|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > 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 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > 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 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > 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 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, 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 > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > 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)); > glob_total_exp_sec := glob_optimal_expect_sec + total_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 2 > 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)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > 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; 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, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, 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)); glob_total_exp_sec := glob_optimal_expect_sec + total_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)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_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 > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #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]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > 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)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #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 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := 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) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > 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) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > 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_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) 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)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := 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) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, 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 > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sqrt 1 $eq_no = 1 > array_tmp1[1] := sqrt(array_x[1]); > #emit pre erf $eq_no = 1 > array_tmp2[1] := erf(array_tmp1[1]); > array_tmp2_a1[1] := -(array_tmp1[1] * array_tmp1[1]); > array_tmp2_a2[1] := exp(array_tmp2_a1[1]); > array_tmp2_c1[1] := 2.0 / sqrt(evalf(Pi)); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[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_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sqrt 2 $eq_no = 1 > array_tmp1[2] := array_x[2] / array_tmp1[1]/2.0; > #emit pre erf $eq_no = 1 > array_tmp2_a1[2] := -ats(2,array_tmp1,array_tmp1,1); > array_tmp2_a2[2] := att(1,array_tmp2_a2,array_tmp1,1); > array_tmp2[2] := array_tmp2_c1[1] * att(1,array_tmp2_a2,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[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_tmp3[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 sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := 0.0; > array_tmp1[3] := -ats(3,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre erf $eq_no = 1 > array_tmp2_a1[3] := -ats(3,array_tmp1,array_tmp1,1); > array_tmp2_a2[3] := att(2,array_tmp2_a2,array_tmp1,1); > array_tmp2[3] := array_tmp2_c1[1] * att(2,array_tmp2_a2,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[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_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := 0.0; > array_tmp1[4] := -ats(4,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre erf $eq_no = 1 > array_tmp2_a1[4] := -ats(4,array_tmp1,array_tmp1,1); > array_tmp2_a2[4] := att(3,array_tmp2_a2,array_tmp1,1); > array_tmp2[4] := array_tmp2_c1[1] * att(3,array_tmp2_a2,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[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_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := 0.0; > array_tmp1[5] := -ats(5,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre erf $eq_no = 1 > array_tmp2_a1[5] := -ats(5,array_tmp1,array_tmp1,1); > array_tmp2_a2[5] := att(4,array_tmp2_a2,array_tmp1,1); > array_tmp2[5] := array_tmp2_c1[1] * att(4,array_tmp2_a2,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[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_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > 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 sqrt LINEAR $eq_no = 1 > array_tmp1[kkk] := 0.0; > array_tmp1[kkk] := -ats(kkk,array_tmp1,array_tmp1,2) /array_tmp1[1] / 2.0; > #emit erf $eq_no = 1 > array_tmp2_a1[kkk] := -ats(kkk,array_tmp1,array_tmp1,1); > array_tmp2_a2[kkk] := att(kkk-1,array_tmp2_a2,array_tmp2_a1,1); > array_tmp2[kkk] := array_tmp2_c1[1] * att(kkk-1,array_tmp2_a2,array_tmp1,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[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 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > 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; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sqrt(array_x[1]); array_tmp2[1] := erf(array_tmp1[1]); array_tmp2_a1[1] := -array_tmp1[1]*array_tmp1[1]; array_tmp2_a2[1] := exp(array_tmp2_a1[1]); array_tmp2_c1[1] := 2.0/sqrt(evalf(Pi)); array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_x[2]/(array_tmp1[1]*2.0); array_tmp2_a1[2] := -ats(2, array_tmp1, array_tmp1, 1); array_tmp2_a2[2] := att(1, array_tmp2_a2, array_tmp1, 1); array_tmp2[2] := array_tmp2_c1[1]*att(1, array_tmp2_a2, array_tmp1, 1); array_tmp3[2] := array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 0.; array_tmp1[3] := -ats(3, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[3] := -ats(3, array_tmp1, array_tmp1, 1); array_tmp2_a2[3] := att(2, array_tmp2_a2, array_tmp1, 1); array_tmp2[3] := array_tmp2_c1[1]*att(2, array_tmp2_a2, array_tmp1, 1); array_tmp3[3] := array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 0.; array_tmp1[4] := -ats(4, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[4] := -ats(4, array_tmp1, array_tmp1, 1); array_tmp2_a2[4] := att(3, array_tmp2_a2, array_tmp1, 1); array_tmp2[4] := array_tmp2_c1[1]*att(3, array_tmp2_a2, array_tmp1, 1); array_tmp3[4] := array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 0.; array_tmp1[5] := -ats(5, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[5] := -ats(5, array_tmp1, array_tmp1, 1); array_tmp2_a2[5] := att(4, array_tmp2_a2, array_tmp1, 1); array_tmp2[5] := array_tmp2_c1[1]*att(4, array_tmp2_a2, array_tmp1, 1); array_tmp3[5] := array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := 0.; array_tmp1[kkk] := -ats(kkk, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0); array_tmp2_a1[kkk] := -ats(kkk, array_tmp1, array_tmp1, 1); array_tmp2_a2[kkk] := att(kkk - 1, array_tmp2_a2, array_tmp2_a1, 1) ; array_tmp2[kkk] := array_tmp2_c1[1]*att(kkk - 1, array_tmp2_a2, array_tmp1, 1); array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp3[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 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > 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 > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_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, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > 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 if 0; > 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 > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > 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 2 > 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 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 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 > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > 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 5 > 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 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > 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 + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_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 + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_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 6 > 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 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_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 + arr_aa[iii_att]*arr_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 > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > 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") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > 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 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > 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 > # End Function number 25 > # Begin Function number 26 > 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 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > 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 > # End Function number 26 > # Begin Function number 27 > 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 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > 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 > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > 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 > # End Function number 29 > # Begin Function number 30 > 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 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > 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 > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > ## Comment 5 > exact_soln_y := proc(x) > ## Comment 6 > return(x * erf(sqrt(x)) - ( 2.0 * (-1.0/2.0 * sqrt(x) / exp(x) + 1.0/4.0 * > sqrt(evalf(Pi)) * erf(sqrt(x))))/sqrt(evalf(Pi))) ; > ## Comment 7 > end; exact_soln_y := proc(x) return x*erf(sqrt(x)) - 2.0* (-1.0*sqrt(x)/(2.0*exp(x)) + 1.0*sqrt(evalf(Pi))*erf(sqrt(x))/4.0)/ sqrt(evalf(Pi)) 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, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_c1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #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/erf_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = erf(sqrt(x));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 1"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"## Comment 2"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 3"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 1.