|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > 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 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 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,""); > value3 := 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 (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 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, ""); value3 := 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_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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 1 > if (iter >= 0) then # if number 2 > 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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > 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 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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)) + 2 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 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > 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 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > 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, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float 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) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*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_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; 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_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_m1[1] * array_const_3D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp4[1] / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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 FULL CONST $eq_no = 1 i = 2 > array_tmp1[2] := array_m1[2] * array_const_3D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - array_tmp2[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp4[2] - array_tmp5[1] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[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_tmp6[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult FULL CONST $eq_no = 1 i = 3 > array_tmp1[3] := array_m1[3] * array_const_3D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - array_tmp2[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp4[3] - array_tmp5[2] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_tmp5[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_tmp6[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 mult FULL CONST $eq_no = 1 i = 4 > array_tmp1[4] := array_m1[4] * array_const_3D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - array_tmp2[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp4[4] - array_tmp5[3] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_tmp5[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_tmp6[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 mult FULL CONST $eq_no = 1 i = 5 > array_tmp1[5] := array_m1[5] * array_const_3D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - array_tmp2[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp4[5] - array_tmp5[4] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_tmp5[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_tmp6[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 mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[kkk] := array_m1[kkk] * array_const_3D0[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp2[kkk] := -ats(kkk,array_x,array_tmp2,2) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp3[kkk] := -ats(kkk,array_x,array_tmp3,2) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp4[kkk] := -ats(kkk,array_x,array_tmp4,2) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp5[kkk] := -ats(kkk,array_x,array_tmp5,2) / array_x[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp6[kkk] := array_tmp5[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp6[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 2 > 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 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_const_3D0[1]; array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_tmp4[1]/array_x[1]; array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[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_m1[2]*array_const_3D0[1]; array_tmp2[2] := (array_tmp1[2] - array_tmp2[1]*array_x[2])/array_x[1]; array_tmp3[2] := (array_tmp2[2] - array_tmp3[1]*array_x[2])/array_x[1]; array_tmp4[2] := (array_tmp3[2] - array_tmp4[1]*array_x[2])/array_x[1]; array_tmp5[2] := (array_tmp4[2] - array_tmp5[1]*array_x[2])/array_x[1]; array_tmp6[2] := array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_m1[3]*array_const_3D0[1]; array_tmp2[3] := (array_tmp1[3] - array_tmp2[2]*array_x[2])/array_x[1]; array_tmp3[3] := (array_tmp2[3] - array_tmp3[2]*array_x[2])/array_x[1]; array_tmp4[3] := (array_tmp3[3] - array_tmp4[2]*array_x[2])/array_x[1]; array_tmp5[3] := (array_tmp4[3] - array_tmp5[2]*array_x[2])/array_x[1]; array_tmp6[3] := array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_m1[4]*array_const_3D0[1]; array_tmp2[4] := (array_tmp1[4] - array_tmp2[3]*array_x[2])/array_x[1]; array_tmp3[4] := (array_tmp2[4] - array_tmp3[3]*array_x[2])/array_x[1]; array_tmp4[4] := (array_tmp3[4] - array_tmp4[3]*array_x[2])/array_x[1]; array_tmp5[4] := (array_tmp4[4] - array_tmp5[3]*array_x[2])/array_x[1]; array_tmp6[4] := array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_m1[5]*array_const_3D0[1]; array_tmp2[5] := (array_tmp1[5] - array_tmp2[4]*array_x[2])/array_x[1]; array_tmp3[5] := (array_tmp2[5] - array_tmp3[4]*array_x[2])/array_x[1]; array_tmp4[5] := (array_tmp3[5] - array_tmp4[4]*array_x[2])/array_x[1]; array_tmp5[5] := (array_tmp4[5] - array_tmp5[4]*array_x[2])/array_x[1]; array_tmp6[5] := array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_m1[kkk]*array_const_3D0[1]; array_tmp2[kkk] := -ats(kkk, array_x, array_tmp2, 2)/array_x[1]; array_tmp3[kkk] := -ats(kkk, array_x, array_tmp3, 2)/array_x[1]; array_tmp4[kkk] := -ats(kkk, array_x, array_tmp4, 2)/array_x[1]; array_tmp5[kkk] := -ats(kkk, array_x, array_tmp5, 2)/array_x[1]; array_tmp6[kkk] := array_tmp5[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp6[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 12 > #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\n", 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 \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", 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\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", 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, "\n") 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 Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # 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 := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # 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"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > 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") else fprintf(file, "No Pole") 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, "\n") 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 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > 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 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > 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 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > 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 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > 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 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > 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(1.0/x/x/x); > end; exact_soln_y := proc(x) return 1.0/(x*x*x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_log10normmin := 0.1; > 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_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > 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_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > 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 := 0.1e-50; > glob_smallish_float := 0.1e-100; > 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_log10abserr := 0.0; > glob_log10relerr := 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/sing5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.0;"); > omniout_str(ALWAYS,"x_end := -0.7;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > 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(1.0/x/x/x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_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..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= 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..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 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 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_3D0[1] := 3.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > x_end := -0.7; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > 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); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > 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); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > 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 3 > 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 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > 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 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > 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,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > 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 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((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 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > 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 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > 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 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-13T01:59:51-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing5") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 156 ") > ; > logitem_str(html_log_file,"sing5 diffeq.mxt") > ; > logitem_str(html_log_file,"sing5 maple results") > ; > logitem_str(html_log_file,"Languages compared - single equations") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, 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; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_log10normmin := 0.1; 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_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; 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_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); 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 := 0.1*10^(-50); glob_smallish_float := 0.1*10^(-100); 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_log10abserr := 0.; glob_log10relerr := 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/sing5postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.0;"); omniout_str(ALWAYS, "x_end := -0.7;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); 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(1.0/x/x/x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_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 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := 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 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 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 <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_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[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_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 <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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 := 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_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_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 := -1.0; x_end := -0.7; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_desired_digits_correct := 10; glob_display_interval := 0.001; 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); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); 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); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. 