours 55 Minutes 47 Seconds Time to Timeout = 58 Seconds Percent Done = 0.0101 % > quit memory used=13.8MB, alloc=4.1MB, time=1.56