|\^/| 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_const_3D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_2D0[1]; > #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := expt(array_tmp2[1] , array_tmp4[1] ) ; > array_tmp5_a1[1] := ln(array_tmp2[1] ) ; > array_tmp5_a1[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp6[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; > #emit pre ln 1 LINEAR $eq_no = 1 > array_tmp8[1] := ln(array_tmp7[1]); > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp9[1] := array_const_3D0[1] * array_tmp8[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp10[1] := array_const_3D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp11[1] := array_tmp10[1] + array_const_2D0[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp12[1] := array_const_2D0[1] * array_tmp11[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp13[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp14[1] := array_tmp13[1] + array_const_1D0[1]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp15[1] := array_tmp12[1] / array_tmp14[1]; > #emit pre add FULL FULL $eq_no = 1 i = 1 > array_tmp16[1] := array_tmp9[1] + array_tmp15[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp17[1] := (array_tmp5[1] * (array_tmp16[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp18[1] := array_const_0D0[1] + array_tmp17[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_tmp18[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_const_3D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp5_a2[1] := (array_tmp5_a1[1] * array_tmp4[2] + array_tmp5_a1[2] * array_tmp4[1]) / glob_h; > array_tmp5[2] := array_tmp5[1] * array_tmp5_a2[1] * glob_h; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp6[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp6[2]; > #emit pre ln 2 LINEAR $eq_no = 1 > array_tmp8[2] := array_tmp7[2] / array_tmp7[1]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp9[2] := array_const_3D0[1] * array_tmp8[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp10[2] := array_const_3D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp11[2] := array_tmp10[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp12[2] := array_const_2D0[1] * array_tmp11[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp13[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp14[2] := array_tmp13[2]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp15[2] := (array_tmp12[2] - array_tmp15[1] * array_tmp14[2]) / array_tmp14[1]; > #emit pre add FULL FULL $eq_no = 1 i = 2 > array_tmp16[2] := array_tmp9[2] + array_tmp15[2]; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp17[2] := ats(2,array_tmp5,array_tmp16,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp18[2] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp5_a1[3] := -array_tmp5_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2; > array_tmp5_a2[2] := (array_tmp5_a1[2] * array_tmp4[2] + array_tmp5_a1[3] * array_tmp4[1]) * 2 / glob_h; > array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/2; > #emit pre ln ID_LINEAR iii = 3 $eq_no = 1 > array_tmp8[3] := - array_tmp7[2] * array_tmp8[2] * 1 / array_tmp7[1] / 2; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp9[3] := array_const_3D0[1] * array_tmp8[3]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp15[3] := - array_tmp15[2] * array_tmp14[2] / array_tmp14[1]; > #emit pre add FULL FULL $eq_no = 1 i = 3 > array_tmp16[3] := array_tmp9[3] + array_tmp15[3]; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp17[3] := ats(3,array_tmp5,array_tmp16,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp18[3] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 4 > array_tmp5_a1[4] := -array_tmp5_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3; > array_tmp5_a2[3] := (array_tmp5_a1[3] * array_tmp4[2] + array_tmp5_a1[4] * array_tmp4[1]) * 3 / glob_h; > array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/3; > #emit pre ln ID_LINEAR iii = 4 $eq_no = 1 > array_tmp8[4] := - array_tmp7[2] * array_tmp8[3] * 2 / array_tmp7[1] / 3; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp9[4] := array_const_3D0[1] * array_tmp8[4]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 4 > array_tmp15[4] := - array_tmp15[3] * array_tmp14[2] / array_tmp14[1]; > #emit pre add FULL FULL $eq_no = 1 i = 4 > array_tmp16[4] := array_tmp9[4] + array_tmp15[4]; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp17[4] := ats(4,array_tmp5,array_tmp16,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp18[4] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 5 > array_tmp5_a1[5] := -array_tmp5_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4; > array_tmp5_a2[4] := (array_tmp5_a1[4] * array_tmp4[2] + array_tmp5_a1[5] * array_tmp4[1]) * 4 / glob_h; > array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/4; > #emit pre ln ID_LINEAR iii = 5 $eq_no = 1 > array_tmp8[5] := - array_tmp7[2] * array_tmp8[4] * 3 / array_tmp7[1] / 4; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp9[5] := array_const_3D0[1] * array_tmp8[5]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 5 > array_tmp15[5] := - array_tmp15[4] * array_tmp14[2] / array_tmp14[1]; > #emit pre add FULL FULL $eq_no = 1 i = 5 > array_tmp16[5] := array_tmp9[5] + array_tmp15[5]; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp17[5] := ats(5,array_tmp5,array_tmp16,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp18[5] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp5_a1[kkk] := -array_tmp5_a1[kkk-1] * array_tmp4[2] * (kkk-2) / array_tmp2[1] / (kkk - 1); > array_tmp5_a2[kkk-1] := (array_tmp5_a1[kkk-1] * array_tmp4[2] + array_tmp5_a1[kkk] * array_tmp4[1]) * (kkk-1) / glob_h; > array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h/(kkk-1); > #emit ln LINEAR $eq_no = 1 > array_tmp8[kkk] := - array_tmp7[2] * array_tmp8[kkk - 1] * (kkk - 2)/ array_tmp7[1] / (kkk - 1); > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp9[kkk] := array_const_3D0[1] * array_tmp8[kkk]; > #emit div LINEAR - LINEAR (NOP) $eq_no = 1 i = 1 > array_tmp15[kkk] := - array_tmp15[kkk-1] * array_tmp14[2] / array_tmp14[1]; > #emit FULL - FULL add $eq_no = 1 > array_tmp16[kkk] := array_tmp9[kkk] + array_tmp15[kkk]; > #emit mult FULL FULL $eq_no = 1 > array_tmp17[kkk] := ats(kkk,array_tmp5,array_tmp16,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp18[kkk] := array_tmp17[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_tmp18[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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := array_const_3D0[1]*array_x[1]; array_tmp4[1] := array_tmp3[1] + array_const_2D0[1]; array_tmp5[1] := expt(array_tmp2[1], array_tmp4[1]); array_tmp5_a1[1] := ln(array_tmp2[1]); array_tmp5_a1[2] := array_tmp2[2]/array_tmp2[1]; array_tmp6[1] := array_const_2D0[1]*array_x[1]; array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; array_tmp8[1] := ln(array_tmp7[1]); array_tmp9[1] := array_const_3D0[1]*array_tmp8[1]; array_tmp10[1] := array_const_3D0[1]*array_x[1]; array_tmp11[1] := array_tmp10[1] + array_const_2D0[1]; array_tmp12[1] := array_const_2D0[1]*array_tmp11[1]; array_tmp13[1] := array_const_2D0[1]*array_x[1]; array_tmp14[1] := array_tmp13[1] + array_const_1D0[1]; array_tmp15[1] := array_tmp12[1]/array_tmp14[1]; array_tmp16[1] := array_tmp9[1] + array_tmp15[1]; array_tmp17[1] := array_tmp5[1]*array_tmp16[1]; array_tmp18[1] := array_const_0D0[1] + array_tmp17[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp18[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_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_const_3D0[1]*array_x[2]; array_tmp4[2] := array_tmp3[2]; array_tmp5_a2[1] := ( array_tmp5_a1[1]*array_tmp4[2] + array_tmp5_a1[2]*array_tmp4[1])/ glob_h; array_tmp5[2] := array_tmp5[1]*array_tmp5_a2[1]*glob_h; array_tmp6[2] := array_const_2D0[1]*array_x[2]; array_tmp7[2] := array_tmp6[2]; array_tmp8[2] := array_tmp7[2]/array_tmp7[1]; array_tmp9[2] := array_const_3D0[1]*array_tmp8[2]; array_tmp10[2] := array_const_3D0[1]*array_x[2]; array_tmp11[2] := array_tmp10[2]; array_tmp12[2] := array_const_2D0[1]*array_tmp11[2]; array_tmp13[2] := array_const_2D0[1]*array_x[2]; array_tmp14[2] := array_tmp13[2]; array_tmp15[2] := (array_tmp12[2] - array_tmp15[1]*array_tmp14[2])/array_tmp14[1]; array_tmp16[2] := array_tmp9[2] + array_tmp15[2]; array_tmp17[2] := ats(2, array_tmp5, array_tmp16, 1); array_tmp18[2] := array_tmp17[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp18[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_tmp5_a1[3] := -1/2*array_tmp5_a1[2]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[2] := 2* (array_tmp5_a1[2]*array_tmp4[2] + array_tmp5_a1[3]*array_tmp4[1])/ glob_h; array_tmp5[3] := 1/2*ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp8[3] := -1/2*array_tmp7[2]*array_tmp8[2]/array_tmp7[1]; array_tmp9[3] := array_const_3D0[1]*array_tmp8[3]; array_tmp15[3] := -array_tmp15[2]*array_tmp14[2]/array_tmp14[1]; array_tmp16[3] := array_tmp9[3] + array_tmp15[3]; array_tmp17[3] := ats(3, array_tmp5, array_tmp16, 1); array_tmp18[3] := array_tmp17[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp18[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_tmp5_a1[4] := -2/3*array_tmp5_a1[3]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[3] := 3* (array_tmp5_a1[3]*array_tmp4[2] + array_tmp5_a1[4]*array_tmp4[1])/ glob_h; array_tmp5[4] := 1/3*ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp8[4] := -2/3*array_tmp7[2]*array_tmp8[3]/array_tmp7[1]; array_tmp9[4] := array_const_3D0[1]*array_tmp8[4]; array_tmp15[4] := -array_tmp15[3]*array_tmp14[2]/array_tmp14[1]; array_tmp16[4] := array_tmp9[4] + array_tmp15[4]; array_tmp17[4] := ats(4, array_tmp5, array_tmp16, 1); array_tmp18[4] := array_tmp17[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp18[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_tmp5_a1[5] := -3/4*array_tmp5_a1[4]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[4] := 4* (array_tmp5_a1[4]*array_tmp4[2] + array_tmp5_a1[5]*array_tmp4[1])/ glob_h; array_tmp5[5] := 1/4*ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp8[5] := -3/4*array_tmp7[2]*array_tmp8[4]/array_tmp7[1]; array_tmp9[5] := array_const_3D0[1]*array_tmp8[5]; array_tmp15[5] := -array_tmp15[4]*array_tmp14[2]/array_tmp14[1]; array_tmp16[5] := array_tmp9[5] + array_tmp15[5]; array_tmp17[5] := ats(5, array_tmp5, array_tmp16, 1); array_tmp18[5] := array_tmp17[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp18[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_tmp5_a1[kkk] := -array_tmp5_a1[kkk - 1]*array_tmp4[2]* (kkk - 2)/(array_tmp2[1]*(kkk - 1)); array_tmp5_a2[kkk - 1] := (array_tmp5_a1[kkk - 1]*array_tmp4[2] + array_tmp5_a1[kkk]*array_tmp4[1])*(kkk - 1)/glob_h; array_tmp5[kkk] := ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/(kkk - 1); array_tmp8[kkk] := -array_tmp7[2]*array_tmp8[kkk - 1]*(kkk - 2)/( array_tmp7[1]*(kkk - 1)); array_tmp9[kkk] := array_const_3D0[1]*array_tmp8[kkk]; array_tmp15[kkk] := -array_tmp15[kkk - 1]*array_tmp14[2]/array_tmp14[1]; array_tmp16[kkk] := array_tmp9[kkk] + array_tmp15[kkk]; array_tmp17[kkk] := ats(kkk, array_tmp5, array_tmp16, 1); array_tmp18[kkk] := array_tmp17[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_tmp18[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 > exact_soln_y := proc(x) > return(expt(2.0*x+1.0,3.0*x+2.0)); > end; exact_soln_y := proc(x) return expt(2.0*x + 1.0, 3.0*x + 2.0) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, 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, > array_const_2D0, > array_const_1D0, > array_const_3D0, > #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, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > 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/expt_lin_lin_newpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > 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,"#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,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(expt(2.0*x+1.0,3.0*x+2.