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_max_h := 0.00001;"); > omniout_str(ALWAYS,"## Comment 4"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"## Comment 5"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"## Comment 6"); > omniout_str(ALWAYS," "); > omniout_str(ALWAYS,"return(x * erf(sqrt(x)) - ( 2.0 * (-1.0/2.0 * sqrt(x) / exp(x) + 1.0/4.0 *"); > omniout_str(ALWAYS,"sqrt(evalf(Pi)) * erf(sqrt(x))))/sqrt(evalf(Pi))) ;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"## Comment 7"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > ## Comment 1 > Digits:=32; > max_terms:=30; > ## Comment 2 > #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_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2_a1:= Array(0..(max_terms + 1),[]); > array_tmp2_a2:= Array(0..(max_terms + 1),[]); > array_tmp2_c1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 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_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > ## Comment 3 > x_start := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_max_h := 0.00001; > ## Comment 4 > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #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); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > 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 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > 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 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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 ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #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 2 > 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 2; > #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 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > 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 2 > 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 2; > #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 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > 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 2 > 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 2; > #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 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > 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 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = erf(sqrt(x));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T05:44:03-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"erf_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = erf(sqrt(x));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"erf_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"erf_sqrt maple results") > ; > logitem_str(html_log_file,"Maple - erf") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > 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, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_c1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; 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/erf_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = erf(sqrt(x));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 1"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "## Comment 2"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 3"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 1.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_max_h := 0.00001;"); omniout_str(ALWAYS, "## Comment 4"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "## Comment 5"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "## Comment 6"); omniout_str(ALWAYS, " "); omniout_str(ALWAYS, "return(x * erf(sqrt(x)) - ( 2.0 * (-1.0/2.0 * sq\ rt(x) / exp(x) + 1.0/4.0 *"); omniout_str(ALWAYS, "sqrt(evalf(Pi)) * erf(sqrt(x))))/sqrt(evalf(Pi))) ;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "## Comment 7"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2_a1 := Array(0 .. max_terms + 1, []); array_tmp2_a2 := Array(0 .. max_terms + 1, []); array_tmp2_c1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); 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_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; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_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_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_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_c1[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_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_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 <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[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; 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_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[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_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a1[term] := 0.; term := term + 1 end do; array_tmp2_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a2[term] := 0.; term := term + 1 end do; array_tmp2_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_c1[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_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.00001; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; 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); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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 glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; 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 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 ) = erf(sqrt(x));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T05:44:03-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "erf_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = erf(sqrt(x));") ; logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "erf_sqrt diffeq.mxt") ; logitem_str(html_log_file, "erf_sqrt maple results"); logitem_str(html_log_file, "Maple - erf"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/erf_sqrtpostode.ode################# diff ( y , x , 1 ) = erf(sqrt(x)); ! #BEGIN FIRST INPUT BLOCK ## Comment 1 Digits:=32; max_terms:=30; ## Comment 2 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## Comment 3 x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.00001; ## Comment 4 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK ## Comment 5 exact_soln_y := proc(x) ## Comment 6 return(x * erf(sqrt(x)) - ( 2.0 * (-1.0/2.0 * sqrt(x) / exp(x) + 1.0/4.0 * sqrt(evalf(Pi)) * erf(sqrt(x))))/sqrt(evalf(Pi))) ; ## Comment 7 end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.9 estimated_steps = 900000 step_error = 1.1111111111111111111111111111111e-16 est_needed_step_err = 1.1111111111111111111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2341973449480526012474060105962e-136 estimated_step_error = 2.2341973449480526012474060105962e-136 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4993376528675699484175962953603e-128 estimated_step_error = 1.4993376528675699484175962953603e-128 best_h = 4.00e-06 opt_iter = 3 bytes used=4000148, alloc=2948580, time=0.28 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0061793331798370324463187113577e-120 estimated_step_error = 1.0061793331798370324463187113577e-120 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.7522326228293276965334836373906e-113 estimated_step_error = 6.7522326228293276965334836373906e-113 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.5311820924946777636297686906444e-105 estimated_step_error = 4.5311820924946777636297686906444e-105 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.023322564278966996812626107045069 y[1] (numeric) = 0.023322564278966996812626107045069 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1121 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1859 Order of pole (six term test) = -0.8415 bytes used=8001248, alloc=3996964, time=0.58 bytes used=12002144, alloc=4259060, time=0.89 bytes used=16003392, alloc=4324584, time=1.21 bytes used=20004560, alloc=4390108, time=1.52 bytes used=24005468, alloc=4390108, time=1.84 bytes used=28006284, alloc=4390108, time=2.16 bytes used=32007364, alloc=4390108, time=2.49 bytes used=36008720, alloc=4390108, time=2.81 bytes used=40010496, alloc=4455632, time=3.13 bytes used=44011260, alloc=4455632, time=3.44 bytes used=48012048, alloc=4455632, time=3.76 bytes used=52013540, alloc=4455632, time=4.08 bytes used=56014784, alloc=4455632, time=4.40 bytes used=60015736, alloc=4455632, time=4.72 bytes used=64016776, alloc=4521156, time=5.05 bytes used=68017960, alloc=4521156, time=5.37 bytes used=72018896, alloc=4521156, time=5.69 bytes used=76020232, alloc=4521156, time=6.01 bytes used=80020996, alloc=4521156, time=6.33 bytes used=84022172, alloc=4521156, time=6.65 bytes used=88024092, alloc=4521156, time=6.97 bytes used=92025048, alloc=4521156, time=7.29 bytes used=96026172, alloc=4521156, time=7.61 bytes used=100026972, alloc=4521156, time=7.93 bytes used=104027896, alloc=4521156, time=8.25 bytes used=108028840, alloc=4521156, time=8.59 bytes used=112029868, alloc=4521156, time=8.91 bytes used=116030728, alloc=4521156, time=9.23 bytes used=120031748, alloc=4521156, time=9.55 bytes used=124032708, alloc=4521156, time=9.87 bytes used=128033652, alloc=4521156, time=10.19 bytes used=132034556, alloc=4521156, time=10.52 bytes used=136035316, alloc=4521156, time=10.84 bytes used=140036376, alloc=4521156, time=11.16 bytes used=144037296, alloc=4521156, time=11.48 bytes used=148038292, alloc=4521156, time=11.81 bytes used=152039236, alloc=4521156, time=12.13 bytes used=156040076, alloc=4586680, time=12.45 bytes used=160043056, alloc=4586680, time=12.77 bytes used=164044024, alloc=4586680, time=13.10 bytes used=168046348, alloc=4586680, time=13.42 bytes used=172047356, alloc=4586680, time=13.74 bytes used=176048276, alloc=4586680, time=14.06 bytes used=180049300, alloc=4586680, time=14.40 bytes