|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sqrt 1 $eq_no = 1 > array_tmp1[1] := sqrt(array_x[1]); > #emit pre arctan $eq_no = 1 > array_tmp2[1] := Si(array_tmp1[1]); > array_tmp2_a1[1] := sin(array_tmp1[1]); > array_tmp2_a2[1] := cos(array_tmp1[1]); > array_tmp2_a3[1] := array_tmp2_a1[1] / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sqrt 2 $eq_no = 1 > array_tmp1[2] := array_x[2] / array_tmp1[1]/2.0; > #emit pre Si $eq_no = 1 > array_tmp2_a1[2] := att(1,array_tmp2_a2,array_tmp1,1); > array_tmp2_a2[2] := -att(1,array_tmp2_a1,array_tmp1,1); > array_tmp2_a3[2] := (array_tmp2_a1[2] - ats(2,array_tmp1,array_tmp2_a3,2))/array_tmp1[1]; > array_tmp2[2] := att(1,array_tmp2_a3,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := 0.0; > array_tmp1[3] := -ats(3,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre Si $eq_no = 1 > array_tmp2_a1[3] := att(2,array_tmp2_a2,array_tmp1,1); > array_tmp2_a2[3] := -att(2,array_tmp2_a1,array_tmp1,1); > array_tmp2_a3[3] := (array_tmp2_a1[3] - ats(3,array_tmp1,array_tmp2_a3,2))/array_tmp1[1]; > array_tmp2[3] := att(2,array_tmp2_a3,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := 0.0; > array_tmp1[4] := -ats(4,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre Si $eq_no = 1 > array_tmp2_a1[4] := att(3,array_tmp2_a2,array_tmp1,1); > array_tmp2_a2[4] := -att(3,array_tmp2_a1,array_tmp1,1); > array_tmp2_a3[4] := (array_tmp2_a1[4] - ats(4,array_tmp1,array_tmp2_a3,2))/array_tmp1[1]; > array_tmp2[4] := att(3,array_tmp2_a3,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := 0.0; > array_tmp1[5] := -ats(5,array_tmp1,array_tmp1,2) / array_tmp1[1] / 2.0; > #emit pre Si $eq_no = 1 > array_tmp2_a1[5] := att(4,array_tmp2_a2,array_tmp1,1); > array_tmp2_a2[5] := -att(4,array_tmp2_a1,array_tmp1,1); > array_tmp2_a3[5] := (array_tmp2_a1[5] - ats(5,array_tmp1,array_tmp2_a3,2))/array_tmp1[1]; > array_tmp2[5] := att(4,array_tmp2_a3,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp1[kkk] := 0.0; > array_tmp1[kkk] := -ats(kkk,array_tmp1,array_tmp1,2) /array_tmp1[1] / 2.0; > #emit Si $eq_no = 1 > array_tmp2_a1[kkk] := att(kkk-1,array_tmp2_a3,array_tmp1,1); > array_tmp2_a3[kkk] := -att(kkk-1,array_tmp2_a1,array_tmp1,1); > array_tmp2_a3[kkk] := (array_tmp2_a1[kkk] - ats(kkk,array_tmp1,array_tmp2_a3,2)) / array_tmp1[1]; > array_tmp2[kkk] := att(kkk-1,array_tmp2_a3,array_tmp1,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sqrt(array_x[1]); array_tmp2[1] := Si(array_tmp1[1]); array_tmp2_a1[1] := sin(array_tmp1[1]); array_tmp2_a2[1] := cos(array_tmp1[1]); array_tmp2_a3[1] := array_tmp2_a1[1]/array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_x[2]/(array_tmp1[1]*2.0); array_tmp2_a1[2] := att(1, array_tmp2_a2, array_tmp1, 1); array_tmp2_a2[2] := -att(1, array_tmp2_a1, array_tmp1, 1); array_tmp2_a3[2] := ( array_tmp2_a1[2] - ats(2, array_tmp1, array_tmp2_a3, 2))/ array_tmp1[1]; array_tmp2[2] := att(1, array_tmp2_a3, array_tmp1, 1); array_tmp3[2] := array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 0.; array_tmp1[3] := -ats(3, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[3] := att(2, array_tmp2_a2, array_tmp1, 1); array_tmp2_a2[3] := -att(2, array_tmp2_a1, array_tmp1, 1); array_tmp2_a3[3] := ( array_tmp2_a1[3] - ats(3, array_tmp1, array_tmp2_a3, 2))/ array_tmp1[1]; array_tmp2[3] := att(2, array_tmp2_a3, array_tmp1, 1); array_tmp3[3] := array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 0.; array_tmp1[4] := -ats(4, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[4] := att(3, array_tmp2_a2, array_tmp1, 1); array_tmp2_a2[4] := -att(3, array_tmp2_a1, array_tmp1, 1); array_tmp2_a3[4] := ( array_tmp2_a1[4] - ats(4, array_tmp1, array_tmp2_a3, 2))/ array_tmp1[1]; array_tmp2[4] := att(3, array_tmp2_a3, array_tmp1, 1); array_tmp3[4] := array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 0.; array_tmp1[5] := -ats(5, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0) ; array_tmp2_a1[5] := att(4, array_tmp2_a2, array_tmp1, 1); array_tmp2_a2[5] := -att(4, array_tmp2_a1, array_tmp1, 1); array_tmp2_a3[5] := ( array_tmp2_a1[5] - ats(5, array_tmp1, array_tmp2_a3, 2))/ array_tmp1[1]; array_tmp2[5] := att(4, array_tmp2_a3, array_tmp1, 1); array_tmp3[5] := array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := 0.; array_tmp1[kkk] := -ats(kkk, array_tmp1, array_tmp1, 2)/(array_tmp1[1]*2.0); array_tmp2_a1[kkk] := att(kkk - 1, array_tmp2_a3, array_tmp1, 1); array_tmp2_a3[kkk] := -att(kkk - 1, array_tmp2_a1, array_tmp1, 1); array_tmp2_a3[kkk] := ( array_tmp2_a1[kkk] - ats(kkk, array_tmp1, array_tmp2_a3, 2))/ array_tmp1[1]; array_tmp2[kkk] := att(kkk - 1, array_tmp2_a3, array_tmp1, 1); array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > ## Comment 5 > exact_soln_y := proc(x) > ## Comment 6 > return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x))); > ## Comment 7 > end; exact_soln_y := proc(x) return x*Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(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, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_a1, > array_tmp2_a2, > array_tmp2_a3, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/Si_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = Si(sqrt(x));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 1"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"## Comment 2"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 3"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 1.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_max_h := 0.001;"); > omniout_str(ALWAYS,"## Comment 4"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"## Comment 5"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"## Comment 6"); > omniout_str(ALWAYS," "); > omniout_str(ALWAYS,"return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"## Comment 7"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > ## Comment 1 > Digits:=32; > max_terms:=30; > ## Comment 2 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2_a1:= Array(0..(max_terms + 1),[]); > array_tmp2_a2:= Array(0..