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_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:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5_c1:= Array(0..(max_terms + 1),[]); > array_tmp5_a1:= Array(0..(max_terms + 1),[]); > array_tmp5_a2:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_tmp15:= Array(0..(max_terms + 1),[]); > array_tmp16:= Array(0..(max_terms + 1),[]); > array_tmp17:= Array(0..(max_terms + 1),[]); > array_tmp18:= 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[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_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp18[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 := 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_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp18 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp18[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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1D0[1] := 1.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_3D0[1] := 3.0; > 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 > 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; > #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 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"); > 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,"2013-05-26T01:11:30-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_lin_lin_new") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_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,"expt_lin_lin_new diffeq.mxt") > ; > logitem_str(html_log_file,"expt_lin_lin_new maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > 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_const_2D0, array_const_1D0, array_const_3D0, 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, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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/expt_lin_lin_newpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 *\ x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.\ 0 ) ) / ( 2.0 * x + 1.0) ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); 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, "#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, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(expt(2.0*x+1.0,3.0*x+2.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; 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 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5_c1 := Array(0 .. max_terms + 1, []); array_tmp5_a1 := Array(0 .. max_terms + 1, []); array_tmp5_a2 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_tmp15 := Array(0 .. max_terms + 1, []); array_tmp16 := Array(0 .. max_terms + 1, []); array_tmp17 := Array(0 .. max_terms + 1, []); array_tmp18 := 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[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp18[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 := 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_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_c1[term] := 0.; term := term + 1 end do; array_tmp5_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a1[term] := 0.; term := term + 1 end do; array_tmp5_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a2[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp18 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp18[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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_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 ) = expt( 2.0 * x + 1.0 , 3.0\ * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * \ x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T01:11:30-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_lin_lin_new"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * \ x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+\ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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, "expt_lin_lin_new diffeq.mxt"); logitem_str(html_log_file, "expt_lin_lin_new maple results"); logitem_str(html_log_file, "All Tests - All Languages"); 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/expt_lin_lin_newpostode.ode################# diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK 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; #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 exact_soln_y := proc(x) return(expt(2.0*x+1.0,3.0*x+2.0)); 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 = 1.0595270250829724090345543846579e-152 estimated_step_error = 1.0595270250829724090345543846579e-152 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 = 1.4732301750687331621919901387752e-142 estimated_step_error = 1.4732301750687331621919901387752e-142 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.8866574970083322734014041551222e-135 estimated_step_error = 9.8866574970083322734014041551222e-135 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 = 6.6347928667115315098678429780350e-127 estimated_step_error = 6.6347928667115315098678429780350e-127 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 = 4.4524929614884137361714297309096e-119 estimated_step_error = 4.4524929614884137361714297309096e-119 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop bytes used=4000964, alloc=2948580, time=0.12 x[1] = 0.1 y[1] (analytic) = 1.5209567545525317650119915799094 y[1] (numeric) = 1.5209567545525317650119915799094 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=8002468, alloc=4128012, time=0.25 bytes used=12003548, alloc=4390108, time=0.37 bytes used=16004460, alloc=4455632, time=0.51 bytes used=20005216, alloc=4521156, time=0.64 bytes used=24005952, alloc=4586680, time=0.77 bytes used=28006752, alloc=4586680, time=0.91 bytes used=32008184, alloc=4652204, time=1.04 bytes used=36010128, alloc=4652204, time=1.18 bytes used=40011560, alloc=4652204, time=1.31 bytes used=44012360, alloc=4652204, time=1.45 bytes used=48013388, alloc=4652204, time=1.58 bytes used=52014416, alloc=4652204, time=1.72 bytes used=56015504, alloc=4652204, time=1.85 bytes used=60016872, alloc=4717728, time=1.99 bytes used=64017692, alloc=4717728, time=2.12 bytes used=68019648, alloc=4717728, time=2.26 bytes used=72020632, alloc=4717728, time=2.39 bytes used=76021724, alloc=4717728, time=2.53 bytes used=80023264, alloc=4717728, time=2.67 bytes used=84024232, alloc=4717728, time=2.80 bytes used=88025188, alloc=4717728, time=2.94 bytes used=92026364, alloc=4717728, time=3.07 bytes used=96027452, alloc=4717728, time=3.21 bytes used=100028512, alloc=4717728, time=3.35 bytes used=104029500, alloc=4717728, time=3.48 bytes used=108030368, alloc=4717728, time=3.62 bytes used=112031372, alloc=4717728, time=3.75 bytes used=116032764, alloc=4717728, time=3.89 bytes used=120033600, alloc=4717728, time=4.02 bytes used=124034864, alloc=4717728, time=4.16 bytes used=128035720, alloc=4783252, time=4.30 bytes used=132036724, alloc=4783252, time=4.43 bytes used=136037856, alloc=4783252, time=4.57 bytes used=140038632, alloc=4783252, time=4.71 bytes used=144039568, alloc=4783252, time=4.84 bytes used=148040612, alloc=4783252, time=4.98 bytes used=152041712, alloc=4783252, time=5.12 bytes used=156042588, alloc=4783252, time=5.25 bytes used=160043384, alloc=4783252, time=5.38 bytes used=164044544, alloc=4783252, time=5.52 bytes used=168045636, alloc=4783252, time=5.66 bytes used=172048016, alloc=4783252, time=5.80 bytes used=176048928, alloc=4783252, time=5.93 bytes used=180050380, alloc=4783252, time=6.07 bytes used=184051896, alloc=4783252, time=6.21 bytes used=188053092, alloc=4783252, time=6.34 bytes used=192054076, alloc=4783252, time=6.48 bytes used=196055408, alloc=4783252, time=6.62 bytes used=200056556, alloc=4783252, time=6.75 bytes used=204058540, alloc=4783252, time=6.89 bytes used=208060144, alloc=4783252, time=7.02 bytes used=212060824, alloc=4783252, time=7.16 bytes used=216063032, alloc=4783252, time=7.30 bytes used=220065484, alloc=4783252, time=7.43 bytes used=224066328, alloc=4783252, time=7.57 bytes used=228069124, alloc=4783252, time=7.70 bytes used=232069968, alloc=4783252, time=7.84 bytes used=236071372, alloc=4783252, time=7.98 bytes used=240072524, alloc=4783252, time=8.12 bytes used=244073316, alloc=4783252, time=8.25 bytes used=248074404, alloc=4783252, time=8.39 bytes used=252075332, alloc=4783252, time=8.52 bytes used=256076092, alloc=4783252, time=8.66 bytes used=260077048, alloc=4783252, time=8.79 bytes used=264077924, alloc=4783252, time=8.93 bytes used=268078956, alloc=4783252, time=9.07 bytes used=272080160, alloc=4783252, time=9.20 bytes used=276081064, alloc=4783252, time=9.34 bytes used=280081812, alloc=4783252, time=9.48 bytes used=284083556, alloc=4783252, time=9.61 bytes used=288084744, alloc=4783252, time=9.75 bytes used=292086596, alloc=4783252, time=9.88 bytes used=296087520, alloc=4783252, time=10.02 bytes used=300089384, alloc=4783252, time=10.16 bytes used=304090648, alloc=4783252, time=10.29 bytes used=308092708, alloc=4783252, time=10.43 bytes used=312093628, alloc=4783252, time=10.57 bytes used=316094276, alloc=4783252, time=10.71 bytes used=320095792, alloc=4783252, time=10.84 bytes used=324096704, alloc=4783252, time=10.98 bytes used=328097356, alloc=4783252, time=11.12 bytes used=332098356, alloc=4783252, time=11.25 bytes used=336099844, alloc=4783252, time=11.39 bytes used=340101908, alloc=4783252, time=11.53 bytes used=344103040, alloc=4783252, time=11.67 bytes used=348103796, alloc=4783252, time=11.81 bytes