used=184051896, alloc=4586680, time=14.72 bytes used=188052912, alloc=4586680, time=15.05 bytes used=192053732, alloc=4586680, time=15.37 bytes used=196054576, alloc=4586680, time=15.69 bytes used=200055728, alloc=4586680, time=16.01 bytes used=204056572, alloc=4586680, time=16.34 bytes used=208057408, alloc=4586680, time=16.66 bytes used=212058464, alloc=4586680, time=16.98 bytes used=216059252, alloc=4586680, time=17.30 bytes used=220060220, alloc=4586680, time=17.62 bytes used=224061272, alloc=4586680, time=17.95 bytes used=228063988, alloc=4586680, time=18.27 bytes used=232064984, alloc=4586680, time=18.59 bytes used=236066692, alloc=4586680, time=18.91 bytes used=240069428, alloc=4586680, time=19.23 bytes used=244070120, alloc=4586680, time=19.56 bytes used=248070940, alloc=4586680, time=19.88 bytes used=252071796, alloc=4586680, time=20.21 bytes used=256072660, alloc=4586680, time=20.54 bytes used=260073668, alloc=4586680, time=20.86 bytes used=264075948, alloc=4586680, time=21.18 bytes used=268079144, alloc=4586680, time=21.51 bytes used=272079960, alloc=4586680, time=21.83 bytes used=276081004, alloc=4586680, time=22.07 bytes used=280081832, alloc=4586680, time=22.21 bytes used=284082784, alloc=4586680, time=22.35 bytes used=288083608, alloc=4586680, time=22.48 bytes used=292085044, alloc=4586680, time=22.62 bytes used=296086560, alloc=4586680, time=22.75 bytes used=300087356, alloc=4586680, time=22.89 bytes used=304088312, alloc=4586680, time=23.03 bytes used=308089020, alloc=4586680, time=23.16 bytes used=312090256, alloc=4586680, time=23.30 bytes used=316091048, alloc=4586680, time=23.43 bytes used=320092088, alloc=4586680, time=23.57 bytes used=324093336, alloc=4586680, time=23.70 bytes used=328094188, alloc=4586680, time=23.84 bytes used=332095812, alloc=4586680, time=23.97 bytes used=336096804, alloc=4586680, time=24.11 bytes used=340097624, alloc=4586680, time=24.25 bytes used=344099476, alloc=4586680, time=24.38 bytes used=348100852, alloc=4586680, time=24.52 bytes used=352101944, alloc=4586680, time=24.65 bytes used=356102816, alloc=4586680, time=24.79 bytes used=360103936, alloc=4586680, time=24.93 bytes used=364106756, alloc=4586680, time=25.06 bytes used=368107616, alloc=4586680, time=25.20 bytes used=372108420, alloc=4586680, time=25.34 bytes used=376109892, alloc=4586680, time=25.47 bytes used=380110832, alloc=4586680, time=25.61 bytes used=384111856, alloc=4586680, time=25.74 bytes used=388114632, alloc=4586680, time=25.88 bytes used=392115324, alloc=4586680, time=26.01 bytes used=396117460, alloc=4586680, time=26.15 bytes used=400120236, alloc=4586680, time=26.29 bytes used=404122572, alloc=4586680, time=26.43 bytes used=408123280, alloc=4586680, time=26.56 bytes used=412127612, alloc=4586680, time=26.70 bytes used=416128344, alloc=4586680, time=26.84 bytes used=420129180, alloc=4586680, time=26.97 bytes used=424130096, alloc=4586680, time=27.11 bytes used=428131108, alloc=4586680, time=27.25 bytes used=432132204, alloc=4586680, time=27.38 bytes used=436132948, alloc=4586680, time=27.52 bytes used=440133988, alloc=4586680, time=27.66 bytes used=444134804, alloc=4586680, time=27.79 bytes used=448135964, alloc=4586680, time=27.92 bytes used=452136864, alloc=4586680, time=28.06 bytes used=456137964, alloc=4586680, time=28.19 bytes used=460138984, alloc=4586680, time=28.33 bytes used=464140848, alloc=4586680, time=28.47 bytes used=468142220, alloc=4586680, time=28.60 bytes used=472143080, alloc=4586680, time=28.74 bytes used=476145064, alloc=4586680, time=28.88 bytes used=480146068, alloc=4586680, time=29.01 bytes used=484146852, alloc=4586680, time=29.15 bytes used=488148408, alloc=4586680, time=29.29 bytes used=492150136, alloc=4586680, time=29.42 bytes used=496151972, alloc=4586680, time=29.56 bytes used=500152812, alloc=4586680, time=29.69 bytes used=504153828, alloc=4586680, time=29.83 bytes used=508155356, alloc=4586680, time=29.96 bytes used=512156264, alloc=4586680, time=30.10 bytes used=516157448, alloc=4586680, time=30.24 bytes used=520158600, alloc=4586680, time=30.38 bytes used=524162524, alloc=4586680, time=30.51 bytes used=528163240, alloc=4586680, time=30.65 bytes used=532164404, alloc=4586680, time=30.78 bytes used=536165432, alloc=4586680, time=30.92 bytes used=540166432, alloc=4586680, time=31.06 bytes used=544167356, alloc=4586680, time=31.19 bytes used=548168444, alloc=4586680, time=31.33 bytes used=552169712, alloc=4586680, time=31.47 bytes used=556171044, alloc=4586680, time=31.60 bytes used=560172068, alloc=4586680, time=31.74 bytes used=564172960, alloc=4586680, time=31.88 bytes used=568173992, alloc=4586680, time=32.01 bytes used=572175068, alloc=4586680, time=32.16 bytes used=576177920, alloc=4586680, time=32.29 bytes used=580179192, alloc=4586680, time=32.43 bytes used=584183344, alloc=4586680, time=32.57 bytes used=588184784, alloc=4586680, time=32.70 bytes used=592185624, alloc=4586680, time=32.84 bytes used=596186392, alloc=4586680, time=32.98 bytes used=600187632, alloc=4586680, time=33.11 bytes used=604188444, alloc=4586680, time=33.25 bytes used=608189384, alloc=4586680, time=33.38 bytes used=612190564, alloc=4586680, time=33.52 bytes used=616191576, alloc=4586680, time=33.65 bytes used=620192608, alloc=4586680, time=33.79 bytes used=624193520, alloc=4586680, time=33.93 bytes used=628195008, alloc=4586680, time=34.06 bytes used=632195912, alloc=4586680, time=34.20 bytes used=636197568, alloc=4586680, time=34.33 bytes used=640198456, alloc=4586680, time=34.47 bytes used=644199352, alloc=4586680, time=34.61 bytes used=648201540, alloc=4586680, time=34.75 bytes used=652202336, alloc=4586680, time=34.88 bytes used=656203376, alloc=4586680, time=35.02 bytes used=660204216, alloc=4586680, time=35.15 bytes used=664205496, alloc=4586680, time=35.29 bytes used=668206464, alloc=4586680, time=35.43 bytes used=672207564, alloc=4586680, time=35.56 bytes used=676208204, alloc=4586680, time=35.70 bytes used=680210068, alloc=4586680, time=35.84 bytes used=684212972, alloc=4586680, time=35.97 bytes used=688214240, alloc=4586680, time=36.11 bytes used=692215460, alloc=4586680, time=36.24 bytes used=696216324, alloc=4652204, time=36.38 bytes used=700217264, alloc=4652204, time=36.52 bytes used=704219132, alloc=4652204, time=36.65 bytes used=708220000, alloc=4652204, time=36.79 bytes used=712220640, alloc=4652204, time=36.92 bytes used=716221700, alloc=4652204, time=37.06 bytes used=720223188, alloc=4652204, time=37.20 bytes used=724224320, alloc=4652204, time=37.33 bytes used=728225296, alloc=4652204, time=37.47 bytes used=732226200, alloc=4652204, time=37.61 bytes used=736226980, alloc=4652204, time=37.74 bytes used=740228256, alloc=4652204, time=37.88 bytes used=744229328, alloc=4652204, time=38.02 bytes used=748230500, alloc=4652204, time=38.16 bytes used=752231308, alloc=4652204, time=38.29 bytes used=756232272, alloc=4652204, time=38.43 bytes used=760233316, alloc=4652204, time=38.57 bytes used=764234392, alloc=4652204, time=38.70 bytes used=768235992, alloc=4652204, time=38.84 bytes used=772237048, alloc=4652204, time=38.97 bytes used=776238288, alloc=4652204, time=39.10 bytes used=780239284, alloc=4652204, time=39.24 bytes used=784241820, alloc=4652204, time=39.37 TOP MAIN SOLVE Loop bytes used=788242668, alloc=4652204, time=39.51 x[1] = 0.11 y[1] (analytic) = 0.026854513745215809780927296994581 y[1] (numeric) = 0.026854513745880644336182361569473 absolute error = 6.64834555255064574892e-13 relative error = 2.4756901635335188355451627347765e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1233 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2042 Order of pole (six term test) = -0.8458 bytes used=792243592, alloc=4652204, time=39.65 bytes used=796244496, alloc=4652204, time=39.78 bytes used=800245628, alloc=4652204, time=39.92 bytes used=804246652, alloc=4652204, time=40.05 bytes used=808247972, alloc=4652204, time=40.19 bytes used=812250484, alloc=4652204, time=40.32 bytes used=816251532, alloc=4652204, time=40.46 bytes used=820252396, alloc=4652204, time=40.59 bytes used=824253264, alloc=4652204, time=40.73 bytes used=828254336, alloc=4652204, time=40.86 bytes used=832255532, alloc=4652204, time=41.00 bytes used=836256656, alloc=4652204, time=41.13 bytes used=840257424, alloc=4652204, time=41.27 bytes used=844258348, alloc=4652204, time=41.40 bytes used=848259524, alloc=4652204, time=41.54 bytes used=852260460, alloc=4652204, time=41.67 bytes used=856262440, alloc=4652204, time=41.81 bytes used=860263440, alloc=4652204, time=41.94 bytes used=864264448, alloc=4652204, time=42.08 bytes used=868265292, alloc=4652204, time=42.21 bytes used=872266988, alloc=4652204, time=42.35 bytes used=876267916, alloc=4652204, time=42.48 bytes used=880269048, alloc=4652204, time=42.62 bytes used=884270080, alloc=4652204, time=42.75 bytes used=888271040, alloc=4652204, time=42.89 bytes used=892272040, alloc=4652204, time=43.02 bytes used=896273332, alloc=4652204, time=43.16 bytes used=900274136, alloc=4652204, time=43.29 bytes used=904275112, alloc=4652204, time=43.43 bytes used=908276032, alloc=4652204, time=43.56 bytes used=912276872, alloc=4652204, time=43.70 bytes used=916277816, alloc=4652204, time=43.83 bytes used=920278652, alloc=4652204, time=43.97 bytes used=924279608, alloc=4652204, time=44.11 bytes used=928283528, alloc=4652204, time=44.24 bytes used=932284444, alloc=4652204, time=44.38 bytes used=936285276, alloc=4652204, time=44.51 bytes used=940286556, alloc=4652204, time=44.64 bytes used=944287492, alloc=4652204, time=44.78 bytes used=948288684, alloc=4652204, time=44.91 bytes used=952291168, alloc=4652204, time=45.05 bytes used=956292224, alloc=4652204, time=45.18 bytes used=960293132, alloc=4652204, time=45.31 bytes used=964294032, alloc=4652204, time=45.45 bytes used=968294976, alloc=4652204, time=45.59 bytes used=972295816, alloc=4652204, time=45.72 bytes used=976297960, alloc=4652204, time=45.85 bytes used=980298996, alloc=4652204, time=45.99 bytes used=984299916, alloc=4652204, time=46.12 bytes used=988301476, alloc=4652204, time=46.26 bytes used=992302724, alloc=4652204, time=46.40 bytes used=996304300, alloc=4652204, time=46.53 bytes used=1000305152, alloc=4652204, time=46.67 bytes used=1004306140, alloc=4652204, time=46.80 