(max_terms + 1),[]); > array_tmp2_a3:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > ## Comment 3 > x_start := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_max_h := 0.001; > ## Comment 4 > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = Si(sqrt(x));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T05:47:09-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"Si_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = Si(sqrt(x));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"Si_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"Si_sqrt maple results") > ; > logitem_str(html_log_file,"Maple - Si") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_a1, array_tmp2_a2, array_tmp2_a3, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/Si_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = Si(sqrt(x));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 1"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "## Comment 2"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 3"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 1.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_max_h := 0.001;"); omniout_str(ALWAYS, "## Comment 4"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "## Comment 5"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "## Comment 6"); omniout_str(ALWAYS, " "); omniout_str(ALWAYS, "return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x)));"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "## Comment 7"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2_a1 := Array(0 .. max_terms + 1, []); array_tmp2_a2 := Array(0 .. max_terms + 1, []); array_tmp2_a3 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a1[term] := 0.; term := term + 1 end do; array_tmp2_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a2[term] := 0.; term := term + 1 end do; array_tmp2_a3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.001; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = Si(sqrt(x));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T05:47:09-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "Si_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = Si(sqrt(x));") ; logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "Si_sqrt diffeq.mxt"); logitem_str(html_log_file, "Si_sqrt maple results"); logitem_str(html_log_file, "Maple - Si"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/Si_sqrtpostode.ode################# diff ( y , x , 1 ) = Si(sqrt(x)); ! #BEGIN FIRST INPUT BLOCK ## Comment 1 Digits:=32; max_terms:=30; ## Comment 2 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## Comment 3 x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.001; ## Comment 4 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK ## Comment 5 exact_soln_y := proc(x) ## Comment 6 return(x * Si(sqrt(x)) - sin(sqrt(x)) + sqrt(x)*cos(sqrt(x))); ## Comment 7 end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.9 estimated_steps = 900000 step_error = 1.1111111111111111111111111111111e-16 est_needed_step_err = 1.1111111111111111111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7934972345263677994492432536923e-136 estimated_step_error = 2.7934972345263677994492432536923e-136 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.8746757545277430858295647309101e-128 estimated_step_error = 1.8746757545277430858295647309101e-128 best_h = 4.00e-06 opt_iter = 3 bytes used=4000260, alloc=3014104, time=0.11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2580621869022487523552569889240e-120 estimated_step_error = 1.2580621869022487523552569889240e-120 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.4425592064326376762845024137538e-113 estimated_step_error = 8.4425592064326376762845024137538e-113 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.6654999468467072467004477432864e-105 estimated_step_error = 5.6654999468467072467004477432864e-105 best_h = 3.200000e-05 opt_iter = 6 bytes used=8001408, alloc=4128012, time=0.23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.8017766936847523362136045928833e-97 estimated_step_error = 3.8017766936847523362136045928833e-97 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.5509588439224448644899615291520e-89 estimated_step_error = 2.5509588439224448644899615291520e-89 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7114227009495059828892151116974e-81 estimated_step_error = 1.7114227009495059828892151116974e-81 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1478501222293516470784396804835e-73 estimated_step_error = 1.1478501222293516470784396804835e-73 best_h = 0.000512 opt_iter = 10 bytes used=12002324, alloc=4259060, time=0.36 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.6941657096191853536892214747610e-66 estimated_step_error = 7.6941657096191853536892214747610e-66 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.1515288845800874120846536268485e-58 estimated_step_error = 5.1515288845800874120846536268485e-58 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.02101172861653694101443709332267 y[1] (numeric) = 0.02101172861653694101443709332267 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1122 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16003572, alloc=4324584, time=0.49 bytes used=20004492, alloc=4455632, time=0.61 TOP MAIN SOLVE Loop bytes used=24005448, alloc=4455632, time=0.74 x[1] = 0.11 y[1] (analytic) = 0.0242329446790716645869461308976 y[1] (numeric) = 0.024232944679071664582905527669564 absolute error = 4.040603228036e-21 relative error = 1.6674008386300623225066515790395e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=28006192, alloc=4455632, time=0.87 bytes used=32007180, alloc=4455632, time=0.99 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.0276022462635188132778091477758 y[1] (numeric) = 0.02760224626351881327109036890219 absolute error = 6.718778873610e-21 relative error = 2.4341420656368967769423524272921e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5261 Order of pole (six term test) = -0.75 bytes used=36008356, alloc=4455632, time=1.12 bytes used=40009172, alloc=4521156, time=1.25 bytes used=44010268, alloc=4521156, time=1.38 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.03111307913423200057866560545161 y[1] (numeric) = 0.031113079134232000570109075485143 absolute error = 8.556529966467e-21 relative error = 2.7501392355129271695423578741170e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1459 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1715 Order of pole (six term test) = -0.75 bytes used=48011116, alloc=4521156, time=1.50 bytes used=52012160, alloc=4521156, time=1.63 TOP MAIN SOLVE Loop bytes used=56013948, alloc=4521156, time=1.76 x[1] = 0.14 y[1] (analytic) = 0.03475965364933978756736821344522 y[1] (numeric) = 0.034759653649339787557513176497292 absolute error = 9.855036947928e-21 relative error = 2.8351942304566613677945378051034e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1571 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=60014880, alloc=4521156, time=1.89 