used=352105092, alloc=4783252, time=11.94 bytes used=356106468, alloc=4783252, time=12.08 bytes used=360107440, alloc=4783252, time=12.22 bytes used=364108140, alloc=4783252, time=12.35 bytes used=368109760, alloc=4783252, time=12.48 bytes used=372110512, alloc=4783252, time=12.62 bytes used=376111504, alloc=4783252, time=12.76 bytes used=380112640, alloc=4783252, time=12.89 bytes used=384113752, alloc=4848776, time=13.03 bytes used=388114616, alloc=4848776, time=13.16 bytes used=392116068, alloc=4848776, time=13.30 bytes used=396116876, alloc=4848776, time=13.44 bytes used=400118392, alloc=4848776, time=13.58 bytes used=404119604, alloc=4848776, time=13.71 bytes used=408120708, alloc=4848776, time=13.85 bytes used=412121632, alloc=4848776, time=13.99 bytes used=416123460, alloc=4848776, time=14.12 bytes used=420124612, alloc=4848776, time=14.26 bytes used=424125484, alloc=4848776, time=14.40 bytes used=428126580, alloc=4848776, time=14.54 bytes used=432127624, alloc=4848776, time=14.67 bytes used=436129360, alloc=4848776, time=14.81 bytes used=440130132, alloc=4848776, time=14.95 bytes used=444133032, alloc=4848776, time=15.09 bytes used=448134192, alloc=4848776, time=15.22 bytes used=452135404, alloc=4848776, time=15.36 bytes used=456136204, alloc=4848776, time=15.49 bytes used=460137120, alloc=4848776, time=15.63 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.5893458251948312793263967179729 y[1] (numeric) = 1.5893458259610241852058987753152 absolute error = 7.661929058795020573423e-10 relative error = 4.8208067352841705358884213444612e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4482 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 = 1.767 Order of pole (six term test) = -97.69 bytes used=464138276, alloc=4848776, time=15.77 bytes used=468139464, alloc=4848776, time=15.90 bytes used=472140328, alloc=4848776, time=16.04 bytes used=476142892, alloc=4848776, time=16.18 bytes used=480145436, alloc=4848776, time=16.32 bytes used=484146240, alloc=4848776, time=16.45 bytes used=488147868, alloc=4848776, time=16.59 bytes used=492148968, alloc=4848776, time=16.73 bytes used=496150060, alloc=4848776, time=16.87 bytes used=500150852, alloc=4848776, time=17.00 bytes used=504155068, alloc=4848776, time=17.14 bytes used=508155916, alloc=4848776, time=17.28 bytes used=512156804, alloc=4848776, time=17.41 bytes used=516158184, alloc=4848776, time=17.56 bytes used=520159392, alloc=4848776, time=17.69 bytes used=524160080, alloc=4848776, time=17.83 bytes used=528162556, alloc=4848776, time=17.96 bytes used=532163368, alloc=4848776, time=18.10 bytes used=536164368, alloc=4848776, time=18.24 bytes used=540165256, alloc=4848776, time=18.38 bytes used=544166104, alloc=4848776, time=18.51 bytes used=548167716, alloc=4848776, time=18.65 bytes used=552168664, alloc=4848776, time=18.79 bytes used=556174356, alloc=4848776, time=18.92 bytes used=560176740, alloc=4848776, time=19.06 bytes used=564177600, alloc=4848776, time=19.20 bytes used=568178704, alloc=4848776, time=19.33 bytes used=572181592, alloc=4848776, time=19.47 bytes used=576182372, alloc=4848776, time=19.61 bytes used=580183556, alloc=4848776, time=19.74 bytes used=584184552, alloc=4848776, time=19.88 bytes used=588185616, alloc=4848776, time=20.02 bytes used=592186768, alloc=4848776, time=20.15 bytes used=596187580, alloc=4848776, time=20.29 bytes used=600188724, alloc=4848776, time=20.43 bytes used=604189420, alloc=4848776, time=20.56 bytes used=608191208, alloc=4848776, time=20.70 bytes used=612192076, alloc=4848776, time=20.84 bytes used=616193268, alloc=4848776, time=20.98 bytes used=620194456, alloc=4848776, time=21.11 bytes used=624197540, alloc=4848776, time=21.25 bytes used=628198580, alloc=4848776, time=21.39 bytes used=632199312, alloc=4848776, time=21.53 bytes used=636200456, alloc=4848776, time=21.66 bytes used=640201752, alloc=4848776, time=21.80 bytes used=644202456, alloc=4848776, time=21.94 bytes used=648203428, alloc=4848776, time=22.08 bytes used=652204528, alloc=4848776, time=22.22 bytes used=656205772, alloc=4848776, time=22.35 bytes used=660206812, alloc=4848776, time=22.49 bytes used=664207836, alloc=4848776, time=22.63 bytes used=668208780, alloc=4848776, time=22.77 bytes used=672209660, alloc=4848776, time=22.90 bytes used=676212412, alloc=4848776, time=23.04 bytes used=680213172, alloc=4848776, time=23.18 bytes used=684213972, alloc=4848776, time=23.32 bytes used=688215796, alloc=4848776, time=23.45 bytes used=692216656, alloc=4848776, time=23.59 bytes used=696217784, alloc=4848776, time=23.73 bytes used=700219364, alloc=4848776, time=23.86 bytes used=704220364, alloc=4848776, time=24.00 bytes used=708221708, alloc=4848776, time=24.14 bytes used=712223156, alloc=4848776, time=24.27 bytes used=716224060, alloc=4848776, time=24.41 bytes used=720225104, alloc=4848776, time=24.55 bytes used=724225748, alloc=4914300, time=24.69 bytes used=728227108, alloc=4914300, time=24.82 bytes used=732229892, alloc=4914300, time=24.96 bytes used=736230744, alloc=4914300, time=25.10 bytes used=740231592, alloc=4914300, time=25.24 bytes used=744232868, alloc=4914300, time=25.37 bytes used=748233644, alloc=4914300, time=25.51 bytes used=752234644, alloc=4914300, time=25.64 bytes used=756235608, alloc=4914300, time=25.78 bytes used=760237056, alloc=4914300, time=25.92 bytes used=764239004, alloc=4914300, time=26.05 bytes used=768240184, alloc=4914300, time=26.19 bytes used=772241124, alloc=4914300, time=26.33 bytes used=776242120, alloc=4914300, time=26.47 bytes used=780246172, alloc=4914300, time=26.60 bytes used=784247088, alloc=4914300, time=26.74 bytes used=788248072, alloc=4914300, time=26.88 bytes used=792249032, alloc=4914300, time=27.02 bytes used=796250480, alloc=4914300, time=27.16 bytes used=800251528, alloc=4914300, time=27.29 bytes used=804252636, alloc=4914300, time=27.43 bytes used=808253620, alloc=4914300, time=27.57 bytes used=812254716, alloc=4914300, time=27.71 bytes used=816255428, alloc=4914300, time=27.85 bytes used=820256180, alloc=4914300, time=27.98 bytes used=824257024, alloc=4914300, time=28.12 bytes used=828258468, alloc=4914300, time=28.26 bytes used=832260248, alloc=4914300, time=28.39 bytes used=836261552, alloc=4914300, time=28.53 bytes used=840262496, alloc=4914300, time=28.67 bytes used=844263532, alloc=4914300, time=28.81 bytes used=848264372, alloc=4914300, time=28.95 bytes used=852265316, alloc=4914300, time=29.08 bytes used=856266580, alloc=4914300, time=29.22 bytes used=860267444, alloc=4914300, time=29.36 bytes used=864268300, alloc=4914300, time=29.50 bytes used=868269768, alloc=4914300, time=29.63 bytes used=872270876, alloc=4914300, time=29.77 bytes used=876271864, alloc=4914300, time=29.91 bytes used=880273080, alloc=4914300, time=30.05 bytes used=884274060, alloc=4914300, time=30.19 bytes used=888275128, alloc=4914300, time=30.33 bytes used=892276020, alloc=4914300, time=30.46 bytes used=896277020, alloc=4914300, time=30.60 bytes used=900279592, alloc=4914300, time=30.74 bytes used=904280436, alloc=4914300, time=30.88 bytes used=908281160, alloc=4914300, time=31.01 bytes used=912281896, alloc=4914300, time=31.15 bytes used=916282832, alloc=4914300, time=31.28 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.6614037140192547633295446461219 y[1] (numeric) = 1.6614037147854476692090467066661 absolute error = 7.661929058795020605442e-10 relative error = 4.6117201942803788775923307281859e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4556 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 = 1.679 Order of pole (six term test) = -81.02 bytes used=920284096, alloc=4914300, time=31.42 bytes used=924284864, alloc=4914300, time=31.56 bytes used=928286564, alloc=4914300, time=31.70 bytes used=932287380, alloc=4914300, time=31.84 bytes used=936288228, alloc=4914300, time=31.97 bytes used=940288996, alloc=4914300, time=32.11 bytes used=944289908, alloc=4914300, time=32.25 bytes used=948290892, alloc=4914300, time=32.39 bytes used=952292072, alloc=4914300, time=32.52 bytes used=956294032, alloc=4914300, time=32.66 bytes used=960294972, alloc=4914300, time=32.80 bytes used=964295920, alloc=4914300, time=32.94 bytes used=968298144, alloc=4914300, time=33.07 bytes used=972301320, alloc=4914300, time=33.21 bytes used=976302044, alloc=4914300, time=33.35 bytes used=980302988, alloc=4914300, time=33.49 bytes used=984304128, alloc=4914300, time=33.62 bytes used=988305692, alloc=4914300, time=33.76 bytes used=992306816, alloc=4914300, time=33.89 bytes used=996308560, alloc=4914300, time=34.03 bytes used=1000309252, alloc=4914300, time=34.17 bytes used=1004309980, alloc=4914300, time=34.31 bytes used=1008311640, alloc=4914300, time=34.45 bytes used=1012312420, alloc=4914300, time=34.58 bytes used=1016313260, alloc=4914300, time=34.72 bytes used=1020314168, alloc=4914300, time=34.86 bytes used=1024315680, alloc=4914300, time=34.99 bytes used=1028316556, alloc=4914300, time=35.13 bytes used=1032317556, alloc=4914300, time=35.27 bytes used=1036318648, alloc=4914300, time=35.41 bytes used=1040319632, alloc=4914300, time=35.55 bytes used=1044320660, alloc=4914300, time=35.69 bytes used=1048321512, alloc=4914300, time=35.83 bytes used=1052322604, alloc=4914300, time=35.97 bytes used=1056323640, alloc=4914300, time=36.10 bytes used=1060326060, alloc=4914300, time=36.24 bytes used=1064326936, alloc=4914300, time=36.38 bytes used=1068327872, alloc=4914300, time=36.52 bytes used=1072328960, alloc=4914300, time=36.66 bytes used=1076330276, alloc=4914300, time=36.79 bytes used=1080331036, alloc=4914300, time=36.93 bytes used=1084331888, alloc=4914300, time=37.07 bytes used=1088332864, alloc=4914300, time=37.21 bytes used=1092335184, alloc=4914300, time=37.35 bytes used=1096340072, alloc=4914300, time=37.48 bytes used=1100340884, alloc=4914300, time=37.62 bytes used=1104341580, alloc=4914300, time=37.76 bytes used=1108343892, alloc=4914300, time=37.90 bytes used=1112344948, alloc=4914300, time=38.03 bytes used=1116346216, alloc=4914300, time=38.17 bytes used=1120347440, alloc=4914300, time=38.31 bytes used=1124348468, alloc=4914300, time=38.45 bytes used=1128349468, alloc=4914300, time=38.59 bytes used=1132354092, alloc=4914300, time=38.72 bytes used=1136354780, alloc=4914300, time=38.86 bytes used=1140355856, alloc=4914300, time=38.99 bytes used=1144357832, alloc=4914300, time=39.13 bytes used=1148360116, alloc=4914300, time=39.27 bytes used=1152363116, alloc=4914300, time=39.41 bytes used=1156364180, alloc=4914300, time=39.55 bytes used=1160365396, alloc=4914300, time=39.68 bytes used=1164366404, alloc=4914300, time=39.82 bytes used=1168367860, alloc=4914300, time=39.96 bytes used=1172369072, alloc=4914300, time=40.09 bytes used=1176370016, alloc=4914300, time=40.23 bytes used=1180370968, alloc=4914300, time=40.37 