bytes used=1008307072, alloc=4652204, time=46.94 bytes used=1012308064, alloc=4652204, time=47.07 bytes used=1016309252, alloc=4652204, time=47.20 bytes used=1020310116, alloc=4652204, time=47.34 bytes used=1024311512, alloc=4652204, time=47.47 bytes used=1028312332, alloc=4652204, time=47.61 bytes used=1032316576, alloc=4652204, time=47.74 bytes used=1036317664, alloc=4652204, time=47.88 bytes used=1040318780, alloc=4652204, time=48.01 bytes used=1044319688, alloc=4652204, time=48.15 bytes used=1048320816, alloc=4652204, time=48.28 bytes used=1052321952, alloc=4652204, time=48.42 bytes used=1056322832, alloc=4652204, time=48.55 bytes used=1060324144, alloc=4652204, time=48.69 bytes used=1064325144, alloc=4652204, time=48.82 bytes used=1068326108, alloc=4652204, time=48.95 bytes used=1072327408, alloc=4652204, time=49.09 bytes used=1076328476, alloc=4652204, time=49.22 bytes used=1080329664, alloc=4652204, time=49.36 bytes used=1084331672, alloc=4652204, time=49.49 bytes used=1088332352, alloc=4652204, time=49.63 bytes used=1092333192, alloc=4652204, time=49.77 bytes used=1096334036, alloc=4652204, time=49.90 bytes used=1100335608, alloc=4652204, time=50.04 bytes used=1104336408, alloc=4652204, time=50.18 bytes used=1108337604, alloc=4652204, time=50.31 bytes used=1112338880, alloc=4652204, time=50.45 bytes used=1116339848, alloc=4652204, time=50.58 bytes used=1120340832, alloc=4652204, time=50.72 bytes used=1124341508, alloc=4652204, time=50.85 bytes used=1128342672, alloc=4652204, time=50.99 bytes used=1132343700, alloc=4652204, time=51.12 bytes used=1136344856, alloc=4652204, time=51.26 bytes used=1140346000, alloc=4652204, time=51.39 bytes used=1144347732, alloc=4652204, time=51.53 bytes used=1148349332, alloc=4652204, time=51.66 bytes used=1152350180, alloc=4652204, time=51.80 bytes used=1156351204, alloc=4652204, time=51.93 bytes used=1160352312, alloc=4652204, time=52.07 bytes used=1164353352, alloc=4652204, time=52.21 bytes used=1168355016, alloc=4652204, time=52.34 bytes used=1172355884, alloc=4652204, time=52.47 bytes used=1176356768, alloc=4652204, time=52.61 bytes used=1180357620, alloc=4652204, time=52.74 bytes used=1184358524, alloc=4652204, time=52.88 bytes used=1188360748, alloc=4652204, time=53.01 bytes used=1192362084, alloc=4652204, time=53.15 bytes used=1196363168, alloc=4652204, time=53.28 bytes used=1200364096, alloc=4652204, time=53.42 bytes used=1204365032, alloc=4652204, time=53.55 bytes used=1208365976, alloc=4652204, time=53.69 bytes used=1212366960, alloc=4652204, time=53.82 bytes used=1216368060, alloc=4652204, time=53.96 bytes used=1220368924, alloc=4652204, time=54.09 bytes used=1224370596, alloc=4652204, time=54.23 bytes used=1228371476, alloc=4652204, time=54.36 bytes used=1232372368, alloc=4652204, time=54.50 bytes used=1236376168, alloc=4652204, time=54.63 bytes used=1240376996, alloc=4652204, time=54.77 bytes used=1244378156, alloc=4652204, time=54.90 bytes used=1248379244, alloc=4652204, time=55.04 bytes used=1252379996, alloc=4652204, time=55.17 bytes used=1256380936, alloc=4652204, time=55.31 bytes used=1260381732, alloc=4652204, time=55.45 bytes used=1264382416, alloc=4652204, time=55.58 bytes used=1268383236, alloc=4652204, time=55.72 bytes used=1272384344, alloc=4652204, time=55.85 bytes used=1276385464, alloc=4652204, time=55.99 bytes used=1280386496, alloc=4652204, time=56.12 bytes used=1284387980, alloc=4652204, time=56.26 bytes used=1288388912, alloc=4652204, time=56.39 bytes used=1292389724, alloc=4652204, time=56.53 bytes used=1296390588, alloc=4652204, time=56.67 bytes used=1300391508, alloc=4652204, time=56.80 bytes used=1304392332, alloc=4652204, time=56.94 bytes used=1308393568, alloc=4652204, time=57.07 bytes used=1312394432, alloc=4652204, time=57.21 bytes used=1316398216, alloc=4652204, time=57.35 bytes used=1320398996, alloc=4652204, time=57.48 bytes used=1324399848, alloc=4652204, time=57.61 bytes used=1328400976, alloc=4652204, time=57.75 bytes used=1332402640, alloc=4652204, time=57.89 bytes used=1336403348, alloc=4652204, time=58.02 bytes used=1340404080, alloc=4652204, time=58.16 bytes used=1344405228, alloc=4652204, time=58.29 bytes used=1348406020, alloc=4652204, time=58.43 bytes used=1352406976, alloc=4652204, time=58.56 bytes used=1356407896, alloc=4652204, time=58.70 bytes used=1360408900, alloc=4652204, time=58.83 bytes used=1364409916, alloc=4652204, time=58.97 bytes used=1368411152, alloc=4652204, time=59.10 bytes used=1372412176, alloc=4652204, time=59.24 bytes used=1376413144, alloc=4652204, time=59.37 bytes used=1380414080, alloc=4652204, time=59.51 bytes used=1384417500, alloc=4652204, time=59.64 bytes used=1388418292, alloc=4652204, time=59.78 bytes used=1392419248, alloc=4652204, time=59.91 bytes used=1396420232, alloc=4652204, time=60.05 bytes used=1400422484, alloc=4652204, time=60.18 bytes used=1404423212, alloc=4652204, time=60.32 bytes used=1408424364, alloc=4652204, time=60.45 bytes used=1412425336, alloc=4652204, time=60.59 bytes used=1416426480, alloc=4652204, time=60.72 bytes used=1420427504, alloc=4652204, time=60.86 bytes used=1424428512, alloc=4652204, time=60.99 bytes used=1428429356, alloc=4652204, time=61.13 bytes used=1432432920, alloc=4652204, time=61.26 bytes used=1436433900, alloc=4652204, time=61.40 bytes used=1440435052, alloc=4652204, time=61.54 bytes used=1444436044, alloc=4652204, time=61.67 bytes used=1448436680, alloc=4652204, time=61.81 bytes used=1452437916, alloc=4652204, time=61.95 bytes used=1456438852, alloc=4652204, time=62.08 bytes used=1460439676, alloc=4652204, time=62.21 bytes used=1464440408, alloc=4652204, time=62.35 bytes used=1468441496, alloc=4652204, time=62.48 bytes used=1472443424, alloc=4652204, time=62.62 bytes used=1476444148, alloc=4652204, time=62.75 bytes used=1480444828, alloc=4652204, time=62.89 bytes used=1484445644, alloc=4652204, time=63.02 bytes used=1488446608, alloc=4652204, time=63.16 bytes used=1492447396, alloc=4652204, time=63.29 bytes used=1496448680, alloc=4652204, time=63.43 bytes used=1500449456, alloc=4652204, time=63.56 bytes used=1504450404, alloc=4652204, time=63.70 bytes used=1508451376, alloc=4652204, time=63.83 bytes used=1512452584, alloc=4652204, time=63.97 bytes used=1516453664, alloc=4652204, time=64.10 bytes used=1520454628, alloc=4652204, time=64.23 bytes used=1524455708, alloc=4652204, time=64.37 bytes used=1528456872, alloc=4652204, time=64.50 bytes used=1532458184, alloc=4652204, time=64.64 bytes used=1536459900, alloc=4652204, time=64.77 bytes used=1540460984, alloc=4652204, time=64.91 bytes used=1544461888, alloc=4652204, time=65.04 bytes used=1548462736, alloc=4652204, time=65.18 bytes used=1552463720, alloc=4652204, time=65.31 bytes used=1556464764, alloc=4652204, time=65.45 bytes used=1560465736, alloc=4652204, time=65.58 bytes used=1564466912, alloc=4652204, time=65.72 bytes used=1568470128, alloc=4652204, time=65.85 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.030538944906449418292473763046309 y[1] (numeric) = 0.03053894490772616843266846326433 absolute error = 1.276750140194700218021e-12 relative error = 4.1807277366844052251875657695435e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2225 Order of pole (six term test) = -0.85 bytes used=1572470836, alloc=4652204, time=65.98 bytes used=1576471956, alloc=4652204, time=66.12 bytes used=1580473192, alloc=4652204, time=66.25 bytes used=1584474296, alloc=4652204, time=66.39 bytes used=1588475220, alloc=4652204, time=66.52 bytes used=1592476204, alloc=4652204, time=66.66 bytes used=1596477132, alloc=4652204, time=66.79 bytes used=1600478208, alloc=4652204, time=66.93 bytes used=1604479248, alloc=4652204, time=67.06 bytes used=1608480256, alloc=4652204, time=67.20 bytes used=1612482172, alloc=4652204, time=67.33 bytes used=1616483592, alloc=4652204, time=67.47 bytes used=1620484632, alloc=4652204, time=67.60 bytes used=1624486608, alloc=4652204, time=67.74 bytes used=1628487308, alloc=4652204, time=67.87 bytes used=1632488400, alloc=4652204, time=68.00 bytes used=1636489196, alloc=4652204, time=68.14 bytes used=1640490168, alloc=4652204, time=68.27 bytes used=1644493484, alloc=4652204, time=68.41 bytes used=1648494404, alloc=4652204, time=68.55 bytes used=1652495252, alloc=4652204, time=68.68 bytes used=1656496608, alloc=4652204, time=68.82 bytes used=1660497544, alloc=4652204, time=68.95 bytes used=1664498792, alloc=4652204, time=69.09 bytes used=1668499812, alloc=4652204, time=69.22 bytes used=1672500780, alloc=4652204, time=69.36 bytes used=1676501892, alloc=4652204, time=69.49 bytes used=1680503292, alloc=4652204, time=69.62 bytes used=1684504060, alloc=4652204, time=69.75 bytes used=1688505252, alloc=4652204, time=69.89 bytes used=1692506392, alloc=4652204, time=70.02 bytes used=1696507348, alloc=4652204, time=70.16 bytes used=1700508244, alloc=4652204, time=70.29 bytes used=1704510080, alloc=4652204, time=70.43 bytes used=1708511144, alloc=4652204, time=70.56 bytes used=1712512420, alloc=4652204, time=70.70 bytes used=1716513280, alloc=4652204, time=70.83 bytes used=1720518964, alloc=4652204, time=70.96 bytes used=1724519660, alloc=4652204, time=71.10 bytes used=1728521044, alloc=4652204, time=71.23 bytes used=1732522132, alloc=4652204, time=71.37 bytes used=1736523152, alloc=4652204, time=71.50 bytes used=1740524072, alloc=4652204, time=71.64 bytes used=1744524884, alloc=4652204, time=71.78 bytes used=1748525984, alloc=4652204, time=71.92 bytes used=1752527464, alloc=4652204, time=72.05 bytes used=1756528392, alloc=4652204, time=72.18 bytes used=1760529280, alloc=4652204, time=72.32 bytes used=1764530256, alloc=4652204, time=72.45 bytes used=1768531060, alloc=4652204, time=72.59 bytes used=1772531924, alloc=4652204, time=72.72 bytes used=1776533000, alloc=4652204, time=72.86 bytes used=1780534236, alloc=4652204, time=73.00 bytes used=1784536648, alloc=4652204, time=73.13 bytes used=1788537468, alloc=4652204, time=73.26 bytes used=1792538860, alloc=4652204, time=73.40 bytes used=1796539900, alloc=4652204, time=73.53 bytes used=1800542560, alloc=4652204, time=73.67 bytes used=1804543628, alloc=4652204, time=73.81 bytes used=1808544528, alloc=4652204, time=73.94 bytes used=1812546372, alloc=4652204, time=74.07 bytes