|\^/| 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_t ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_t[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 > ; > if (glob_type_given_pole = 4) then # if number 2 > rad_given := sqrt(expt(array_t[1] - array_given_rad_poles[2,1],2.0) + expt(array_given_rad_poles[2,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[2,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 3 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 3; > if (array_poles[2,1] <> glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4, array_poles[2,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 3; > if ((array_real_poles[2,1] > 0.0) and (array_real_poles[2,1] <> glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4, array_real_poles[2,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 3; > if ((array_complex_poles[2,1] > 0.0) and (array_complex_poles[2,1] <> glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4, array_complex_poles[2,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 3 > ; > 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_t; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_t[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; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_t[1] - array_given_rad_poles[2, 1], 2.0) + expt(array_given_rad_poles[2, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_poles[2, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if 0. < array_real_poles[2, 1] and array_real_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_real_poles[2, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if 0. < array_complex_poles[2, 1] and array_complex_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_complex_poles[2, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") 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 3 > ret := 1.0; > else > ret := -1.0; > fi;# end if 3; > 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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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_x2[1]) < min_size) then # if number 3 > min_size := omniabs(array_x2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (omniabs(array_x1[1]) < min_size) then # if number 3 > min_size := omniabs(array_x1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < 1.0) then # if number 3 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_x2[1]) < min_size then min_size := omniabs(array_x2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_x1[1]) < min_size then min_size := omniabs(array_x1[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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_x2[no_terms-3] + array_x2[no_terms - 2] * hn_div_ho + array_x2[no_terms - 1] * hn_div_ho_2 + array_x2[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > est_tmp := omniabs(array_x1[no_terms-3] + array_x1[no_terms - 2] * hn_div_ho + array_x1[no_terms - 1] * hn_div_ho_2 + array_x1[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_x2[no_terms - 3] + array_x2[no_terms - 2]*hn_div_ho + array_x2[no_terms - 1]*hn_div_ho_2 + array_x2[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; est_tmp := omniabs(array_x1[no_terms - 3] + array_x1[no_terms - 2]*hn_div_ho + array_x1[no_terms - 1]*hn_div_ho_2 + array_x1[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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_t[1]) >= glob_check_sign * glob_next_display) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_t[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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 3 > if (iter >= 0) then # if number 4 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 5 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 6 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 5; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > 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," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 5 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 6 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 5; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 5; > 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 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[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, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[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[2] := relerr else array_last_rel_error[2] := 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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_x2_higher[1,1]); > if (tmp < glob_normmax) then # if number 4 > glob_normmax := tmp; > fi;# end if 4 > fi;# end if 3; > if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 4 > glob_normmax := tmp; > fi;# end if 4 > fi;# end if 3; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 3 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 4 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 4 > fi;# end if 3; > if ( not glob_reached_optimal_h) then # if number 3 > 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_t[1]; > fi;# end if 3; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_x2_higher[1, 1]) then tmp := omniabs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_x1_higher[1, 1]) then tmp := omniabs(array_x1_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_t[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(t_start,t_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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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(t_end),convfloat(t_start),convfloat(array_t[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(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[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 3 > 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 3; > 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(t_start, t_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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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(t_end), convfloat(t_start), convfloat(array_t[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(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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 - 2 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_x2_higher[1,n]) = 0.0) or (omniabs(array_x2_higher[1,n+1]) = 0.0)) then # if number 3 > found_sing := 0; > else > tmp_rad := omniabs(array_x2_higher[1,n] * glob_h / array_x2_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 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 > if (tmp_rad < rad_c) then # if number 6 > rad_c := tmp_rad; > fi;# end if 6; > elif > (cnt > 0) then # if number 6 > found_sing := 0; > fi;# end if 6 > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_pole[1]) then # if number 6 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 6; > fi;# end if 5; > #BOTTOM radius ratio test in Henrici1 > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > #TOP radius ratio test in Henrici2 > 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_x1_higher[1,n]) = 0.0) or (omniabs(array_x1_higher[1,n+1]) = 0.0)) then # if number 5 > found_sing := 0; > else > tmp_rad := omniabs(array_x1_higher[1,n] * glob_h / array_x1_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 6 > if (tmp_rad < rad_c) then # if number 7 > rad_c := tmp_rad; > fi;# end if 7; > elif > (cnt = 0) then # if number 7 > if (tmp_rad < rad_c) then # if number 8 > rad_c := tmp_rad; > fi;# end if 8; > elif > (cnt > 0) then # if number 8 > found_sing := 0; > fi;# end if 8 > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_pole[1]) then # if number 8 > array_pole[1] := rad_c; > array_poles[2,1] := rad_c; > fi;# end if 8; > fi;# end if 7; > #BOTTOM radius ratio test in Henrici2 > #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 - 2 - 1; > while ((m >= 10) and ((omniabs(array_x2_higher[1,m]) = 0.0) or (omniabs(array_x2_higher[1,m-1]) = 0.0) or (omniabs(array_x2_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 7 > rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 8 > 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 8 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 7; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #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_x1_higher[1,m]) = 0.0) or (omniabs(array_x1_higher[1,m-1]) = 0.0) or (omniabs(array_x1_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 7 > rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 8 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[2,1] := rcs; > array_real_poles[2,2] := ord_no; > else > array_real_poles[2,1] := glob_large_float; > array_real_poles[2,2] := glob_large_float; > fi;# end if 8 > else > array_real_poles[2,1] := glob_large_float; > array_real_poles[2,2] := glob_large_float; > fi;# end if 7; > #BOTTOM RADII REAL EQ = 2 > #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 - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_x2_higher[1,n]) <> 0.0) then # if number 7 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 7; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 7 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_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 8 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9 > 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 10 > if (rcs > 0.0) then # if number 11 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 11 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 10 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 9 > fi;# end if 8; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 7; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #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_x1_higher[1,n]) <> 0.0) then # if number 7 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 7; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 7 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_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 8 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9 > 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 10 > if (rcs > 0.0) then # if number 11 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 11 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 10 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 9 > fi;# end if 8; > array_complex_poles[2,1] := rad_c; > array_complex_poles[2,2] := ord_no; > fi;# end if 7; > #BOTTOM RADII COMPLEX EQ = 2 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 7 