bytes used=1184373564, alloc=4914300, time=40.51 bytes used=1188376796, alloc=4914300, time=40.64 bytes used=1192377648, alloc=4914300, time=40.78 bytes used=1196378672, alloc=4914300, time=40.92 bytes used=1200380508, alloc=4914300, time=41.06 bytes used=1204381888, alloc=4914300, time=41.19 bytes used=1208382856, alloc=4914300, time=41.34 bytes used=1212383904, alloc=4914300, time=41.47 bytes used=1216385160, alloc=4914300, time=41.61 bytes used=1220386068, alloc=4914300, time=41.75 bytes used=1224388000, alloc=4914300, time=41.89 bytes used=1228388720, alloc=4914300, time=42.02 bytes used=1232389744, alloc=4914300, time=42.16 bytes used=1236390976, alloc=4914300, time=42.30 bytes used=1240392344, alloc=4914300, time=42.44 bytes used=1244393076, alloc=4914300, time=42.58 bytes used=1248393908, alloc=4914300, time=42.71 bytes used=1252395596, alloc=4914300, time=42.85 bytes used=1256396396, alloc=4914300, time=42.99 bytes used=1260397740, alloc=4914300, time=43.12 bytes used=1264398604, alloc=4914300, time=43.26 bytes used=1268399552, alloc=4914300, time=43.40 bytes used=1272400432, alloc=4914300, time=43.54 bytes used=1276401496, alloc=4914300, time=43.67 bytes used=1280402288, alloc=4914300, time=43.81 bytes used=1284403312, alloc=4914300, time=43.95 bytes used=1288406868, alloc=4914300, time=44.09 bytes used=1292407800, alloc=4914300, time=44.23 bytes used=1296409052, alloc=4914300, time=44.36 bytes used=1300411480, alloc=4914300, time=44.50 bytes used=1304412552, alloc=4914300, time=44.64 bytes used=1308413456, alloc=4914300, time=44.78 bytes used=1312414160, alloc=4914300, time=44.92 bytes used=1316414900, alloc=4914300, time=45.05 bytes used=1320416000, alloc=4914300, time=45.19 bytes used=1324416744, alloc=4914300, time=45.33 bytes used=1328418316, alloc=4914300, time=45.47 bytes used=1332419004, alloc=4914300, time=45.61 bytes used=1336420116, alloc=4914300, time=45.74 bytes used=1340421020, alloc=4914300, time=45.88 bytes used=1344421784, alloc=4914300, time=46.02 bytes used=1348422844, alloc=4914300, time=46.16 bytes used=1352423752, alloc=4914300, time=46.30 bytes used=1356425448, alloc=4914300, time=46.43 bytes used=1360426892, alloc=4914300, time=46.57 bytes used=1364427716, alloc=4914300, time=46.71 bytes used=1368429508, alloc=4914300, time=46.84 bytes used=1372431976, alloc=4914300, time=46.98 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.7373431362782306797502262616139 y[1] (numeric) = 1.7373431370444235856297283253093 absolute error = 7.661929058795020636954e-10 relative error = 4.4101414964049934063310787774798e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4629 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 = 1.672 Order of pole (six term test) = -74.57 bytes used=1376432984, alloc=4914300, time=47.12 bytes used=1380434208, alloc=4914300, time=47.26 bytes used=1384435620, alloc=4914300, time=47.40 bytes used=1388436780, alloc=4914300, time=47.54 bytes used=1392437668, alloc=4914300, time=47.68 bytes used=1396438900, alloc=4914300, time=47.81 bytes used=1400441772, alloc=4914300, time=47.95 bytes used=1404442552, alloc=4914300, time=48.09 bytes used=1408443720, alloc=4979824, time=48.23 bytes used=1412445488, alloc=4979824, time=48.37 bytes used=1416448864, alloc=4979824, time=48.50 bytes used=1420449672, alloc=4979824, time=48.64 bytes used=1424450672, alloc=4979824, time=48.78 bytes used=1428451404, alloc=4979824, time=48.91 bytes used=1432452408, alloc=4979824, time=49.05 bytes used=1436454368, alloc=4979824, time=49.19 bytes used=1440455096, alloc=4979824, time=49.33 bytes used=1444456148, alloc=4979824, time=49.46 bytes used=1448457116, alloc=4979824, time=49.60 bytes used=1452458168, alloc=4979824, time=49.74 bytes used=1456459108, alloc=4979824, time=49.88 bytes used=1460460084, alloc=4979824, time=50.01 bytes used=1464460960, alloc=4979824, time=50.15 bytes used=1468462952, alloc=4979824, time=50.29 bytes used=1472464092, alloc=4979824, time=50.43 bytes used=1476464908, alloc=4979824, time=50.57 bytes used=1480466044, alloc=4979824, time=50.70 bytes used=1484467016, alloc=4979824, time=50.84 bytes used=1488469216, alloc=4979824, time=50.98 bytes used=1492469996, alloc=4979824, time=51.12 bytes used=1496470868, alloc=4979824, time=51.26 bytes used=1500471948, alloc=4979824, time=51.39 bytes used=1504473016, alloc=4979824, time=51.53 bytes used=1508475500, alloc=4979824, time=51.67 bytes used=1512476456, alloc=4979824, time=51.81 bytes used=1516477492, alloc=4979824, time=51.94 bytes used=1520478488, alloc=4979824, time=52.08 bytes used=1524479480, alloc=4979824, time=52.22 bytes used=1528481852, alloc=4979824, time=52.36 bytes used=1532482624, alloc=4979824, time=52.50 bytes used=1536483484, alloc=4979824, time=52.63 bytes used=1540484552, alloc=4979824, time=52.77 bytes used=1544488920, alloc=4979824, time=52.91 bytes used=1548489888, alloc=4979824, time=53.05 bytes used=1552491684, alloc=4979824, time=53.19 bytes used=1556492624, alloc=4979824, time=53.33 bytes used=1560493704, alloc=4979824, time=53.46 bytes used=1564494576, alloc=4979824, time=53.60 bytes used=1568495668, alloc=4979824, time=53.73 bytes used=1572497028, alloc=4979824, time=53.87 bytes used=1576497728, alloc=4979824, time=54.01 bytes used=1580498892, alloc=4979824, time=54.14 bytes used=1584499636, alloc=4979824, time=54.28 bytes used=1588501740, alloc=4979824, time=54.42 bytes used=1592502624, alloc=4979824, time=54.56 bytes used=1596503472, alloc=4979824, time=54.70 bytes used=1600505020, alloc=4979824, time=54.83 bytes used=1604505968, alloc=4979824, time=54.97 bytes used=1608506684, alloc=4979824, time=55.11 bytes used=1612507656, alloc=4979824, time=55.25 bytes used=1616509712, alloc=4979824, time=55.39 bytes used=1620510832, alloc=4979824, time=55.53 bytes used=1624511848, alloc=4979824, time=55.66 bytes used=1628512676, alloc=4979824, time=55.80 bytes used=1632513668, alloc=4979824, time=55.94 bytes used=1636517304, alloc=4979824, time=56.08 bytes used=1640518004, alloc=4979824, time=56.22 bytes used=1644519032, alloc=4979824, time=56.36 bytes used=1648519928, alloc=4979824, time=56.49 bytes used=1652521136, alloc=4979824, time=56.63 bytes used=1656522132, alloc=4979824, time=56.77 bytes used=1660522960, alloc=4979824, time=56.91 bytes used=1664523984, alloc=4979824, time=57.05 bytes used=1668525268, alloc=4979824, time=57.18 bytes used=1672526952, alloc=4979824, time=57.32 bytes used=1676527844, alloc=4979824, time=57.46 bytes used=1680528856, alloc=4979824, time=57.59 bytes used=1684529776, alloc=4979824, time=57.73 bytes used=1688530604, alloc=4979824, time=57.87 bytes used=1692531748, alloc=4979824, time=58.01 bytes used=1696534004, alloc=4979824, time=58.15 bytes used=1700534936, alloc=4979824, time=58.28 bytes used=1704535860, alloc=4979824, time=58.42 bytes used=1708538120, alloc=4979824, time=58.56 bytes used=1712538780, alloc=4979824, time=58.70 bytes used=1716539916, alloc=4979824, time=58.84 bytes used=1720541016, alloc=4979824, time=58.97 bytes used=1724542552, alloc=4979824, time=59.11 bytes used=1728543332, alloc=4979824, time=59.25 bytes used=1732544676, alloc=4979824, time=59.39 bytes used=1736545444, alloc=4979824, time=59.53 bytes used=1740546392, alloc=4979824, time=59.67 bytes used=1744547088, alloc=4979824, time=59.81 bytes used=1748548188, alloc=4979824, time=59.95 bytes used=1752549144, alloc=4979824, time=60.09 bytes used=1756550384, alloc=4979824, time=60.22 bytes used=1760551768, alloc=4979824, time=60.36 bytes used=1764552936, alloc=4979824, time=60.50 bytes used=1768553832, alloc=4979824, time=60.64 bytes used=1772554792, alloc=4979824, time=60.77 bytes used=1776555948, alloc=4979824, time=60.91 bytes used=1780557284, alloc=4979824, time=61.05 bytes used=1784558208, alloc=4979824, time=61.19 bytes used=1788559124, alloc=4979824, time=61.32 bytes used=1792560064, alloc=4979824, time=61.46 bytes used=1796561000, alloc=4979824, time=61.60 bytes used=1800564692, alloc=4979824, time=61.74 bytes used=1804565388, alloc=4979824, time=61.88 bytes used=1808566524, alloc=4979824, time=62.01 bytes used=1812567496, alloc=4979824, time=62.15 bytes used=1816568576, alloc=4979824, time=62.29 bytes used=1820569656, alloc=4979824, time=62.43 bytes used=1824570628, alloc=4979824, time=62.57 bytes used=1828571836, alloc=4979824, time=62.71 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.8173899685524985781622358939287 y[1] (numeric) = 1.8173899693186914840417379607324 absolute error = 7.661929058795020668037e-10 relative error = 4.2158970784336053551518827040396e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4703 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 = 1.715 Order of pole (six term test) = -73.13 bytes used=1832572800, alloc=4979824, time=62.84 bytes used=1836575472, alloc=4979824, time=62.98 bytes used=1840576448, alloc=4979824, time=63.12 bytes used=1844577524, alloc=4979824, time=63.26 bytes used=1848579452, alloc=4979824, time=63.40 bytes used=1852580808, alloc=4979824, time=63.54 bytes used=1856581724, alloc=4979824, time=63.67 bytes used=1860583600, alloc=4979824, time=63.81 bytes used=1864584624, alloc=4979824, time=63.95 bytes used=1868585832, alloc=4979824, time=64.09 bytes used=1872587268, alloc=4979824, time=64.23 bytes used=1876587972, alloc=4979824, time=64.36 bytes used=1880588892, alloc=4979824, time=64.50 bytes used=1884589996, alloc=4979824, time=64.64 bytes used=1888590928, alloc=4979824, time=64.78 bytes used=1892591756, alloc=4979824, time=64.91 bytes used=1896592744, alloc=4979824, time=65.05 bytes used=1900593676, alloc=4979824, time=65.19 bytes used=1904594520, alloc=4979824, time=65.33 bytes used=1908596592, alloc=4979824, time=65.46 bytes used=1912598076, alloc=4979824, time=65.60 bytes used=1916599048, alloc=4979824, time=65.74 bytes used=1920600040, alloc=4979824, time=65.88 bytes used=1924601304, alloc=4979824, time=66.01 bytes used=1928602200, alloc=4979824, time=66.15 bytes used=1932603124, alloc=4979824, time=66.29 bytes used=1936604160, alloc=4979824, time=66.43 bytes used=1940605444, alloc=4979824, time=66.57 bytes used=1944606200, alloc=4979824, time=66.71 bytes used=1948607096, alloc=4979824, time=66.84 bytes used=1952608104, alloc=4979824, time=66.98 bytes used=1956609848, alloc=4979824, time=67.12 bytes used=1960612976, alloc=4979824, time=67.26 bytes used=1964613772, alloc=4979824, time=67.40 bytes used=1968616464, alloc=4979824, time=67.54 bytes used=1972618204, alloc=4979824, time=67.67 bytes used=1976619228, alloc=4979824, time=67.81 bytes used=1980620088, alloc=4979824, time=67.95 bytes used=1984622208, alloc=4979824, time=68.09 bytes used=1988623136, alloc=4979824, time=68.22 bytes used=1992624120, alloc=4979824, time=68.36 bytes used=1996625792, alloc=4979824, time=68.50 bytes