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(); 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, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < 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_log10normmin := -glob_large_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and 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 ) = m1 * 3.0 / x / x / x / x ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-13T01:59:51-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing5"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 156 "); logitem_str(html_log_file, "sing5 diffeq.mxt"); logitem_str(html_log_file, "sing5 maple results") ; logitem_str(html_log_file, "Languages compared - single equations"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; x_end := -0.7; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; 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(1.0/x/x/x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.3 estimated_steps = 300 step_error = 3.3333333333333333333333333333333e-13 est_needed_step_err = 3.3333333333333333333333333333333e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.0404069204059829059829059829059e-78 max_value3 = 4.0404069204059829059829059829059e-78 value3 = 4.0404069204059829059829059829059e-78 best_h = 0.001 START of Soultion x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.999 y[1] (analytic) = -1.0030060100150210280360450550661 y[1] (numeric) = -1.0030060100150210175150131366772 absolute error = 1.05210319183889e-17 relative error = 1.0489500375208456548311100000000e-15 % Correct digits = 16 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.998 y[1] (analytic) = -1.0060240802406737966195482277442 y[1] (numeric) = -1.0060240802406737754822986403582 absolute error = 2.11372495873860e-17 relative error = 2.1010679567758735932911999999998e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used Radius of convergence = 0.998 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -0.997 y[1] (analytic) = -1.0090542712201234910283314761 y[1] (numeric) = -1.0090542712201234591787206587356 absolute error = 3.18496108173644e-17 relative error = 3.1563823399560697169961200000000e-15 % Correct digits = 16 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.996 y[1] (analytic) = -1.0120966438616192807876074547054 y[1] (numeric) = -1.0120966438616192381285234235307 absolute error = 4.26590840311747e-17 relative error = 4.2149219928652721990419200000005e-15 % Correct digits = 16 h = 0.001 Complex estimate of poles used Radius of convergence = 0.8319 Order of pole = 4.877e-27 TOP MAIN SOLVE Loop x[1] = -0.995 y[1] (analytic) = -1.0151512594410653301861952371894 y[1] (numeric) = -1.0151512594410652766195468446405 absolute error = 5.35666483925489e-17 relative error = 5.2767159469459058598887500000003e-15 % Correct digits = 16 h = 0.001 Complex estimate of poles used Radius of convergence = 0.7904 Order of pole = 2.517e-27 TOP MAIN SOLVE Loop x[1] = -0.994 y[1] (analytic) = -1.0182181796046125218370125452544 y[1] (numeric) = -1.0182181796046124572637186090651 absolute error = 6.45732939361893e-17 relative error = 6.3417934613251510827511200000000e-15 % Correct digits = 16 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.993 y[1] (analytic) = -1.0212974663712710812022922527324 y[1] (numeric) = -1.0212974663712710055222705531658 absolute error = 7.56800216995666e-17 relative error = 7.4101840248818094738856200000005e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used Radius of convergence = 0.993 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -0.992 y[1] (analytic) = -1.0243891821355442919002383270116 y[1] (numeric) = -1.0243891821355442050123944705604 absolute error = 8.68878438564512e-17 relative error = 8.4819173583340755327385599999993e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used Radius of convergence = 0.992 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -0.991 y[1] (analytic) = -1.0274933896700834935271733588728 y[1] (numeric) = -1.0274933896700833953293895066732 absolute error = 9.81977838521996e-17 relative error = 9.5570234163481867049291599999994e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used Radius of convergence = 0.991 Order of pole = 2.8e-29 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = -1.0306101521283645556678920621376 y[1] (numeric) = -1.0306101521283644460570155213115 absolute error = 1.096108765408261e-16 relative error = 1.0635532389668702400389999999999e-14 % Correct digits = 15 h = 0.001 NO POLE memory used=3.8MB, alloc=3.0MB, time=0.19 TOP MAIN SOLVE Loop x[1] = -0.989 y[1] (analytic) = -1.0337395330473860237271816069859 y[1] (numeric) = -1.033739533047385902599013283106 absolute error = 1.211281683238799e-16 relative error = 1.1717474707270139261955310000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.8443 Order of pole = 6.53e-28 TOP MAIN SOLVE Loop x[1] = -0.988 y[1] (analytic) = -1.0368815963503891341975628073193 y[1] (numeric) = -1.0368815963503890014468455161625 absolute error = 1.327507172911568e-16 relative error = 1.2802881038530545581864960000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.987 y[1] (analytic) = -1.040036406349599898982511894951 y[1] (numeric) = -1.0400364063495997545029185316821 absolute error = 1.444795933632689e-16 relative error = 1.3891782295426997113052670000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.2284 Order of pole = 3.678e-27 TOP MAIN SOLVE Loop x[1] = -0.986 y[1] (analytic) = -1.0432040277489934604210102726637 y[1] (numeric) = -1.0432040277489933041051318365619 absolute error = 1.563158784361018e-16 relative error = 1.4984209634753552359506080000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.985 y[1] (analytic) = -1.0463845256470809207085121942383 y[1] (numeric) = -1.0463845256470807524478456670545 absolute error = 1.682606665271838e-16 relative error = 1.6080194460361684881967499999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.985 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -0.984 y[1] (analytic) = -1.0495779655397188514815943321043 y[1] (numeric) = -1.04957796553971867116653040811 absolute error = 1.803150639239943e-16 relative error = 1.7179768425423436854174720000001e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.8016 Order of pole = 4.759e-27 TOP MAIN SOLVE Loop x[1] = -0.983 y[1] (analytic) = -1.0527844133229416914289368831288 y[1] (numeric) = -1.0527844133229414989487475488867 absolute error = 1.924801893342421e-16 relative error = 1.8282963434717834166926270000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.982 y[1] (analytic) = -1.0560039352958172419101671644937 y[1] (numeric) = -1.0560039352958170371529931263562 absolute error = 2.047571740381375e-16 relative error = 1.9389811646940415423210000000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.981 y[1] (analytic) = -1.0592365981633254727067612653502 y[1] (numeric) = -1.0592365981633252555595992226599 absolute error = 2.171471620426903e-16 relative error = 2.0500345477036473568213229999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.981 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = -1.0624824690392608521959387670103 y[1] (numeric) = -1.06248246903926062254462852895 absolute error = 2.296513102380603e-16 relative error = 2.1614597598558044987760000000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.979 y[1] (analytic) = -1.0657416154491584184295952209222 y[1] (numeric) = -1.0657416154491581761588066649297 absolute error = 2.422707885559925e-16 relative error = 2.2732600946045173353095749999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.979 Order of pole = 2.2e-29 TOP MAIN SOLVE Loop x[1] = -0.978 y[1] (analytic) = -1.0690141053332438098160963061637 y[1] (numeric) = -1.0690141053332435548093161758011 absolute error = 2.550067801303626e-16 relative error = 2.3854388717431312679423520000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.977 y[1] (analytic) = -1.0723000070494074763435096902299 y[1] (numeric) = -1.0723000070494072084830282303612 absolute error = 2.678604814598687e-16 relative error = 2.4979994376473664910442709999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.976 y[1] (analytic) = -1.0755993893762032945488829461497 y[1] (numeric) = -1.0755993893762030137157803732551 absolute error = 2.808331025728946e-16 relative error = 2.6109451655208218297384959999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.975 y[1] (analytic) = -1.0789123215158718117297998954803 y[1] (numeric) = -1.0789123215158715178039327009 absolute error = 2.939258671945803e-16 relative error = 2.7242794556430170024531250000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.975 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.974 y[1] (analytic) = -1.0822388730973883472119790717858 y[1] (numeric) = -1.0822388730973880400719661556567 absolute error = 3.071400129161291e-16 relative error = 2.8380057356199792612973840000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.974 Order of pole = 1.4e-29 TOP MAIN SOLVE Loop x[1] = -0.973 y[1] (analytic) = -1.0855791141795361808304364754183 y[1] (numeric) = -1.0855791141795358603536451090342 absolute error = 3.204767913663841e-16 relative error = 2.9521274606374080538845970000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.972 y[1] (analytic) = -1.0889331152540050611520445424867 y[1] (numeric) = -1.0889331152540047272145761567797 absolute error = 3.339374683857070e-16 relative error = 3.0666481137164479182393600000002e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.971 y[1] (analytic) = -1.0923009472485152683645087474632 y[1] (numeric) = -1.0923009472485149208411845452694 absolute error = 3.475233242021938e-16 relative error = 3.1815712059721110705281180000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.971 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = -1.0956826815299674691811853752658 y[1] (numeric) = -1.0956826815299671079455317650077 absolute error = 3.612356536102581e-16 relative error = 3.2969002768743509090130000000001e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.5668 Order of pole = 6.327e-27 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.42 x[1] = -0.969 y[1] (analytic) = -1.0990783899076186035631160806292 y[1] (numeric) = -1.0990783899076182284873499290099 absolute error = 3.750757661516193e-16 relative error = 3.4126388945118440065133370000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.969 Order of pole = 6.7e-29 TOP MAIN SOLVE Loop x[1] = -0.968 y[1] (analytic) = -1.1024881446362840455394987810185 y[1] (numeric) = -1.1024881446362836564945124822888 absolute error = 3.890449862987297e-16 relative error = 3.5287906558585030966359040000002e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.967 y[1] (analytic) = -1.1059120184195662829158966860222 y[1] (numeric) = -1.1059120184195658797712430453467 absolute error = 4.031446536406755e-16 relative error = 3.6453591870427482740305649999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.966 y[1] (analytic) = -1.1093500844131103631961590004675 y[1] (numeric) = -1.1093500844131099458200359288804 absolute error = 4.173761230715871e-16 relative error = 3.7623481436195627420342159999997e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.965 y[1] (analytic) = -1.1128024162278863556096439352199 y[1] (numeric) = -1.1128024162278859238688789536224 absolute error = 4.317407649815975e-16 relative error = 3.8797612108453854731968749999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.965 Order of pole = 5.2e-29 TOP MAIN SOLVE Loop x[1] = -0.964 y[1] (analytic) = -1.1162690879334990817302578077933 y[1] (numeric) = -1.1162690879334986354902923574094 absolute error = 4.462399654503839e-16 relative error = 3.9976021039558547829196159999998e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.963 y[1] (analytic) = -1.1197501740615253697984187777124 y[1] (numeric) = -1.1197501740615249089232923343826 absolute error = 4.608751264433298e-16 relative error = 4.1158745684464321370424059999998e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.962 y[1] (analytic) = -1.1232457496088790905116906474093 y[1] (numeric) = -1.1232457496088786148640246370609 absolute error = 4.756476660103484e-16 relative error = 4.2345823803559619183139519999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.961 y[1] (analytic) = -1.1267558900412042347348866939516 y[1] (numeric) = -1.126755890041203744175868206548 absolute error = 4.905590184874036e-16 relative error = 4.3537293465531774713265160000002e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = -1.1302806712962962962962962962964 y[1] (numeric) = -1.1302806712962957906856615955269 absolute error = 5.056106347007695e-16 relative error = 4.4733193050262000435199999999996e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.96 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -0.959 y[1] (analytic) = -1.1338201697875522257837239681508 y[1] (numeric) = -1.1338201697875517049797417940834 absolute error = 5.208039821740674e-16 relative error = 4.5933561251750551279892459999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.958 y[1] (analytic) = -1.1373744624074492240326423195072 y[1] (numeric) = -1.137374462407448687892096981384 absolute error = 5.361405453381232e-16 relative error = 4.7138437081072601390275840000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.958 Order of pole = 5.6e-29 TOP MAIN SOLVE Loop x[1] = -0.957 y[1] (analytic) = -1.1409436265310526468093437893195 y[1] (numeric) = -1.1409436265310520951875180456358 absolute error = 5.516218257436837e-16 relative error = 4.8347859869364931312396410000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.956 y[1] (analytic) = -1.1445277400195532950349324516209 y[1] (numeric) = -1.1445277400195527277855901745853 absolute error = 5.672493422770356e-16 relative error = 4.9561869270843939656424960000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.955 y[1] (analytic) = -1.1481268812238343677717340059826 y[1] (numeric) = -1.1481268812238337847471026274124 absolute error = 5.830246313785702e-16 relative error = 5.0780505265855366475552500000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.955 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -0.954 y[1] (analytic) = -1.1517411289880683581026319837056 y[1] (numeric) = -1.1517411289880677591533847193699 absolute error = 5.989492472643357e-16 relative error = 5.2003808163955965504390479999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.954 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.953 y[1] (analytic) = -1.1553705626533441749763796331014 y[1] (numeric) = -1.1553705626533435599516174824792 absolute error = 6.150247621506222e-16 relative error = 5.3231818607027587907072939999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.952 y[1] (analytic) = -1.1590152620613247770685140096572 y[1] (numeric) = -1.1590152620613241458157475280329 absolute error = 6.312527664816243e-16 relative error = 5.4464577572424065216701440000002e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.951 y[1] (analytic) = -1.1626753075579356077185414125254 y[1] (numeric) = -1.1626753075579349600836722522996 absolute error = 6.476348691602258e-16 relative error = 5.5702126376151188243225580000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.951 Order of pole = 8.4e-29 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = -1.1663507799970841230500072896924 y[1] (numeric) = -1.166350779997083458877309507739 absolute error = 6.641726977819534e-16 relative error = 5.6944506676080229632499999999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.949 y[1] (analytic) = -1.170041760744410708461350868743 y[1] (numeric) = -1.170041760744410027593451996597 absolute error = 6.808678988721460e-16 relative error = 5.8191760475195372819895399999998e-14 % Correct digits = 15 h = 0.001 NO POLE memory used=11.4MB, alloc=4.3MB, time=0.67 TOP MAIN SOLVE Loop x[1] = -0.948 y[1] (analytic) = -1.1737483316810712817925229113796 y[1] (numeric) = -1.1737483316810705840703847849916 absolute error = 6.977221381263880e-16 relative error = 5.9443930124875505629209600000002e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.6453 Order of pole = 4.632e-27 TOP MAIN SOLVE Loop x[1] = -0.947 y[1] (analytic) = -1.1774705752075518846256681452278 y[1] (numeric) = -1.1774705752075511698885674909741 absolute error = 7.147371006542537e-16 relative error = 6.0701058328210665430180510000003e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.946 y[1] (analytic) = -1.1812085742475155663682023490042 y[1] (numeric) = -1.1812085742475148344537111225913 absolute error = 7.319144912264129e-16 relative error = 6.1963188143353619436831440000005e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.945 y[1] (analytic) = -1.1849624122516818689938143480878 y[1] (numeric) = -1.1849624122516811197377798229402 absolute error = 7.492560345251476e-16 relative error = 6.3230362986906983903804999999997e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.944 y[1] (analytic) = -1.1887321732017392235817683404827 y[1] (numeric) = -1.1887321732017384568182929421531 absolute error = 7.667634753983296e-16 relative error = 6.4502626637346215902576640000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.943 y[1] (analytic) = -1.1925179416142905730978515695743 y[1] (numeric) = -1.1925179416142897886592724526611 absolute error = 7.844385791169132e-16 relative error = 6.5780023238479119725415239999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.942 y[1] (analytic) = -1.196319802544832539201892566443 y[1] (numeric) = -1.1963198025448317369187609304517 absolute error = 8.022831316359913e-16 relative error = 6.7062597302941947646507439999998e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.941 y[1] (analytic) = -1.2001378415917684542474589010426 y[1] (numeric) = -1.2001378415917676339485190415709 absolute error = 8.202989398594717e-16 relative error = 6.8350393715732827362482569999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.941 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = -1.2039721449004555830596303323926 y[1] (numeric) = -1.2039721449004547445717984239661 absolute error = 8.384878319084265e-16 relative error = 6.9643457737782851607600000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.94 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -0.939 y[1] (analytic) = -1.207822799167286862537140083043 y[1] (numeric) = -1.2078227991672860056854826898745 absolute error = 8.568516573931685e-16 relative error = 7.0941835009565184568620150000003e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.938 y[1] (analytic) = -1.2116898916438074906261973616586 y[1] (numeric) = -1.2116898916438066152339096725464 absolute error = 8.753922876891122e-16 relative error = 7.2245571554742780195799840000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.938 Order of pole = 2.9e-29 TOP MAIN SOLVE Loop x[1] = -0.937 y[1] (analytic) = -1.2155735101408666997554690332752 y[1] (numeric) = -1.2155735101408658056438528168003 absolute error = 8.941116162164749e-16 relative error = 7.3554713783855062963497969999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.937 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -0.936 y[1] (analytic) = -1.2194737430328050534055355444793 y[1] (numeric) = -1.2194737430328041403939768206038 absolute error = 9.130115587238755e-16 relative error = 7.4869308498044027452492799999995e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.936 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -0.935 y[1] (analytic) = -1.2233906792616776081121812551163 y[1] (numeric) = -1.2233906792616766760181276792253 absolute error = 9.320940535758910e-16 relative error = 7.6189402892820339435912499999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.935 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.934 y[1] (analytic) = -1.2273244083415132868716750738552 y[1] (numeric) = -1.2273244083415123355106130292266 absolute error = 9.513610620446286e-16 relative error = 7.7515044561869776120081440000002e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.933 y[1] (analytic) = -1.2312750203626108136282941788923 y[1] (numeric) = -1.2312750203626098428137255735179 absolute error = 9.708145686053744e-16 relative error = 7.8846281500900526442413280000003e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.932 y[1] (analytic) = -1.2352426059958715622802997500976 y[1] (numeric) = -1.2352426059958705718237185137174 absolute error = 9.904565812363802e-16 relative error = 8.0183162111531838783535359999998e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used Radius of convergence = 0.7155 Order of pole = 2.932e-27 TOP MAIN SOLVE Loop x[1] = -0.931 y[1] (analytic) = -1.2392272564971696774409549695412 y[1] (numeric) = -1.2392272564971686671518232466902 absolute error = 1.0102891317228510e-15 relative error = 8.1525735205224518177384099999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.931 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = -1.2432290637117598280365559073895 y[1] (numeric) = -1.2432290637117587977222799421926 absolute error = 1.0303142759651969e-15 relative error = 8.2874050007253788289329999999992e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.929 y[1] (analytic) = -1.2472481200787229587144071821765 y[1] (numeric) = -1.2472481200787219081803128905642 absolute error = 1.0505340942916123e-15 relative error = 8.4228156160724892766299470000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.929 Order of pole = 4.3e-29 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.91 x[1] = -0.928 y[1] (analytic) = -1.2512845186354504079708065111321 y[1] (numeric) = -1.2512845186354493370201147360807 absolute error = 1.0709506917750514e-15 relative error = 8.5588103730632224258785279999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.928 Order of pole = 4.2e-29 TOP MAIN SOLVE Loop x[1] = -0.927 y[1] (analytic) = -1.2553383530221667658930037737743 y[1] (numeric) = -1.2553383530221656743268052191133 absolute error = 1.0915661985546610e-15 relative error = 8.6953943207962046784876300000000e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.926 y[1] (analytic) = -1.2594097174864918484403777354619 y[1] (numeric) = -1.259409717486490736057607573717 absolute error = 1.1123827701617449e-15 relative error = 8.8325725513839865450184239999995e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.925 y[1] (analytic) = -1.2634987068880421692693423884075 y[1] (numeric) = -1.2634987068880410358667545380843 absolute error = 1.1334025878503232e-15 relative error = 8.9703502003722532889999999999993e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.925 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.924 y[1] (analytic) = -1.2676054167030722942343789029571 y[1] (numeric) = -1.2676054167030711396065199705978 absolute error = 1.1546278589323593e-15 relative error = 9.1087324471635861019432319999998e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.923 y[1] (analytic) = -1.2717299430291564678747211762303 y[1] (numeric) = -1.2717299430291552918139040585049 absolute error = 1.1760608171177254e-15 relative error = 9.2477245154458260775976180000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.923 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop x[1] = -0.922 y[1] (analytic) = -1.2758723825899109054232445840927 y[1] (numeric) = -1.2758723825899097077195217251154 absolute error = 1.1977037228589773e-15 relative error = 9.3873316736250849208393040000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.922 Order of pole = 4.4e-29 TOP MAIN SOLVE Loop x[1] = -0.921 y[1] (analytic) = -1.280032832739757148151669518471 y[1] (numeric) = -1.2800328327397559285928058174583 absolute error = 1.2195588637010127e-15 relative error = 9.5275592352634646728150470000001e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = -1.2842113914687268841949535629161 y[1] (numeric) = -1.2842113914687256425663989272272 absolute error = 1.2416285546356889e-15 relative error = 9.6684125595215531816319999999999e-14 % Correct digits = 15 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.919 y[1] (analytic) = -1.288408157407308641378378008257 y[1] (numeric) = -1.2884081574073073774632395467841 absolute error = 1.2639151384614729e-15 relative error = 9.8098970516057305277125110000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.919 Order of pole = 1.3e-29 TOP MAIN SOLVE Loop x[1] = -0.918 y[1] (analytic) = -1.2926232298313367630040146085453 y[1] (numeric) = -1.2926232298313354765830284603415 absolute error = 