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_x2[term] := array_x2[term]* ratio; > array_x2_higher[1,term] := array_x2_higher[1,term]* ratio; > array_t[term] := array_t[term]* ratio; > array_x1[term] := array_x1[term]* ratio; > array_x1_higher[1,term] := array_x1_higher[1,term]* ratio; > array_t[term] := array_t[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 7; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 7 > display_poles(); > fi;# end if 7 > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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 - 12; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_x2_higher[1, n]) = 0. or omniabs(array_x2_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_x2_higher[1, n]*glob_h/array_x2_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; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[2, 1] := glob_large_float; array_poles[2, 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_x1_higher[1, n]) = 0. or omniabs(array_x1_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_x1_higher[1, n]*glob_h/array_x1_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[2, 1] := rad_c end if end if; n := glob_max_terms; m := n - 3; while 10 <= m and (omniabs(array_x2_higher[1, m]) = 0. or omniabs(array_x2_higher[1, m - 1]) = 0. or omniabs(array_x2_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_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; m := n - 2; while 10 <= m and (omniabs(array_x1_higher[1, m]) = 0. or omniabs(array_x1_higher[1, m - 1]) = 0. or omniabs(array_x1_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_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[2, 1] := rcs; array_real_poles[2, 2] := ord_no else array_real_poles[2, 1] := glob_large_float; array_real_poles[2, 2] := glob_large_float end if else array_real_poles[2, 1] := glob_large_float; array_real_poles[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_x2_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_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_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; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_x1_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_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_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[2, 1] := rad_c; array_complex_poles[2, 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_x2[term] := array_x2[term]*ratio; array_x2_higher[1, term] := array_x2_higher[1, term]*ratio; array_t[term] := array_t[term]*ratio; array_x1[term] := array_x1[term]*ratio; array_x1_higher[1, term] := array_x1_higher[1, term]*ratio; array_t[term] := array_t[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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 7 > 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_x2[iii]) > array_norms[iii]) then # if number 8 > array_norms[iii] := omniabs(array_x2[iii]); > fi;# end if 8; > iii := iii + 1; > od;# end do number 1 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_x1[iii]) > array_norms[iii]) then # if number 8 > array_norms[iii] := omniabs(array_x1[iii]); > fi;# end if 8; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 7; > 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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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_x2[iii]) then array_norms[iii] := omniabs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_x1[iii]) then array_norms[iii] := omniabs(array_x1[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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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 diff $eq_no = 1 i = 1 order_d = 1 > array_tmp1[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_3D0[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 mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_2D0[1] * array_x2[1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; > #emit pre diff $eq_no = 1 i = 1 order_d = 2 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; > #emit pre diff $eq_no = 1 i = 1 order_d = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; > #emit pre add FULL FULL $eq_no = 1 i = 1 > array_tmp10[1] := array_tmp9[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_x2_set_initial[1,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[1] * expt(glob_h , (2)) * factorial_3(0,2); > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_x2_higher[3,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp12[1] := array_const_4D0[1] * array_x2[1]; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp13[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp14[1] := array_const_2D0[1] * array_tmp13[1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp16[1] := array_const_2D0[1] * array_x1[1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_x1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_x1_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp1[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_const_3D0[1] * array_tmp1[2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_const_2D0[1] * array_x2[2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; > #emit pre diff $eq_no = 1 i = 2 order_d = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; > #emit pre add FULL FULL $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_x2_set_initial[1,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[2] * expt(glob_h , (2)) * factorial_3(1,3); > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_x2_higher[2,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[3,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp12[2] := array_const_4D0[1] * array_x2[2]; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp13[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp14[2] := array_const_2D0[1] * array_tmp13[2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp16[2] := array_const_2D0[1] * array_x1[2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_x1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp1[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_const_3D0[1] * array_tmp1[3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_const_2D0[1] * array_x2[3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; > #emit pre diff $eq_no = 1 i = 3 order_d = 2 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; > #emit pre add FULL FULL $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_x2_set_initial[1,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[3] * expt(glob_h , (2)) * factorial_3(2,4); > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_x2_higher[2,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp12[3] := array_const_4D0[1] * array_x2[3]; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp13[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp14[3] := array_const_2D0[1] * array_tmp13[3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp16[3] := array_const_2D0[1] * array_x1[3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_x1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_x1_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp1[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_const_3D0[1] * array_tmp1[4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_const_2D0[1] * array_x2[4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; > #emit pre diff $eq_no = 1 i = 4 order_d = 2 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; > #emit pre add FULL FULL $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_x2_set_initial[1,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[4] * expt(glob_h , (2)) * factorial_3(3,5); > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_x2_higher[2,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_x2_higher[3,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp12[4] := array_const_4D0[1] * array_x2[4]; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp13[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp14[4] := array_const_2D0[1] * array_tmp13[4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp16[4] := array_const_2D0[1] * array_x1[4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_x1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_x1_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp1[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_const_3D0[1] * array_tmp1[5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_const_2D0[1] * array_x2[5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; > #emit pre diff $eq_no = 1 i = 5 order_d = 2 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; > #emit pre add FULL FULL $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_x2_set_initial[1,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[5] * expt(glob_h , (2)) * factorial_3(4,6); > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_x2_higher[2,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_x2_higher[3,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp12[5] := array_const_4D0[1] * array_x2[5]; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp13[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp14[5] := array_const_2D0[1] * array_tmp13[5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp16[5] := array_const_2D0[1] * array_x1[5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_x1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_x1_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 diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp2[kkk] := array_const_3D0[1] * array_tmp1[kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := array_const_2D0[1] * array_x2[kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; > #emit FULL - FULL add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_x2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp10[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x2[kkk + order_d] := temporary; > array_x2_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_x2_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; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp12[kkk] := array_const_4D0[1] * array_x2[kkk]; > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp14[kkk] := array_const_2D0[1] * array_tmp13[kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp16[kkk] := array_const_2D0[1] * array_x1[kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_x1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp17[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_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_x1_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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; array_tmp8[1] := array_x1_higher[2, 1]; array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; array_tmp10[1] := array_tmp9[1] + array_x1[1]; if