bytes used=64016096, alloc=4521156, time=2.01 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.03853680550514419831820980956466 y[1] (numeric) = 0.03853680550514419830741401738675 absolute error = 1.0795792177910e-20 relative error = 2.8014237393052447149951991779228e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=68017100, alloc=4521156, time=2.14 bytes used=72017996, alloc=4521156, time=2.27 bytes used=76018812, alloc=4521156, time=2.40 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.04243988965272320273635241812664 y[1] (numeric) = 0.042439889652723202724860127541383 absolute error = 1.1492290585257e-20 relative error = 2.7078983190804748920386492408582e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1795 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=80020136, alloc=4521156, time=2.52 bytes used=84021128, alloc=4586680, time=2.65 TOP MAIN SOLVE Loop bytes used=88022212, alloc=4586680, time=2.79 x[1] = 0.17 y[1] (analytic) = 0.04646469786246896746347503888234 y[1] (numeric) = 0.04646469786246896745145722913717 absolute error = 1.2017809745170e-20 relative error = 2.5864388015050823953171096147814e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1907 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=92023048, alloc=4586680, time=2.91 bytes used=96023696, alloc=4586680, time=3.04 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.05060739355700686104977308733273 y[1] (numeric) = 0.050607393557006861037352090060139 absolute error = 1.2420997272591e-20 relative error = 2.4543839149904702599500640280461e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.202 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=100024628, alloc=4586680, time=3.17 bytes used=104025380, alloc=4586680, time=3.30 bytes used=108026200, alloc=4586680, time=3.42 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.05486445951916478534735693006468 y[1] (numeric) = 0.054864459519164785334621979688214 absolute error = 1.2734950376466e-20 relative error = 2.3211657397294756333550617736473e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2132 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=112027392, alloc=4586680, time=3.55 bytes used=116028384, alloc=4586680, time=3.68 TOP MAIN SOLVE Loop bytes used=120029292, alloc=4586680, time=3.81 x[1] = 0.2 y[1] (analytic) = 0.0592326553757257311850347617666 y[1] (numeric) = 0.059232655375725731172052080747057 absolute error = 1.2982681019543e-20 relative error = 2.1918114150363520504991871668470e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2244 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=124030236, alloc=4586680, time=3.94 bytes used=128031096, alloc=4586680, time=4.07 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.0637089826239078639394934553792 y[1] (numeric) = 0.063708982623907863926312953062056 absolute error = 1.3180502317144e-20 relative error = 2.0688609006601520438858679735921e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2356 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3674 Order of pole (six term test) = -0.75 bytes used=132032004, alloc=4586680, time=4.20 bytes used=136033132, alloc=4586680, time=4.32 bytes used=140034296, alloc=4586680, time=4.45 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.0682906555612834706531438647202 y[1] (numeric) = 0.068290655561283470639803682935907 absolute error = 1.3340181784293e-20 relative error = 1.9534417519717073109719372772849e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=144035356, alloc=4586680, time=4.58 bytes used=148036500, alloc=4586680, time=4.71 TOP MAIN SOLVE Loop bytes used=152037320, alloc=4586680, time=4.84 x[1] = 0.23 y[1] (analytic) = 0.07297507689552925974513803766118 y[1] (numeric) = 0.072975076895529259731667695094419 absolute error = 1.3470342566761e-20 relative error = 1.8458826136004039168936200868426e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.258 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=156038328, alloc=4586680, time=4.97 bytes used=160039284, alloc=4586680, time=5.09 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.07775981710693572198563031071952 y[1] (numeric) = 0.077759817106935721972052916174535 absolute error = 1.3577394544985e-20 relative error = 1.7460682200825258404261761245590e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2693 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=164039972, alloc=4586680, time=5.22 bytes used=168041148, alloc=4586680, time=5.35 bytes used=172042184, alloc=4586680, time=5.48 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.08264259685175003007525953297954 y[1] (numeric) = 0.082642596851750030061593368107921 absolute error = 1.3666164871619e-20 relative error = 1.6536465929470132414951124338802e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2805 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=176043328, alloc=4652204, time=5.61 bytes used=180044256, alloc=4652204, time=5.74 TOP MAIN SOLVE Loop bytes used=184045180, alloc=4652204, time=5.87 x[1] = 0.26 y[1] (analytic) = 0.08762127185292661212609148179727 y[1] (numeric) = 0.087621271852926612112351149400529 absolute error = 1.3740332396741e-20 relative error = 1.5681503025662898125231386961176e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=188046396, alloc=4652204, time=6.00 bytes used=192048596, alloc=4652204, time=6.13 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.09269381984325844644578324423321 y[1] (numeric) = 0.092693819843258446431980512497045 absolute error = 1.3802731736165e-20 relative error = 1.4890670984867026773012015680421e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3029 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=196049740, alloc=4652204, time=6.26 bytes used=200050580, alloc=4652204, time=6.39 bytes used=204051512, alloc=4652204, time=6.52 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.09785832921543259067893378612129 y[1] (numeric) = 0.0978583292154325906650782169168 absolute error = 1.3855569204490e-20 relative error = 1.4158804176992764052150736215316e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3141 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=208052484, alloc=4652204, time=6.64 bytes used=212053368, alloc=4652204, time=6.77 TOP MAIN SOLVE Loop bytes used=216054204, alloc=4652204, time=6.90 x[1] = 0.29 y[1] (analytic) = 0.10311298910210522186354368864912 y[1] (numeric) = 0.10311298910210522184964311042855 absolute error = 1.390057822057e-20 relative error = 