1.2864209861482038e-15 relative error = 9.9520181632203666942080159999995e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used Radius of convergence = 0.918 Order of pole = 6.2e-29 TOP MAIN SOLVE Loop x[1] = -0.917 y[1] (analytic) = -1.2968567086669230820396754298098 y[1] (numeric) = -1.2968567086669217728911782227665 absolute error = 1.3091484972070433e-15 relative error = 1.0094781393024949585137228999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.917 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -0.916 y[1] (analytic) = -1.3011086944954317136938005355821 y[1] (numeric) = -1.3011086944954303815937004698861 absolute error = 1.3321001000656960e-15 relative error = 1.0238192287096219226460160000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.915 y[1] (analytic) = -1.3053792885584973909547331992383 y[1] (numeric) = -1.3053792885584960356764807502589 absolute error = 1.3552782524489794e-15 relative error = 1.0382256439395360520209750000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.914 y[1] (analytic) = -1.3096685927630877723231885321479 y[1] (numeric) = -1.3096685927630863936377467673233 absolute error = 1.3786854417648246e-15 relative error = 1.0526979492240306141490224000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.914 Order of pole = 2.9e-29 TOP MAIN SOLVE Loop x[1] = -0.913 y[1] (analytic) = -1.3139767096866101556731673040805 y[1] (numeric) = -1.3139767096866087533489818082857 absolute error = 1.4023241854957948e-15 relative error = 1.0672367136783238323604156000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.912 y[1] (analytic) = -1.3183037425820630369398411387039 y[1] (numeric) = -1.3183037425820616107428095425013 absolute error = 1.4261970315962026e-15 relative error = 1.0818425113493321650249728000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.911 y[1] (analytic) = -1.3226497953832329571537875774513 y[1] (numeric) = -1.3226497953832315068472286825362 absolute error = 1.4503065588949151e-15 relative error = 1.0965159212644750464181680999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.911 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = -1.3270149727099370862201438218827 y[1] (numeric) = -1.3270149727099356115647663179501 absolute error = 1.4746553775039326e-15 relative error = 1.1112575274810159933146000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.91 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -0.909 y[1] (analytic) = -1.3313993798733119967795472727922 y[1] (numeric) = -1.3313993798733104975334180399582 absolute error = 1.4992461292328340e-15 relative error = 1.1260679191359494971117860000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.908 y[1] (analytic) = -1.335803122881149086485921319016 y[1] (numeric) = -1.335803122881147562404433309843 absolute error = 1.5240814880091730e-15 relative error = 1.1409476904964352859109760000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.908 Order of pole = 2.8e-29 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.16 x[1] = -0.907 y[1] (analytic) = -1.3402263084432771120950394467669 y[1] (numeric) = -1.340226308443275562930879141842 absolute error = 1.5491641603049249e-15 relative error = 1.1558974410107923508025107000001e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.6633 Order of pole = 1.674e-27 TOP MAIN SOLVE Loop x[1] = -0.906 y[1] (analytic) = -1.3446690439769923038781642926751 y[1] (numeric) = -1.344669043976990729381278723603 absolute error = 1.5744968855690721e-15 relative error = 1.1709177753600552288456935999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.905 y[1] (analytic) = -1.3491314376125365340577269732354 y[1] (numeric) = -1.34913143761253493397529030681 absolute error = 1.6000824366664254e-15 relative error = 1.1860093035101007522276750000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.904 y[1] (analytic) = -1.3536135981986240182078138633596 y[1] (numeric) = -1.3536135981986223922841935405788 absolute error = 1.6259236203227808e-15 relative error = 1.2011726407643542773645312000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.903 y[1] (analytic) = -1.3581156353080170338720028735771 y[1] (numeric) = -1.3581156353080153818487252970725 absolute error = 1.6520232775765046e-15 relative error = 1.2164084078170781755614042000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.902 y[1] (analytic) = -1.3626376592431511460256912140318 y[1] (numeric) = -1.3626376592431494676414069773793 absolute error = 1.6783842842366525e-15 relative error = 1.2317172308072538333902200000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.902 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.901 y[1] (analytic) = -1.3671797810418104344503459655956 y[1] (numeric) = -1.3671797810418087294407946178744 absolute error = 1.7050095513477212e-15 relative error = 1.2470997413730619075109611999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.901 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = -1.3717421124828532235939643347051 y[1] (numeric) = -1.3717421124828514916919386735676 absolute error = 1.7319020256611375e-15 relative error = 1.2625565767069692375000000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.9 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.899 y[1] (analytic) = -1.3763247660919888210663417729105 y[1] (numeric) = -1.3763247660919870620016516593205 absolute error = 1.7590646901135900e-15 relative error = 1.2780883796114297028794100000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.898 y[1] (analytic) = -1.3809278551476057765604156102339 y[1] (numeric) = -1.3809278551476039900598512979243 absolute error = 1.7865005643123096e-15 relative error = 1.2936957985552059321892031999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.897 y[1] (analytic) = -1.3855514936866521787028949919356 y[1] (numeric) = -1.3855514936866503644901899645265 absolute error = 1.8142127050274091e-15 relative error = 1.3093794877303205518620843000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.897 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -0.896 y[1] (analytic) = -1.3901957965105685131195335276968 y[1] (numeric) = -1.3901957965105666709153268363052 absolute error = 1.8422042066913916e-15 relative error = 1.3251401071096439899160576000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.895 y[1] (analytic) = -1.3948608791912736108536914731631 y[1] (numeric) = -1.3948608791912717403754895672234 absolute error = 1.8704782019059397e-15 relative error = 1.3409783225051262866322875000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.895 Order of pole = 3.5e-29 TOP MAIN SOLVE Loop x[1] = -0.894 y[1] (analytic) = -1.399546858077204222202225496714 y[1] (numeric) = -1.3995468580772023231643635406119 absolute error = 1.8990378619561021e-15 relative error = 1.3568948056266824128880664000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.893 y[1] (analytic) = -1.4042538502994087570312061028052 y[1] (numeric) = -1.4042538502994068291448087708139 absolute error = 1.9278863973319913e-15 relative error = 1.3728902341417372232629741000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.892 y[1] (analytic) = -1.4089819737776957387064797029497 y[1] (numeric) = -1.4089819737776937816794214448367 absolute error = 1.9570270582581130e-15 relative error = 1.3889652917354398340525439999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.892 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -0.891 y[1] (analytic) = -1.413731347226837524921662636677 y[1] (numeric) = -1.4137313472268355384585274062318 absolute error = 1.9864631352304452e-15 relative error = 1.4051206681715540296466892000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.891 Order of pole = 4.2e-29 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = -1.4185020901628298549297912390473 y[1] (numeric) = -1.4185020901628278387318316776546 absolute error = 2.0161979595613927e-15 relative error = 1.4213570593540354503263000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.89 Order of pole = 5.3e-29 TOP MAIN SOLVE Loop x[1] = -0.889 y[1] (analytic) = -1.4232943229092077889855832511187 y[1] (numeric) = -1.4232943229092057427506793183812 absolute error = 2.0462349039327375e-15 relative error = 1.4376751673893012549926375000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.889 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -0.888 y[1] (analytic) = -1.4281081666034186121841344631703 y[1] (numeric) = -1.4281081666034165356067515064556 absolute error = 2.0765773829567147e-15 relative error = 1.4540757006492030371203584000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.887 y[1] (analytic) = -1.4329437432032522813399387588215 y[1] (numeric) = -1.4329437432032501741110850134809 absolute error = 2.1072288537453406e-15 relative error = 1.4705593738347103082484818000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.887 Order of pole = 9.8e-29 memory used=22.8MB, alloc=4.3MB, time=1.41 TOP MAIN SOLVE Loop x[1] = -0.886 y[1] (analytic) = -1.4378011754933300000884535283164 y[1] (numeric) = -1.4378011754933278618956370401895 absolute error = 2.1381928164881269e-15 relative error = 1.4871269080403155062972663999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.885 y[1] (analytic) = -1.4426805870916515140121253696644 y[1] (numeric) = -1.4426805870916493445393103313561 absolute error = 2.1694728150383083e-15 relative error = 1.5037790308191654311667375000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.884 y[1] (analytic) = -1.4475821024562017242949487676374 y[1] (numeric) = -1.447582102456199523222511259911 absolute error = 2.2010724375077264e-15 relative error = 1.5205164762489334520083456000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.884 Order of pole = 6.5e-29 TOP MAIN SOLVE Loop x[1] = -0.883 y[1] (analytic) = -1.4525058468916172251953750000215 y[1] (numeric) = -1.45250584689161499220005812952 absolute error = 2.2329953168705015e-15 relative error = 1.5373399849984374440815805000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.883 Order of pole = 4.2e-29 TOP MAIN SOLVE Loop x[1] = -0.882 y[1] (analytic) = -1.4574519465559133774978583909607 y[1] (numeric) = -1.4574519465559111122527268153255 absolute error = 2.2652451315756352e-15 relative error = 1.5542503043950147937204736000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.881 y[1] (analytic) = -1.4624205284672725370596775546123 y[1] (numeric) = -1.4624205284672702392340713859272 absolute error = 2.2978256061686851e-15 relative error = 1.5712481884926631531888690999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.881 Order of pole = 5.4e-29 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = -1.4674117205108940646130728775357 y[1] (numeric) = -1.4674117205108917338725609548776 absolute error = 2.3307405119226581e-15 relative error = 1.5883343981409576607232000000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.879 y[1] (analytic) = -1.4724256514459067501143879634775 y[1] (numeric) = -1.4724256514459043861207204852097 absolute error = 2.3639936674782678e-15 relative error = 1.6055097010547530775973642000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.879 Order of pole = 2.6e-29 TOP MAIN SOLVE Loop x[1] = -0.878 y[1] (analytic) = -1.4774624509123442921529995342211 y[1] (numeric) = -1.477462450912341894564060040515 absolute error = 2.3975889394937061e-15 relative error = 1.6227748718846808649429272000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.878 Order of pole = 1.1e-29 TOP MAIN SOLVE Loop x[1] = -0.877 y[1] (analytic) = -1.4825222494381844802445926880049 y[1] (numeric) = -1.4825222494381820487143493839216 absolute error = 2.4315302433040833e-15 relative error = 1.6401306922884524514588789000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.877 Order of pole = 5.5e-29 TOP MAIN SOLVE Loop x[1] = -0.876 y[1] (analytic) = -1.4876051784464527352370300107803 y[1] (numeric) = -1.4876051784464502694154864200913 absolute error = 2.4658215435906890e-15 relative error = 1.6575779510029769403680640000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.876 Order of pole = 3.4e-29 TOP MAIN SOLVE Loop x[1] = -0.875 y[1] (analytic) = -1.4927113702623906705539358600583 y[1] (numeric) = -1.4927113702623881700870807998244 absolute error = 2.5004668550602339e-15 relative error = 1.6751174439173051322265625000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.875 