not array_x2_set_initial[1, 3] then if 1 <= glob_max_terms then temporary := array_tmp10[1]*expt(glob_h, 2)*factorial_3(0, 2); array_x2[3] := temporary; array_x2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 2] := temporary; temporary := temporary*1.0/glob_h; array_x2_higher[3, 1] := temporary end if end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp14[1] := array_const_2D0[1]*array_tmp13[1]; array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; if not array_x1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp17[1]*expt(glob_h, 1)*factorial_3(0, 1); array_x1[2] := temporary; array_x1_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_x1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp2[2] := array_const_3D0[1]*array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; array_tmp4[2] := array_const_2D0[1]*array_x2[2]; array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; array_tmp8[2] := array_x1_higher[2, 2]; array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; array_tmp10[2] := array_tmp9[2] + array_x1[2]; if not array_x2_set_initial[1, 4] then if 2 <= glob_max_terms then temporary := array_tmp10[2]*expt(glob_h, 2)*factorial_3(1, 3); array_x2[4] := temporary; array_x2_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[2, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[3, 2] := temporary end if end if; kkk := 3; array_tmp12[2] := array_const_4D0[1]*array_x2[2]; array_tmp13[2] := array_x2_higher[2, 2]; array_tmp14[2] := array_const_2D0[1]*array_tmp13[2]; array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; array_tmp16[2] := array_const_2D0[1]*array_x1[2]; array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; if not array_x1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp17[2]*expt(glob_h, 1)*factorial_3(1, 2); array_x1[3] := temporary; array_x1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp2[3] := array_const_3D0[1]*array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; array_tmp4[3] := array_const_2D0[1]*array_x2[3]; array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; array_tmp8[3] := array_x1_higher[2, 3]; array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; array_tmp10[3] := array_tmp9[3] + array_x1[3]; if not array_x2_set_initial[1, 5] then if 3 <= glob_max_terms then temporary := array_tmp10[3]*expt(glob_h, 2)*factorial_3(2, 4); array_x2[5] := temporary; array_x2_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_x2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 3] := temporary end if end if; kkk := 4; array_tmp12[3] := array_const_4D0[1]*array_x2[3]; array_tmp13[3] := array_x2_higher[2, 3]; array_tmp14[3] := array_const_2D0[1]*array_tmp13[3]; array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; array_tmp16[3] := array_const_2D0[1]*array_x1[3]; array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; if not array_x1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp17[3]*expt(glob_h, 1)*factorial_3(2, 3); array_x1[4] := temporary; array_x1_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_x1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp2[4] := array_const_3D0[1]*array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; array_tmp4[4] := array_const_2D0[1]*array_x2[4]; array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; array_tmp8[4] := array_x1_higher[2, 4]; array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; array_tmp10[4] := array_tmp9[4] + array_x1[4]; if not array_x2_set_initial[1, 6] then if 4 <= glob_max_terms then temporary := array_tmp10[4]*expt(glob_h, 2)*factorial_3(3, 5); array_x2[6] := temporary; array_x2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_x2_higher[2, 5] := temporary; temporary := temporary*4.0/glob_h; array_x2_higher[3, 4] := temporary end if end if; kkk := 5; array_tmp12[4] := array_const_4D0[1]*array_x2[4]; array_tmp13[4] := array_x2_higher[2, 4]; array_tmp14[4] := array_const_2D0[1]*array_tmp13[4]; array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; array_tmp16[4] := array_const_2D0[1]*array_x1[4]; array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; if not array_x1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp17[4]*expt(glob_h, 1)*factorial_3(3, 4); array_x1[5] := temporary; array_x1_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_x1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp2[5] := array_const_3D0[1]*array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; array_tmp4[5] := array_const_2D0[1]*array_x2[5]; array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; array_tmp8[5] := array_x1_higher[2, 5]; array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; array_tmp10[5] := array_tmp9[5] + array_x1[5]; if not array_x2_set_initial[1, 7] then if 5 <= glob_max_terms then temporary := array_tmp10[5]*expt(glob_h, 2)*factorial_3(4, 6); array_x2[7] := temporary; array_x2_higher[1, 7] := temporary; temporary := temporary*6.0/glob_h; array_x2_higher[2, 6] := temporary; temporary := temporary*5.0/glob_h; array_x2_higher[3, 5] := temporary end if end if; kkk := 6; array_tmp12[5] := array_const_4D0[1]*array_x2[5]; array_tmp13[5] := array_x2_higher[2, 5]; array_tmp14[5] := array_const_2D0[1]*array_tmp13[5]; array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; array_tmp16[5] := array_const_2D0[1]*array_x1[5]; array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; if not array_x1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp17[5]*expt(glob_h, 1)*factorial_3(4, 5); array_x1[6] := temporary; array_x1_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_x1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp2[kkk] := array_const_3D0[1]*array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; array_tmp4[kkk] := array_const_2D0[1]*array_x2[kkk]; array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d < glob_max_terms then if not array_x2_set_initial[1, kkk + order_d] then temporary := array_tmp10[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_x2[kkk + order_d] := temporary; array_x2_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_x2_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp12[kkk] := array_const_4D0[1]*array_x2[kkk]; array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp14[kkk] := array_const_2D0[1]*array_tmp13[kkk]; array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; array_tmp16[kkk] := array_const_2D0[1]*array_x1[kkk]; array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_x1_set_initial[2, kkk + order_d] then temporary := array_tmp17[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_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_x1_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return(2.0 * c1 + 6.0 * c3 * exp(-t)); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x1p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return( - 6.0 * c3 * exp(-t)); > end; exact_soln_x1p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return -6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 2.0*c2*exp(2.0*t) - c3*exp(-t) 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, > t_start,t_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_2, > array_const_0D0, > array_const_3D0, > array_const_1, > array_const_2D0, > array_const_4D0, > #END CONST > array_x2_init, > array_x1_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_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_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 := 2; > 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/mtest6_rev_sm_hpostode.ode#################"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"## problem from Boyce DePrima -"); > omniout_str(ALWAYS,"## _Elementary Differential Equations and Boundary Value Problems_"); > omniout_str(ALWAYS,"## page 269"); > omniout_str(ALWAYS,"##"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 0.8;"); > omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"## I think following line should be omitted"); > omniout_str(ALWAYS,"## diff(x1,1,exact_soln_x1p(t_start));"); > omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_max_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return(2.0 * c1 + 6.0 * c3 * exp(-t));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x1p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return( - 6.0 * c3 * exp(-t));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_x2_init:= Array(0..(max_terms + 1),[]); > array_x1_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..(3 + 1),[]); > array_last_rel_error:= Array(0..(3 + 1),[]); > array_type_pole:= Array(0..(3 + 1),[]); > array_type_real_pole:= Array(0..(3 + 1),[]); > array_type_complex_pole:= Array(0..(3 + 1),[]); > array_x2:= Array(0..(max_terms + 1),[]); > array_t:= Array(0..(max_terms + 1),[]); > array_x1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_tmp15:= Array(0..(max_terms + 1),[]); > array_tmp16:= Array(0..(max_terms + 1),[]); > array_tmp17:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(3+ 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_x2_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x1_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 <= 3) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) 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_x2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x2_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x2_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x2_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x2_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x1_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x1_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x1_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 <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_x1_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 <=3) 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 <=3) 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 <=3) 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 <=3) 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 <=3) 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_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_t := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_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_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2[1] := 2; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_3D0[1] := 3.0; > array_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_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_4D0[1] := 4.0; > 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 > ## problem from Boyce DePrima - > ## _Elementary Differential Equations and Boundary Value Problems_ > ## page 269 > ## > t_start := 0.5; > t_end := 0.8; > array_x1_init[0 + 1] := exact_soln_x1(t_start); > ## I think following line should be omitted > ## diff(x1,1,exact_soln_x1p(t_start)); > array_x2_init[0 + 1] := exact_soln_x2(t_start); > array_x2_init[1 + 1] := exact_soln_x2p(t_start); > glob_max_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > #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_x2_set_initial[1,1] := true; > array_x2_set_initial[1,2] := true; > array_x2_set_initial[1,3] := false; > array_x2_set_initial[1,4] := false; > array_x2_set_initial[1,5] := false; > array_x2_set_initial[1,6] := false; > array_x2_set_initial[1,7] := false; > array_x2_set_initial[1,8] := false; > array_x2_set_initial[1,9] := false; > array_x2_set_initial[1,10] := false; > array_x2_set_initial[1,11] := false; > array_x2_set_initial[1,12] := false; > array_x2_set_initial[1,13] := false; > array_x2_set_initial[1,14] := false; > array_x2_set_initial[1,15] := false; > array_x2_set_initial[1,16] := false; > array_x2_set_initial[1,17] := false; > array_x2_set_initial[1,18] := false; > array_x2_set_initial[1,19] := false; > array_x2_set_initial[1,20] := false; > array_x2_set_initial[1,21] := false; > array_x2_set_initial[1,22] := false; > array_x2_set_initial[1,23] := false; > array_x2_set_initial[1,24] := false; > array_x2_set_initial[1,25] := false; > array_x2_set_initial[1,26] := false; > array_x2_set_initial[1,27] := false; > array_x2_set_initial[1,28] := false; > array_x2_set_initial[1,29] := false; > array_x2_set_initial[1,30] := false; > array_x1_set_initial[2,1] := true; > array_x1_set_initial[2,2] := false; > array_x1_set_initial[2,3] := false; > array_x1_set_initial[2,4] := false; > array_x1_set_initial[2,5] := false; > array_x1_set_initial[2,6] := false; > array_x1_set_initial[2,7] := false; > array_x1_set_initial[2,8] := false; > array_x1_set_initial[2,9] := false; > array_x1_set_initial[2,10] := false; > array_x1_set_initial[2,11] := false; > array_x1_set_initial[2,12] := false; > array_x1_set_initial[2,13] := false; > array_x1_set_initial[2,14] := false; > array_x1_set_initial[2,15] := false; > array_x1_set_initial[2,16] := false; > array_x1_set_initial[2,17] := false; > array_x1_set_initial[2,18] := false; > array_x1_set_initial[2,19] := false; > array_x1_set_initial[2,20] := false; > array_x1_set_initial[2,21] := false; > array_x1_set_initial[2,22] := false; > array_x1_set_initial[2,23] := false; > array_x1_set_initial[2,24] := false; > array_x1_set_initial[2,25] := false; > array_x1_set_initial[2,26] := false; > array_x1_set_initial[2,27] := false; > array_x1_set_initial[2,28] := false; > array_x1_set_initial[2,29] := false; > array_x1_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(t_start,t_end); > glob_h := check_sign(t_start,t_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 7 > glob_h := glob_max_h; > fi;# end if 7; > if (glob_display_interval < glob_h) then # if number 7 > glob_h := glob_display_interval; > fi;# end if 7; > 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(t_start,t_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_t[1] := t_start; > array_t[2] := glob_h; > glob_next_display := t_start; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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 > ; > order_diff := 2; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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 > ; > if (glob_subiter_method = 1 ) then # if number 7 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 8 > subiter := 1; > while (subiter <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + glob_max_terms) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 8; > 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 8 > 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 9 > 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 9; > 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 9 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 9; > if (opt_iter > 100) then # if number 9 > glob_h := glob_max_h; > found_h := false; > fi;# end if 9; > if (glob_display_interval < glob_h) then # if number 9 > glob_h := glob_display_interval; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > glob_next_display := t_start; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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 > ; > order_diff := 2; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_t[1]) < (glob_check_sign * t_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 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 10 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 11 > subiter := 1; > while (subiter <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + glob_max_terms) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 11; > display_alot(current_iter); > if (glob_look_poles) then # if number 11 > #left paren 0004C > check_for_pole(); > fi;# end if 11;#was right paren 0004C > if (reached_interval()) then # if number 11 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 11; > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > #Jump Series array_x2; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[3,iii] := array_x2_higher[3,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 := 3; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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 := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[2,iii] := array_x2_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 := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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 := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[2,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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 := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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 := 3; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_x2_higher[ord,term_no] := array_x2_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 > #Jump Series array_x1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[2,iii] := array_x1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[1,iii] := array_x1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[1,iii] := array_x1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #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_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_x1_higher[ord,term_no] := array_x1_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 11 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 11; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 11 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 11; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if (glob_html_log) then # if number 11 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T03:26:08-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6_rev_sm_h") > ; > logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[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 12 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 12; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"mtest6_rev_sm_h diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6_rev_sm_h maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 12 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 12; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 11; > if (glob_html_log) then # if number 11 > fclose(html_log_file); > fi;# end if 11 > ; > ;; > fi;# end if 10 > #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, t_start, t_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_2, array_const_0D0, array_const_3D0, array_const_1, array_const_2D0, array_const_4D0, array_x2_init, array_x1_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_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_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 := 2; 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/mtest6_rev_sm_hpostode.ode#################"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1)+x1;"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "## problem from Boyce DePrima -"); omniout_str(ALWAYS, "## _Elementary Differential Equations and Bounda\ ry Value Problems_"); omniout_str(ALWAYS, "## page 269"); omniout_str(ALWAYS, "##"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 0.8;"); omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "## I think following line should be omitted"); omniout_str(ALWAYS, "## diff(x1,1,exact_soln_x1p(t_start));"); omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);") ; omniout_str(ALWAYS, "glob_max_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return(2.0 * c1 + 6.0 * c3 * exp(-t));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x1p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return( - 6.0 * c3 * exp(-t));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));"); 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 := 64; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_x2_init := Array(0 .. max_terms + 1, []); array_x1_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 .. 4, []); array_last_rel_error := Array(0 .. 4, []); array_type_pole := Array(0 .. 4, []); array_type_real_pole := Array(0 .. 4, []); array_type_complex_pole := Array(0 .. 4, []); array_x2 := Array(0 .. max_terms + 1, []); array_t := Array(0 .. max_terms + 1, []); array_x1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_tmp15 := Array(0 .. max_terms + 1, []); array_tmp16 := Array(0 .. max_terms + 1, []); array_tmp17 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 4, 0 .. 4, []); array_given_rad_poles := Array(0 .. 4, 0 .. 4, []); array_given_ord_poles := Array(0 .. 4, 0 .. 4, []); array_real_poles := Array(0 .. 4, 0 .. 4, []); array_complex_poles := Array(0 .. 4, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_x2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1_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 <= 3 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 3 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 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 <= 3 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 <= 3 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 <= 3 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 <= 3 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_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_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_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; 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; t_start := 0.5; t_end := 0.8; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_max_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; 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_x2_set_initial[1, 1] := true; array_x2_set_initial[1, 2] := true; array_x2_set_initial[1, 3] := false; array_x2_set_initial[1, 4] := false; array_x2_set_initial[1, 5] := false; array_x2_set_initial[1, 6] := false; array_x2_set_initial[1, 7] := false; array_x2_set_initial[1, 8] := false; array_x2_set_initial[1, 9] := false; array_x2_set_initial[1, 10] := false; array_x2_set_initial[1, 11] := false; array_x2_set_initial[1, 12] := false; array_x2_set_initial[1, 13] := false; array_x2_set_initial[1, 14] := false; array_x2_set_initial[1, 15] := false; array_x2_set_initial[1, 16] := false; array_x2_set_initial[1, 17] := false; array_x2_set_initial[1, 18] := false; array_x2_set_initial[1, 19] := false; array_x2_set_initial[1, 20] := false; array_x2_set_initial[1, 21] := false; array_x2_set_initial[1, 22] := false; array_x2_set_initial[1, 23] := false; array_x2_set_initial[1, 24] := false; array_x2_set_initial[1, 25] := false; array_x2_set_initial[1, 26] := false; array_x2_set_initial[1, 27] := false; array_x2_set_initial[1, 28] := false; array_x2_set_initial[1, 29] := false; array_x2_set_initial[1, 30] := false; array_x1_set_initial[2, 1] := true; array_x1_set_initial[2, 2] := false; array_x1_set_initial[2, 3] := false; array_x1_set_initial[2, 4] := false; array_x1_set_initial[2, 5] := false; array_x1_set_initial[2, 6] := false; array_x1_set_initial[2, 7] := false; array_x1_set_initial[2, 8] := false; array_x1_set_initial[2, 9] := false; array_x1_set_initial[2, 10] := false; array_x1_set_initial[2, 11] := false; array_x1_set_initial[2, 12] := false; array_x1_set_initial[2, 13] := false; array_x1_set_initial[2, 14] := false; array_x1_set_initial[2, 15] := false; array_x1_set_initial[2, 16] := false; array_x1_set_initial[2, 17] := false; array_x1_set_initial[2, 18] := false; array_x1_set_initial[2, 19] := false; array_x1_set_initial[2, 20] := false; array_x1_set_initial[2, 21] := false; array_x1_set_initial[2, 22] := false; array_x1_set_initial[2, 23] := false; array_x1_set_initial[2, 24] := false; array_x1_set_initial[2, 25] := false; array_x1_set_initial[2, 26] := false; array_x1_set_initial[2, 27] := false; array_x1_set_initial[2, 28] := false; array_x1_set_initial[2, 29] := false; array_x1_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(t_start, t_end); glob_h := check_sign(t_start, t_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(t_start, t_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_t[1] := t_start; array_t[2] := glob_h; glob_next_display := t_start; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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_t[1] := t_start; array_t[2] := glob_h; glob_next_display := t_start; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_t[1] < glob_check_sign*t_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 3; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_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 := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_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 := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 \ - diff(x1,t,2) - diff (x1,t,1)+x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T03:26:08-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6_rev_sm_h"); logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1\ ) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[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, "mtest6_rev_sm_h diffeq.mxt"); logitem_str(html_log_file, "mtest6_rev_sm_h maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 *\ diff (x2,t ,1) - 2.0 * x1;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); 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/mtest6_rev_sm_hpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## problem from Boyce DePrima - ## _Elementary Differential Equations and Boundary Value Problems_ ## page 269 ## t_start := 0.5; t_end := 0.8; array_x1_init[0 + 1] := exact_soln_x1(t_start); ## I think following line should be omitted ## diff(x1,1,exact_soln_x1p(t_start)); array_x2_init[0 + 1] := exact_soln_x2(t_start); array_x2_init[1 + 1] := exact_soln_x2p(t_start); glob_max_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); end; exact_soln_x1p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( - 6.0 * c3 * exp(-t)); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); 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 = 0.3 estimated_steps = 300000 step_error = 3.3333333333333333333333333333333e-16 est_needed_step_err = 3.3333333333333333333333333333333e-16 opt_iter = 1 bytes used=4000004, alloc=3210676, time=0.14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1158013774365979338391678604982e-178 estimated_step_error = 2.1158013774365979338391678604982e-178 best_h = 2.0e-06 opt_iter = 2 bytes used=8000868, alloc=4848776, time=0.28 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4198903214825858626085046185924e-170 estimated_step_error = 1.4198903214825858626085046185924e-170 best_h = 4.00e-06 opt_iter = 3 bytes used=12001832, alloc=4848776, time=0.44 bytes used=16002624, alloc=4914300, time=0.59 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.5287233537605262951698596080266e-163 estimated_step_error = 9.5287233537605262951698596080266e-163 best_h = 8.000e-06 opt_iter = 4 bytes used=20003552, alloc=4914300, time=0.74 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.3946189437624795102738106461558e-155 estimated_step_error = 6.3946189437624795102738106461558e-155 best_h = 1.60000e-05 opt_iter = 5 bytes used=24004212, alloc=4914300, time=0.89 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.2913574018014516751056109669648e-147 estimated_step_error = 4.2913574018014516751056109669648e-147 best_h = 3.200000e-05 opt_iter = 6 bytes used=28004940, alloc=4914300, time=1.04 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8798829091270685721220365466171e-139 estimated_step_error = 2.8798829091270685721220365466171e-139 best_h = 6.4000000e-05 opt_iter = 7 bytes used=32005800, alloc=4914300, time=1.19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9326589954065832399494506349008e-131 estimated_step_error = 1.9326589954065832399494506349008e-131 best_h = 0.000128 opt_iter = 8 bytes used=36006696, alloc=4914300, time=1.35 bytes used=40007516, alloc=4914300, time=1.50 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2969885711609859332831343834859e-123 estimated_step_error = 1.2969885711609859332831343834859e-123 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop bytes used=44008908, alloc=4914300, time=1.65 t[1] = 0.5 x2[1] (analytic) = 1.0007256155636055990741531973548 x2[1] (numeric) = 1.0007256155636055990741531973548 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.0001 x1[1] (analytic) = 2.001091755187482740162486839163 x1[1] (numeric) = 2.001091755187482740162486839163 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.573e+04 Order of pole (six term test) = 1.303e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 4.800e+27 Order of pole (six term test) = 1.274e+54 bytes used=48009568, alloc=4914300, time=1.81 bytes used=52010908, alloc=4979824, time=1.96 bytes used=56011584, alloc=4979824, time=2.11 bytes used=60012676, alloc=4979824, time=2.27 bytes used=64013588, alloc=4979824, time=2.42 bytes used=68014880, alloc=4979824, time=2.57 bytes used=72015544, alloc=4979824, time=2.73 bytes used=76016304, alloc=4979824, time=2.88 bytes used=80017316, alloc=4979824, time=3.04 bytes used=84018092, alloc=4979824, time=3.19 bytes used=88018952, alloc=4979824, time=3.35 bytes used=92019636, alloc=4979824, time=3.51 bytes used=96020384, alloc=4979824, time=3.66 bytes used=100021664, alloc=4979824, time=3.82 bytes used=104022604, alloc=4979824, time=3.97 bytes used=108023512, alloc=4979824, time=4.12 bytes used=112024336, alloc=5045348, time=4.28 bytes used=116025132, alloc=5045348, time=4.43 bytes used=120026000, alloc=5045348, time=4.59 bytes used=124026780, alloc=5045348, time=4.74 bytes used=128027884, alloc=5045348, time=4.90 bytes used=132028900, alloc=5045348, time=5.05 bytes used=136029684, alloc=5045348, time=5.21 bytes used=140030504, alloc=5045348, time=5.36 bytes used=144031256, alloc=5045348, time=5.52 bytes used=148031912, alloc=5045348, time=5.67 bytes used=152032652, alloc=5045348, time=5.82 bytes used=156033400, alloc=5045348, time=5.98 bytes used=160034264, alloc=5045348, time=6.14 bytes used=164034976, alloc=5045348, time=6.29 bytes used=168035684, alloc=5045348, time=6.45 bytes used=172036352, alloc=5045348, time=6.60 bytes used=176037024, alloc=5045348, time=6.75 bytes used=180037732, alloc=5045348, time=6.91 bytes used=184038736, alloc=5045348, time=7.06 bytes used=188039548, alloc=5045348, time=7.22 bytes used=192040640, alloc=5045348, time=7.37 bytes used=196041304, alloc=5045348, time=7.53 bytes used=200042060, alloc=5045348, time=7.68 bytes used=204043100, alloc=5045348, time=7.83 bytes used=208043916, alloc=5045348, time=7.99 bytes used=212045104, alloc=5045348, time=8.14 bytes used=216045860, alloc=5045348, time=8.29 bytes used=220046720, alloc=5045348, time=8.45 bytes used=224047568, alloc=5045348, time=8.61 bytes used=228048316, alloc=5045348, time=8.76 bytes used=232049008, alloc=5045348, time=8.91 bytes used=236049692, alloc=5045348, time=9.07 bytes used=240050508, alloc=5045348, time=9.22 bytes used=244051216, alloc=5045348, time=9.38 bytes used=248051904, alloc=5045348, time=9.54 bytes used=252052636, alloc=5045348, time=9.69 bytes used=256053320, alloc=5045348, time=9.85 bytes used=260054200, alloc=5045348, time=10.00 bytes used=264055088, alloc=5045348, time=10.15 bytes used=268055808, alloc=5045348, time=10.31 bytes used=272056520, alloc=5045348, time=10.46 bytes used=276057448, alloc=5045348, time=10.62 bytes used=280058440, alloc=5045348, time=10.77 bytes used=284059264, alloc=5045348, time=10.93 bytes used=288060008, alloc=5045348, time=11.08 bytes used=292061004, alloc=5045348, time=11.24 bytes used=296061900, alloc=5045348, time=11.39 bytes used=300062588, alloc=5045348, time=11.55 bytes used=304063336, alloc=5045348, time=11.70 bytes used=308064036, alloc=5045348, time=11.86 bytes used=312064780, alloc=5045348, time=12.01 bytes used=316065588, alloc=5045348, time=12.17 bytes used=320066300, alloc=5045348, time=12.32 bytes used=324067172, alloc=5045348, time=12.48 bytes used=328067956, alloc=5045348, time=12.63 bytes used=332068644, alloc=5045348, time=12.79 bytes used=336069532, alloc=5045348, time=12.94 bytes