used=2000626548, alloc=4979824, time=68.64 bytes used=2004627432, alloc=4979824, time=68.78 bytes used=2008628568, alloc=4979824, time=68.91 bytes used=2012630140, alloc=4979824, time=69.05 bytes used=2016631776, alloc=4979824, time=69.19 bytes used=2020633244, alloc=4979824, time=69.33 bytes used=2024634064, alloc=4979824, time=69.46 bytes used=2028635056, alloc=4979824, time=69.60 bytes used=2032637160, alloc=4979824, time=69.74 bytes used=2036637896, alloc=4979824, time=69.88 bytes used=2040638936, alloc=4979824, time=70.01 bytes used=2044640144, alloc=4979824, time=70.15 bytes used=2048641380, alloc=4979824, time=70.29 bytes used=2052643248, alloc=4979824, time=70.42 bytes used=2056644372, alloc=4979824, time=70.56 bytes used=2060645204, alloc=4979824, time=70.70 bytes used=2064646180, alloc=4979824, time=70.84 bytes used=2068647192, alloc=4979824, time=70.98 bytes used=2072648608, alloc=4979824, time=71.12 bytes used=2076649576, alloc=4979824, time=71.26 bytes used=2080651004, alloc=4979824, time=71.40 bytes used=2084651828, alloc=4979824, time=71.53 bytes used=2088652768, alloc=4979824, time=71.67 bytes used=2092653816, alloc=4979824, time=71.81 bytes used=2096654880, alloc=4979824, time=71.95 bytes used=2100655764, alloc=4979824, time=72.09 bytes used=2104657836, alloc=4979824, time=72.23 bytes used=2108659924, alloc=4979824, time=72.36 bytes used=2112660780, alloc=4979824, time=72.50 bytes used=2116662752, alloc=4979824, time=72.64 bytes used=2120664512, alloc=4979824, time=72.78 bytes used=2124667364, alloc=4979824, time=72.91 bytes used=2128668232, alloc=4979824, time=73.05 bytes used=2132669264, alloc=4979824, time=73.19 bytes used=2136670168, alloc=4979824, time=73.33 bytes used=2140671324, alloc=4979824, time=73.46 bytes used=2144672520, alloc=4979824, time=73.60 bytes used=2148673416, alloc=4979824, time=73.74 bytes used=2152674376, alloc=4979824, time=73.88 bytes used=2156675144, alloc=4979824, time=74.01 bytes used=2160677076, alloc=4979824, time=74.15 bytes used=2164677760, alloc=4979824, time=74.29 bytes used=2168679752, alloc=4979824, time=74.43 bytes used=2172680476, alloc=4979824, time=74.57 bytes used=2176681560, alloc=4979824, time=74.70 bytes used=2180682480, alloc=4979824, time=74.84 bytes used=2184683148, alloc=4979824, time=74.98 bytes used=2188684056, alloc=4979824, time=75.12 bytes used=2192684988, alloc=4979824, time=75.25 bytes used=2196686032, alloc=4979824, time=75.39 bytes used=2200686848, alloc=4979824, time=75.53 bytes used=2204687968, alloc=4979824, time=75.67 bytes used=2208689120, alloc=4979824, time=75.81 bytes used=2212690164, alloc=4979824, time=75.95 bytes used=2216690948, alloc=4979824, time=76.08 bytes used=2220692364, alloc=4979824, time=76.22 bytes used=2224693112, alloc=4979824, time=76.36 bytes used=2228694172, alloc=4979824, time=76.49 bytes used=2232695948, alloc=4979824, time=76.63 bytes used=2236698476, alloc=4979824, time=76.77 bytes used=2240699800, alloc=4979824, time=76.91 bytes used=2244700684, alloc=4979824, time=77.05 bytes used=2248702568, alloc=4979824, time=77.19 bytes used=2252703952, alloc=4979824, time=77.33 bytes used=2256705572, alloc=4979824, time=77.47 bytes used=2260706356, alloc=4979824, time=77.60 bytes used=2264707440, alloc=4979824, time=77.74 bytes used=2268709144, alloc=4979824, time=77.88 bytes used=2272710008, alloc=4979824, time=78.02 bytes used=2276711032, alloc=4979824, time=78.15 bytes used=2280713584, alloc=4979824, time=78.29 bytes used=2284714392, alloc=4979824, time=78.43 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.9017841044837866283034228181341 y[1] (numeric) = 1.9017841052499795341829248880055 absolute error = 7.661929058795020698714e-10 relative error = 4.0288111782671287501249435500042e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4777 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 = 1.797 Order of pole (six term test) = -75.2 bytes used=2288716220, alloc=4979824, time=78.57 bytes used=2292717136, alloc=4979824, time=78.71 bytes used=2296718152, alloc=4979824, time=78.85 bytes used=2300719164, alloc=4979824, time=78.98 bytes used=2304720240, alloc=4979824, time=79.12 bytes used=2308721996, alloc=4979824, time=79.26 bytes used=2312722924, alloc=4979824, time=79.40 bytes used=2316723868, alloc=4979824, time=79.54 bytes used=2320724900, alloc=4979824, time=79.67 bytes used=2324726064, alloc=4979824, time=79.81 bytes used=2328727904, alloc=4979824, time=79.95 bytes used=2332728840, alloc=4979824, time=80.09 bytes used=2336730296, alloc=4979824, time=80.23 bytes used=2340731456, alloc=4979824, time=80.37 bytes used=2344733868, alloc=4979824, time=80.50 bytes used=2348734592, alloc=4979824, time=80.64 bytes used=2352735900, alloc=4979824, time=80.78 bytes used=2356736732, alloc=4979824, time=80.92 bytes used=2360737688, alloc=4979824, time=81.06 bytes used=2364738832, alloc=4979824, time=81.19 bytes used=2368739788, alloc=4979824, time=81.33 bytes used=2372742108, alloc=4979824, time=81.47 bytes used=2376743280, alloc=4979824, time=81.61 bytes used=2380744544, alloc=4979824, time=81.75 bytes used=2384745364, alloc=4979824, time=81.88 bytes used=2388746308, alloc=4979824, time=82.02 bytes used=2392747256, alloc=4979824, time=82.16 bytes used=2396748088, alloc=4979824, time=82.30 bytes used=2400748808, alloc=4979824, time=82.44 bytes used=2404750148, alloc=4979824, time=82.57 bytes used=2408750932, alloc=4979824, time=82.71 bytes used=2412751928, alloc=4979824, time=82.85 bytes used=2416753408, alloc=4979824, time=82.99 bytes used=2420754220, alloc=4979824, time=83.13 bytes used=2424756788, alloc=4979824, time=83.27 bytes used=2428757624, alloc=4979824, time=83.41 bytes used=2432758648, alloc=4979824, time=83.54 bytes used=2436760724, alloc=4979824, time=83.68 bytes used=2440761724, alloc=4979824, time=83.82 bytes used=2444762680, alloc=4979824, time=83.96 bytes used=2448763588, alloc=4979824, time=84.10 bytes used=2452764484, alloc=4979824, time=84.24 bytes used=2456766740, alloc=4979824, time=84.38 bytes used=2460767840, alloc=4979824, time=84.51 bytes used=2464768732, alloc=4979824, time=84.65 bytes used=2468769956, alloc=4979824, time=84.79 bytes used=2472771072, alloc=4979824, time=84.93 bytes used=2476773168, alloc=4979824, time=85.07 bytes used=2480773948, alloc=4979824, time=85.20 bytes used=2484774672, alloc=4979824, time=85.34 bytes used=2488775768, alloc=4979824, time=85.48 bytes used=2492776680, alloc=4979824, time=85.62 bytes used=2496779196, alloc=4979824, time=85.76 bytes used=2500779996, alloc=4979824, time=85.89 bytes used=2504780936, alloc=4979824, time=86.03 bytes used=2508781848, alloc=4979824, time=86.17 bytes used=2512783096, alloc=4979824, time=86.31 bytes used=2516785188, alloc=4979824, time=86.45 bytes used=2520785864, alloc=4979824, time=86.58 bytes used=2524786576, alloc=4979824, time=86.72 bytes used=2528787692, alloc=4979824, time=86.86 bytes used=2532789016, alloc=4979824, time=87.00 bytes used=2536789844, alloc=4979824, time=87.14 bytes used=2540790972, alloc=4979824, time=87.28 bytes used=2544792092, alloc=4979824, time=87.41 bytes used=2548793136, alloc=4979824, time=87.55 bytes used=2552794936, alloc=4979824, time=87.69 bytes used=2556795876, alloc=4979824, time=87.83 bytes used=2560796672, alloc=4979824, time=87.97 bytes used=2564797716, alloc=4979824, time=88.11 bytes used=2568799700, alloc=4979824, time=88.25 bytes used=2572801832, alloc=4979824, time=88.38 bytes used=2576802584, alloc=4979824, time=88.52 bytes used=2580803540, alloc=4979824, time=88.66 bytes used=2584804480, alloc=4979824, time=88.80 bytes used=2588806600, alloc=4979824, time=88.94 bytes used=2592807496, alloc=4979824, time=89.08 bytes used=2596808856, alloc=4979824, time=89.22 bytes used=2600809752, alloc=4979824, time=89.35 bytes used=2604810884, alloc=4979824, time=89.49 bytes used=2608814344, alloc=4979824, time=89.63 bytes used=2612815188, alloc=4979824, time=89.77 bytes used=2616816300, alloc=4979824, time=89.91 bytes used=2620817272, alloc=4979824, time=90.04 bytes used=2624819380, alloc=4979824, time=90.18 bytes used=2628820664, alloc=4979824, time=90.32 bytes used=2632821572, alloc=4979824, time=90.46 bytes used=2636822480, alloc=4979824, time=90.60 bytes used=2640823684, alloc=4979824, time=90.74 bytes used=2644824948, alloc=4979824, time=90.87 bytes used=2648826136, alloc=4979824, time=91.01 bytes used=2652826984, alloc=4979824, time=91.15 bytes used=2656827932, alloc=4979824, time=91.29 bytes used=2660828940, alloc=4979824, time=91.43 bytes used=2664830840, alloc=4979824, time=91.57 bytes used=2668831740, alloc=4979824, time=91.71 bytes used=2672832628, alloc=4979824, time=91.85 bytes used=2676834668, alloc=4979824, time=91.99 bytes used=2680835496, alloc=4979824, time=92.12 bytes used=2684836640, alloc=4979824, time=92.26 bytes used=2688837548, alloc=4979824, time=92.40 bytes used=2692839592, alloc=4979824, time=92.54 bytes used=2696840528, alloc=4979824, time=92.67 bytes used=2700841220, alloc=4979824, time=92.81 bytes used=2704843172, alloc=4979824, time=92.95 bytes used=2708844120, alloc=4979824, time=93.09 bytes used=2712845356, alloc=4979824, time=93.23 bytes used=2716847868, alloc=4979824, time=93.37 bytes used=2720848804, alloc=4979824, time=93.51 bytes used=2724849716, alloc=4979824, time=93.64 bytes used=2728850888, alloc=4979824, time=93.78 bytes used=2732852100, alloc=4979824, time=93.92 bytes used=2736853216, alloc=4979824, time=94.06 TOP MAIN SOLVE Loop bytes used=2740854088, alloc=4979824, time=94.20 x[1] = 0.16 y[1] (analytic) = 1.9907803683431329730340501323101 y[1] (numeric) = 1.9907803691093258789135522052153 absolute error = 7.661929058795020729052e-10 relative error = 3.8487063568804505482648817426553e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4851 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 = 1.921 Order of pole (six term test) = -80.66 bytes used=2744854864, alloc=4979824, time=94.34 bytes used=2748855856, alloc=4979824, time=94.47 bytes used=2752857756, alloc=4979824, time=94.61 bytes used=2756858680, alloc=4979824, time=94.75 bytes used=2760860176, alloc=4979824, time=94.89 bytes used=2764862096, alloc=4979824, time=95.03 bytes used=2768862740, alloc=4979824, time=95.17 bytes used=2772865364, alloc=4979824, time=95.31 bytes used=2776866912, alloc=4979824, time=95.45 bytes used=2780868028, alloc=4979824, time=95.59 bytes used=2784869116, alloc=4979824, time=95.73 bytes used=2788869888, alloc=4979824, time=95.86 bytes used=2792871308, alloc=4979824, time=96.00 bytes used=2796872392, alloc=4979824, time=96.14 bytes used=2800873068, alloc=4979824, time=96.28 bytes used=2804874288, alloc=4979824, time=96.42 bytes used=2808875260, alloc=4979824, time=96.56 bytes used=2812877228, alloc=4979824, time=96.70 bytes