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.874 y[1] (analytic) = -1.4978409581206903445924520343095 y[1] (numeric) = -1.4978409581206878091222089000778 absolute error = 2.5354702431342317e-15 relative error = 1.6927499741464094229364808000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.874 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -0.873 y[1] (analytic) = -1.5029940761727948822787179358928 y[1] (numeric) = -1.5029940761727923114428932872085 absolute error = 2.5708358246486843e-15 relative error = 1.7104763521058101230316131000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.873 Order of pole = 2.4e-29 TOP MAIN SOLVE Loop x[1] = -0.872 y[1] (analytic) = -1.5081708594942661515688065672661 y[1] (numeric) = -1.5081708594942635450010380030288 absolute error = 2.6065677685642373e-15 relative error = 1.7282973955870595411874304000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.872 Order of pole = 2.3e-29 TOP MAIN SOLVE Loop x[1] = -0.871 y[1] (analytic) = -1.513371444092220188565446317884 y[1] (numeric) = -1.5133714440922175458951496309106 absolute error = 2.6426702966869734e-15 relative error = 1.7462139298340938050071274000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = -1.5185959669128310729032365835843 y[1] (numeric) = -1.5185959669128283937555521835669 absolute error = 2.6791476844000174e-15 relative error = 1.7642267876204646579522000000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.869 y[1] (analytic) = -1.5238445658489039631386022470804 y[1] (numeric) = -1.5238445658489012471343408409567 absolute error = 2.7160042614061237e-15 relative error = 1.7823368093274597983122433000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.868 y[1] (analytic) = -1.529117379747518010066828056647 y[1] (numeric) = -1.5291173797475152568224155752164 absolute error = 2.7532444124814306e-15 relative error = 1.8005448430231273317489791999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.868 Order of pole = 3e-30 TOP MAIN SOLVE Loop x[1] = -0.867 y[1] (analytic) = -1.5344145484177398741785901072737 y[1] (numeric) = -1.5344145484177370833060118667187 absolute error = 2.7908725782405550e-15 relative error = 1.8188517445422109625914650000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.66 x[1] = -0.866 y[1] (analytic) = -1.5397362126384085818639004496732 y[1] (numeric) = -1.539736212638405752970644536455 absolute error = 2.8288932559132182e-15 relative error = 1.8372583775670119036337072000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.865 y[1] (analytic) = -1.5450825141659924634737665268303 y[1] (numeric) = -1.545082514165989596162766394246 absolute error = 2.8673110001325843e-15 relative error = 1.8557656137091854980053875000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.865 Order of pole = 1.2e-29 TOP MAIN SOLVE Loop x[1] = -0.864 y[1] (analytic) = -1.5504535957425189249606259208454 y[1] (numeric) = -1.5504535957425160188302021853392 absolute error = 2.9061304237355062e-15 relative error = 1.8743743325924874169417728000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.3368 Order of pole = 2.717e-27 TOP MAIN SOLVE Loop x[1] = -0.863 y[1] (analytic) = -1.5558496011035778135392574546282 y[1] (numeric) = -1.5558496011035748681830588797571 absolute error = 2.9453561985748711e-15 relative error = 1.8930854219364802544001016999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.863 Order of pole = 2.2e-29 TOP MAIN SOLVE Loop x[1] = -0.862 y[1] (analytic) = -1.561270674986399146641923482474 y[1] (numeric) = -1.5612706749863961616488671382321 absolute error = 2.9849930563442419e-15 relative error = 1.9118997776412122571321831999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.861 y[1] (analytic) = -1.5667169631380059823865198193511 y[1] (numeric) = -1.5667169631380029573407304043533 absolute error = 3.0250457894149978e-15 relative error = 1.9308183038728823179047618000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = -1.5721886123234432188360773265248 y[1] (numeric) = -1.5721886123234401533168256403491 absolute error = 3.0655192516861757e-15 relative error = 1.9498419131505021710391999999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.86 Order of pole = 5.8e-29 TOP MAIN SOLVE Loop x[1] = -0.859 y[1] (analytic) = -1.5776857703340831185036747275529 y[1] (numeric) = -1.5776857703340800120853152803317 absolute error = 3.1064183594472212e-15 relative error = 1.9689715264335692475721148000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.859 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -0.858 y[1] (analytic) = -1.5832085859960083638503121118408 y[1] (numeric) = -1.5832085859960052161022198579789 absolute error = 3.1477480922538619e-15 relative error = 1.9882080732107639689228728000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.857 y[1] (analytic) = -1.5887572091784734589362098299482 y[1] (numeric) = -1.5887572091784702694227160126327 absolute error = 3.1895134938173155e-15 relative error = 2.0075524915896829537721914999999e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.333 Order of pole = 5.130e-27 TOP MAIN SOLVE Loop x[1] = -0.856 y[1] (analytic) = -1.594331790802445301920014236235 y[1] (numeric) = -1.5943317908024420702003413291813 absolute error = 3.2317196729070537e-15 relative error = 2.0270057283876228023342592000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.856 Order of pole = 4.1e-29 TOP MAIN SOLVE Loop x[1] = -0.855 y[1] (analytic) = -1.5999324828492237627572116456687 y[1] (numeric) = -1.599932482849220488385407378324 absolute error = 3.2743718042673447e-15 relative error = 2.0465687392234279887164624999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.855 Order of pole = 6.2e-29 TOP MAIN SOLVE Loop x[1] = -0.854 y[1] (analytic) = -1.6055594383691431102304025318619 y[1] (numeric) = -1.6055594383691397927552729840631 absolute error = 3.3174751295477988e-15 relative error = 2.0662424886104151948961632000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.853 y[1] (analytic) = -1.6112128114903551423517233516925 y[1] (numeric) = -1.6112128114903517813167651035404 absolute error = 3.3610349582481521e-15 relative error = 2.0860279500503906852335517000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.852 y[1] (analytic) = -1.6168927574276948842134041806586 y[1] (numeric) = -1.6168927574276914791567355031416 absolute error = 3.4050566686775170e-15 relative error = 2.1059261061287710239135360000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.852 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop x[1] = -0.851 y[1] (analytic) = -1.6225994324916297275280245597819 y[1] (numeric) = -1.622599432491626277982315631437 absolute error = 3.4495457089283449e-15 relative error = 2.1259379486108254754910898999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = -1.6283329940972928963973132505598 y[1] (numeric) = -1.6283329940972894018897153852203 absolute error = 3.4945075978653395e-15 relative error = 2.1460644785390516204374999999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.849 y[1] (analytic) = -1.6340936007736021342791937713569 y[1] (numeric) = -1.6340936007735985943312676417861 absolute error = 3.5399479261295708e-15 relative error = 2.1663067063317005271169691999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.849 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -0.848 y[1] (analytic) = -1.6398814121724645176890990549246 y[1] (numeric) = -1.6398814121724609318167418968841 absolute error = 3.5858723571580405e-15 relative error = 2.1866656518824656712437759999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.847 y[1] (analytic) = -1.6456965890780683128752868101502 y[1] (numeric) = -1.6456965890780646805886585911944 absolute error = 3.6322866282189558e-15 relative error = 2.2071423446613511337093033999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.846 y[1] (analytic) = -1.6515392934162628025509332405935 y[1] (numeric) = -1.6515392934162591233543817776216 absolute error = 3.6791965514629719e-15 relative error = 2.2277378238167340473378183999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.91 x[1] = -0.845 y[1] (analytic) = -1.6574096882640270207501477684324 y[1] (numeric) = -1.6574096882640232941421327777629 absolute error = 3.7266080149906695e-15 relative error = 2.2484531382786373073281875000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.844 y[1] (analytic) = -1.6633079378590283450027469863256 y[1] (numeric) = -1.6633079378590245704757630497878 absolute error = 3.7745269839365378e-15 relative error = 2.2692893468632284462138751999999e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.5773 Order of pole = 8.694e-27 TOP MAIN SOLVE Loop x[1] = -0.843 y[1] (analytic) = -1.6692342076092719062956949212883 y[1] (numeric) = -1.6692342076092680833361933515528 absolute error = 3.8229595015697355e-15 relative error = 2.2902475183785591020951985000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.842 y[1] (analytic) = -1.6751886641028417887096331295281 y[1] (numeric) = -1.6751886641028379167979427176127 absolute error = 3.8719116904119154e-15 relative error = 2.3113287317315646656815952000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.841 y[1] (analytic) = -1.6811714751177350021889945367492 y[1] (numeric) = -1.6811714751177310807992411643579 absolute error = 3.9213897533723913e-15 relative error = 2.3325340760363367427775073000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = -1.6871828096317892236259583198358 y[1] (numeric) = -1.6871828096317852522259834188941 absolute error = 3.9713999749009417e-15 relative error = 2.3538646507236877493568000000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.839 y[1] (analytic) = -1.6932228378327053133141317009617 y[1] (numeric) = -1.6932228378327012913654095424168 absolute error = 4.0219487221585449e-15 relative error = 2.3753215656520241059398831000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.839 Order of pole = 1.5e-29 TOP MAIN SOLVE Loop x[1] = -0.838 y[1] (analytic) = -1.699291731128165625859544239898 y[1] (numeric) = -1.6992917311281615528170980335537 absolute error = 4.0730424462063443e-15 relative error = 2.3969059412195441030585095999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.837 y[1] (analytic) = -1.7053896621560491468265513132913 y[1] (numeric) = -1.705389662156045022138868100139 absolute error = 4.1246876832131523e-15 relative error = 2.4186189084777792459923319000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.837 Order of pole = 4.7e-29 TOP MAIN SOLVE Loop x[1] = -0.836 y[1] (analytic) = -1.7115168047947444987468410876636 y[1] (numeric) = -1.7115168047947403218557854058593 absolute error = 4.1768910556818043e-15 relative error = 2.4404616092464966891721408000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.835 y[1] (analytic) = -1.7176733341735618726332340160297 y[1] (numeric) = -1.7176733341735576429739603213517 absolute error = 4.2296592736946780e-15 relative error = 2.4624351962299795102392500000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.835 Order of pole = 8e-30 TOP MAIN SOLVE Loop x[1] = -0.834 y[1] (analytic) = -1.7238594266832449538187023660578 y[1] (numeric) = -1.7238594266832406708195661873553 absolute error = 4.2829991361787025e-15 relative error = 2.4845408331347039391390599999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.834 Order of pole = 3.5e-29 TOP MAIN SOLVE Loop x[1] = -0.833 y[1] (analytic) = -1.7300752599865839237874028365729 y[1] (numeric) = -1.7300752599865795868698706463862 absolute error = 4.3369175321901867e-15 relative error = 2.5067796947884324104105579000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.7266 Order of pole = 3.64e-28 TOP MAIN SOLVE Loop x[1] = -0.832 y[1] (analytic) = -1.7363210130291306326809285389167 y[1] (numeric) = -1.7363210130291262412594863191159 absolute error = 4.3914214422198008e-15 relative error = 2.5291529672607406116306944000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.832 Order of pole = 2.3e-29 TOP MAIN SOLVE Loop x[1] = -0.831 y[1] (analytic) = -1.7425968660500170503519060230893 y[1] (numeric) = -1.7425968660500126038339665050387 absolute error = 4.4465179395180506e-15 relative error = 2.5516618479849968930612646000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = -1.7489030005928781172009856817312 