used=340070500, alloc=5045348, time=13.10 bytes used=344071200, alloc=5045348, time=13.26 bytes used=348071884, alloc=5045348, time=13.41 bytes used=352072708, alloc=5110872, time=13.57 bytes used=356073400, alloc=5110872, time=13.72 bytes used=360074300, alloc=5110872, time=13.88 bytes used=364075312, alloc=5110872, time=14.03 bytes used=368076360, alloc=5110872, time=14.19 bytes used=372077160, alloc=5110872, time=14.34 bytes used=376077900, alloc=5110872, time=14.50 bytes used=380078804, alloc=5110872, time=14.65 bytes used=384079524, alloc=5110872, time=14.81 bytes used=388080296, alloc=5110872, time=14.96 bytes used=392081000, alloc=5110872, time=15.12 bytes used=396081684, alloc=5110872, time=15.27 bytes used=400082476, alloc=5110872, time=15.43 bytes used=404083308, alloc=5110872, time=15.59 bytes used=408084132, alloc=5110872, time=15.74 bytes used=412085184, alloc=5110872, time=15.90 bytes used=416086064, alloc=5110872, time=16.05 bytes used=420086908, alloc=5110872, time=16.20 bytes used=424087668, alloc=5110872, time=16.36 bytes used=428088344, alloc=5110872, time=16.51 bytes used=432089116, alloc=5110872, time=16.67 bytes used=436090112, alloc=5110872, time=16.82 bytes used=440090952, alloc=5110872, time=16.98 bytes used=444091780, alloc=5110872, time=17.13 bytes used=448092772, alloc=5110872, time=17.29 bytes used=452093548, alloc=5110872, time=17.44 bytes used=456094296, alloc=5110872, time=17.60 bytes used=460095172, alloc=5110872, time=17.76 bytes used=464095900, alloc=5110872, time=17.91 bytes used=468097108, alloc=5110872, time=18.06 bytes used=472097896, alloc=5110872, time=18.22 bytes used=476098820, alloc=5110872, time=18.37 bytes used=480099564, alloc=5110872, time=18.53 bytes used=484100824, alloc=5110872, time=18.68 bytes used=488101952, alloc=5110872, time=18.84 bytes used=492102676, alloc=5110872, time=19.00 bytes used=496103504, alloc=5110872, time=19.15 bytes used=500104284, alloc=5110872, time=19.30 bytes used=504105024, alloc=5110872, time=19.46 bytes used=508105696, alloc=5110872, time=19.61 bytes used=512106596, alloc=5110872, time=19.77 TOP MAIN SOLVE Loop bytes used=516107440, alloc=5110872, time=19.92 t[1] = 0.51 x2[1] (analytic) = 1.0007347876264365393661995311595 x2[1] (numeric) = 1.0007348429461450453830298675891 absolute error = 5.5319708506016830336429565547572e-08 relative error = 5.5279090114599951870891924380675e-06 % Correct digits = 8 h = 0.0001 x1[1] (analytic) = 2.0010808920418620786970381472244 x1[1] (numeric) = 2.0010807828654335314007942343835 absolute error = 1.0917642854729624391284082515233e-07 relative error = 5.4558728226071283748098831279477e-06 % Correct digits = 8 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.581e+04 Order of pole (six term test) = 1.316e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 4.435e+27 Order of pole (six term test) = -1.340e+54 bytes used=520108252, alloc=5110872, time=20.08 bytes used=524109192, alloc=5110872, time=20.23 bytes used=528110072, alloc=5110872, time=20.39 bytes used=532110776, alloc=5110872, time=20.55 bytes used=536111576, alloc=5110872, time=20.70 bytes used=540112280, alloc=5110872, time=20.86 bytes used=544113168, alloc=5110872, time=21.01 bytes used=548113912, alloc=5110872, time=21.17 bytes used=552115028, alloc=5110872, time=21.32 bytes used=556115740, alloc=5110872, time=21.47 bytes used=560116556, alloc=5110872, time=21.63 bytes used=564117748, alloc=5110872, time=21.79 bytes used=568118568, alloc=5110872, time=21.94 bytes used=572119600, alloc=5110872, time=22.10 bytes used=576120508, alloc=5110872, time=22.25 bytes used=580121280, alloc=5110872, time=22.40 bytes used=584122088, alloc=5110872, time=22.56 bytes used=588122916, alloc=5110872, time=22.71 bytes used=592123632, alloc=5110872, time=22.87 bytes used=596124428, alloc=5110872, time=23.02 bytes used=600125372, alloc=5110872, time=23.18 bytes used=604126144, alloc=5110872, time=23.33 bytes used=608127108, alloc=5110872, time=23.49 bytes used=612127812, alloc=5110872, time=23.65 bytes used=616128508, alloc=5110872, time=23.80 bytes used=620129804, alloc=5110872, time=23.96 bytes used=624130672, alloc=5110872, time=24.11 bytes used=628131336, alloc=5110872, time=24.27 bytes used=632132120, alloc=5110872, time=24.42 bytes used=636132976, alloc=5110872, time=24.58 bytes used=640134004, alloc=5110872, time=24.73 bytes used=644135020, alloc=5110872, time=24.89 bytes used=648135676, alloc=5110872, time=25.05 bytes used=652136560, alloc=5110872, time=25.20 bytes used=656137344, alloc=5110872, time=25.36 bytes used=660138372, alloc=5110872, time=25.51 bytes used=664139224, alloc=5110872, time=25.67 bytes used=668139880, alloc=5110872, time=25.83 bytes used=672140564, alloc=5110872, time=25.98 bytes used=676141256, alloc=5110872, time=26.14 bytes used=680142020, alloc=5110872, time=26.29 bytes used=684142844, alloc=5110872, time=26.44 bytes used=688144092, alloc=5110872, time=26.60 bytes used=692145092, alloc=5110872, time=26.75 bytes used=696146396, alloc=5110872, time=26.91 bytes used=700147120, alloc=5110872, time=27.07 bytes used=704148088, alloc=5110872, time=27.23 bytes used=708148856, alloc=5110872, time=27.38 bytes used=712150044, alloc=5110872, time=27.54 bytes used=716151276, alloc=5110872, time=27.70 bytes used=720152060, alloc=5110872, time=27.85 bytes used=724152720, alloc=5110872, time=28.00 bytes used=728153376, alloc=5110872, time=28.16 bytes used=732154180, alloc=5110872, time=28.31 bytes used=736154856, alloc=5110872, time=28.47 bytes used=740155524, alloc=5110872, time=28.62 bytes used=744156452, alloc=5110872, time=28.78 bytes used=748157264, alloc=5110872, time=28.94 bytes used=752158268, alloc=5110872, time=29.09 bytes used=756159024, alloc=5110872, time=29.24 bytes used=760159884, alloc=5110872, time=29.40 bytes used=764160552, alloc=5110872, time=29.56 bytes used=768161272, alloc=5110872, time=29.71 bytes used=772162072, alloc=5110872, time=29.87 bytes used=776162872, alloc=5110872, time=30.03 bytes used=780163556, alloc=5110872, time=30.18 bytes used=784164348, alloc=5110872, time=30.33 bytes used=788165396, alloc=5110872, time=30.49 bytes used=792166056, alloc=5110872, time=30.64 bytes used=796167012, alloc=5110872, time=30.80 bytes used=800167764, alloc=5110872, time=30.95 bytes used=804168556, alloc=5110872, time=31.11 bytes used=808169332, alloc=5110872, time=31.27 bytes used=812170280, alloc=5110872, time=31.42 bytes used=816171060, alloc=5110872, time=31.58 bytes used=820171924, alloc=5110872, time=31.74 bytes used=824172928, alloc=5110872, time=31.89 bytes used=828173648, alloc=5110872, time=32.04 bytes used=832174456, alloc=5110872, time=32.20 bytes used=836175120, alloc=5110872, time=32.35 bytes used=840175784, alloc=5110872, time=32.51 bytes used=844176784, alloc=5110872, time=32.66 bytes used=848177680, alloc=5110872, time=32.82 bytes used=852178400, alloc=5110872, time=32.98 bytes used=856179080, alloc=5110872, time=33.14 bytes used=860180012, alloc=5110872, time=33.30 bytes used=864180680, alloc=5110872, time=33.45 bytes used=868181560, alloc=5110872, time=33.60 bytes used=872182576, alloc=5110872, time=33.76 bytes used=876183336, alloc=5110872, time=33.92 bytes used=880184216, alloc=5110872, time=34.07 bytes used=884184900, alloc=5110872, time=34.23 bytes used=888185576, alloc=5110872, time=34.38 bytes used=892186580, alloc=5110872, time=34.54 bytes used=896187332, alloc=5110872, time=34.69 bytes used=900187988, alloc=5110872, time=34.85 bytes used=904188676, alloc=5110872, time=35.01 bytes used=908189392, alloc=5110872, time=35.16 bytes used=912190288, alloc=5110872, time=35.32 bytes used=916191012, alloc=5110872, time=35.47 bytes used=920191868, alloc=5110872, time=35.63 bytes used=924192620, alloc=5110872, time=35.78 bytes used=928193424, alloc=5110872, time=35.94 bytes used=932194268, alloc=5110872, time=36.10 bytes used=936195004, alloc=5110872, time=36.25 bytes used=940196052, alloc=5110872, time=36.40 bytes used=944196796, alloc=5110872, time=36.56 bytes used=948197664, alloc=5110872, time=36.72 bytes used=952198452, alloc=5110872, time=36.87 bytes used=956199168, alloc=5110872, time=37.02 bytes used=960200408, alloc=5110872, time=37.18 bytes used=964201172, alloc=5110872, time=37.33 bytes used=968201864, alloc=5110872, time=37.49 bytes used=972202584, alloc=5110872, time=37.64 bytes used=976203324, alloc=5110872, time=37.80 bytes used=980204056, alloc=5110872, time=37.96 bytes used=984204780, alloc=5110872, time=38.11 TOP MAIN SOLVE Loop bytes used=988205620, alloc=5110872, time=38.27 t[1] = 0.52 x2[1] (analytic) = 1.000744199567261370205597366143 x2[1] (numeric) = 1.0007444238070847829267772204405 absolute error = 2.2423982341272117985429747798384e-07 relative error = 2.2407306833223340431872172083163e-05 % Correct digits = 7 h = 0.0001 x1[1] (analytic) = 2.0010701369863463498101608136496 x1[1] (numeric) = 2.0010697002697144267897951467495 absolute error = 4.3671663192302036566690008078862e-07 relative error = 2.1824154178859756745016717156998e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.589e+04 Order of pole (six term test) = 1.329e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 6.209e+27 Order of pole (six term test) = -7.376e+53 bytes used=992206408, alloc=5110872, time=38.42 bytes used=996207396, alloc=5110872, time=38.57 bytes used=1000208104, alloc=5110872, time=38.73 bytes used=1004208804, alloc=5110872, time=38.88 bytes used=1008209644, alloc=5110872, time=39.05 bytes used=1012210408, alloc=5110872, time=39.20 bytes used=1016211716, alloc=5110872, time=39.36 bytes used=1020212564, alloc=5110872, time=39.51 bytes used=1024213348, alloc=5110872, time=39.67 bytes used=1028214244, alloc=5110872, time=39.82 bytes used=1032215708, alloc=5110872, time=39.98 bytes used=1036216656, alloc=5110872, time=40.14 bytes used=1040217516, alloc=5110872, time=40.29 bytes used=1044218236, alloc=5110872, time=40.45 bytes used=1048219068, alloc=5110872, time=40.60 bytes used=1052219800, alloc=5110872, time=40.76 bytes used=1056220504, alloc=5110872, time=40.91 bytes used=1060221488, alloc=5110872, time=41.07 bytes used=1064222208, alloc=5110872, time=41.22 bytes used=1068222952, alloc=5110872, time=41.38 bytes used=1072223820, alloc=5110872, time=41.53 bytes used=1076224552, alloc=5110872, time=41.69 bytes used=1080225292, alloc=5110872, time=41.84 bytes used=1084226136, alloc=5110872, time=42.00 bytes used=1088226884, alloc=5110872, time=42.15 bytes used=1092227560, alloc=5110872, time=42.31 bytes used=1096228280, alloc=5110872, time=42.46 bytes used=1100229508, alloc=5110872, time=42.62 bytes used=1104230420, alloc=5110872, time=42.78 bytes used=1108231396, alloc=5110872, time=42.93 bytes