used=1816547132, alloc=4652204, time=74.21 bytes used=1820548288, alloc=4652204, time=74.35 bytes used=1824549008, alloc=4652204, time=74.48 bytes used=1828549816, alloc=4652204, time=74.62 bytes used=1832550720, alloc=4652204, time=74.75 bytes used=1836551544, alloc=4652204, time=74.89 bytes used=1840552380, alloc=4652204, time=75.02 bytes used=1844553696, alloc=4652204, time=75.16 bytes used=1848554604, alloc=4652204, time=75.29 bytes used=1852555824, alloc=4652204, time=75.43 bytes used=1856556948, alloc=4652204, time=75.56 bytes used=1860557796, alloc=4652204, time=75.70 bytes used=1864559580, alloc=4652204, time=75.83 bytes used=1868560756, alloc=4652204, time=75.97 bytes used=1872561812, alloc=4652204, time=76.10 bytes used=1876562800, alloc=4652204, time=76.23 bytes used=1880563648, alloc=4652204, time=76.37 bytes used=1884564704, alloc=4652204, time=76.50 bytes used=1888565596, alloc=4652204, time=76.64 bytes used=1892566796, alloc=4652204, time=76.77 bytes used=1896568216, alloc=4652204, time=76.91 bytes used=1900569992, alloc=4652204, time=77.04 bytes used=1904571188, alloc=4652204, time=77.18 bytes used=1908572048, alloc=4652204, time=77.31 bytes used=1912573200, alloc=4652204, time=77.45 bytes used=1916574116, alloc=4652204, time=77.58 bytes used=1920575300, alloc=4652204, time=77.72 bytes used=1924576164, alloc=4652204, time=77.85 bytes used=1928577176, alloc=4652204, time=77.99 bytes used=1932577952, alloc=4652204, time=78.12 bytes used=1936579048, alloc=4652204, time=78.25 bytes used=1940579864, alloc=4652204, time=78.39 bytes used=1944580856, alloc=4652204, time=78.52 bytes used=1948581956, alloc=4652204, time=78.66 bytes used=1952583012, alloc=4652204, time=78.79 bytes used=1956583988, alloc=4652204, time=78.92 bytes used=1960584924, alloc=4652204, time=79.06 bytes used=1964587244, alloc=4652204, time=79.19 bytes used=1968588832, alloc=4652204, time=79.33 bytes used=1972589500, alloc=4652204, time=79.46 bytes used=1976590320, alloc=4652204, time=79.60 bytes used=1980591160, alloc=4652204, time=79.73 bytes used=1984592308, alloc=4652204, time=79.87 bytes used=1988593212, alloc=4652204, time=80.00 bytes used=1992596668, alloc=4652204, time=80.13 bytes used=1996597600, alloc=4652204, time=80.27 bytes used=2000598532, alloc=4652204, time=80.40 bytes used=2004599260, alloc=4652204, time=80.54 bytes used=2008600424, alloc=4652204, time=80.67 bytes used=2012603236, alloc=4652204, time=80.81 bytes used=2016606688, alloc=4652204, time=80.94 bytes used=2020607428, alloc=4652204, time=81.08 bytes used=2024608528, alloc=4652204, time=81.21 bytes used=2028609692, alloc=4652204, time=81.35 bytes used=2032610512, alloc=4652204, time=81.48 bytes used=2036611692, alloc=4652204, time=81.62 bytes used=2040612808, alloc=4652204, time=81.75 bytes used=2044613660, alloc=4652204, time=81.88 bytes used=2048614448, alloc=4652204, time=82.02 bytes used=2052615472, alloc=4652204, time=82.15 bytes used=2056616380, alloc=4652204, time=82.29 bytes used=2060618860, alloc=4652204, time=82.42 bytes used=2064620004, alloc=4652204, time=82.56 bytes used=2068621128, alloc=4652204, time=82.69 bytes used=2072622224, alloc=4652204, time=82.83 bytes used=2076623280, alloc=4652204, time=82.96 bytes used=2080624044, alloc=4652204, time=83.09 bytes used=2084625096, alloc=4652204, time=83.23 bytes used=2088626444, alloc=4652204, time=83.36 bytes used=2092627504, alloc=4652204, time=83.50 bytes used=2096628412, alloc=4652204, time=83.63 bytes used=2100630080, alloc=4652204, time=83.76 bytes used=2104632320, alloc=4652204, time=83.90 bytes used=2108633704, alloc=4652204, time=84.03 bytes used=2112634492, alloc=4652204, time=84.17 bytes used=2116635240, alloc=4652204, time=84.30 bytes used=2120636296, alloc=4652204, time=84.44 bytes used=2124637300, alloc=4652204, time=84.57 bytes used=2128638100, alloc=4652204, time=84.71 bytes used=2132638968, alloc=4652204, time=84.84 bytes used=2136639908, alloc=4652204, time=84.98 bytes used=2140641212, alloc=4652204, time=85.11 bytes used=2144642144, alloc=4652204, time=85.24 bytes used=2148643188, alloc=4652204, time=85.38 bytes used=2152644404, alloc=4652204, time=85.51 bytes used=2156645332, alloc=4652204, time=85.65 bytes used=2160646460, alloc=4652204, time=85.79 bytes used=2164647384, alloc=4652204, time=85.92 bytes used=2168648492, alloc=4652204, time=86.06 bytes used=2172650472, alloc=4652204, time=86.19 bytes used=2176651368, alloc=4652204, time=86.32 bytes used=2180652748, alloc=4652204, time=86.46 bytes used=2184653628, alloc=4652204, time=86.59 bytes used=2188654540, alloc=4652204, time=86.73 bytes used=2192655388, alloc=4652204, time=86.86 bytes used=2196656688, alloc=4652204, time=87.00 bytes used=2200657628, alloc=4652204, time=87.13 bytes used=2204658296, alloc=4652204, time=87.27 bytes used=2208659140, alloc=4652204, time=87.40 bytes used=2212660052, alloc=4652204, time=87.54 bytes used=2216661992, alloc=4652204, time=87.67 bytes used=2220663124, alloc=4652204, time=87.81 bytes used=2224665016, alloc=4652204, time=87.94 bytes used=2228665932, alloc=4652204, time=88.08 bytes used=2232666712, alloc=4652204, time=88.21 bytes used=2236667724, alloc=4652204, time=88.35 bytes used=2240668428, alloc=4652204, time=88.48 bytes used=2244669404, alloc=4652204, time=88.62 bytes used=2248670476, alloc=4652204, time=88.75 bytes used=2252671512, alloc=4652204, time=88.89 bytes used=2256672348, alloc=4652204, time=89.02 bytes used=2260673664, alloc=4652204, time=89.16 bytes used=2264676436, alloc=4652204, time=89.29 bytes used=2268677152, alloc=4652204, time=89.42 bytes used=2272678268, alloc=4652204, time=89.56 bytes used=2276679160, alloc=4652204, time=89.70 bytes used=2280681932, alloc=4652204, time=89.83 bytes used=2284682844, alloc=4652204, time=89.96 bytes used=2288683788, alloc=4652204, time=90.10 bytes used=2292684884, alloc=4652204, time=90.23 bytes used=2296685876, alloc=4652204, time=90.37 bytes used=2300686920, alloc=4652204, time=90.50 bytes used=2304687868, alloc=4652204, time=90.64 bytes used=2308688728, alloc=4652204, time=90.77 bytes used=2312689616, alloc=4652204, time=90.91 bytes used=2316690468, alloc=4652204, time=91.04 bytes used=2320693944, alloc=4652204, time=91.18 bytes used=2324694708, alloc=4652204, time=91.31 bytes used=2328697296, alloc=4652204, time=91.45 bytes used=2332698084, alloc=4652204, time=91.58 bytes used=2336699172, alloc=4652204, time=91.72 bytes used=2340700216, alloc=4652204, time=91.85 bytes used=2344701124, alloc=4652204, time=91.99 bytes used=2348702108, alloc=4652204, time=92.12 bytes used=2352703024, alloc=4652204, time=92.25 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.03436790066218024633325872694657 y[1] (numeric) = 0.034367900664023900327751744134213 absolute error = 1.843653994493017187643e-12 relative error = 5.3644649774079585478937845279303e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1458 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2407 Order of pole (six term test) = -0.854 bytes used=2356704012, alloc=4652204, time=92.39 bytes used=2360705052, alloc=4652204, time=92.52 bytes used=2364706024, alloc=4652204, time=92.66 bytes used=2368706952, alloc=4652204, time=92.79 bytes used=2372711004, alloc=4652204, time=92.93 bytes used=2376711860, alloc=4652204, time=93.06 bytes used=2380712872, alloc=4652204, time=93.20 bytes used=2384715116, alloc=4652204, time=93.33 bytes used=2388717688, alloc=4652204, time=93.47 bytes used=2392718620, alloc=4652204, time=93.60 bytes used=2396719692, alloc=4652204, time=93.73 bytes used=2400720616, alloc=4652204, time=93.87 bytes used=2404721412, alloc=4652204, time=94.01 bytes used=2408722984, alloc=4652204, time=94.14 bytes used=2412723756, alloc=4652204, time=94.27 bytes used=2416724828, alloc=4652204, time=94.41 bytes used=2420726120, alloc=4652204, time=94.54 bytes used=2424730360, alloc=4652204, time=94.68 bytes used=2428731020, alloc=4652204, time=94.81 bytes used=2432732000, alloc=4652204, time=94.94 bytes used=2436732764, alloc=4652204, time=95.08 bytes used=2440733704, alloc=4652204, time=95.21 bytes used=2444735136, alloc=4652204, time=95.35 bytes used=2448736300, alloc=4652204, time=95.48 bytes used=2452737196, alloc=4652204, time=95.62 bytes used=2456738172, alloc=4652204, time=95.75 bytes used=2460739632, alloc=4652204, time=95.89 bytes used=2464740676, alloc=4652204, time=96.02 bytes used=2468741480, alloc=4652204, time=96.16 bytes used=2472742336, alloc=4652204, time=96.29 bytes used=2476744852, alloc=4652204, time=96.43 bytes used=2480745632, alloc=4652204, time=96.56 bytes used=2484746696, alloc=4652204, time=96.70 bytes used=2488747592, alloc=4652204, time=96.83 bytes used=2492748408, alloc=4652204, time=96.97 bytes used=2496750176, alloc=4652204, time=97.10 bytes used=2500751208, alloc=4652204, time=97.24 bytes used=2504752156, alloc=4652204, time=97.37 bytes used=2508753488, alloc=4652204, time=97.51 bytes used=2512754292, alloc=4652204, time=97.65 bytes used=2516755476, alloc=4652204, time=97.78 bytes used=2520756512, alloc=4652204, time=97.92 bytes used=2524757308, alloc=4652204, time=98.05 bytes used=2528758204, alloc=4652204, time=98.19 bytes used=2532759164, alloc=4652204, time=98.32 bytes used=2536760332, alloc=4652204, time=98.46 bytes used=2540761804, alloc=4652204, time=98.59 bytes used=2544762636, alloc=4652204, time=98.73 bytes used=2548763472, alloc=4652204, time=98.86 bytes used=2552766564, alloc=4652204, time=98.99 bytes used=2556767200, alloc=4652204, time=99.13 bytes used=2560768108, alloc=4652204, time=99.26 bytes used=2564768984, alloc=4652204, time=99.40 bytes used=2568769736, alloc=4652204, time=99.53 bytes used=2572771032, alloc=4652204, time=99.67 bytes used=2576772568, alloc=4652204, time=99.80 bytes used=2580773712, alloc=4652204, time=99.94 bytes used=2584774556, alloc=4652204, time=100.07 bytes used=2588776268, alloc=4652204, time=100.21 bytes used=2592777112, alloc=4652204, time=100.34 bytes used=2596778064, alloc=4652204, time=100.47 bytes used=2600779460, alloc=4652204, time=100.61 bytes used=2604780676, alloc=4652204, time=100.75 bytes used=2608781792, alloc=4652204, time=100.88 bytes used=2612782732, alloc=4652204, time=101.02 bytes used=2616783704, alloc=4652204, time=101.15 