y[1] (numeric) = -1.7489030005928736149867942401365 absolute error = 4.5022141914415947e-15 relative error = 2.5743075458818151087288999999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.83 Order of pole = 9.6e-29 TOP MAIN SOLVE Loop x[1] = -0.829 y[1] (analytic) = -1.7552395995168801295747360388632 y[1] (numeric) = -1.755239599516875571057275218109 absolute error = 4.5585174608207542e-15 relative error = 2.5970912814839983119074638000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.829 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -0.828 y[1] (analytic) = -1.7616068470078558082235302646312 y[1] (numeric) = -1.761606847007851192788422916052 absolute error = 4.6154351073485792e-15 relative error = 2.6200142870629957708253183999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.827 y[1] (analytic) = -1.7680049285895472122228234362272 y[1] (numeric) = -1.768004928589542539248234444395 absolute error = 4.6729745889918322e-15 relative error = 2.6430778067568899034983125999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.827 Order of pole = 5.0e-29 TOP MAIN SOLVE Loop x[1] = -0.826 y[1] (analytic) = -1.774434031134957674850919505327 y[1] (numeric) = -1.7744340311349529437074560810586 absolute error = 4.7311434634242684e-15 relative error = 2.6662830966999375773215584000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.825 y[1] (analytic) = -1.7808943428778139521941174833737 y[1] (numeric) = -1.7808943428778091622447280007863 absolute error = 4.7899493894825874e-15 relative error = 2.6896314251536834905281250000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.16 x[1] = -0.824 y[1] (analytic) = -1.7873860534241397897187495138309 y[1] (numeric) = -1.787386053424134940318620868386 absolute error = 4.8494001286454449e-15 relative error = 2.7131240726396677474520576000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.824 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -0.823 y[1] (analytic) = -1.7939093537639421267118651337083 y[1] (numeric) = -1.7939093537639372172083185977888 absolute error = 4.9095035465359195e-15 relative error = 2.7367623320737496950497564999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.823 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -0.822 y[1] (analytic) = -1.8004644362830111733510061160912 y[1] (numeric) = -1.8004644362830062030833916682595 absolute error = 4.9702676144478317e-15 relative error = 2.7605475089020674832226616000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.821 y[1] (analytic) = -1.8070514947748356102215296773666 y[1] (numeric) = -1.8070514947748305785211187810365 absolute error = 5.0317004108963301e-15 relative error = 2.7844809212386590275228961000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = -1.8136707244526341753601950058762 y[1] (numeric) = -1.8136707244526290815500718127241 absolute error = 5.0938101231931521e-15 relative error = 2.8085639000047618870728000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.82 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -0.819 y[1] (analytic) = -1.8203223219615049193691959147911 y[1] (numeric) = -1.8203223219614997627641468677999 absolute error = 5.1566050490469912e-15 relative error = 2.8327977890698194598643208000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.818 y[1] (analytic) = -1.8270064853906934248185150415763 y[1] (numeric) = -1.8270064853906882047249168521809 absolute error = 5.2200935981893954e-15 relative error = 2.8571839453942126642410128000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.818 Order of pole = 9.8e-29 TOP MAIN SOLVE Loop x[1] = -0.817 y[1] (analytic) = -1.8337234142859813020394545286774 y[1] (numeric) = -1.8337234142859760177551605020371 absolute error = 5.2842842940266403e-15 relative error = 2.8817237391737428035878738999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.816 y[1] (analytic) = -1.8404733096621962895115754875575 y[1] (numeric) = -1.8404733096621909403258001695356 absolute error = 5.3491857753180219e-15 relative error = 2.9064185539858879408410624000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.815 y[1] (analytic) = -1.8472563740158453033622144170508 y[1] (numeric) = -1.8472563740158398885554165360236 absolute error = 5.4148067978810272e-15 relative error = 2.9312697869378581129148000000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.814 y[1] (analytic) = -1.8540728113378717970354503022977 y[1] (numeric) = -1.8540728113378663158792139784549 absolute error = 5.4811562363238428e-15 relative error = 2.9562788488164716163417632000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.813 y[1] (analytic) = -1.8609228271265388089491339578728 y[1] (numeric) = -1.8609228271265332607060481521953 absolute error = 5.5482430858056775e-15 relative error = 2.9814471642398788882674675000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.813 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -0.812 y[1] (analytic) = -1.867806628400439092947676191544 y[1] (numeric) = -1.8678066284004334768712123661636 absolute error = 5.6160764638253804e-15 relative error = 3.0067761718111590709395712000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.811 y[1] (analytic) = -1.8747244237116337435780916486818 y[1] (numeric) = -1.8747244237116280589124796098396 absolute error = 5.6846656120388422e-15 relative error = 3.0322673242738132571378482000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.811 Order of pole = 7.5e-29 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = -1.8816764231589207456707329694172 y[1] (numeric) = -1.8816764231589149916508348637361 absolute error = 5.7540198981056811e-15 relative error = 3.0579220886691812694650999999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.809 y[1] (analytic) = -1.888662838401234895397702429192 y[1] (numeric) = -1.8886628384012290712488848634697 absolute error = 5.8241488175657223e-15 relative error = 3.0837419464958082807706766999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.809 Order of pole = 6.1e-29 TOP MAIN SOLVE Loop x[1] = -0.808 y[1] (analytic) = -1.8956838826711805579146288317687 y[1] (numeric) = -1.8956838826711746628526330859799 absolute error = 5.8950619957457888e-15 relative error = 3.1097283938707875565715455999998e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.6907 Order of pole = 2.319e-27 TOP MAIN SOLVE Loop x[1] = -0.807 y[1] (analytic) = -1.9027397707886987448689363638825 y[1] (numeric) = -1.9027397707886927780997466665519 absolute error = 5.9667691896973306e-15 relative error = 3.1358829416931058627269558000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.806 y[1] (analytic) = -1.909830719174870013483557663832 y[1] (numeric) = -1.9098307191748639742032674983996 absolute error = 6.0392802901654324e-15 relative error = 3.1622071158090201391407584000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.806 Order of pole = 4.7e-29 TOP MAIN SOLVE Loop x[1] = -0.805 y[1] (analytic) = -1.9169569458658547076029627528077 y[1] (numeric) = -1.9169569458658485949976391630628 absolute error = 6.1126053235897449e-15 relative error = 3.1887024571794917732521125000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.805 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.804 y[1] (analytic) = -1.924118670526972080022155995597 y[1] (numeric) = -1.9241186705269658932677018576974 absolute error = 6.1867544541378996e-15 relative error = 3.2153705220497076242982143999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.804 Order of pole = 3.6e-29 memory used=38.1MB, alloc=4.4MB, time=2.41 TOP MAIN SOLVE Loop x[1] = -0.803 y[1] (analytic) = -1.931316114466919854612763229623 y[1] (numeric) = -1.9313161144669135928747774576471 absolute error = 6.2617379857719759e-15 relative error = 3.2422128821207165325067893000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.802 y[1] (analytic) = -1.9385495006521358062173810937547 y[1] (numeric) = -1.9385495006521294686510167451552 absolute error = 6.3375663643485995e-15 relative error = 3.2692311247232102274239960000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.802 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -0.801 y[1] (analytic) = -1.9458190537213029560079440864848 y[1] (numeric) = -1.9458190537212965417577643332249 absolute error = 6.4142501797532599e-15 relative error = 3.2964268529934769153850198999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = -1.953125 y[1] (numeric) = -1.9531249999999935081998319305478 absolute error = 6.4918001680694522e-15 relative error = 3.3238016860515595264000000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.8 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -0.799 y[1] (analytic) = -1.9604675675154986086865545815472 y[1] (numeric) = -1.9604675675154920384593407982931 absolute error = 6.5702272137832541e-15 relative error = 3.3513572591816481173545858999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.798 y[1] (analytic) = -1.9678469860117092563067016414472 y[1] (numeric) = -1.9678469860117026067643496174867 absolute error = 6.6495423520239605e-15 relative error = 3.3790952240147363815091160000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.797 y[1] (analytic) = -1.975263486964277259099813210591 y[1] (numeric) = -1.9752634869642705293430423691756 absolute error = 6.7297567708414154e-15 relative error = 3.4070172487135754939504242000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.797 Order of pole = 6.8e-29 TOP MAIN SOLVE Loop x[1] = -0.796 y[1] (analytic) = -1.9827173035958307230199125726357 y[1] (numeric) = -1.9827173035958239121380990519507 absolute error = 6.8108818135206850e-15 relative error = 3.4351250181599549881801599999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.795 y[1] (analytic) = -1.9902086708913821228013480678431 y[1] (numeric) = -1.9902086708913752298723671331076 absolute error = 6.8929289809347355e-15 relative error = 3.4634202341443445824880625000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.795 Order of pole = 1.3e-29 TOP MAIN SOLVE Loop x[1] = -0.794 y[1] (analytic) = -1.9977378256138852559804559230874 y[1] (numeric) = -1.9977378256138782800705219872994 absolute error = 6.9759099339357880e-15 relative error = 3.4919046155579295001929919999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.794 Order of pole = 4.8e-29 TOP MAIN SOLVE Loop x[1] = -0.793 y[1] (analytic) = -2.0053050063199493374930471312832 y[1] (numeric) = -2.0053050063199422776565513452511 absolute error = 7.0598364957860321e-15 relative error = 3.5205798985870705465419496999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.793 Order of pole = 4.5e-29 TOP MAIN SOLVE Loop x[1] = -0.792 y[1] (analytic) = -2.0129104533757120227888516838625 y[1] (numeric) = -2.0129104533757048780681970554581 absolute error = 7.1447206546284044e-15 relative error = 3.5494478369102265143887871999998e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.791 y[1] (analytic) = -2.020554408972873170036153638601 y[1] (numeric) = -2.0205544089728659394615876404651 absolute error = 7.2305745659981359e-15 relative error = 3.5785102018973692174258888999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.791 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = -2.0282371171448911749374795908639 y[1] (numeric) = -2.0282371171448838575269242150648 absolute error = 7.3174105553757991e-15 relative error = 3.6077687828119286124649000000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.79 Order of pole = 4.5e-29 TOP MAIN SOLVE Loop x[1] = -0.789 y[1] (analytic) = -2.0359588237833437349451661012474 y[1] (numeric) = -2.0359588237833363297040453186549 absolute error = 7.4052411207825925e-15 relative error = 3.6372253870153025096313824999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.789 Order of pole = 5.2e-29 TOP MAIN SOLVE Loop x[1] = -0.788 y[1] (analytic) = -2.0437197766544549232588128793716 y[1] (numeric) = -2.0437197766544474291798774607581 absolute error = 7.4940789354186135e-15 relative error = 3.6668818401739655264214720000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.787 y[1] (analytic) = -2.0515202254157904769099931792492 y[1] (numeric) = -2.051520225415782892973142834355 absolute error = 7.5839368503448942e-15 relative error = 3.6967399864692169525229625999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.786 y[1] (analytic) = -2.0593604216331232274981882982627 