used=1112232208, alloc=5110872, time=43.09 bytes used=1116232876, alloc=5110872, time=43.24 bytes used=1120233748, alloc=5110872, time=43.40 bytes used=1124234916, alloc=5110872, time=43.55 bytes used=1128235956, alloc=5110872, time=43.71 bytes used=1132236792, alloc=5110872, time=43.86 bytes used=1136237504, alloc=5110872, time=44.02 bytes used=1140238264, alloc=5110872, time=44.18 bytes used=1144238924, alloc=5110872, time=44.33 bytes used=1148239832, alloc=5110872, time=44.48 bytes used=1152240588, alloc=5110872, time=44.64 bytes used=1156241480, alloc=5110872, time=44.80 bytes used=1160242244, alloc=5110872, time=44.96 bytes used=1164242960, alloc=5110872, time=45.12 bytes used=1168243752, alloc=5110872, time=45.27 bytes used=1172244644, alloc=5110872, time=45.43 bytes used=1176245296, alloc=5110872, time=45.59 bytes used=1180246072, alloc=5110872, time=45.74 bytes used=1184246844, alloc=5110872, time=45.90 bytes used=1188247584, alloc=5110872, time=46.05 bytes used=1192248476, alloc=5110872, time=46.21 bytes used=1196249200, alloc=5110872, time=46.36 bytes used=1200250204, alloc=5110872, time=46.52 bytes used=1204251124, alloc=5110872, time=46.68 bytes used=1208251936, alloc=5110872, time=46.83 bytes used=1212253020, alloc=5110872, time=46.99 bytes used=1216253760, alloc=5110872, time=47.14 bytes used=1220254620, alloc=5110872, time=47.30 bytes used=1224255416, alloc=5110872, time=47.45 bytes used=1228256652, alloc=5110872, time=47.61 bytes used=1232257400, alloc=5110872, time=47.76 bytes used=1236258468, alloc=5110872, time=47.91 bytes used=1240259168, alloc=5110872, time=48.07 bytes used=1244260064, alloc=5110872, time=48.22 bytes used=1248260760, alloc=5110872, time=48.38 bytes used=1252261480, alloc=5110872, time=48.53 bytes used=1256262204, alloc=5110872, time=48.69 bytes used=1260262892, alloc=5110872, time=48.84 bytes used=1264263744, alloc=5110872, time=49.00 bytes used=1268264572, alloc=5110872, time=49.15 bytes used=1272265232, alloc=5110872, time=49.31 bytes used=1276266364, alloc=5110872, time=49.46 bytes used=1280267236, alloc=5110872, time=49.62 bytes used=1284267948, alloc=5110872, time=49.77 bytes used=1288268784, alloc=5110872, time=49.93 bytes used=1292269612, alloc=5110872, time=50.09 bytes used=1296270408, alloc=5110872, time=50.24 bytes used=1300271320, alloc=5110872, time=50.40 bytes used=1304271976, alloc=5110872, time=50.55 bytes used=1308272808, alloc=5110872, time=50.71 bytes used=1312273712, alloc=5110872, time=50.86 bytes used=1316274380, alloc=5110872, time=51.02 bytes used=1320275160, alloc=5110872, time=51.18 bytes used=1324275980, alloc=5110872, time=51.33 bytes used=1328277368, alloc=5110872, time=51.49 bytes used=1332278168, alloc=5110872, time=51.65 bytes used=1336278944, alloc=5110872, time=51.80 bytes used=1340279704, alloc=5110872, time=51.95 bytes used=1344280428, alloc=5110872, time=52.11 bytes used=1348281120, alloc=5110872, time=52.27 bytes used=1352282116, alloc=5110872, time=52.42 bytes used=1356282892, alloc=5110872, time=52.57 bytes used=1360283708, alloc=5110872, time=52.73 bytes used=1364284408, alloc=5110872, time=52.88 bytes used=1368285164, alloc=5110872, time=53.04 bytes used=1372286056, alloc=5110872, time=53.19 bytes used=1376286796, alloc=5110872, time=53.35 bytes used=1380287516, alloc=5110872, time=53.50 bytes used=1384288280, alloc=5110872, time=53.66 bytes used=1388288956, alloc=5110872, time=53.81 bytes used=1392289736, alloc=5110872, time=53.97 bytes used=1396290500, alloc=5110872, time=54.12 bytes used=1400291168, alloc=5110872, time=54.28 bytes used=1404291920, alloc=5110872, time=54.43 bytes used=1408292604, alloc=5110872, time=54.59 bytes used=1412293800, alloc=5110872, time=54.75 bytes used=1416294516, alloc=5110872, time=54.90 bytes used=1420295260, alloc=5110872, time=55.06 bytes used=1424296048, alloc=5110872, time=55.21 bytes used=1428296988, alloc=5110872, time=55.37 bytes used=1432297816, alloc=5110872, time=55.52 bytes used=1436298528, alloc=5110872, time=55.68 bytes used=1440299380, alloc=5110872, time=55.84 bytes used=1444300192, alloc=5110872, time=55.99 bytes used=1448300840, alloc=5110872, time=56.15 bytes used=1452301616, alloc=5110872, time=56.30 bytes used=1456302436, alloc=5110872, time=56.46 TOP MAIN SOLVE Loop bytes used=1460303164, alloc=5110872, time=56.61 t[1] = 0.53 x2[1] (analytic) = 1.0007538556887570982080529143471 x2[1] (numeric) = 1.0007543669662728092922294867088 absolute error = 5.1127751571108417657236166266000e-07 relative error = 5.1089237658665169546403960391323e-05 % Correct digits = 7 h = 0.0001 x1[1] (analytic) = 2.0010594889454210393528278357407 x1[1] (numeric) = 2.0010585062920566188918108460945 absolute error = 9.8265336442046101698964624539146e-07 relative error = 4.9106654242364851477123150024894e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.597e+04 Order of pole (six term test) = 1.342e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 4.468e+27 Order of pole (six term test) = -1.023e+54 bytes used=1464303896, alloc=5110872, time=56.77 bytes used=1468304676, alloc=5110872, time=56.93 bytes used=1472305412, alloc=5110872, time=57.09 bytes used=1476306112, alloc=5110872, time=57.24 bytes used=1480307128, alloc=5110872, time=57.40 bytes used=1484307892, alloc=5110872, time=57.56 bytes used=1488308776, alloc=5110872, time=57.71 bytes used=1492309468, alloc=5110872, time=57.87 bytes used=1496310236, alloc=5110872, time=58.02 bytes used=1500310952, alloc=5110872, time=58.18 bytes used=1504311652, alloc=5110872, time=58.34 bytes used=1508312376, alloc=5110872, time=58.49 bytes used=1512313108, alloc=5110872, time=58.64 bytes used=1516314060, alloc=5110872, time=58.80 bytes used=1520314848, alloc=5110872, time=58.95 bytes used=1524315620, alloc=5110872, time=59.11 bytes used=1528316484, alloc=5110872, time=59.26 bytes used=1532317228, alloc=5110872, time=59.42 bytes used=1536318112, alloc=5110872, time=59.57 bytes used=1540318772, alloc=5110872, time=59.73 bytes used=1544319676, alloc=5110872, time=59.88 bytes used=1548320624, alloc=5110872, time=60.04 bytes used=1552321396, alloc=5110872, time=60.19 bytes used=1556322124, alloc=5110872, time=60.35 bytes used=1560323064, alloc=5110872, time=60.51 bytes used=1564323908, alloc=5110872, time=60.66 bytes used=1568325016, alloc=5110872, time=60.81 bytes used=1572325672, alloc=5110872, time=60.97 bytes used=1576326492, alloc=5110872, time=61.13 bytes used=1580327480, alloc=5110872, time=61.28 bytes used=1584328320, alloc=5110872, time=61.44 bytes used=1588329108, alloc=5110872, time=61.59 bytes used=1592330012, alloc=5110872, time=61.75 bytes used=1596330868, alloc=5110872, time=61.90 bytes used=1600331688, alloc=5110872, time=62.06 bytes used=1604332476, alloc=5110872, time=62.21 bytes used=1608333152, alloc=5110872, time=62.37 bytes used=1612334024, alloc=5110872, time=62.52 bytes used=1616334716, alloc=5110872, time=62.68 bytes used=1620335836, alloc=5110872, time=62.83 bytes used=1624336736, alloc=5110872, time=62.99 bytes used=1628337412, alloc=5110872, time=63.14 bytes used=1632338072, alloc=5110872, time=63.30 bytes used=1636338792, alloc=5110872, time=63.45 bytes used=1640339688, alloc=5110872, time=63.61 bytes used=1644340504, alloc=5110872, time=63.76 bytes used=1648341244, alloc=5110872, time=63.92 bytes used=1652341952, alloc=5110872, time=64.08 bytes used=1656342712, alloc=5110872, time=64.23 bytes used=1660343452, alloc=5110872, time=64.39 bytes used=1664344348, alloc=5110872, time=64.54 bytes used=1668345108, alloc=5110872, time=64.69 bytes used=1672345960, alloc=5110872, time=64.85 bytes used=1676346640, alloc=5110872, time=65.00 bytes used=1680347316, alloc=5110872, time=65.16 bytes used=1684348188, alloc=5110872, time=65.32 bytes used=1688348936, alloc=5110872, time=65.47 bytes used=1692350020, alloc=5110872, time=65.63 bytes used=1696350740, alloc=5110872, time=65.78 bytes used=1700351624, alloc=5110872, time=65.94 bytes used=1704352300, alloc=5110872, time=66.09 bytes used=1708353004, alloc=5110872, time=66.25 bytes used=1712353796, alloc=5110872, time=66.40 bytes used=1716354636, alloc=5110872, time=66.56 bytes used=1720355420, alloc=5110872, time=66.72 bytes used=1724356316, alloc=5110872, time=66.87 bytes used=1728357036, alloc=5110872, time=67.03 bytes used=1732357940, alloc=5110872, time=67.18 bytes used=1736358656, alloc=5110872, time=67.34 bytes used=1740359364, alloc=5110872, time=67.49 bytes used=1744360244, alloc=5110872, time=67.65 bytes used=1748360980, alloc=5110872, time=67.80 bytes used=1752361816, alloc=5110872, time=67.96 bytes used=1756362708, alloc=5110872, time=68.11 bytes used=1760363644, alloc=5110872, time=68.27 bytes used=1764364412, alloc=5110872, time=68.42 bytes used=1768365204, alloc=5110872, time=68.58 bytes used=1772365988, alloc=5110872, time=68.74 bytes used=1776366776, alloc=5110872, time=68.89 bytes used=1780367556, alloc=5110872, time=69.05 bytes used=1784368372, alloc=5110872, time=69.20 bytes used=1788369068, alloc=5110872, time=69.36 bytes used=1792369756, alloc=5110872, time=69.51 bytes used=1796370780, alloc=5110872, time=69.67 bytes used=1800371484, alloc=5110872, time=69.82 bytes used=1804372220, alloc=5110872, time=69.98 bytes used=1808373068, alloc=5110872, time=70.13 bytes used=1812373764, alloc=5110872, time=70.29 bytes used=1816375356, alloc=5110872, time=70.45 bytes used=1820376252, alloc=5110872, time=70.60 bytes used=1824377248, alloc=5110872, time=70.76 bytes used=1828378068, alloc=5110872, time=70.91 bytes used=1832378888, alloc=5110872, time=71.07 bytes used=1836379724, alloc=5110872, time=71.22 bytes used=1840380612, alloc=5110872, time=71.38 bytes used=1844381496, alloc=5110872, time=71.53 bytes used=1848382824, alloc=5110872, time=71.68 bytes used=1852383548, alloc=5110872, time=71.84 bytes used=1856384640, alloc=5110872, time=71.99 bytes used=1860385436, alloc=5110872, time=72.15 bytes used=1864386240, alloc=5110872, time=72.30 bytes used=1868386936, alloc=5110872, time=72.46 bytes used=1872388148, alloc=5110872, time=72.62 bytes used=1876389292, alloc=5110872, time=72.77 bytes used=1880389984, alloc=5110872, time=72.92 bytes used=1884390692, alloc=5110872, time=73.08 bytes used=1888391668, alloc=5110872, time=73.24 bytes used=1892392568, alloc=5110872, time=73.39 bytes used=1896393296, alloc=5110872, time=73.54 bytes used=1900394076, alloc=5110872, time=73.70 bytes used=1904395080, alloc=5110872, time=73.85 bytes used=1908395744, alloc=5110872, time=74.01 bytes used=1912396476, alloc=5110872, time=74.17 bytes used=1916397144, alloc=5110872, time=74.32 bytes used=1920397904, alloc=5110872, time=74.47 bytes used=1924398724, alloc=5110872, time=74.63 bytes