bytes used=2620784648, alloc=4652204, time=101.29 bytes used=2624786004, alloc=4652204, time=101.42 bytes used=2628787096, alloc=4652204, time=101.56 bytes used=2632788164, alloc=4652204, time=101.69 bytes used=2636791240, alloc=4652204, time=101.83 bytes used=2640792004, alloc=4652204, time=101.96 bytes used=2644792936, alloc=4652204, time=102.10 bytes used=2648794004, alloc=4652204, time=102.23 bytes used=2652795984, alloc=4652204, time=102.37 bytes used=2656797928, alloc=4652204, time=102.50 bytes used=2660799264, alloc=4652204, time=102.64 bytes used=2664800256, alloc=4652204, time=102.77 bytes used=2668801264, alloc=4652204, time=102.91 bytes used=2672802200, alloc=4652204, time=103.04 bytes used=2676803164, alloc=4652204, time=103.18 bytes used=2680804092, alloc=4652204, time=103.31 bytes used=2684804964, alloc=4652204, time=103.45 bytes used=2688807864, alloc=4652204, time=103.59 bytes used=2692809272, alloc=4652204, time=103.72 bytes used=2696810020, alloc=4652204, time=103.86 bytes used=2700811060, alloc=4652204, time=103.99 bytes used=2704811836, alloc=4652204, time=104.13 bytes used=2708813172, alloc=4652204, time=104.26 bytes used=2712814116, alloc=4652204, time=104.40 bytes used=2716815384, alloc=4652204, time=104.53 bytes used=2720816160, alloc=4652204, time=104.67 bytes used=2724817688, alloc=4652204, time=104.80 bytes used=2728820964, alloc=4652204, time=104.94 bytes used=2732821944, alloc=4652204, time=105.08 bytes used=2736823272, alloc=4652204, time=105.21 bytes used=2740824420, alloc=4652204, time=105.34 bytes used=2744825396, alloc=4652204, time=105.48 bytes used=2748827168, alloc=4652204, time=105.62 bytes used=2752828188, alloc=4652204, time=105.75 bytes used=2756830040, alloc=4652204, time=105.88 bytes used=2760831080, alloc=4652204, time=106.02 bytes used=2764832036, alloc=4652204, time=106.16 bytes used=2768833124, alloc=4652204, time=106.29 bytes used=2772838004, alloc=4652204, time=106.43 bytes used=2776839248, alloc=4652204, time=106.56 bytes used=2780840136, alloc=4652204, time=106.70 bytes used=2784841460, alloc=4652204, time=106.83 bytes used=2788845624, alloc=4652204, time=106.97 bytes used=2792846452, alloc=4652204, time=107.10 bytes used=2796848624, alloc=4652204, time=107.23 bytes used=2800849620, alloc=4652204, time=107.37 bytes used=2804850436, alloc=4652204, time=107.51 bytes used=2808851796, alloc=4652204, time=107.64 bytes used=2812852632, alloc=4652204, time=107.78 bytes used=2816853484, alloc=4652204, time=107.91 bytes used=2820854484, alloc=4652204, time=108.05 bytes used=2824855380, alloc=4652204, time=108.18 bytes used=2828856408, alloc=4652204, time=108.31 bytes used=2832857368, alloc=4652204, time=108.45 bytes used=2836858340, alloc=4652204, time=108.58 bytes used=2840859468, alloc=4652204, time=108.71 bytes used=2844860336, alloc=4652204, time=108.85 bytes used=2848863020, alloc=4652204, time=108.98 bytes used=2852867616, alloc=4652204, time=109.12 bytes used=2856868336, alloc=4652204, time=109.25 bytes used=2860869172, alloc=4652204, time=109.39 bytes used=2864870336, alloc=4652204, time=109.53 bytes used=2868871360, alloc=4652204, time=109.66 bytes used=2872872268, alloc=4652204, time=109.80 bytes used=2876873368, alloc=4652204, time=109.93 bytes used=2880874636, alloc=4652204, time=110.07 bytes used=2884875900, alloc=4652204, time=110.20 bytes used=2888877884, alloc=4652204, time=110.34 bytes used=2892879076, alloc=4652204, time=110.47 bytes used=2896880396, alloc=4652204, time=110.60 bytes used=2900881216, alloc=4652204, time=110.74 bytes used=2904882472, alloc=4652204, time=110.87 bytes used=2908883368, alloc=4652204, time=111.01 bytes used=2912884204, alloc=4652204, time=111.14 bytes used=2916885212, alloc=4652204, time=111.27 bytes used=2920886224, alloc=4652204, time=111.41 bytes used=2924887208, alloc=4652204, time=111.54 bytes used=2928890604, alloc=4652204, time=111.68 bytes used=2932891352, alloc=4652204, time=111.81 bytes used=2936892412, alloc=4652204, time=111.95 bytes used=2940895456, alloc=4652204, time=112.08 bytes used=2944896692, alloc=4652204, time=112.22 bytes used=2948897408, alloc=4652204, time=112.35 bytes used=2952902264, alloc=4652204, time=112.49 bytes used=2956903200, alloc=4652204, time=112.62 bytes used=2960904372, alloc=4652204, time=112.76 bytes used=2964905660, alloc=4652204, time=112.90 bytes used=2968907108, alloc=4652204, time=113.03 bytes used=2972908328, alloc=4652204, time=113.17 bytes used=2976909308, alloc=4652204, time=113.30 bytes used=2980911316, alloc=4652204, time=113.44 bytes used=2984912264, alloc=4652204, time=113.57 bytes used=2988913180, alloc=4652204, time=113.71 bytes used=2992914388, alloc=4652204, time=113.84 bytes used=2996916752, alloc=4652204, time=113.98 bytes used=3000917804, alloc=4652204, time=114.11 bytes used=3004920300, alloc=4652204, time=114.24 bytes used=3008921260, alloc=4652204, time=114.38 bytes used=3012922172, alloc=4652204, time=114.52 bytes used=3016923048, alloc=4652204, time=114.65 bytes used=3020924000, alloc=4652204, time=114.79 bytes used=3024924956, alloc=4652204, time=114.92 bytes used=3028926744, alloc=4652204, time=115.05 bytes used=3032927952, alloc=4652204, time=115.19 bytes used=3036928980, alloc=4652204, time=115.33 bytes used=3040929968, alloc=4652204, time=115.46 bytes used=3044931108, alloc=4652204, time=115.59 bytes used=3048932124, alloc=4652204, time=115.73 bytes used=3052933152, alloc=4652204, time=115.87 bytes used=3056933872, alloc=4652204, time=116.00 bytes used=3060934868, alloc=4652204, time=116.14 bytes used=3064935960, alloc=4652204, time=116.27 bytes used=3068937572, alloc=4652204, time=116.41 bytes used=3072938480, alloc=4652204, time=116.55 bytes used=3076939304, alloc=4652204, time=116.68 bytes used=3080940560, alloc=4652204, time=116.81 bytes used=3084941404, alloc=4652204, time=116.95 bytes used=3088942252, alloc=4652204, time=117.08 bytes used=3092943816, alloc=4652204, time=117.22 bytes used=3096944664, alloc=4652204, time=117.36 bytes used=3100947896, alloc=4652204, time=117.49 bytes used=3104948956, alloc=4652204, time=117.63 bytes used=3108949680, alloc=4652204, time=117.76 bytes used=3112950588, alloc=4652204, time=117.90 bytes used=3116951620, alloc=4652204, time=118.03 bytes used=3120952532, alloc=4652204, time=118.17 bytes used=3124953572, alloc=4652204, time=118.31 bytes used=3128955564, alloc=4652204, time=118.44 bytes used=3132956380, alloc=4652204, time=118.58 TOP MAIN SOLVE Loop bytes used=3136957432, alloc=4652204, time=118.71 x[1] = 0.14 y[1] (analytic) = 0.038334319936214754393346335556751 y[1] (numeric) = 0.038334319938586507435223151088851 absolute error = 2.371753041876815532100e-12 relative error = 6.1870226100873136648397235664113e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.157 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2589 Order of pole (six term test) = -0.8578 bytes used=3140960924, alloc=4652204, time=118.85 bytes used=3144961724, alloc=4652204, time=118.98 bytes used=3148964972, alloc=4652204, time=119.12 bytes used=3152966184, alloc=4652204, time=119.26 bytes used=3156967112, alloc=4652204, time=119.39 bytes used=3160968244, alloc=4652204, time=119.53 bytes used=3164970280, alloc=4652204, time=119.66 bytes used=3168971352, alloc=4652204, time=119.80 bytes used=3172972604, alloc=4652204, time=119.93 bytes used=3176974384, alloc=4652204, time=120.06 bytes used=3180975032, alloc=4652204, time=120.20 bytes used=3184975988, alloc=4652204, time=120.34 bytes used=3188976836, alloc=4652204, time=120.47 bytes used=3192977944, alloc=4652204, time=120.61 bytes used=3196979220, alloc=4652204, time=120.74 bytes used=3200980288, alloc=4652204, time=120.87 bytes used=3204981376, alloc=4652204, time=121.01 bytes used=3208982632, alloc=4652204, time=121.14 bytes used=3212984036, alloc=4652204, time=121.28 bytes used=3216984912, alloc=4652204, time=121.42 bytes used=3220986268, alloc=4652204, time=121.55 bytes used=3224987052, alloc=4652204, time=121.69 bytes used=3228988408, alloc=4652204, time=121.82 bytes used=3232990036, alloc=4652204, time=121.96 bytes used=3236991460, alloc=4652204, time=122.09 bytes used=3240992616, alloc=4652204, time=122.22 bytes used=3244993532, alloc=4652204, time=122.36 bytes used=3248994328, alloc=4652204, time=122.50 bytes used=3252995208, alloc=4652204, time=122.63 bytes used=3256996216, alloc=4652204, time=122.77 bytes used=3260997336, alloc=4652204, time=122.90 bytes used=3264998408, alloc=4652204, time=123.03 bytes used=3268999448, alloc=4652204, time=123.17 bytes used=3273000220, alloc=4652204, time=123.31 bytes used=3277001396, alloc=4652204, time=123.44 bytes used=3281002296, alloc=4652204, time=123.58 bytes used=3285003388, alloc=4652204, time=123.71 bytes used=3289004800, alloc=4652204, time=123.85 bytes used=3293005588, alloc=4652204, time=123.98 bytes used=3297006572, alloc=4652204, time=124.12 bytes used=3301007296, alloc=4652204, time=124.25 bytes used=3305008260, alloc=4652204, time=124.39 bytes used=3309009592, alloc=4652204, time=124.52 bytes used=3313010568, alloc=4652204, time=124.66 bytes used=3317012144, alloc=4652204, time=124.79 bytes used=3321012924, alloc=4652204, time=124.93 bytes used=3325013588, alloc=4652204, time=125.06 bytes used=3329014424, alloc=4652204, time=125.20 bytes used=3333015404, alloc=4652204, time=125.33 bytes used=3337016368, alloc=4652204, time=125.47 bytes used=3341018496, alloc=4652204, time=125.60 bytes used=3345019360, alloc=4652204, time=125.74 bytes used=3349020272, alloc=4652204, time=125.87 bytes used=3353021000, alloc=4652204, time=126.01 bytes used=3357022160, alloc=4652204, time=126.15 bytes used=3361023484, alloc=4652204, time=126.28 bytes used=3365024420, alloc=4652204, time=126.41 bytes used=3369025816, alloc=4652204, time=126.55 bytes used=3373028932, alloc=4652204, time=126.69 bytes used=3377030756, alloc=4652204, time=126.82 bytes used=3381032444, alloc=4652204, time=126.96 bytes used=3385033532, alloc=4652204, time=127.09 bytes used=3389035700, alloc=4652204, time=127.23 bytes used=3393036844, alloc=4652204, time=127.37 bytes used=3397038620, alloc=4652204, time=127.50 bytes used=3401039524, alloc=4652204, time=127.64 bytes used=3405040584, alloc=4652204, time=127.77 bytes