y[1] (numeric) = -2.0593604216331155526702910882884 absolute error = 7.6748278972099743e-15 relative error = 3.7268016888096003601572408000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.786 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -0.785 y[1] (analytic) = -2.0672406187974706277408703548134 y[1] (numeric) = -2.067240618797462860975579332998 absolute error = 7.7667652910218154e-15 relative error = 3.7570688290460357829690250000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.784 y[1] (analytic) = -2.0751610723423063519451929043171 y[1] (numeric) = -2.0751610723422984921827599384507 absolute error = 7.8597624329658664e-15 relative error = 3.7875433081897009811193856000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.783 y[1] (analytic) = -2.0831220396609479738041654095807 y[1] (numeric) = -2.0831220396609400199712521394716 absolute error = 7.9538329132701091e-15 relative error = 3.8182270466327007498017516999999e-13 % Correct digits = 14 h = 0.001 memory used=41.9MB, alloc=4.4MB, time=2.66 Complex estimate of poles used Radius of convergence = 0.7022 Order of pole = 7.134e-27 TOP MAIN SOLVE Loop x[1] = -0.782 y[1] (analytic) = -2.0911237801241227505718763491408 y[1] (numeric) = -2.0911237801241147015813622312116 absolute error = 8.0489905141179292e-15 relative error = 3.8491219843715638832308256000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.781 y[1] (analytic) = -2.0991665550977135686857719189918 y[1] (numeric) = -2.0991665550977054234365593093185 absolute error = 8.1452492126096733e-15 relative error = 3.8802300812336075788139553000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = -2.1072506279606871322847654208601 y[1] (numeric) = -2.1072506279606788896615816470916 absolute error = 8.2426231837737685e-15 relative error = 3.9115533171062093892120000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.78 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -0.779 y[1] (analytic) = -2.1153762641232065028257122097987 y[1] (numeric) = -2.1153762641231981616989085814988 absolute error = 8.3411268036282999e-15 relative error = 3.9430936921690282877607861000003e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.779 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -0.778 y[1] (analytic) = -2.1235437310449301251332969635414 y[1] (numeric) = -2.1235437310449216843586446695825 absolute error = 8.4407746522939589e-15 relative error = 3.9748532271292171694478728000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.8045 Order of pole = 8.9e-29 TOP MAIN SOLVE Loop x[1] = -0.777 y[1] (analytic) = -2.1317532982534995027355010062484 y[1] (numeric) = -2.1317532982534909611539838469609 absolute error = 8.5415815171592875e-15 relative error = 4.0068339634596672183589874999998e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.1538 Order of pole = 2.302e-27 TOP MAIN SOLVE Loop x[1] = -0.776 y[1] (analytic) = -2.140005237363217713244502686066 y[1] (numeric) = -2.1400052373632090696821065868942 absolute error = 8.6435623960991718e-15 relative error = 4.0390379636403299452013568000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.775 y[1] (analytic) = -2.1482998220939209828471686079689 y[1] (numeric) = -2.1482998220939122361146678604218 absolute error = 8.7467325007475471e-15 relative error = 4.0714673114026589946265624999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.775 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -0.774 y[1] (analytic) = -2.1566373282900455676763749335044 y[1] (numeric) = -2.156637328290036716569115108207 absolute error = 8.8511072598252974e-15 relative error = 4.1041241119772152956666576000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.1896 Order of pole = 7.1e-29 TOP MAIN SOLVE Loop x[1] = -0.773 y[1] (analytic) = -2.1650180339398922189505167310244 y[1] (numeric) = -2.1650180339398832622481942066649 absolute error = 8.9567023225243595e-15 relative error = 4.1370104923444836399331615000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.772 y[1] (analytic) = -2.1734422191950905383000858109763 y[1] (numeric) = -2.173442219195081474766523861928 absolute error = 9.0635335619490483e-15 relative error = 4.1701286014889433167649984000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.771 y[1] (analytic) = -2.1819101663902655596535974109681 y[1] (numeric) = -2.1819101663902563880365187953174 absolute error = 9.1716170786156507e-15 relative error = 4.2034806106564411996919577000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = -2.1904221600629089244370067443099 y[1] (numeric) = -2.1904221600628996434678027329588 absolute error = 9.2809692040113511e-15 relative error = 4.2370687136149141517362999999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.77 Order of pole = 6.5e-29 TOP MAIN SOLVE Loop x[1] = -0.769 y[1] (analytic) = -2.1989784869734570476577724679092 y[1] (numeric) = -2.1989784869734476560512682543366 absolute error = 9.3916065042135726e-15 relative error = 4.2708951269185084873513134000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.769 Order of pole = 5e-30 TOP MAIN SOLVE Loop x[1] = -0.768 y[1] (analytic) = -2.2075794361255787037037037037036 y[1] (numeric) = -2.2075794361255692001579201328625 absolute error = 9.5035457835708411e-15 relative error = 4.3049620901751458157821952000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.767 y[1] (analytic) = -2.2162252987866744923945940476183 y[1] (numeric) = -2.2162252987866648755905056013203 absolute error = 9.6168040884462980e-15 relative error = 4.3392718663175838845615739999998e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.766 y[1] (analytic) = -2.224916368508590677988441363673 y[1] (numeric) = -2.2249163685085809465897303386606 absolute error = 9.7313987110250124e-15 relative error = 4.3738267418780232066431903999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.765 y[1] (analytic) = -2.2336529411485499264709372435661 y[1] (numeric) = -2.2336529411485400791237440572985 absolute error = 9.8473471931862676e-15 relative error = 4.4086290272663115940006500000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.764 y[1] (analytic) = -2.2424353148903014995541679804348 y[1] (numeric) = -2.2424353148902915348868375384218 absolute error = 9.9646673304420130e-15 relative error = 4.4436810570517964521166719999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.764 Order of pole = 1.7e-29 TOP MAIN SOLVE Loop x[1] = -0.763 y[1] (analytic) = -2.251263790265493497385507179126 y[1] (numeric) = -2.2512637902654834140083312364231 absolute error = 1.00833771759427029e-14 relative error = 4.4789851902488785897022463000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.91 x[1] = -0.762 y[1] (analytic) = -2.2601386701752697760280326626562 y[1] (numeric) = -2.2601386701752595725329881108885 absolute error = 1.02034950445517677e-14 relative error = 4.5145438106063220525518855999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.761 y[1] (analytic) = -2.2690602599120942003271299638595 y[1] (numeric) = -2.2690602599120838752876129738788 absolute error = 1.03250395169899807e-14 relative error = 4.5503593269003722604661366999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.761 Order of pole = 6.4e-29 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = -2.2780288671818049278320454876804 y[1] (numeric) = -2.2780288671817944798026014366624 absolute error = 1.04480294440510180e-14 relative error = 4.5864341732317396775680000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.76 Order of pole = 4.3e-29 TOP MAIN SOLVE Loop x[1] = -0.759 y[1] (analytic) = -2.2870448021259014550039521392055 y[1] (numeric) = -2.287044802125890882520001249678 absolute error = 1.05724839508895275e-14 relative error = 4.6227708093265039278211725000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.759 Order of pole = 3.3e-29 TOP MAIN SOLVE Loop x[1] = -0.758 y[1] (analytic) = -2.2961083773440671930216527244822 y[1] (numeric) = -2.2961083773440564945992113414295 absolute error = 1.06984224413830527e-14 relative error = 4.6593717208409957169742824000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.757 y[1] (analytic) = -2.3052199079169303771005742987441 y[1] (numeric) = -2.3052199079169195512359717295603 absolute error = 1.08258646025691838e-14 relative error = 4.6962394196707148330064934000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.6282 Order of pole = 7.061e-27 TOP MAIN SOLVE Loop x[1] = -0.756 y[1] (analytic) = -2.3143797114290661503785436486089 y[1] (numeric) = -2.314379711429055195548134489276 absolute error = 1.09548304091593329e-14 relative error = 4.7333764442633420971808064000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.755 y[1] (analytic) = -2.3235881079922427011014678977424 y[1] (numeric) = -2.3235881079922316157613397671786 absolute error = 1.10853401281305638e-14 relative error = 4.7707853599359065957217249999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.755 Order of pole = 1.1e-29 TOP MAIN SOLVE Loop x[1] = -0.754 y[1] (analytic) = -2.3328454202689143700721089984511 y[1] (numeric) = -2.3328454202689031526577856015231 absolute error = 1.12174143233969280e-14 relative error = 4.8084687591961672508113919999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.754 Order of pole = 8e-30 TOP MAIN SOLVE Loop x[1] = -0.753 y[1] (analytic) = -2.342151973495964684114420054234 y[1] (numeric) = -2.3421519734959533330405594924399 absolute error = 1.13510738605617941e-14 relative error = 4.8464292620682715800677157000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.753 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -0.752 y[1] (analytic) = -2.3515080955087023106633404929544 y[1] (numeric) = -2.3515080955086908243234287402701 absolute error = 1.14863399117526843e-14 relative error = 4.8846695164227540667551743999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.751 y[1] (analytic) = -2.3609141167651129685246164405216 y[1] (numeric) = -2.3609141167651013452906559003607 absolute error = 1.16232339605401609e-14 relative error = 4.9231921983109370771084358999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.751 Order of pole = 4.9e-29 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = -2.3703703703703703703703703703703 y[1] (numeric) = -2.3703703703703586085925634280284 absolute error = 1.17617778069423419e-14 relative error = 4.9620000123038004890625000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.75 Order of pole = 4.4e-29 TOP MAIN SOLVE Loop x[1] = -0.749 y[1] (analytic) = -2.3798771921016093136531990931554 y[1] (numeric) = -2.3798771921015974116596265765046 absolute error = 1.19019935725166508e-14 relative error = 5.0010956918353847979726492000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.749 Order of pole = 4.3e-29 TOP MAIN SOLVE Loop x[1] = -0.748 y[1] (analytic) = -2.3894349204329640783441040138989 y[1] (numeric) = -2.3894349204329520344403984734598 absolute error = 1.20439037055404391e-14 relative error = 5.0404819995507939829783872000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.747 y[1] (analytic) = -2.3990438965608753322372917444871 y[1] (numeric) = -2.3990438965608631447063054623287 absolute error = 1.21875309862821584e-14 relative error = 5.0801617276588677321893232000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.747 Order of pole = 1.0e-29 TOP MAIN SOLVE Loop x[1] = -0.746 y[1] (analytic) = -2.4087044644296687875277359910374 y[1] (numeric) = -2.4087044644296564546292036262524 absolute error = 1.23328985323647850e-14 relative error = 5.1201376982895904340387600000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.746 Order of pole = 4.2e-29 TOP MAIN SOLVE Loop x[1] = -0.745 y[1] (analytic) = -2.4184169707574088959654456583219 y[1] (numeric) = -2.4184169707573964159356414350822 absolute error = 1.24800298042232397e-14 relative error = 5.1604127638563076927969124999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.745 Order of pole = 5.7e-29 TOP MAIN SOLVE Loop x[1] = -0.744 y[1] (analytic) = -2.4281817650620309141338982566198 y[1] (numeric) = -2.4281817650620182851852875990414 absolute error = 1.26289486106575784e-14 relative error = 5.2009898074228212680134656000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.743 y[1] (analytic) = -2.4379991996877547152995106274908 y[1] (numeric) = -2.4379991996877419356203961437222 absolute error = 1.27796791144837686e-14 