1.3480918690859866414553848371397e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3254 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=220055232, alloc=4652204, time=7.03 bytes used=224056092, alloc=4652204, time=7.16 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.10845608066211933050373087816212 y[1] (numeric) = 0.10845608066211933048979174562147 absolute error = 1.393913254065e-20 relative error = 1.2852329215247539691520827170561e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3366 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3929 Order of pole (six term test) = -0.75 bytes used=228057000, alloc=4652204, time=7.29 bytes used=232057896, alloc=4652204, time=7.42 bytes used=236058680, alloc=4652204, time=7.54 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.1138859693904133281896463623123 y[1] (numeric) = 0.11388596939041332817567403259883 absolute error = 1.397232971347e-20 relative error = 1.2268701568997805057812088158364e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3478 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=240059724, alloc=4652204, time=7.67 bytes used=244060920, alloc=4652204, time=7.80 TOP MAIN SOLVE Loop bytes used=248062140, alloc=4652204, time=7.93 x[1] = 0.32 y[1] (analytic) = 0.11940109830182609816376755995711 y[1] (numeric) = 0.11940109830182609814976650671044 absolute error = 1.400105324667e-20 relative error = 1.1726067386145534725604320237705e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.359 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=252063112, alloc=4652204, time=8.06 bytes used=256064012, alloc=4652204, time=8.19 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.12499998186496788596664318429292 y[1] (numeric) = 0.12499998186496788595261716491613 absolute error = 1.402601937679e-20 relative error = 1.1220817129351031891812368528977e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3702 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=260065308, alloc=4652204, time=8.32 bytes used=264066380, alloc=4652204, time=8.45 bytes used=268067564, alloc=4652204, time=8.57 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.13068120058313194952274967679503 y[1] (numeric) = 0.13068120058313194950870186421088 absolute error = 1.404781258415e-20 relative error = 1.0749681301874465383618249765943e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3815 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=272068424, alloc=4652204, time=8.71 bytes used=276069472, alloc=4652204, time=8.84 TOP MAIN SOLVE Loop bytes used=280070308, alloc=4652204, time=8.97 x[1] = 0.35 y[1] (analytic) = 0.13644339613601686663871970248489 y[1] (numeric) = 0.13644339613601686662465278968872 absolute error = 1.406691279617e-20 relative error = 1.0309705852049491014115159526205e-17 % Correct digits = 19 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3927 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=284071388, alloc=4652204, time=9.10 bytes used=288073996, alloc=4652204, time=9.23 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.14228526700968044522749929915703 y[1] (numeric) = 0.14228526700968044521341558276183 absolute error = 1.408371639520e-20 relative error = 9.8982253687880472647108520202513e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4039 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=292074916, alloc=4652204, time=9.36 bytes used=296076056, alloc=4652204, time=9.49 bytes used=300077076, alloc=4652204, time=9.62 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.1482055645533135708706721697601 y[1] (numeric) = 0.14820556455331357085657361719358 absolute error = 1.409855256652e-20 relative error = 9.5128361806201732331272354687505e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4151 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=304077884, alloc=4652204, time=9.75 bytes used=308078740, alloc=4652204, time=9.88 TOP MAIN SOLVE Loop bytes used=312079976, alloc=4652204, time=10.00 x[1] = 0.38 y[1] (analytic) = 0.15420308941061341619435798007207 y[1] (numeric) = 0.1542030894106134161802462839594 absolute error = 1.411169611267e-20 relative error = 9.1513705507502802054502564909581e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4263 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=316081060, alloc=4652204, time=10.13 bytes used=320081952, alloc=4652204, time=10.26 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.16027668828114320969946369125599 y[1] (numeric) = 0.16027668828114320968534031368962 absolute error = 1.412337756637e-20 relative error = 8.8118725922237790186896886111371e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4376 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=324082952, alloc=4652204, time=10.39 bytes used=328085340, alloc=4652204, time=10.52 bytes used=332086592, alloc=4652204, time=10.65 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.16642525097339690401226591334186 y[1] (numeric) = 0.16642525097339690399813212211841 absolute error = 1.413379122345e-20 relative error = 8.4925761810683933973944053034988e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4488 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5979 Order of pole (six term test) = -0.75 bytes used=336087528, alloc=4652204, time=10.77 bytes used=340088580, alloc=4652204, time=10.90 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.17264770771658263461500700740523 y[1] (numeric) = 0.17264770771658263460086390584286 absolute error = 1.414310156237e-20 relative error = 8.1918849369186091156129435084555e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=344089444, alloc=4652204, time=11.03 bytes used=348090452, alloc=4652204, time=11.16 bytes used=352091604, alloc=4652204, time=11.29 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.17894302670258953540380865243176 y[1] (numeric) = 0.17894302670258953538965720402723 absolute error = 1.415144840453e-20 relative error = 7.9083542205029721717574366658619e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4712 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=356092828, alloc=4652204, time=11.42 bytes used=360094212, alloc=4652204, time=11.55 bytes used=364095260, alloc=4652204, time=11.67 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.1853102118333601316561250900761 y[1] (numeric) = 0.18531021183336013164196613899127 absolute error = 1.415895108483e-20 relative error = 7.6406750306682563245294362063467e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4824 