used=3409041428, alloc=4652204, time=127.91 bytes used=3413042640, alloc=4652204, time=128.04 bytes used=3417043324, alloc=4652204, time=128.18 bytes used=3421044380, alloc=4652204, time=128.31 bytes used=3425045560, alloc=4652204, time=128.45 bytes used=3429047760, alloc=4652204, time=128.59 bytes used=3433048596, alloc=4652204, time=128.72 bytes used=3437049836, alloc=4652204, time=128.86 bytes used=3441050976, alloc=4652204, time=128.99 bytes used=3445052080, alloc=4652204, time=129.13 bytes used=3449052936, alloc=4652204, time=129.26 bytes used=3453053732, alloc=4652204, time=129.40 bytes used=3457054688, alloc=4652204, time=129.53 bytes used=3461055628, alloc=4652204, time=129.67 bytes used=3465057320, alloc=4652204, time=129.81 bytes used=3469058000, alloc=4652204, time=129.94 bytes used=3473059536, alloc=4652204, time=130.08 bytes used=3477060244, alloc=4652204, time=130.21 bytes used=3481061348, alloc=4652204, time=130.35 bytes used=3485062288, alloc=4652204, time=130.48 bytes used=3489063180, alloc=4652204, time=130.62 bytes used=3493064188, alloc=4652204, time=130.75 bytes used=3497065052, alloc=4652204, time=130.89 bytes used=3501065940, alloc=4652204, time=131.03 bytes used=3505068484, alloc=4652204, time=131.16 bytes used=3509069624, alloc=4652204, time=131.30 bytes used=3513070420, alloc=4652204, time=131.44 bytes used=3517071248, alloc=4652204, time=131.57 bytes used=3521072056, alloc=4652204, time=131.71 bytes used=3525073020, alloc=4652204, time=131.84 bytes used=3529074344, alloc=4652204, time=131.98 bytes used=3533075440, alloc=4652204, time=132.11 bytes used=3537076504, alloc=4652204, time=132.25 bytes used=3541077404, alloc=4652204, time=132.38 bytes used=3545078808, alloc=4652204, time=132.52 bytes used=3549079552, alloc=4652204, time=132.65 bytes used=3553080308, alloc=4652204, time=132.79 bytes used=3557081424, alloc=4652204, time=132.93 bytes used=3561082508, alloc=4652204, time=133.06 bytes used=3565083420, alloc=4652204, time=133.20 bytes used=3569084216, alloc=4652204, time=133.34 bytes used=3573085324, alloc=4652204, time=133.47 bytes used=3577086220, alloc=4652204, time=133.61 bytes used=3581087276, alloc=4652204, time=133.75 bytes used=3585088140, alloc=4652204, time=133.88 bytes used=3589089676, alloc=4652204, time=134.01 bytes used=3593091216, alloc=4717728, time=134.15 bytes used=3597092520, alloc=4717728, time=134.28 bytes used=3601093648, alloc=4717728, time=134.42 bytes used=3605095116, alloc=4717728, time=134.55 bytes used=3609095948, alloc=4717728, time=134.69 bytes used=3613096904, alloc=4717728, time=134.82 bytes used=3617097728, alloc=4717728, time=134.96 bytes used=3621098784, alloc=4717728, time=135.09 bytes used=3625099736, alloc=4717728, time=135.23 bytes used=3629100792, alloc=4717728, time=135.37 bytes used=3633102116, alloc=4717728, time=135.50 bytes used=3637103152, alloc=4717728, time=135.63 bytes used=3641104408, alloc=4717728, time=135.77 bytes used=3645105268, alloc=4717728, time=135.91 bytes used=3649106480, alloc=4717728, time=136.04 bytes used=3653107372, alloc=4717728, time=136.18 bytes used=3657108428, alloc=4717728, time=136.31 bytes used=3661112268, alloc=4717728, time=136.45 bytes used=3665113340, alloc=4717728, time=136.58 bytes used=3669114572, alloc=4717728, time=136.72 bytes used=3673115864, alloc=4717728, time=136.85 bytes used=3677116628, alloc=4717728, time=136.99 bytes used=3681117648, alloc=4717728, time=137.12 bytes used=3685118560, alloc=4717728, time=137.26 bytes used=3689119532, alloc=4717728, time=137.39 bytes used=3693120444, alloc=4717728, time=137.53 bytes used=3697121448, alloc=4717728, time=137.66 bytes used=3701122520, alloc=4717728, time=137.80 bytes used=3705123404, alloc=4717728, time=137.94 bytes used=3709126596, alloc=4717728, time=138.07 bytes used=3713127564, alloc=4717728, time=138.21 bytes used=3717128352, alloc=4717728, time=138.34 bytes used=3721129704, alloc=4717728, time=138.48 bytes used=3725130792, alloc=4717728, time=138.61 bytes used=3729131636, alloc=4717728, time=138.75 bytes used=3733133804, alloc=4717728, time=138.88 bytes used=3737134576, alloc=4717728, time=139.02 bytes used=3741135616, alloc=4717728, time=139.15 bytes used=3745136712, alloc=4717728, time=139.29 bytes used=3749137760, alloc=4717728, time=139.43 bytes used=3753138540, alloc=4717728, time=139.56 bytes used=3757139732, alloc=4717728, time=139.69 bytes used=3761140516, alloc=4717728, time=139.83 bytes used=3765141480, alloc=4717728, time=139.96 bytes used=3769142616, alloc=4717728, time=140.10 bytes used=3773146132, alloc=4717728, time=140.23 bytes used=3777147980, alloc=4717728, time=140.37 bytes used=3781148920, alloc=4717728, time=140.51 bytes used=3785149924, alloc=4717728, time=140.64 bytes used=3789150692, alloc=4717728, time=140.77 bytes used=3793151908, alloc=4717728, time=140.91 bytes used=3797154664, alloc=4717728, time=141.05 bytes used=3801155524, alloc=4717728, time=141.18 bytes used=3805156556, alloc=4717728, time=141.31 bytes used=3809158676, alloc=4717728, time=141.45 bytes used=3813159408, alloc=4717728, time=141.59 bytes used=3817160884, alloc=4717728, time=141.72 bytes used=3821161760, alloc=4717728, time=141.86 bytes used=3825164072, alloc=4717728, time=141.99 bytes used=3829165300, alloc=4717728, time=142.13 bytes used=3833166184, alloc=4717728, time=142.26 bytes used=3837168352, alloc=4717728, time=142.40 bytes used=3841169804, alloc=4717728, time=142.53 bytes used=3845170556, alloc=4717728, time=142.66 bytes used=3849172396, alloc=4717728, time=142.80 bytes used=3853173332, alloc=4717728, time=142.93 bytes used=3857174404, alloc=4717728, time=143.07 bytes used=3861175468, alloc=4717728, time=143.21 bytes used=3865176520, alloc=4717728, time=143.34 bytes used=3869179828, alloc=4717728, time=143.47 bytes used=3873180928, alloc=4717728, time=143.61 bytes used=3877182164, alloc=4717728, time=143.74 bytes used=3881183080, alloc=4717728, time=143.88 bytes used=3885184552, alloc=4717728, time=144.02 bytes used=3889185740, alloc=4717728, time=144.15 bytes used=3893186840, alloc=4717728, time=144.29 bytes used=3897187836, alloc=4717728, time=144.42 bytes used=3901189028, alloc=4717728, time=144.56 bytes used=3905189944, alloc=4717728, time=144.69 bytes used=3909190736, alloc=4717728, time=144.82 bytes used=3913191952, alloc=4717728, time=144.96 bytes used=3917192792, alloc=4717728, time=145.10 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.04243187703788402981872271482688 y[1] (numeric) = 0.042431877040750044075031678385552 absolute error = 2.866014256308963558672e-12 relative error = 6.7543895212321826309397472955236e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1682 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.277 Order of pole (six term test) = -0.8614 bytes used=3921193584, alloc=4717728, time=145.23 bytes used=3925195220, alloc=4717728, time=145.37 bytes used=3929197272, alloc=4717728, time=145.50 bytes used=3933198176, alloc=4717728, time=145.64 bytes used=3937199068, alloc=4717728, time=145.77 bytes used=3941200212, alloc=4717728, time=145.91 bytes used=3945203052, alloc=4717728, time=146.04 bytes used=3949205132, alloc=4717728, time=146.18 bytes used=3953205848, alloc=4717728, time=146.31 bytes used=3957206892, alloc=4717728, time=146.45 bytes used=3961207940, alloc=4717728, time=146.58 bytes used=3965209116, alloc=4717728, time=146.72 bytes used=3969210132, alloc=4717728, time=146.85 bytes used=3973211124, alloc=4717728, time=146.99 bytes used=3977212248, alloc=4717728, time=147.12 bytes used=3981213396, alloc=4717728, time=147.26 bytes used=3985214228, alloc=4717728, time=147.39 bytes used=3989215116, alloc=4717728, time=147.52 bytes used=3993217684, alloc=4717728, time=147.66 bytes used=3997218368, alloc=4717728, time=147.79 bytes used=4001219476, alloc=4717728, time=147.93 bytes used=4005220300, alloc=4717728, time=148.06 bytes used=4009221072, alloc=4717728, time=148.20 bytes used=4013222256, alloc=4717728, time=148.33 bytes used=4017223160, alloc=4717728, time=148.47 bytes used=4021225676, alloc=4717728, time=148.60 bytes used=4025226508, alloc=4717728, time=148.74 bytes used=4029227308, alloc=4717728, time=148.88 bytes used=4033228368, alloc=4717728, time=149.01 bytes used=4037229280, alloc=4717728, time=149.15 bytes used=4041231992, alloc=4717728, time=149.28 bytes used=4045233172, alloc=4717728, time=149.41 bytes used=4049234128, alloc=4717728, time=149.55 bytes used=4053235208, alloc=4717728, time=149.69 bytes used=4057236260, alloc=4717728, time=149.82 bytes used=4061237260, alloc=4717728, time=149.96 bytes used=4065238212, alloc=4717728, time=150.09 bytes used=4069239324, alloc=4717728, time=150.23 bytes used=4073240148, alloc=4717728, time=150.37 bytes used=4077241484, alloc=4717728, time=150.50 bytes used=4081242312, alloc=4717728, time=150.64 bytes used=4085243236, alloc=4717728, time=150.77 bytes used=4089244156, alloc=4717728, time=150.91 bytes used=4093244996, alloc=4717728, time=151.04 bytes used=4097245940, alloc=4717728, time=151.18 bytes used=4101247032, alloc=4717728, time=151.31 bytes used=4105247876, alloc=4717728, time=151.45 bytes used=4109248764, alloc=4717728, time=151.58 bytes used=4113249976, alloc=4717728, time=151.72 bytes used=4117250760, alloc=4717728, time=151.85 bytes used=4121251852, alloc=4717728, time=151.99 bytes used=4125252936, alloc=4717728, time=152.12 bytes used=4129253656, alloc=4717728, time=152.26 bytes used=4133254792, alloc=4717728, time=152.39 bytes used=4137256076, alloc=4717728, time=152.53 bytes used=4141257036, alloc=4717728, time=152.66 bytes used=4145257952, alloc=4717728, time=152.80 bytes used=4149258908, alloc=4717728, time=152.93 bytes used=4153259732, alloc=4717728, time=153.07 bytes used=4157260820, alloc=4717728, time=153.20 bytes used=4161262512, alloc=4717728, time=153.34 bytes used=4165263512, alloc=4717728, time=153.48 bytes used=4169264676, alloc=4717728, time=153.61 bytes used=4173265904, alloc=4717728, time=153.75 bytes used=4177266604, alloc=4717728, time=153.88 bytes used=4181267692, alloc=4717728, time=154.02 bytes used=4185268640, alloc=4717728, time=154.16 bytes used=4189269540, alloc=4717728, time=154.29 bytes used=4193270644, alloc=4717728, time=154.43 bytes