relative error = 5.2418717430754359290930202000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.742 y[1] (analytic) = -2.4478696298317837698449525251352 y[1] (numeric) = -2.4478696298317708375991142412395 absolute error = 1.29322458382838957e-14 relative error = 5.2830615163000295861137015999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=3.15 x[1] = -0.741 y[1] (analytic) = -2.4577934135712927625423710988308 y[1] (numeric) = -2.4577934135712796758687008411395 absolute error = 1.30866736702576913e-14 relative error = 5.3245621043642236769512173000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.741 Order of pole = 3e-30 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = -2.4677709118907073618541843523582 y[1] (numeric) = -2.4677709118906941188663141750519 absolute error = 1.32429878701773063e-14 relative error = 5.3663765167047287681112000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.74 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -0.739 y[1] (analytic) = -2.4778024887092797040802114816317 y[1] (numeric) = -2.4778024887092663028661360343396 absolute error = 1.34012140754472921e-14 relative error = 5.4085077953199421000096899000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.738 y[1] (analytic) = -2.4878885109089632035119273057289 y[1] (numeric) = -2.4878885109089496421336200339312 absolute error = 1.35613783072717977e-14 relative error = 5.4509590151678768480508743999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.738 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -0.737 y[1] (analytic) = -2.4980293483625903488191476787313 y[1] (numeric) = -2.4980293483625766253121707477075 absolute error = 1.37235069769310238e-14 relative error = 5.4937332845695010353531614000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.736 y[1] (analytic) = -2.5082253739623571956932686775704 y[1] (numeric) = -2.5082253739623433080663765085432 absolute error = 1.38876268921690272e-14 relative error = 5.5368337456175695115845632000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.735 y[1] (analytic) = -2.51847696364861831631629929958 y[1] (numeric) = -2.518476963648604262551035604581 absolute error = 1.40537652636949990e-14 relative error = 5.5802635745910286635596250000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.734 y[1] (analytic) = -2.5287844964389960175285630760685 y[1] (numeric) = -2.5287844964389817955788512758727 absolute error = 1.42219497118001958e-14 relative error = 5.6240259823750796957038032000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.734 Order of pole = 4.4e-29 TOP MAIN SOLVE Loop x[1] = -0.733 y[1] (analytic) = -2.5391483544578076916425330983765 y[1] (numeric) = -2.5391483544577932994342600056367 absolute error = 1.43922082730927398e-14 relative error = 5.6681242148869844795368125999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.733 Order of pole = 2.9e-29 TOP MAIN SOLVE Loop x[1] = -0.732 y[1] (analytic) = -2.5495689229658152167084632797622 y[1] (numeric) = -2.5495689229658006521390559272089 absolute error = 1.45645694073525533e-14 relative error = 5.7125615535077009482148544000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.732 Order of pole = 2.4e-29 TOP MAIN SOLVE Loop x[1] = -0.731 y[1] (analytic) = -2.5600465903903003766921674358228 y[1] (numeric) = -2.5600465903902856376301629270852 absolute error = 1.47390620045087376e-14 relative error = 5.7573413155194355723844016000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = -2.5705817483554703264895878586282 y[1] (numeric) = -2.5705817483554554107741961168725 absolute error = 1.49157153917417557e-14 relative error = 5.8024668545492025771469000000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.729 y[1] (analytic) = -2.5811747917131971819900315081167 y[1] (numeric) = -2.5811747917131820874306907952913 absolute error = 1.50945593407128254e-14 relative error = 5.8479415610184804250396206000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.728 y[1] (analytic) = -2.5918261185740958715237184021148 y[1] (numeric) = -2.591826118574080595899643479134 absolute error = 1.52756240749229808e-14 relative error = 5.8937688625990582089916415999998e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.1331 Order of pole = 3.096e-27 TOP MAIN SOLVE Loop x[1] = -0.727 y[1] (analytic) = -2.6025361303389444420034101395271 y[1] (numeric) = -2.6025361303389289830631329352176 absolute error = 1.54589402772043095e-14 relative error = 5.9399522246751654923924385000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.726 y[1] (analytic) = -2.6133052317304510709084415550069 y[1] (numeric) = -2.6133052317304354263693442090798 absolute error = 1.56445390973459271e-14 relative error = 5.9864951508119815591878696000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.725 y[1] (analytic) = -2.6241338308253720939767928164335 y[1] (numeric) = -2.6241338308253562615246329591332 absolute error = 1.58324521598573003e-14 relative error = 6.0334011832306202658859375000003e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.725 Order of pole = 7.3e-29 TOP MAIN SOLVE Loop x[1] = -0.724 y[1] (analytic) = -2.6350223390869854180814979946004 y[1] (numeric) = -2.6350223390869693953699261230123 absolute error = 1.60227115718715881e-14 relative error = 6.0806739032896897722676544000001e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.584 Order of pole = 5.829e-27 TOP MAIN SOLVE Loop x[1] = -0.723 y[1] (analytic) = -2.6459711713979237492865370258804 y[1] (numeric) = -2.6459711713979075339366058341575 absolute error = 1.62153499311917229e-14 relative error = 6.1283169319735268006111342999998e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.4073 Order of pole = 6.249e-27 TOP MAIN SOLVE Loop x[1] = -0.722 y[1] (analytic) = -2.6569807460933721275195165332327 y[1] (numeric) = -2.6569807460933557171191820512192 absolute error = 1.64104003344820135e-14 relative error = 6.1763339303872080300911480000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.722 Order of pole = 3.1e-29 TOP MAIN SOLVE Loop x[1] = -0.721 y[1] (analytic) = -2.6680514849946343216792995658351 y[1] (numeric) = -2.6680514849946177137829139577272 absolute error = 1.66078963856081079e-14 relative error = 6.2247286002584420859864519000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.721 Order of pole = 6e-30 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=3.40 x[1] = -0.72 y[1] (analytic) = -2.6791838134430727023319615912208 y[1] (numeric) = -2.6791838134430558944597574630096 absolute error = 1.68078722041282112e-14 relative error = 6.2735046844464465739776000000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.719 y[1] (analytic) = -2.6903781603344262734539803107741 y[1] (numeric) = -2.6903781603344092630915463722542 absolute error = 1.70103624339385199e-14 relative error = 6.3226659674579183627511841000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.719 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -0.718 y[1] (analytic) = -2.7016349581535116099736495494029 y[1] (numeric) = -2.7016349581534943945713974735105 absolute error = 1.72154022520758924e-14 relative error = 6.3722162759702057498974368000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.718 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -0.717 y[1] (analytic) = -2.7129546430093115141568769223607 y[1] (numeric) = -2.7129546430092940911294992415222 absolute error = 1.74230273776808385e-14 relative error = 6.4221594793617928064602004999999e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.716 y[1] (analytic) = -2.7243376546704562711986161585216 y[1] (numeric) = -2.7243376546704386379245350345439 absolute error = 1.76332740811239777e-14 relative error = 6.4724994902502088408281792000004e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.715 y[1] (analytic) = -2.7357844366011024527333393292608 y[1] (numeric) = -2.7357844366010846065541460300785 absolute error = 1.78461791932991823e-14 relative error = 6.5232402650374777469920125000002e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.715 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -0.714 y[1] (analytic) = -2.747295435997214286384625800669 y[1] (numeric) = -2.7472954359971962246045107139836 absolute error = 1.80617801150866854e-14 relative error = 6.5743858044632225553073776000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.714 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -0.713 y[1] (analytic) = -2.7588711038232526799529061806125 y[1] (numeric) = -2.7588711038232343998380791911026 absolute error = 1.82801148269895099e-14 relative error = 6.6259401541655449029057603000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.712 y[1] (analytic) = -2.7705118948492770604097485137645 y[1] (numeric) = -2.770511894849258559187849567124 absolute error = 1.85012218989466405e-14 relative error = 6.6779074052497992738019839999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.712 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -0.711 y[1] (analytic) = -2.7822182676884652605452394936406 y[1] (numeric) = -2.7822182676884465354047391672084 absolute error = 1.87251405003264322e-14 relative error = 6.7302916948653835341772782000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.711 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = -2.7939906848350567599207624241782 y[1] (numeric) = -2.7939906848350378080103523203475 absolute error = 1.89519104101038307e-14 relative error = 6.7830972067906721496676999999997e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.709 y[1] (analytic) = -2.805829612702724661731917576432 y[1] (numeric) = -2.8058296127027054801598903513876 absolute error = 1.91815720272250444e-14 relative error = 6.8363281720262163937218075999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.709 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -0.708 y[1] (analytic) = -2.8177355216633818633049323626257 y[1] (numeric) = -2.8177355216633624491385511992281 absolute error = 1.94141663811633976e-14 relative error = 6.8899888693963424488730112000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.707 y[1] (analytic) = -2.8297088860864269552544896847392 y[1] (numeric) = -2.8297088860864073055193470145753 absolute error = 1.96497351426701639e-14 relative error = 6.9440836261592768999625276999998e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.707 Order of pole = 3.8e-29 TOP MAIN SOLVE Loop x[1] = -0.706 y[1] (analytic) = -2.8417501843784354628416497000919 y[1] (numeric) = -2.8417501843784155745210149758278 absolute error = 1.98883206347242641e-14 relative error = 6.9986168186259328504690056000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used Radius of convergence = 0.706 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -0.705 y[1] (analytic) = -2.8538598990233021228080126397455 y[1] (numeric) = -2.8538598990232819928421689549461 absolute error = 2.01299658436847994e-14 relative error = 7.0535928727874933823584250000000e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.704 y[1] (analytic) = -2.8660385166228399699474079639368 y[1] (numeric) = -2.86603851662281959523297731347 absolute error = 2.03747144306504668e-14 relative error = 7.1090162649519282744983552000002e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.703 y[1] (analytic) = -2.8782865279378420899305255604119 y[1] (numeric) = -2.878286527937821467319782530412 absolute error = 2.06226107430299999e-14 relative error = 7.1648915223895855940671073000001e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used Radius of convergence = 0.579 Order of pole = 1.575e-27 TOP MAIN SOLVE Loop x[1] = -0.702 y[1] (analytic) = -2.890604427929611978442750920247 y[1] (numeric) = -2.8906044279295911047429245923868 absolute error = 2.08736998263278602e-14 relative error = 7.2212232239879997222365616000001e-13 % Correct digits = 14 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -0.701 y[1] (analytic) = -2.9029927158019685315531547212295 y[1] (numeric) = -2.9029927158019474035257185717304 absolute error = 2.11280274361494991e-14 relative error = 7.2780160009160613050746091000000e-13 % Correct digits = 14 h = 0.001 NO POLE Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 300 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Time to Timeout = 2 Minutes 56 Seconds Percent Done = 100.3 % > quit memory used=57.0MB, alloc=4.4MB, time=3.63