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=368096176, alloc=4652204, time=11.81 bytes used=372097100, alloc=4652204, time=11.93 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.19174830065207680268522342109599 y[1] (numeric) = 0.19174830065207680267105770925556 absolute error = 1.416571184043e-20 relative error = 7.3876596518752891935862310084123e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4937 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=376098000, alloc=4652204, time=12.06 bytes used=380099064, alloc=4652204, time=12.19 bytes used=384100032, alloc=4652204, time=12.32 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.1982563624392836852608743680207 y[1] (numeric) = 0.19825636243928368524670254944311 absolute error = 1.417181857759e-20 relative error = 7.1482288907273486123640172361545e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5049 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=388100940, alloc=4652204, time=12.45 bytes used=392102140, alloc=4652204, time=12.58 TOP MAIN SOLVE Loop bytes used=396103332, alloc=4717728, time=12.71 x[1] = 0.46 y[1] (analytic) = 0.20483349645738424032739463660336 y[1] (numeric) = 0.20483349645738424031321728946168 absolute error = 1.417734714168e-20 relative error = 6.9214007410304630062180620139244e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5161 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=400104148, alloc=4717728, time=12.84 bytes used=404105228, alloc=4717728, time=12.97 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.21147883032894414147392841058774 y[1] (numeric) = 0.21147883032894414145974604739959 absolute error = 1.418236318815e-20 relative error = 6.7062803241771688271589307229717e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5273 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=408106552, alloc=4717728, time=13.10 bytes used=412107940, alloc=4717728, time=13.23 bytes used=416108756, alloc=4717728, time=13.36 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.21819151853594202238755819189924 y[1] (numeric) = 0.2181915185359420223733712681684 absolute error = 1.418692373084e-20 relative error = 6.5020509623993617274559544961488e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5385 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7307 Order of pole (six term test) = -0.75 bytes used=420109692, alloc=4717728, time=13.49 bytes used=424110592, alloc=4717728, time=13.61 TOP MAIN SOLVE Loop bytes used=428111532, alloc=4717728, time=13.74 x[1] = 0.49 y[1] (analytic) = 0.22497074102859038704234597934801 y[1] (numeric) = 0.22497074102859038702815490091879 absolute error = 1.419107842922e-20 relative error = 6.3079662556725667863638470280180e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5498 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=432112584, alloc=4717728, time=13.87 bytes used=436113648, alloc=4717728, time=14.00 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.23181570193363150761099449299946 y[1] (numeric) = 0.23181570193363150759679962233728 absolute error = 1.419487066218e-20 relative error = 6.1233430452627279160528528885217e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.561 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4776 Order of pole (six term test) = -0.75 bytes used=440115724, alloc=4717728, time=14.13 bytes used=444116624, alloc=4717728, time=14.26 bytes used=448118804, alloc=4717728, time=14.39 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.23872562835312814792158035069624 y[1] (numeric) = 0.23872562835312814790738201226857 absolute error = 1.419833842767e-20 relative error = 5.9475551601303185665585194557049e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5722 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2733 Order of pole (six term test) = -0.75 bytes used=452119460, alloc=4717728, time=14.52 bytes used=456120260, alloc=4717728, time=14.65 TOP MAIN SOLVE Loop bytes used=460121252, alloc=4717728, time=14.78 x[1] = 0.52 y[1] (analytic) = 0.24569976924574120962724244197333 y[1] (numeric) = 0.24569976924574120961304092687451 absolute error = 1.420151509882e-20 relative error = 5.7800278536753893470638791796894e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5834 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=464122336, alloc=4717728, time=14.90 bytes used=468123080, alloc=4717728, time=15.03 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.252737394383336592027233416646 y[1] (numeric) = 0.25273739438333659201302898658395 absolute error = 1.420443006205e-20 relative error = 5.6202328494791676655538703119356e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5946 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=472124188, alloc=4717728, time=15.16 bytes used=476125160, alloc=4717728, time=15.29 bytes used=480126544, alloc=4717728, time=15.42 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.25983779337650903834691957291989 y[1] (numeric) = 0.25983779337650903833271246366303 absolute error = 1.420710925686e-20 relative error = 5.4676839239754764380987551681262e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6059 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=484127344, alloc=4717728, time=15.55 bytes used=488128260, alloc=4717728, time=15.67 TOP MAIN SOLVE Loop bytes used=492129380, alloc=4717728, time=15.80 x[1] = 0.55 y[1] (analytic) = 0.26700027476326612021203093917204 y[1] (numeric) = 0.26700027476326612019782136353751 absolute error = 1.420957563453e-20 relative error = 5.3219329632259061843885802857052e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6171 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=496130440, alloc=4717728, time=15.93 bytes used=500132240, alloc=4717728, time=16.06 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.27422416515569312869459758597341 y[1] (numeric) = 0.2742241651556931286803857364249 absolute error = 1.421184954851e-20 relative error = 5.1825664380967666237039974234973e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6283 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=504133464, alloc=4717728, time=16.19 bytes used=508134256, alloc=4717728, time=16.32 bytes used=512135216, alloc=4717728, time=16.45 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.28150880843992995365617709626816 y[1] (numeric) = 0.28150880843992995364196314717991 absolute error = 1.421394908825e-20 relative error = 5.0492022494859368250494906996184e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6395 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=516136840, alloc=4717728, time=16.58 