used=2816879208, alloc=4979824, time=96.84 bytes used=2820880336, alloc=4979824, time=96.97 bytes used=2824881252, alloc=4979824, time=97.11 bytes used=2828882472, alloc=4979824, time=97.25 bytes used=2832883348, alloc=4979824, time=97.39 bytes used=2836886128, alloc=4979824, time=97.53 bytes used=2840887680, alloc=4979824, time=97.67 bytes used=2844888464, alloc=4979824, time=97.80 bytes used=2848889412, alloc=4979824, time=97.94 bytes used=2852890692, alloc=4979824, time=98.08 bytes used=2856891692, alloc=4979824, time=98.22 bytes used=2860892800, alloc=4979824, time=98.36 bytes used=2864893768, alloc=4979824, time=98.49 bytes used=2868894876, alloc=4979824, time=98.63 bytes used=2872895840, alloc=4979824, time=98.77 bytes used=2876896716, alloc=4979824, time=98.91 bytes used=2880897764, alloc=4979824, time=99.05 bytes used=2884898724, alloc=4979824, time=99.19 bytes used=2888900704, alloc=4979824, time=99.32 bytes used=2892901772, alloc=4979824, time=99.46 bytes used=2896902548, alloc=4979824, time=99.60 bytes used=2900903364, alloc=4979824, time=99.74 bytes used=2904904252, alloc=4979824, time=99.88 bytes used=2908906224, alloc=4979824, time=100.02 bytes used=2912907180, alloc=4979824, time=100.15 bytes used=2916908680, alloc=5045348, time=100.29 bytes used=2920909532, alloc=5045348, time=100.43 bytes used=2924910568, alloc=5045348, time=100.57 bytes used=2928913320, alloc=5045348, time=100.71 bytes used=2932914192, alloc=5045348, time=100.85 bytes used=2936915252, alloc=5045348, time=100.99 bytes used=2940916288, alloc=5045348, time=101.13 bytes used=2944917256, alloc=5045348, time=101.27 bytes used=2948918296, alloc=5045348, time=101.41 bytes used=2952919312, alloc=5045348, time=101.54 bytes used=2956920396, alloc=5045348, time=101.68 bytes used=2960921460, alloc=5045348, time=101.82 bytes used=2964922744, alloc=5045348, time=101.96 bytes used=2968923820, alloc=5045348, time=102.10 bytes used=2972924724, alloc=5045348, time=102.24 bytes used=2976925804, alloc=5045348, time=102.37 bytes used=2980926720, alloc=5045348, time=102.51 bytes used=2984928212, alloc=5045348, time=102.65 bytes used=2988929292, alloc=5045348, time=102.79 bytes used=2992931080, alloc=5045348, time=102.93 bytes used=2996931976, alloc=5045348, time=103.07 bytes used=3000932944, alloc=5045348, time=103.21 bytes used=3004933828, alloc=5045348, time=103.34 bytes used=3008934744, alloc=5045348, time=103.48 bytes used=3012936320, alloc=5045348, time=103.62 bytes used=3016937164, alloc=5045348, time=103.76 bytes used=3020938992, alloc=5045348, time=103.90 bytes used=3024942300, alloc=5045348, time=104.04 bytes used=3028943348, alloc=5045348, time=104.18 bytes used=3032944488, alloc=5045348, time=104.32 bytes used=3036946136, alloc=5045348, time=104.45 bytes used=3040946888, alloc=5045348, time=104.59 bytes used=3044947932, alloc=5045348, time=104.73 bytes used=3048948808, alloc=5045348, time=104.87 bytes used=3052949760, alloc=5045348, time=105.01 bytes used=3056952048, alloc=5045348, time=105.15 bytes used=3060952856, alloc=5045348, time=105.29 bytes used=3064953952, alloc=5045348, time=105.43 bytes used=3068954820, alloc=5045348, time=105.57 bytes used=3072957128, alloc=5045348, time=105.71 bytes used=3076957796, alloc=5045348, time=105.84 bytes used=3080959076, alloc=5045348, time=105.98 bytes used=3084960196, alloc=5045348, time=106.12 bytes used=3088961012, alloc=5045348, time=106.26 bytes used=3092962312, alloc=5045348, time=106.40 bytes used=3096963420, alloc=5045348, time=106.54 bytes used=3100964944, alloc=5045348, time=106.68 bytes used=3104965816, alloc=5045348, time=106.82 bytes used=3108967568, alloc=5045348, time=106.96 bytes used=3112968432, alloc=5045348, time=107.10 bytes used=3116971160, alloc=5045348, time=107.23 bytes used=3120972164, alloc=5045348, time=107.37 bytes used=3124974152, alloc=5045348, time=107.51 bytes used=3128975572, alloc=5045348, time=107.65 bytes used=3132976460, alloc=5045348, time=107.79 bytes used=3136977372, alloc=5045348, time=107.93 bytes used=3140978320, alloc=5045348, time=108.07 bytes used=3144979260, alloc=5045348, time=108.20 bytes used=3148980224, alloc=5045348, time=108.34 bytes used=3152981216, alloc=5045348, time=108.48 bytes used=3156982284, alloc=5045348, time=108.62 bytes used=3160983276, alloc=5045348, time=108.76 bytes used=3164985440, alloc=5045348, time=108.89 bytes used=3168987080, alloc=5045348, time=109.03 bytes used=3172988044, alloc=5045348, time=109.17 bytes used=3176988964, alloc=5045348, time=109.31 bytes used=3180990316, alloc=5045348, time=109.45 bytes used=3184991344, alloc=5045348, time=109.59 bytes used=3188992384, alloc=5045348, time=109.72 bytes used=3192993252, alloc=5045348, time=109.86 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 2.0846494904998704894881066824681 y[1] (numeric) = 2.0846494912660633953676087583735 absolute error = 7.661929058795020759054e-10 relative error = 3.6754039917558489732623888517485e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4912 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 = 2.098 Order of pole (six term test) = -90.52 bytes used=3196994352, alloc=5045348, time=110.00 bytes used=3200995172, alloc=5045348, time=110.14 bytes used=3204996100, alloc=5045348, time=110.28 bytes used=3208997096, alloc=5045348, time=110.42 bytes used=3212998076, alloc=5045348, time=110.56 bytes used=3216999752, alloc=5045348, time=110.69 bytes used=3221000720, alloc=5045348, time=110.83 bytes used=3225001728, alloc=5045348, time=110.97 bytes used=3229003112, alloc=5045348, time=111.11 bytes used=3233004000, alloc=5045348, time=111.25 bytes used=3237005420, alloc=5045348, time=111.38 bytes used=3241006132, alloc=5045348, time=111.52 bytes used=3245007096, alloc=5045348, time=111.66 bytes used=3249008728, alloc=5045348, time=111.80 bytes used=3253009720, alloc=5045348, time=111.94 bytes used=3257012500, alloc=5045348, time=112.08 bytes used=3261013492, alloc=5045348, time=112.21 bytes used=3265014468, alloc=5045348, time=112.35 bytes used=3269015512, alloc=5045348, time=112.49 bytes used=3273016652, alloc=5045348, time=112.63 bytes used=3277019440, alloc=5045348, time=112.77 bytes used=3281020324, alloc=5045348, time=112.91 bytes used=3285021996, alloc=5045348, time=113.05 bytes used=3289022760, alloc=5045348, time=113.19 bytes used=3293023724, alloc=5045348, time=113.33 bytes used=3297026464, alloc=5045348, time=113.47 bytes used=3301027300, alloc=5045348, time=113.60 bytes used=3305028312, alloc=5045348, time=113.74 bytes used=3309029196, alloc=5045348, time=113.88 bytes used=3313030344, alloc=5045348, time=114.02 bytes used=3317031340, alloc=5045348, time=114.16 bytes used=3321032256, alloc=5045348, time=114.30 bytes used=3325033940, alloc=5045348, time=114.44 bytes used=3329034648, alloc=5045348, time=114.58 bytes used=3333035636, alloc=5045348, time=114.71 bytes used=3337038480, alloc=5045348, time=114.85 bytes used=3341039888, alloc=5045348, time=114.99 bytes used=3345040796, alloc=5045348, time=115.13 bytes used=3349041792, alloc=5045348, time=115.27 bytes used=3353042632, alloc=5045348, time=115.41 bytes used=3357045596, alloc=5045348, time=115.55 bytes used=3361046532, alloc=5045348, time=115.68 bytes used=3365047332, alloc=5045348, time=115.82 bytes used=3369048336, alloc=5045348, time=115.96 bytes used=3373049308, alloc=5045348, time=116.10 bytes used=3377050800, alloc=5045348, time=116.24 bytes used=3381051708, alloc=5045348, time=116.38 bytes used=3385052520, alloc=5045348, time=116.51 bytes used=3389054140, alloc=5045348, time=116.65 bytes used=3393054932, alloc=5045348, time=116.79 bytes used=3397059356, alloc=5045348, time=116.93 bytes used=3401060372, alloc=5045348, time=117.07 bytes used=3405061376, alloc=5045348, time=117.21 bytes used=3409062220, alloc=5045348, time=117.35 bytes used=3413063268, alloc=5045348, time=117.48 bytes used=3417065380, alloc=5045348, time=117.62 bytes used=3421066344, alloc=5045348, time=117.76 bytes used=3425067316, alloc=5045348, time=117.90 bytes used=3429068280, alloc=5045348, time=118.04 bytes used=3433069228, alloc=5045348, time=118.17 bytes used=3437070120, alloc=5045348, time=118.31 bytes used=3441070924, alloc=5045348, time=118.45 bytes used=3445072076, alloc=5045348, time=118.59 bytes used=3449073104, alloc=5045348, time=118.73 bytes used=3453074100, alloc=5045348, time=118.87 bytes used=3457075768, alloc=5045348, time=119.01 bytes used=3461077388, alloc=5045348, time=119.15 bytes used=3465078536, alloc=5045348, time=119.29 bytes used=3469079300, alloc=5045348, time=119.42 bytes used=3473080420, alloc=5045348, time=119.56 bytes used=3477082664, alloc=5045348, time=119.70 bytes used=3481083484, alloc=5045348, time=119.84 bytes used=3485084452, alloc=5045348, time=119.98 bytes used=3489085548, alloc=5045348, time=120.12 bytes used=3493086672, alloc=5045348, time=120.26 bytes used=3497089196, alloc=5045348, time=120.40 bytes used=3501089944, alloc=5045348, time=120.53 bytes used=3505090908, alloc=5045348, time=120.67 bytes used=3509092416, alloc=5045348, time=120.81 bytes used=3513093208, alloc=5045348, time=120.95 bytes used=3517094188, alloc=5045348, time=121.09 bytes used=3521095012, alloc=5045348, time=121.23 bytes used=3525096468, alloc=5045348, time=121.36 bytes used=3529097888, alloc=5045348, time=121.50 bytes used=3533099040, alloc=5045348, time=121.64 bytes used=3537100396, alloc=5045348, time=121.78 bytes used=3541101828, alloc=5045348, time=121.92 bytes used=3545102820, alloc=5045348, time=122.06 bytes used=3549103852, alloc=5045348, time=122.19 bytes used=3553104920, alloc=5045348, time=122.33 bytes used=3557106708, alloc=5045348, time=122.47 bytes used=3561107956, alloc=5045348, time=122.60 bytes used=3565108928, alloc=5045348, time=122.74 bytes used=3569110248, alloc=5045348, time=122.88 bytes used=3573111332, alloc=5045348, time=123.02 bytes used=3577112376, alloc=5045348, time=123.16 bytes used=3581113380, alloc=5045348, time=123.30 bytes used=3585114620, alloc=5045348, time=123.43 bytes used=3589115692, alloc=5045348, time=123.57 bytes used=3593116568, alloc=5045348, time=123.71 bytes used=3597117516, alloc=5045348, time=123.85 bytes used=3601118280, alloc=5045348, time=123.99 bytes used=3605119328, alloc=5045348, time=124.13 bytes used=3609120128, alloc=5045348, time=124.27 bytes used=3613121088, alloc=5045348, time=124.40 bytes used=3617122504, alloc=5045348, time=124.54 bytes used=3621124360, alloc=5045348, time=124.68 bytes used=3625125116, alloc=5045348, time=124.82 bytes used=3629126120, alloc=5045348, time=124.96 bytes used=3633127016, alloc=5045348, time=125.09 bytes used=3637128032, alloc=5045348, time=125.23 bytes used=3641130212, alloc=5045348, time=125.37 bytes used=3645130888, alloc=5045348, time=125.51 bytes used=3649131720, alloc=5045348, time=125.64 