used=4197271488, alloc=4717728, time=154.56 bytes used=4201272368, alloc=4717728, time=154.70 bytes used=4205273304, alloc=4717728, time=154.83 bytes used=4209274440, alloc=4717728, time=154.97 bytes used=4213275500, alloc=4717728, time=155.10 bytes used=4217276720, alloc=4717728, time=155.24 bytes used=4221277672, alloc=4717728, time=155.38 bytes used=4225283512, alloc=4717728, time=155.51 bytes used=4229284208, alloc=4717728, time=155.65 bytes used=4233285276, alloc=4717728, time=155.78 bytes used=4237286444, alloc=4717728, time=155.92 bytes used=4241287236, alloc=4717728, time=156.06 bytes used=4245288392, alloc=4717728, time=156.19 bytes used=4249289444, alloc=4717728, time=156.32 bytes used=4253290752, alloc=4717728, time=156.46 bytes used=4257293668, alloc=4717728, time=156.59 bytes used=4261294400, alloc=4717728, time=156.73 bytes used=4265295384, alloc=4717728, time=156.87 bytes used=4269296364, alloc=4717728, time=157.01 bytes used=4273297304, alloc=4717728, time=157.14 bytes used=4277298536, alloc=4717728, time=157.28 bytes used=4281299460, alloc=4717728, time=157.41 bytes used=4285300456, alloc=4717728, time=157.55 bytes used=4289301916, alloc=4717728, time=157.68 bytes used=4293303728, alloc=4717728, time=157.82 bytes used=4297304576, alloc=4717728, time=157.95 bytes used=4301305460, alloc=4717728, time=158.09 bytes used=4305307692, alloc=4717728, time=158.22 bytes used=4309309792, alloc=4717728, time=158.36 bytes used=4313310728, alloc=4717728, time=158.50 bytes used=4317311736, alloc=4717728, time=158.63 bytes used=4321312708, alloc=4717728, time=158.77 bytes used=4325313552, alloc=4717728, time=158.90 bytes used=4329314896, alloc=4717728, time=159.04 bytes used=4333315788, alloc=4717728, time=159.18 bytes used=4337316600, alloc=4717728, time=159.31 bytes used=4341317580, alloc=4717728, time=159.44 bytes used=4345318524, alloc=4717728, time=159.58 bytes used=4349320228, alloc=4717728, time=159.71 bytes used=4353320976, alloc=4717728, time=159.85 bytes used=4357322412, alloc=4717728, time=159.98 bytes used=4361323260, alloc=4717728, time=160.12 bytes used=4365324368, alloc=4717728, time=160.25 bytes used=4369325340, alloc=4717728, time=160.39 bytes used=4373326520, alloc=4717728, time=160.53 bytes used=4377327444, alloc=4717728, time=160.66 bytes used=4381328324, alloc=4717728, time=160.80 bytes used=4385329272, alloc=4717728, time=160.93 bytes used=4389330448, alloc=4717728, time=161.06 bytes used=4393331456, alloc=4717728, time=161.20 bytes used=4397332204, alloc=4717728, time=161.33 bytes used=4401333140, alloc=4717728, time=161.47 bytes used=4405336076, alloc=4717728, time=161.61 bytes used=4409336884, alloc=4717728, time=161.74 bytes used=4413337900, alloc=4717728, time=161.87 bytes used=4417338928, alloc=4717728, time=162.01 bytes used=4421340064, alloc=4717728, time=162.15 bytes used=4425341456, alloc=4717728, time=162.28 bytes used=4429342408, alloc=4717728, time=162.42 bytes used=4433344236, alloc=4717728, time=162.55 bytes used=4437345160, alloc=4717728, time=162.69 bytes used=4441348216, alloc=4717728, time=162.82 bytes used=4445349300, alloc=4717728, time=162.96 bytes used=4449350388, alloc=4717728, time=163.10 bytes used=4453351488, alloc=4717728, time=163.23 bytes used=4457353892, alloc=4717728, time=163.37 bytes used=4461356952, alloc=4717728, time=163.50 bytes used=4465357824, alloc=4717728, time=163.64 bytes used=4469358752, alloc=4717728, time=163.77 bytes used=4473359628, alloc=4717728, time=163.91 bytes used=4477360484, alloc=4717728, time=164.04 bytes used=4481361448, alloc=4717728, time=164.18 bytes used=4485362496, alloc=4717728, time=164.31 bytes used=4489363744, alloc=4717728, time=164.45 bytes used=4493364836, alloc=4717728, time=164.58 bytes used=4497370252, alloc=4717728, time=164.72 bytes used=4501371376, alloc=4717728, time=164.85 bytes used=4505373404, alloc=4717728, time=164.99 bytes used=4509374324, alloc=4717728, time=165.12 bytes used=4513376444, alloc=4717728, time=165.25 bytes used=4517377596, alloc=4717728, time=165.39 bytes used=4521378408, alloc=4717728, time=165.52 bytes used=4525379644, alloc=4717728, time=165.66 bytes used=4529380900, alloc=4717728, time=165.79 bytes used=4533381620, alloc=4717728, time=165.92 bytes used=4537382560, alloc=4717728, time=166.06 bytes used=4541383540, alloc=4717728, time=166.19 bytes used=4545384556, alloc=4717728, time=166.33 bytes used=4549385692, alloc=4717728, time=166.46 bytes used=4553386800, alloc=4717728, time=166.60 bytes used=4557388852, alloc=4717728, time=166.73 bytes used=4561390292, alloc=4717728, time=166.87 bytes used=4565392176, alloc=4717728, time=167.00 bytes used=4569393076, alloc=4717728, time=167.14 bytes used=4573394408, alloc=4717728, time=167.27 bytes used=4577395344, alloc=4717728, time=167.41 bytes used=4581397192, alloc=4717728, time=167.54 bytes used=4585401136, alloc=4717728, time=167.68 bytes used=4589402116, alloc=4717728, time=167.81 bytes used=4593405180, alloc=4717728, time=167.95 bytes used=4597406068, alloc=4717728, time=168.09 bytes used=4601407812, alloc=4717728, time=168.22 bytes used=4605408660, alloc=4717728, time=168.35 bytes used=4609409916, alloc=4717728, time=168.49 bytes used=4613415860, alloc=4717728, time=168.63 bytes used=4617417088, alloc=4717728, time=168.76 bytes used=4621418116, alloc=4717728, time=168.90 bytes used=4625419120, alloc=4717728, time=169.03 bytes used=4629419968, alloc=4717728, time=169.16 bytes used=4633420784, alloc=4717728, time=169.30 bytes used=4637421680, alloc=4717728, time=169.44 bytes used=4641422972, alloc=4717728, time=169.57 bytes used=4645424540, alloc=4717728, time=169.70 bytes used=4649425560, alloc=4717728, time=169.84 bytes used=4653426396, alloc=4717728, time=169.97 bytes used=4657427344, alloc=4717728, time=170.11 bytes used=4661428332, alloc=4717728, time=170.24 bytes used=4665429704, alloc=4717728, time=170.38 bytes used=4669430632, alloc=4717728, time=170.51 bytes used=4673431464, alloc=4717728, time=170.64 bytes used=4677432372, alloc=4717728, time=170.78 bytes used=4681433192, alloc=4717728, time=170.91 bytes used=4685434300, alloc=4717728, time=171.04 bytes used=4689436420, alloc=4717728, time=171.18 bytes used=4693437284, alloc=4717728, time=171.32 bytes used=4697438472, alloc=4717728, time=171.45 bytes used=4701439556, alloc=4717728, time=171.58 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.046654859051994282834197886797537 y[1] (numeric) = 0.046654859055324761115526324472792 absolute error = 3.330478281328437675255e-12 relative error = 7.1385453712694795726841767453049e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1794 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2951 Order of pole (six term test) = -0.8649 bytes used=4705440288, alloc=4717728, time=171.72 bytes used=4709441348, alloc=4717728, time=171.85 bytes used=4713442308, alloc=4717728, time=171.99 bytes used=4717443180, alloc=4717728, time=172.12 bytes used=4721443956, alloc=4717728, time=172.26 bytes used=4725444884, alloc=4717728, time=172.39 bytes used=4729446128, alloc=4717728, time=172.53 bytes used=4733451320, alloc=4717728, time=172.66 bytes used=4737453068, alloc=4717728, time=172.80 bytes used=4741454336, alloc=4717728, time=172.93 bytes used=4745455384, alloc=4717728, time=173.07 bytes used=4749456428, alloc=4717728, time=173.20 bytes used=4753457632, alloc=4717728, time=173.34 bytes used=4757458560, alloc=4717728, time=173.47 bytes used=4761459732, alloc=4717728, time=173.61 bytes used=4765460888, alloc=4717728, time=173.74 bytes used=4769462724, alloc=4717728, time=173.87 bytes used=4773463884, alloc=4717728, time=174.01 bytes used=4777464868, alloc=4717728, time=174.14 bytes used=4781465972, alloc=4717728, time=174.28 bytes used=4785467036, alloc=4717728, time=174.42 bytes used=4789467956, alloc=4717728, time=174.55 bytes used=4793469104, alloc=4717728, time=174.69 bytes used=4797469980, alloc=4717728, time=174.83 bytes used=4801471112, alloc=4717728, time=174.96 bytes used=4805472384, alloc=4717728, time=175.10 bytes used=4809473928, alloc=4717728, time=175.23 bytes used=4813474876, alloc=4717728, time=175.37 bytes used=4817476224, alloc=4717728, time=175.50 bytes used=4821477180, alloc=4717728, time=175.64 bytes used=4825478396, alloc=4717728, time=175.77 bytes used=4829479808, alloc=4717728, time=175.91 bytes used=4833482820, alloc=4717728, time=176.04 bytes used=4837483624, alloc=4717728, time=176.18 bytes used=4841484940, alloc=4717728, time=176.32 bytes used=4845485656, alloc=4717728, time=176.45 bytes used=4849486880, alloc=4717728, time=176.59 bytes used=4853488776, alloc=4717728, time=176.72 bytes used=4857489624, alloc=4717728, time=176.86 bytes used=4861490676, alloc=4717728, time=176.99 bytes used=4865492436, alloc=4717728, time=177.13 bytes used=4869493240, alloc=4717728, time=177.27 bytes used=4873494064, alloc=4717728, time=177.40 bytes used=4877495500, alloc=4717728, time=177.53 bytes used=4881496952, alloc=4717728, time=177.67 bytes used=4885498184, alloc=4717728, time=177.81 bytes used=4889499000, alloc=4717728, time=177.94 bytes used=4893500120, alloc=4717728, time=178.07 bytes used=4897501020, alloc=4717728, time=178.21 bytes used=4901502404, alloc=4717728, time=178.34 bytes used=4905503216, alloc=4717728, time=178.47 bytes used=4909506864, alloc=4717728, time=178.61 bytes used=4913507740, alloc=4717728, time=178.75 bytes used=4917508476, alloc=4717728, time=178.88 bytes used=4921509604, alloc=4717728, time=179.01 bytes used=4925510488, alloc=4717728, time=179.15 bytes used=4929511728, alloc=4717728, time=179.28 bytes used=4933512908, alloc=4717728, time=179.42 bytes used=4937513940, alloc=4717728, time=179.55 bytes used=4941514764, alloc=4717728, time=179.69 bytes used=4945515824, alloc=4717728, time=179.83 bytes used=4949517000, alloc=4717728, time=179.96 bytes used=4953518128, alloc=4717728, time=180.10 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = erf(sqrt(x)); Iterations = 6320 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 39 Minutes 43 Seconds Optimized Time Remaining = 39 Minutes 39 Seconds Expected Total Time = 42 Minutes 39 Seconds Time to Timeout Unknown Percent Done = 7.023 % > quit bytes used=4954408248, alloc=4717728, time=180.12