bytes used=520137696, alloc=4717728, time=16.71 TOP MAIN SOLVE Loop bytes used=524138768, alloc=4717728, time=16.83 x[1] = 0.58 y[1] (analytic) = 0.28885356502524293556735739340893 y[1] (numeric) = 0.28885356502524293555314150304387 absolute error = 1.421589036506e-20 relative error = 4.9214869007476754641017949602048e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6507 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=528139928, alloc=4717728, time=16.96 bytes used=532140780, alloc=4717728, time=17.09 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.29625781113837574911119902618758 y[1] (numeric) = 0.29625781113837574909698133842984 absolute error = 1.421768775774e-20 relative error = 4.7990929599824860537032119018224e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.662 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=536141640, alloc=4717728, time=17.22 bytes used=540142880, alloc=4717728, time=17.35 bytes used=544143760, alloc=4717728, time=17.48 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.3037209381597201121017272675031 y[1] (numeric) = 0.30372093815972011208750791337886 absolute error = 1.421935412424e-20 relative error = 4.6817167793556454483647708409475e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6732 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=548144632, alloc=4717728, time=17.61 bytes used=552145624, alloc=4717728, time=17.73 TOP MAIN SOLVE Loop bytes used=556146712, alloc=4717728, time=17.86 x[1] = 0.61 y[1] (analytic) = 0.31124235199816507030331787757062 y[1] (numeric) = 0.31124235199816507028909697658619 absolute error = 1.422090098443e-20 relative error = 4.5690764425639089568725249333864e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6844 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1652 Order of pole (six term test) = -0.75 bytes used=560147840, alloc=4717728, time=17.99 bytes used=564148936, alloc=4717728, time=18.12 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.31882147250176757398043480450662 y[1] (numeric) = 0.31882147250176757396621246582828 absolute error = 1.422233867834e-20 relative error = 4.4609099151128066247325388992131e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6956 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=568149964, alloc=4717728, time=18.25 bytes used=572151196, alloc=4717728, time=18.38 bytes used=576152144, alloc=4717728, time=18.51 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.32645773290164116217850611633425 y[1] (numeric) = 0.3264577329016411621642824398307 absolute error = 1.422367650355e-20 relative error = 4.3569733751215715193248293714335e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7068 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=580153168, alloc=4717728, time=18.64 bytes used=584154192, alloc=4717728, time=18.77 TOP MAIN SOLVE Loop bytes used=588155604, alloc=4717728, time=18.90 x[1] = 0.64 y[1] (analytic) = 0.33415057928668737367191479071961 y[1] (numeric) = 0.33415057928668737365768986788487 absolute error = 1.422492283474e-20 relative error = 4.2570397050054504539850715512049e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.718 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=592156748, alloc=4717728, time=19.03 bytes used=596157844, alloc=4717728, time=19.16 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.34189947010699910143662624273517 y[1] (numeric) = 0.34189947010699910142240015750733 absolute error = 1.422608522784e-20 relative error = 4.1608971266869403052138612559668e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7293 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=600158828, alloc=4717728, time=19.28 bytes used=604160068, alloc=4717728, time=19.41 bytes used=608160928, alloc=4717728, time=19.54 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.34970387570394918680215167774942 y[1] (numeric) = 0.34970387570394918678792450723831 absolute error = 1.422717051111e-20 relative error = 4.0683479651093078632117364521278e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7405 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=612162044, alloc=4717728, time=19.67 bytes used=616163256, alloc=4717728, time=19.80 TOP MAIN SOLVE Loop bytes used=620164040, alloc=4717728, time=19.93 x[1] = 0.67 y[1] (analytic) = 0.35756327786514344930166323559463 y[1] (numeric) = 0.35756327786514344928743505072971 absolute error = 1.422818486492e-20 relative error = 3.9792075265307926882267901114680e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7517 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=624164856, alloc=4717728, time=20.06 bytes used=628165980, alloc=4717728, time=20.19 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.36547716940256711007416462988609 y[1] (numeric) = 0.3654771694025671100599354959944 absolute error = 1.422913389169e-20 relative error = 3.8933030796287147298960911460827e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7629 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=632167476, alloc=4717728, time=20.32 bytes used=636169200, alloc=4717728, time=20.45 bytes used=640170072, alloc=4717728, time=20.58 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.37344505375238897584772666954199 y[1] (numeric) = 0.37344505375238897583349664686455 absolute error = 1.423002267744e-20 relative error = 3.8104729288703207846530823144751e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7741 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=644171016, alloc=4717728, time=20.71 bytes used=648171836, alloc=4717728, time=20.84 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.3814664445950103717571801853617 y[1] (numeric) = 0.38146644459501037174294932951572 absolute error = 1.423085584598e-20 relative error = 3.7305655707380510587993295822671e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7854 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5233 Order of pole (six term test) = -0.75 bytes used=652172560, alloc=4717728, time=20.97 bytes used=656173796, alloc=4717728, time=21.10 bytes used=660174776, alloc=4717728, time=21.22 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.38954086549405701862250238081336 y[1] (numeric) = 0.3895408654940570186082707432066 absolute error = 1.423163760676e-20 relative error = 3.6534389244912542288636375543186e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7966 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=664175656, alloc=4717728, time=21.36 bytes used=668176804, alloc=4717728, time=21.48 