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 2.183679149148485113444865832242 y[1] (numeric) = 2.1836791499146780193243679111208 absolute error = 7.661929058795020788788e-10 relative error = 3.5087247418114296412386187475819e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4968 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 = 2.359 Order of pole (six term test) = -107.6 bytes used=3653133380, alloc=5045348, time=125.78 bytes used=3657134408, alloc=5045348, time=125.92 bytes used=3661138336, alloc=5045348, time=126.06 bytes used=3665139036, alloc=5045348, time=126.20 bytes used=3669141540, alloc=5045348, time=126.34 bytes used=3673142372, alloc=5045348, time=126.47 bytes used=3677143264, alloc=5045348, time=126.61 bytes used=3681144260, alloc=5045348, time=126.75 bytes used=3685145164, alloc=5045348, time=126.89 bytes used=3689146012, alloc=5045348, time=127.02 bytes used=3693146836, alloc=5045348, time=127.16 bytes used=3697147748, alloc=5045348, time=127.30 bytes used=3701150512, alloc=5045348, time=127.44 bytes used=3705151364, alloc=5045348, time=127.58 bytes used=3709152692, alloc=5045348, time=127.71 bytes used=3713153492, alloc=5045348, time=127.85 bytes used=3717155328, alloc=5045348, time=127.99 bytes used=3721157392, alloc=5045348, time=128.13 bytes used=3725158164, alloc=5045348, time=128.26 bytes used=3729159480, alloc=5045348, time=128.40 bytes used=3733161516, alloc=5045348, time=128.54 bytes used=3737162328, alloc=5045348, time=128.68 bytes used=3741163188, alloc=5045348, time=128.82 bytes used=3745164088, alloc=5045348, time=128.95 bytes used=3749165040, alloc=5045348, time=129.09 bytes used=3753165916, alloc=5045348, time=129.23 bytes used=3757167132, alloc=5045348, time=129.37 bytes used=3761168272, alloc=5045348, time=129.51 bytes used=3765169064, alloc=5045348, time=129.65 bytes used=3769169808, alloc=5045348, time=129.78 bytes used=3773170644, alloc=5045348, time=129.92 bytes used=3777171348, alloc=5045348, time=130.06 bytes used=3781172296, alloc=5045348, time=130.20 bytes used=3785174872, alloc=5045348, time=130.34 bytes used=3789175508, alloc=5045348, time=130.48 bytes used=3793176592, alloc=5045348, time=130.62 bytes used=3797177416, alloc=5045348, time=130.76 bytes used=3801179188, alloc=5045348, time=130.89 bytes used=3805180276, alloc=5045348, time=131.03 bytes used=3809181256, alloc=5045348, time=131.17 bytes used=3813182340, alloc=5045348, time=131.31 bytes used=3817183704, alloc=5045348, time=131.45 bytes used=3821185164, alloc=5045348, time=131.58 bytes used=3825186136, alloc=5045348, time=131.72 bytes used=3829187120, alloc=5045348, time=131.86 bytes used=3833187924, alloc=5045348, time=132.00 bytes used=3837188996, alloc=5045348, time=132.14 bytes used=3841190880, alloc=5045348, time=132.27 bytes used=3845192856, alloc=5045348, time=132.41 bytes used=3849195360, alloc=5045348, time=132.54 bytes used=3853196152, alloc=5045348, time=132.68 bytes used=3857197016, alloc=5045348, time=132.82 bytes used=3861198064, alloc=5045348, time=132.96 bytes used=3865199028, alloc=5045348, time=133.10 bytes used=3869199696, alloc=5045348, time=133.24 bytes used=3873200800, alloc=5045348, time=133.37 bytes used=3877201860, alloc=5045348, time=133.51 bytes used=3881202848, alloc=5045348, time=133.65 bytes used=3885204712, alloc=5045348, time=133.79 bytes used=3889205692, alloc=5045348, time=133.93 bytes used=3893207344, alloc=5045348, time=134.07 bytes used=3897208052, alloc=5045348, time=134.20 bytes used=3901209144, alloc=5045348, time=134.34 bytes used=3905210092, alloc=5045348, time=134.48 bytes used=3909211076, alloc=5045348, time=134.62 bytes used=3913212124, alloc=5045348, time=134.76 bytes used=3917213000, alloc=5045348, time=134.89 bytes used=3921215664, alloc=5045348, time=135.03 bytes used=3925217252, alloc=5045348, time=135.17 bytes used=3929218664, alloc=5045348, time=135.31 bytes used=3933219316, alloc=5045348, time=135.45 bytes used=3937220328, alloc=5045348, time=135.58 bytes used=3941221452, alloc=5045348, time=135.72 bytes used=3945222756, alloc=5045348, time=135.86 bytes used=3949223680, alloc=5045348, time=136.00 bytes used=3953224528, alloc=5045348, time=136.14 bytes used=3957225444, alloc=5045348, time=136.28 bytes used=3961226544, alloc=5045348, time=136.42 bytes used=3965228352, alloc=5045348, time=136.56 bytes used=3969230008, alloc=5045348, time=136.70 bytes used=3973231012, alloc=5045348, time=136.83 bytes used=3977231964, alloc=5045348, time=136.97 bytes used=3981232800, alloc=5045348, time=137.11 bytes used=3985234128, alloc=5045348, time=137.25 bytes used=3989235052, alloc=5045348, time=137.39 bytes used=3993237088, alloc=5045348, time=137.53 bytes used=3997237864, alloc=5045348, time=137.66 bytes used=4001239072, alloc=5045348, time=137.80 bytes used=4005239812, alloc=5045348, time=137.94 bytes used=4009240980, alloc=5045348, time=138.08 bytes used=4013241796, alloc=5045348, time=138.22 bytes used=4017243500, alloc=5045348, time=138.36 bytes used=4021244252, alloc=5045348, time=138.50 bytes used=4025245404, alloc=5045348, time=138.63 bytes used=4029246132, alloc=5045348, time=138.77 bytes used=4033247392, alloc=5045348, time=138.91 bytes used=4037249676, alloc=5045348, time=139.05 bytes used=4041250660, alloc=5045348, time=139.19 bytes used=4045252880, alloc=5045348, time=139.33 bytes used=4049253772, alloc=5045348, time=139.47 bytes used=4053255164, alloc=5045348, time=139.61 bytes used=4057256392, alloc=5045348, time=139.75 bytes used=4061257780, alloc=5045348, time=139.88 bytes used=4065258964, alloc=5045348, time=140.02 bytes used=4069259848, alloc=5045348, time=140.16 bytes used=4073260704, alloc=5045348, time=140.30 bytes used=4077261648, alloc=5045348, time=140.44 bytes used=4081263240, alloc=5045348, time=140.57 bytes used=4085263936, alloc=5045348, time=140.71 bytes used=4089264792, alloc=5045348, time=140.85 bytes used=4093266052, alloc=5045348, time=140.99 bytes used=4097267176, alloc=5045348, time=141.12 bytes used=4101268028, alloc=5045348, time=141.26 bytes used=4105269648, alloc=5045348, time=141.40 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 2.2881750829646272864030775953138 y[1] (numeric) = 2.2881750837308201922825796771422 absolute error = 7.661929058795020818284e-10 relative error = 3.3484889840107860138331308011069e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5018 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 = 2.775 Order of pole (six term test) = -140 bytes used=4109270712, alloc=5045348, time=141.54 bytes used=4113271668, alloc=5045348, time=141.67 bytes used=4117272648, alloc=5045348, time=141.81 bytes used=4121273512, alloc=5045348, time=141.95 bytes used=4125275168, alloc=5045348, time=142.09 bytes used=4129275900, alloc=5045348, time=142.23 bytes used=4133277516, alloc=5045348, time=142.37 bytes used=4137278676, alloc=5045348, time=142.51 bytes used=4141279572, alloc=5045348, time=142.65 bytes used=4145280684, alloc=5045348, time=142.79 bytes used=4149281608, alloc=5045348, time=142.92 bytes used=4153282924, alloc=5045348, time=143.06 bytes used=4157283992, alloc=5045348, time=143.20 bytes used=4161285480, alloc=5045348, time=143.34 bytes used=4165287296, alloc=5045348, time=143.47 bytes used=4169288952, alloc=5045348, time=143.61 bytes used=4173289864, alloc=5045348, time=143.75 bytes used=4177291124, alloc=5045348, time=143.89 bytes used=4181291936, alloc=5045348, time=144.03 bytes used=4185293484, alloc=5045348, time=144.17 bytes used=4189294448, alloc=5045348, time=144.31 bytes used=4193295224, alloc=5045348, time=144.44 bytes used=4197296092, alloc=5045348, time=144.58 bytes used=4201297748, alloc=5045348, time=144.72 bytes used=4205299024, alloc=5045348, time=144.86 bytes used=4209299848, alloc=5045348, time=145.00 bytes used=4213300868, alloc=5045348, time=145.13 bytes used=4217301740, alloc=5045348, time=145.27 bytes used=4221302588, alloc=5045348, time=145.41 bytes used=4225303580, alloc=5045348, time=145.55 bytes used=4229304580, alloc=5045348, time=145.69 bytes used=4233305476, alloc=5045348, time=145.82 bytes used=4237307400, alloc=5045348, time=145.96 bytes used=4241308308, alloc=5045348, time=146.10 bytes used=4245309256, alloc=5045348, time=146.24 bytes used=4249310292, alloc=5045348, time=146.38 bytes used=4253311480, alloc=5045348, time=146.52 bytes used=4257312692, alloc=5045348, time=146.66 bytes used=4261313648, alloc=5045348, time=146.79 bytes used=4265314632, alloc=5045348, time=146.93 bytes used=4269315420, alloc=5045348, time=147.06 bytes used=4273316724, alloc=5045348, time=147.20 bytes used=4277317572, alloc=5045348, time=147.34 bytes used=4281319108, alloc=5045348, time=147.48 bytes used=4285320256, alloc=5045348, time=147.62 bytes used=4289321568, alloc=5045348, time=147.75 bytes used=4293322528, alloc=5045348, time=147.89 bytes used=4297323620, alloc=5045348, time=148.03 bytes used=4301324480, alloc=5045348, time=148.17 bytes used=4305325852, alloc=5045348, time=148.31 bytes used=4309328116, alloc=5045348, time=148.45 bytes used=4313329012, alloc=5045348, time=148.59 bytes used=4317329912, alloc=5045348, time=148.73 bytes used=4321331532, alloc=5045348, time=148.87 bytes used=4325333144, alloc=5045348, time=149.00 bytes used=4329334456, alloc=5045348, time=149.14 bytes used=4333335536, alloc=5045348, time=149.28 bytes used=4337336732, alloc=5045348, time=149.42 bytes used=4341337736, alloc=5045348, time=149.56 bytes used=4345338688, alloc=5045348, time=149.70 bytes used=4349339704, alloc=5045348, time=149.83 bytes used=4353340608, alloc=5045348, time=149.97 bytes used=4357341796, alloc=5045348, time=150.11 bytes used=4361342948, alloc=5045348, time=150.25 bytes used=4365343940, alloc=5045348, time=150.39 bytes used=4369344972, alloc=5045348, time=150.52 bytes used=4373346368, alloc=5045348, time=150.66 bytes used=4377347428, alloc=5045348, time=150.80 bytes used=4381348236, alloc=5045348, time=150.94 bytes used=4385350788, alloc=5045348, time=151.08 bytes used=4389351816, alloc=5045348, time=151.22 bytes used=4393353108, alloc=5045348, time=151.35 bytes used=4397355480, alloc=5045348, time=151.49 bytes used=4401357612, alloc=5045348, time=151.63 bytes used=4405359224, alloc=5045348, time=151.77 bytes used=4409360104, alloc=5045348, time=151.91 bytes used=4413362180, alloc=5045348, time=152.05 bytes used=4417363628, alloc=5045348, time=152.19 bytes used=4421364736, alloc=5045348, time=152.32 bytes used=4425365416, alloc=5045348, time=152.46 bytes used=4429366444, alloc=5045348, time=152.60 bytes used=4433367420, alloc=5045348, time=152.74 bytes used=4437368388, alloc=5045348, time=152.88 bytes used=4441369360, alloc=5045348, time=153.02 bytes used=4445370732, alloc=5045348, time=153.15 bytes used=4449371460, alloc=5045348, time=153.29 