bytes used=672177828, alloc=4717728, time=21.61 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.39766784955311305291452998148413 y[1] (numeric) = 0.39766784955311305290029760968691 absolute error = 1.423237179722e-20 relative error = 3.5789596300565669133628035835997e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8078 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=676178836, alloc=4717728, time=21.74 bytes used=680179896, alloc=4717728, time=21.87 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.40584693908908825136674503319275 y[1] (numeric) = 0.40584693908908825135251197127255 absolute error = 1.423306192020e-20 relative error = 3.5070024064110713622355810138461e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.819 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=684181072, alloc=4717728, time=22.00 bytes used=688181872, alloc=4717728, time=22.13 bytes used=692182868, alloc=4717728, time=22.25 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.41407768532119318847729432173213 y[1] (numeric) = 0.414077685321193188463060610555 absolute error = 1.423371117713e-20 relative error = 3.4374494646069001429848639768622e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8302 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=696183696, alloc=4717728, time=22.38 bytes used=700184524, alloc=4717728, time=22.51 TOP MAIN SOLVE Loop bytes used=704185720, alloc=4717728, time=22.64 x[1] = 0.75 y[1] (analytic) = 0.42235964807457335695436084521896 y[1] (numeric) = 0.4223596480745733569401265227212 absolute error = 1.423432249776e-20 relative error = 3.3701899702423125903000877308984e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8415 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=708186856, alloc=4717728, time=22.77 bytes used=712187708, alloc=4717728, time=22.90 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.4306923954977229567889229319278 y[1] (numeric) = 0.43069239549772295677468803336145 absolute error = 1.423489856635e-20 relative error = 3.3051195505552544635870867904582e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8527 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=716188536, alloc=4717728, time=23.03 bytes used=720189652, alloc=4717728, time=23.16 bytes used=724190500, alloc=4717728, time=23.29 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.43907550379286276358809156616832 y[1] (numeric) = 0.43907550379286276357385612432323 absolute error = 1.423544184509e-20 relative error = 3.2421398420362979004639259114104e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8639 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=728191552, alloc=4717728, time=23.42 bytes used=732192348, alloc=4717728, time=23.55 TOP MAIN SOLVE Loop bytes used=736193292, alloc=4717728, time=23.68 x[1] = 0.78 y[1] (analytic) = 0.44750855695852480400976127263357 y[1] (numeric) = 0.44750855695852480399552531803849 absolute error = 1.423595459508e-20 relative error = 3.1811580747939511570680639132344e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8751 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.186 Order of pole (six term test) = -0.75 bytes used=740195936, alloc=4717728, time=23.80 bytes used=744196840, alloc=4717728, time=23.93 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.45599114654364001485177203774162 y[1] (numeric) = 0.45599114654364001483753559884646 absolute error = 1.423643889516e-20 relative error = 3.1220866902944399392347211608231e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8863 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=748197900, alloc=4717728, time=24.07 bytes used=752199068, alloc=4717728, time=24.19 bytes used=756200264, alloc=4717728, time=24.32 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.46452287141247410580008615162259 y[1] (numeric) = 0.46452287141247410578584925496404 absolute error = 1.423689665855e-20 relative error = 3.0648429893795942472291938557979e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8976 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=760201436, alloc=4717728, time=24.45 bytes used=764202628, alloc=4717728, time=24.58 TOP MAIN SOLVE Loop bytes used=768203752, alloc=4717728, time=24.71 x[1] = 0.81 y[1] (analytic) = 0.47310333751980189792187140402686 y[1] (numeric) = 0.47310333751980189790763407437894 absolute error = 1.423732964792e-20 relative error = 3.0093488079280547922452634670378e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9088 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.367 Order of pole (six term test) = -0.75 bytes used=772205312, alloc=4717728, time=24.84 bytes used=776206424, alloc=4717728, time=24.97 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0.48173215769575184105218496698933 y[1] (numeric) = 0.48173215769575184103794722750028 absolute error = 1.423773948905e-20 relative error = 2.9555302176945692453610449447154e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=780207592, alloc=4717728, time=25.10 bytes used=784208376, alloc=4717728, time=25.23 bytes used=788209332, alloc=4717728, time=25.36 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.49040895143979055513623865085879 y[1] (numeric) = 0.49040895143979055512200052317607 absolute error = 1.423812768272e-20 relative error = 2.9033172500049830756121144192884e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9312 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=792210404, alloc=4717728, time=25.49 bytes used=796211472, alloc=4717728, time=25.62 TOP MAIN SOLVE Loop bytes used=800212696, alloc=4717728, time=25.75 x[1] = 0.84 y[1] (analytic) = 0.49913334472335239115583054753454 y[1] (numeric) = 0.49913334472335239114159205191859 absolute error = 1.423849561595e-20 relative error = 2.8526436405168984292835143164688e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=804213628, alloc=4717728, time=25.88 bytes used=808214500, alloc=4717728, time=26.01 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.50790496980065143408757155422775 y[1] (numeric) = 0.5079049698006514340733327096561 absolute error = 1.423884457165e-20 relative error = 2.8034465930188929986851669414658e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9537 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=812215320, alloc=4717728, time=26.14 bytes used=816216484, alloc=4717728, time=26.27 bytes used=820217576, alloc=4717728, time=26.39 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.51672346502724331419153257735065 y[1] (numeric) = 0.51672346502724331417729340161303 