bytes used=4453372500, alloc=5045348, time=153.43 bytes used=4457373332, alloc=5045348, time=153.57 bytes used=4461374228, alloc=5045348, time=153.71 bytes used=4465375216, alloc=5045348, time=153.85 bytes used=4469376220, alloc=5045348, time=153.99 bytes used=4473377480, alloc=5045348, time=154.12 bytes used=4477378976, alloc=5045348, time=154.27 bytes used=4481379804, alloc=5045348, time=154.41 bytes used=4485380888, alloc=5045348, time=154.54 bytes used=4489382088, alloc=5045348, time=154.68 bytes used=4493382756, alloc=5045348, time=154.82 bytes used=4497383784, alloc=5045348, time=154.96 bytes used=4501384844, alloc=5045348, time=155.10 bytes used=4505385692, alloc=5045348, time=155.24 bytes used=4509386580, alloc=5045348, time=155.38 bytes used=4513387648, alloc=5045348, time=155.52 bytes used=4517388360, alloc=5045348, time=155.65 bytes used=4521389588, alloc=5045348, time=155.79 bytes used=4525390436, alloc=5045348, time=155.93 bytes used=4529391720, alloc=5045348, time=156.07 bytes used=4533393268, alloc=5045348, time=156.21 bytes used=4537394832, alloc=5045348, time=156.35 bytes used=4541395896, alloc=5045348, time=156.49 bytes used=4545396576, alloc=5045348, time=156.62 bytes used=4549397932, alloc=5045348, time=156.76 bytes used=4553399228, alloc=5045348, time=156.90 bytes used=4557400560, alloc=5045348, time=157.04 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 2.3984622796991397319664026633917 y[1] (numeric) = 2.3984622804653326378459047481514 absolute error = 7.661929058795020847597e-10 relative error = 3.1945172219911351514951470013159e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5062 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 = 3.569 Order of pole (six term test) = -217.7 bytes used=4561401544, alloc=5045348, time=157.18 bytes used=4565402572, alloc=5045348, time=157.32 bytes used=4569403632, alloc=5045348, time=157.45 bytes used=4573405672, alloc=5045348, time=157.59 bytes used=4577406596, alloc=5045348, time=157.73 bytes used=4581407512, alloc=5045348, time=157.87 bytes used=4585409048, alloc=5045348, time=158.01 bytes used=4589409904, alloc=5045348, time=158.15 bytes used=4593410872, alloc=5045348, time=158.28 bytes used=4597412040, alloc=5045348, time=158.42 bytes used=4601412968, alloc=5045348, time=158.56 bytes used=4605415264, alloc=5045348, time=158.70 bytes used=4609416248, alloc=5045348, time=158.84 bytes used=4613417412, alloc=5045348, time=158.98 bytes used=4617418364, alloc=5045348, time=159.11 bytes used=4621419268, alloc=5045348, time=159.25 bytes used=4625420348, alloc=5045348, time=159.39 bytes used=4629422644, alloc=5045348, time=159.53 bytes used=4633423636, alloc=5045348, time=159.67 bytes used=4637424792, alloc=5045348, time=159.81 bytes used=4641425856, alloc=5045348, time=159.95 bytes used=4645427688, alloc=5045348, time=160.09 bytes used=4649428928, alloc=5045348, time=160.22 bytes used=4653430152, alloc=5045348, time=160.36 bytes used=4657431132, alloc=5045348, time=160.50 bytes used=4661432224, alloc=5045348, time=160.64 bytes used=4665433360, alloc=5045348, time=160.78 bytes used=4669434332, alloc=5045348, time=160.92 bytes used=4673435244, alloc=5045348, time=161.06 bytes used=4677436220, alloc=5045348, time=161.20 bytes used=4681437008, alloc=5045348, time=161.34 bytes used=4685438104, alloc=5045348, time=161.47 bytes used=4689439240, alloc=5045348, time=161.61 bytes used=4693440184, alloc=5045348, time=161.75 bytes used=4697442476, alloc=5045348, time=161.88 bytes used=4701443248, alloc=5045348, time=162.02 bytes used=4705444200, alloc=5045348, time=162.16 bytes used=4709444932, alloc=5045348, time=162.30 bytes used=4713445692, alloc=5045348, time=162.44 bytes used=4717446740, alloc=5045348, time=162.58 bytes used=4721452268, alloc=5045348, time=162.72 bytes used=4725454228, alloc=5045348, time=162.86 bytes used=4729455092, alloc=5045348, time=162.99 bytes used=4733456108, alloc=5045348, time=163.13 bytes used=4737457040, alloc=5045348, time=163.27 bytes used=4741458400, alloc=5045348, time=163.41 bytes used=4745460944, alloc=5045348, time=163.55 bytes used=4749462000, alloc=5045348, time=163.69 bytes used=4753462688, alloc=5045348, time=163.83 bytes used=4757463668, alloc=5045348, time=163.97 bytes used=4761464624, alloc=5045348, time=164.11 bytes used=4765465500, alloc=5045348, time=164.25 bytes used=4769466944, alloc=5045348, time=164.38 bytes used=4773468160, alloc=5045348, time=164.52 bytes used=4777469300, alloc=5045348, time=164.66 bytes used=4781470056, alloc=5045348, time=164.80 bytes used=4785471644, alloc=5045348, time=164.94 bytes used=4789473088, alloc=5045348, time=165.08 bytes used=4793473936, alloc=5045348, time=165.22 bytes used=4797474792, alloc=5045348, time=165.35 bytes used=4801475752, alloc=5045348, time=165.49 bytes used=4805476824, alloc=5045348, time=165.63 bytes used=4809478808, alloc=5045348, time=165.77 bytes used=4813479732, alloc=5045348, time=165.91 bytes used=4817480396, alloc=5045348, time=166.05 bytes used=4821481380, alloc=5045348, time=166.19 bytes used=4825482840, alloc=5045348, time=166.33 bytes used=4829483616, alloc=5045348, time=166.47 bytes used=4833485224, alloc=5045348, time=166.61 bytes used=4837486152, alloc=5045348, time=166.75 bytes used=4841487336, alloc=5045348, time=166.88 bytes used=4845488384, alloc=5045348, time=167.02 bytes used=4849489472, alloc=5045348, time=167.16 bytes used=4853492700, alloc=5045348, time=167.30 bytes used=4857493452, alloc=5045348, time=167.44 bytes used=4861496312, alloc=5045348, time=167.57 bytes used=4865497220, alloc=5045348, time=167.71 bytes used=4869500024, alloc=5045348, time=167.85 bytes used=4873501076, alloc=5045348, time=167.99 bytes used=4877502044, alloc=5045348, time=168.13 bytes used=4881503404, alloc=5045348, time=168.27 bytes used=4885504344, alloc=5045348, time=168.40 bytes used=4889505764, alloc=5045348, time=168.54 bytes used=4893506616, alloc=5045348, time=168.68 bytes used=4897507760, alloc=5045348, time=168.82 bytes used=4901508760, alloc=5045348, time=168.96 bytes used=4905509740, alloc=5045348, time=169.09 bytes used=4909510456, alloc=5045348, time=169.23 bytes used=4913511436, alloc=5045348, time=169.37 bytes used=4917512472, alloc=5045348, time=169.51 bytes used=4921514344, alloc=5045348, time=169.64 bytes used=4925515384, alloc=5045348, time=169.78 bytes used=4929517864, alloc=5045348, time=169.92 bytes used=4933518872, alloc=5045348, time=170.06 bytes used=4937519988, alloc=5045348, time=170.19 bytes used=4941521904, alloc=5045348, time=170.33 bytes used=4945523124, alloc=5045348, time=170.47 bytes used=4949524436, alloc=5045348, time=170.61 bytes used=4953526872, alloc=5045348, time=170.75 bytes used=4957528052, alloc=5045348, time=170.88 bytes used=4961529036, alloc=5045348, time=171.02 bytes used=4965530128, alloc=5045348, time=171.16 bytes used=4969531200, alloc=5045348, time=171.30 bytes used=4973532136, alloc=5045348, time=171.44 bytes used=4977533552, alloc=5045348, time=171.57 bytes used=4981534416, alloc=5045348, time=171.71 bytes used=4985535528, alloc=5045348, time=171.85 bytes used=4989536692, alloc=5045348, time=171.99 bytes used=4993538864, alloc=5045348, time=172.13 bytes used=4997540224, alloc=5045348, time=172.27 bytes used=5001541004, alloc=5045348, time=172.41 bytes used=5005541812, alloc=5045348, time=172.55 bytes used=5009542868, alloc=5045348, time=172.69 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 2.5148862460818292520626668752815 y[1] (numeric) = 2.5148862468480221579421689629547 absolute error = 7.661929058795020876732e-10 relative error = 3.0466304671760956397117481114120e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5098 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 = 6.215 Order of pole (six term test) = -619.4 bytes used=5013543732, alloc=5045348, time=172.83 bytes used=5017546184, alloc=5045348, time=172.97 bytes used=5021547676, alloc=5045348, time=173.10 bytes used=5025549556, alloc=5045348, time=173.24 bytes used=5029550392, alloc=5045348, time=173.38 bytes used=5033551332, alloc=5045348, time=173.52 bytes used=5037553312, alloc=5045348, time=173.66 bytes used=5041554236, alloc=5045348, time=173.80 bytes used=5045555728, alloc=5045348, time=173.94 bytes used=5049556680, alloc=5045348, time=174.07 bytes used=5053557740, alloc=5045348, time=174.21 bytes used=5057558600, alloc=5045348, time=174.35 bytes used=5061559660, alloc=5045348, time=174.49 bytes used=5065560532, alloc=5045348, time=174.63 bytes used=5069562148, alloc=5045348, time=174.76 bytes used=5073562980, alloc=5045348, time=174.90 bytes used=5077564852, alloc=5045348, time=175.04 bytes used=5081565828, alloc=5045348, time=175.18 bytes used=5085566752, alloc=5045348, time=175.32 bytes used=5089567900, alloc=5045348, time=175.46 bytes used=5093569572, alloc=5045348, time=175.59 bytes used=5097570508, alloc=5045348, time=175.73 bytes used=5101571484, alloc=5045348, time=175.87 bytes used=5105572384, alloc=5045348, time=176.01 bytes used=5109573420, alloc=5045348, time=176.15 bytes used=5113574568, alloc=5045348, time=176.29 bytes used=5117575540, alloc=5045348, time=176.43 bytes used=5121576668, alloc=5045348, time=176.57 bytes used=5125577676, alloc=5045348, time=176.70 bytes used=5129578728, alloc=5045348, time=176.84 bytes used=5133579816, alloc=5045348, time=176.98 bytes used=5137580812, alloc=5045348, time=177.12 bytes used=5141582172, alloc=5045348, time=177.26 bytes used=5145583120, alloc=5045348, time=177.39 bytes used=5149583960, alloc=5045348, time=177.53 bytes used=5153585176, alloc=5045348, time=177.67 bytes used=5157586200, alloc=5045348, time=177.81 bytes used=5161587172, alloc=5045348, time=177.95 bytes used=5165588040, alloc=5045348, time=178.09 bytes used=5169589012, alloc=5045348, time=178.23 bytes used=5173590052, alloc=5045348, time=178.37 bytes used=5177591248, alloc=5045348, time=178.50 bytes used=5181593224, alloc=5045348, time=178.64 bytes used=5185594228, alloc=5045348, time=178.78 bytes used=5189595856, alloc=5045348, time=178.92 bytes used=5193596788, alloc=5045348, time=179.06 bytes used=5197598360, alloc=5045348, time=179.19 bytes used=5201599572, alloc=5045348, time=179.33 bytes used=5205600568, alloc=5045348, time=179.47 bytes used=5209602180, alloc=5045348, time=179.61 bytes used=5213603860, alloc=5045348, time=179.75 bytes used=5217605124, alloc=5045348, time=179.89 bytes used=5221606292, alloc=5045348, time=180.02 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; Iterations = 11466 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 20 Minutes 32 Seconds Optimized Time Remaining = 20 Minutes 32 Seconds Expected Total Time = 23 Minutes 32 Seconds Time to Timeout Unknown Percent Done = 12.74 % > quit bytes used=5223147148, alloc=5045348, time=180.07