absolute error = 1.423917573762e-20 relative error = 2.7556665608110645992759863416237e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9649 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=824218428, alloc=4717728, time=26.52 bytes used=828219164, alloc=4717728, time=26.65 TOP MAIN SOLVE Loop bytes used=832219896, alloc=4717728, time=26.78 x[1] = 0.87 y[1] (analytic) = 0.52558847468593187074164261123563 y[1] (numeric) = 0.525588474685931870727403121021 absolute error = 1.423949021463e-20 relative error = 2.7092470441135303639286819156728e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9761 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=836220820, alloc=4717728, time=26.91 bytes used=840221712, alloc=4717728, time=27.04 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0.53449964881964131977406275271287 y[1] (numeric) = 0.53449964881964131975982296368922 absolute error = 1.423978902365e-20 relative error = 2.6641344021640316637865950920141e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9873 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.859 Order of pole (six term test) = -0.75 bytes used=844222624, alloc=4717728, time=27.17 bytes used=848223724, alloc=4717728, time=27.30 bytes used=852224516, alloc=4717728, time=27.43 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.54345664307089829129628488942734 y[1] (numeric) = 0.54345664307089829128204481631486 absolute error = 1.424007311248e-20 relative error = 2.6202776788252946056075554173532e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9985 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.183 Order of pole (six term test) = -0.75 bytes used=856225420, alloc=4717728, time=27.56 bytes used=860226404, alloc=4717728, time=27.68 TOP MAIN SOLVE Loop bytes used=864227204, alloc=4717728, time=27.81 x[1] = 0.9 y[1] (analytic) = 0.55245911852759008150266303407261 y[1] (numeric) = 0.55245911852759008148842269071085 absolute error = 1.424034336176e-20 relative error = 2.5776284405827632678321687283029e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.53 Order of pole (six term test) = -0.75 bytes used=868228324, alloc=4717728, time=27.94 bytes used=872229288, alloc=4717728, time=28.07 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.56150674157468585659107857799664 y[1] (numeric) = 0.56150674157468585657683797740624 absolute error = 1.424060059040e-20 relative error = 2.5361406259279723445976386310696e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.021 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2575 Order of pole (six term test) = -0.75 bytes used=876230580, alloc=4717728, time=28.20 bytes used=880231820, alloc=4717728, time=28.32 bytes used=884233084, alloc=4717728, time=28.45 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.57059918375162647793731703614644 y[1] (numeric) = 0.57059918375162647792307619058594 absolute error = 1.424084556050e-20 relative error = 2.4957704052200034092658318938440e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.032 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=888234036, alloc=4717728, time=28.58 bytes used=892234756, alloc=4717728, time=28.71 TOP MAIN SOLVE Loop bytes used=896236056, alloc=4717728, time=28.84 x[1] = 0.93 y[1] (analytic) = 0.57973612161510621268402163268504 y[1] (numeric) = 0.57973612161510621266978055370315 absolute error = 1.424107898189e-20 relative error = 2.4564760502097579671190976435508e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.043 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=900237008, alloc=4717728, time=28.96 bytes used=904237992, alloc=4717728, time=29.09 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.58891723660698595736683624368667 y[1] (numeric) = 0.58891723660698595735259494217047 absolute error = 1.424130151620e-20 relative error = 2.4182178124468677394770655596279e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.055 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=908238836, alloc=4717728, time=29.22 bytes used=912239944, alloc=4717728, time=29.35 bytes used=916240896, alloc=4717728, time=29.48 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.59814221492709283336382336582135 y[1] (numeric) = 0.59814221492709283334958185204069 absolute error = 1.424151378066e-20 relative error = 2.3809578099074463216086969538405e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.066 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=920241724, alloc=4717728, time=29.61 bytes used=924242596, alloc=4717728, time=29.73 TOP MAIN SOLVE Loop bytes used=928243460, alloc=4717728, time=29.86 x[1] = 0.96 y[1] (analytic) = 0.60741074741067520123436905096897 y[1] (numeric) = 0.60741074741067520122012733461755 absolute error = 1.424171635142e-20 relative error = 2.3446599211704535663198664244588e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=932244432, alloc=4717728, time=29.99 bytes used=936245528, alloc=4717728, time=30.12 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.61672252941029536799001774696194 y[1] (numeric) = 0.61672252941029536797577583719517 absolute error = 1.424190976677e-20 relative error = 2.3092896866258458643567661961682e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.088 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=940246588, alloc=4717728, time=30.25 bytes used=944248172, alloc=4717728, time=30.38 bytes used=948249400, alloc=4717728, time=30.51 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.62607726068195460143106106972141 y[1] (numeric) = 0.62607726068195460141681897519155 absolute error = 1.424209452986e-20 relative error = 2.2748142161155637211918527806110e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=952250236, alloc=4717728, time=30.64 bytes used=956251628, alloc=4717728, time=30.77 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.63547464527525658684329825001407 y[1] (numeric) = 0.63547464527525658682905597890259 absolute error = 1.424227111148e-20 relative error = 2.2412021026127554763554562219621e-18 % Correct digits = 20 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.111 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=960252436, alloc=4717728, time=30.90 bytes used=964253372, alloc=4717728, time=31.03 bytes used=968254548, alloc=4717728, time=31.16 Finished! diff ( y , x , 1 ) = Si(sqrt(x)); Iterations = 900 Total Elapsed Time = 31 Seconds Elapsed Time(since restart) = 30 Seconds Time to Timeout = 2 Minutes 28 Seconds Percent Done = 100.1 % > quit bytes used=969710424, alloc=4717728, time=31.20