used=1928399400, alloc=5110872, time=74.79 TOP MAIN SOLVE Loop bytes used=1932400084, alloc=5110872, time=74.94 t[1] = 0.54 x2[1] (analytic) = 1.0007637603859253016627203164665 x2[1] (numeric) = 1.0007646814386052129465369345331 absolute error = 9.2105267991128381661806666202041e-07 relative error = 9.2034975322857170654153176435346e-05 % Correct digits = 7 h = 0.0001 x1[1] (analytic) = 2.0010489468542731813969777772086 x1[1] (numeric) = 2.0010471998130530135802422561648 absolute error = 1.7470412201678167355210437628634e-06 relative error = 8.7306271189129757302527869511055e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.605e+04 Order of pole (six term test) = 1.356e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 5.080e+27 Order of pole (six term test) = -2.778e+52 bytes used=1936400912, alloc=5110872, time=75.10 bytes used=1940401700, alloc=5110872, time=75.25 bytes used=1944402392, alloc=5110872, time=75.41 bytes used=1948403192, alloc=5110872, time=75.57 bytes used=1952403872, alloc=5110872, time=75.72 bytes used=1956404644, alloc=5110872, time=75.88 bytes used=1960405392, alloc=5110872, time=76.03 bytes used=1964406112, alloc=5110872, time=76.19 bytes used=1968406780, alloc=5110872, time=76.35 bytes used=1972407440, alloc=5110872, time=76.50 bytes used=1976408308, alloc=5110872, time=76.65 bytes used=1980409008, alloc=5110872, time=76.81 bytes used=1984409724, alloc=5110872, time=76.97 bytes used=1988410632, alloc=5110872, time=77.12 bytes used=1992411420, alloc=5110872, time=77.28 bytes used=1996412356, alloc=5110872, time=77.43 bytes used=2000413608, alloc=5110872, time=77.59 bytes used=2004414416, alloc=5110872, time=77.74 bytes used=2008415220, alloc=5110872, time=77.90 bytes used=2012416080, alloc=5110872, time=78.06 bytes used=2016417096, alloc=5110872, time=78.21 bytes used=2020417804, alloc=5110872, time=78.37 bytes used=2024418580, alloc=5110872, time=78.52 bytes used=2028419260, alloc=5110872, time=78.68 bytes used=2032420280, alloc=5110872, time=78.83 bytes used=2036420988, alloc=5110872, time=78.99 bytes used=2040421720, alloc=5110872, time=79.14 bytes used=2044422456, alloc=5110872, time=79.29 bytes used=2048423396, alloc=5110872, time=79.45 bytes used=2052424332, alloc=5110872, time=79.60 bytes used=2056425068, alloc=5110872, time=79.76 bytes used=2060425876, alloc=5110872, time=79.91 bytes used=2064426744, alloc=5110872, time=80.07 bytes used=2068427736, alloc=5110872, time=80.23 bytes used=2072428716, alloc=5110872, time=80.38 bytes used=2076429440, alloc=5110872, time=80.54 bytes used=2080430168, alloc=5110872, time=80.69 bytes used=2084431060, alloc=5110872, time=80.85 bytes used=2088431740, alloc=5110872, time=81.01 bytes used=2092432584, alloc=5110872, time=81.16 bytes used=2096433292, alloc=5110872, time=81.32 bytes used=2100434176, alloc=5110872, time=81.47 bytes used=2104435456, alloc=5110872, time=81.63 bytes used=2108436184, alloc=5110872, time=81.78 bytes used=2112436844, alloc=5110872, time=81.94 bytes used=2116437552, alloc=5110872, time=82.09 bytes used=2120438268, alloc=5110872, time=82.25 bytes used=2124439048, alloc=5110872, time=82.40 bytes used=2128440036, alloc=5110872, time=82.56 bytes used=2132440720, alloc=5110872, time=82.71 bytes used=2136441788, alloc=5110872, time=82.87 bytes used=2140442544, alloc=5110872, time=83.02 bytes used=2144443496, alloc=5110872, time=83.18 bytes used=2148444324, alloc=5110872, time=83.33 bytes used=2152444980, alloc=5110872, time=83.49 bytes used=2156445688, alloc=5110872, time=83.64 bytes used=2160446396, alloc=5110872, time=83.80 bytes used=2164447292, alloc=5110872, time=83.95 bytes used=2168448308, alloc=5110872, time=84.11 bytes used=2172449256, alloc=5110872, time=84.27 bytes used=2176450796, alloc=5110872, time=84.42 bytes used=2180451516, alloc=5110872, time=84.58 bytes used=2184452196, alloc=5110872, time=84.73 bytes used=2188452932, alloc=5110872, time=84.88 bytes used=2192453980, alloc=5110872, time=85.04 bytes used=2196454984, alloc=5110872, time=85.19 bytes used=2200455932, alloc=5110872, time=85.35 bytes used=2204456728, alloc=5110872, time=85.50 bytes used=2208457540, alloc=5110872, time=85.66 bytes used=2212458344, alloc=5110872, time=85.81 bytes used=2216459024, alloc=5110872, time=85.97 bytes used=2220459740, alloc=5110872, time=86.12 bytes used=2224460568, alloc=5110872, time=86.28 bytes used=2228461332, alloc=5110872, time=86.44 bytes used=2232462120, alloc=5110872, time=86.59 bytes used=2236463264, alloc=5110872, time=86.74 bytes used=2240464104, alloc=5110872, time=86.90 bytes used=2244464784, alloc=5110872, time=87.05 bytes used=2248465744, alloc=5110872, time=87.21 bytes used=2252466400, alloc=5110872, time=87.36 bytes used=2256467216, alloc=5110872, time=87.52 bytes used=2260468116, alloc=5110872, time=87.67 bytes used=2264468892, alloc=5110872, time=87.83 bytes used=2268469732, alloc=5110872, time=87.98 bytes used=2272470584, alloc=5110872, time=88.14 bytes used=2276471332, alloc=5110872, time=88.29 bytes used=2280472076, alloc=5110872, time=88.45 bytes used=2284472944, alloc=5110872, time=88.61 bytes used=2288473756, alloc=5110872, time=88.76 bytes used=2292474464, alloc=5110872, time=88.91 bytes used=2296475388, alloc=5110872, time=89.07 bytes used=2300476168, alloc=5110872, time=89.22 bytes used=2304476932, alloc=5110872, time=89.38 bytes used=2308477656, alloc=5110872, time=89.53 bytes used=2312478484, alloc=5110872, time=89.69 bytes used=2316479340, alloc=5110872, time=89.84 bytes used=2320480052, alloc=5110872, time=90.00 bytes used=2324480988, alloc=5110872, time=90.15 bytes used=2328481776, alloc=5110872, time=90.31 bytes used=2332482484, alloc=5110872, time=90.47 bytes used=2336483212, alloc=5110872, time=90.62 bytes used=2340483996, alloc=5110872, time=90.78 bytes used=2344484732, alloc=5110872, time=90.93 bytes used=2348485536, alloc=5110872, time=91.09 bytes used=2352486332, alloc=5110872, time=91.24 bytes used=2356487252, alloc=5110872, time=91.40 bytes used=2360488268, alloc=5110872, time=91.55 bytes used=2364489072, alloc=5110872, time=91.71 bytes used=2368490292, alloc=5110872, time=91.86 bytes used=2372490988, alloc=5110872, time=92.02 bytes used=2376491668, alloc=5110872, time=92.17 bytes used=2380492484, alloc=5110872, time=92.33 bytes used=2384493320, alloc=5110872, time=92.49 bytes used=2388494228, alloc=5110872, time=92.64 bytes used=2392495252, alloc=5110872, time=92.80 bytes used=2396496004, alloc=5110872, time=92.95 bytes used=2400496900, alloc=5110872, time=93.11 TOP MAIN SOLVE Loop bytes used=2404497664, alloc=5110872, time=93.27 bytes used=2408498740, alloc=5110872, time=93.43 t[1] = 0.55 x2[1] (analytic) = 1.0007739181479034326310074925802 x2[1] (numeric) = 1.0007753764381360060543037329804 absolute error = 1.4582902325734232962404002540424e-06 relative error = 0.00014571625080639880938589051826771 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.0010385096586848760515748659368 x1[1] (numeric) = 2.001035779702046288397314940137 absolute error = 2.7299566385876542599257997805830e-06 relative error = 0.00013642699155516503354307852901987 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.613e+04 Order of pole (six term test) = 1.369e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 4.594e+27 Order of pole (six term test) = 1.677e+54 bytes used=2412499644, alloc=5110872, time=93.58 bytes used=2416500320, alloc=5110872, time=93.74 bytes used=2420501128, alloc=5110872, time=93.89 bytes used=2424501900, alloc=5110872, time=94.05 bytes used=2428502632, alloc=5110872, time=94.20 bytes used=2432503420, alloc=5110872, time=94.36 bytes used=2436504148, alloc=5110872, time=94.51 bytes used=2440504884, alloc=5110872, time=94.67 bytes used=2444505776, alloc=5110872, time=94.82 bytes used=2448506588, alloc=5110872, time=94.98 bytes used=2452507252, alloc=5110872, time=95.13 bytes used=2456508012, alloc=5110872, time=95.28 bytes used=2460508796, alloc=5110872, time=95.44 bytes used=2464509424, alloc=5110872, time=95.59 bytes used=2468510220, alloc=5110872, time=95.75 bytes used=2472511148, alloc=5110872, time=95.91 bytes used=2476511872, alloc=5110872, time=96.06 bytes used=2480513028, alloc=5110872, time=96.22 bytes used=2484514364, alloc=5110872, time=96.37 bytes used=2488515500, alloc=5110872, time=96.53 bytes used=2492516264, alloc=5110872, time=96.68 bytes used=2496517152, alloc=5110872, time=96.84 bytes used=2500517916, alloc=5110872, time=96.99 bytes used=2504518856, alloc=5110872, time=97.15 bytes used=2508519724, alloc=5110872, time=97.30 bytes used=2512520392, alloc=5110872, time=97.46 bytes used=2516521184, alloc=5110872, time=97.61 bytes used=2520522136, alloc=5110872, time=97.77 bytes used=2524522824, alloc=5110872, time=97.92 bytes used=2528523500, alloc=5110872, time=98.08 bytes used=2532524696, alloc=5110872, time=98.23 bytes used=2536525472, alloc=5110872, time=98.39 bytes used=2540526852, alloc=5110872, time=98.55 bytes used=2544527752, alloc=5110872, time=98.70 bytes used=2548528488, alloc=5110872, time=98.86 bytes used=2552529212, alloc=5110872, time=99.01 bytes used=2556529940, alloc=5110872, time=99.17 bytes used=2560530640, alloc=5110872, time=99.32 bytes used=2564531316, alloc=5110872, time=99.48 bytes used=2568531980, alloc=5110872, time=99.63 bytes used=2572532676, alloc=5110872, time=99.79 bytes used=2576533448, alloc=5110872, time=99.95 bytes used=2580534128, alloc=5110872, time=100.10 bytes used=2584534804, alloc=5110872, time=100.26 bytes used=2588535484, alloc=5110872, time=100.41 bytes used=2592536180, alloc=5110872, time=100.57 bytes used=2596536904, alloc=5110872, time=100.72 bytes used=2600537596, alloc=5110872, time=100.88 bytes used=2604538260, alloc=5110872, time=101.03 bytes used=2608539188, alloc=5110872, time=101.18 bytes used=2612539944, alloc=5110872, time=101.34 bytes used=2616540664, alloc=5110872, time=101.49 bytes used=2620541448, alloc=5110872, time=101.65 bytes used=2624542308, alloc=5110872, time=101.80 bytes used=2628543168, alloc=5110872, time=101.96 bytes used=2632543976, alloc=5110872, time=102.11 bytes used=2636544736, alloc=5110872, time=102.27 bytes used=2640545444, alloc=5110872, time=102.42 bytes used=2644547032, alloc=5110872, time=102.58 bytes used=2648547736, alloc=5110872, time=102.73 bytes used=2652548572, alloc=5110872, time=102.89 bytes used=2656549500, alloc=5110872, time=103.05 bytes used=2660550716, alloc=5110872, time=103.20 bytes used=2664551552, alloc=5110872, time=103.36 bytes used=2668552284, alloc=5110872, time=103.52 bytes used=2672553036, alloc=5110872, time=103.67 bytes used=2676554248, alloc=5110872, time=103.83 bytes used=2680555288, alloc=5110872, time=103.98 bytes used=2684556008, alloc=5110872, time=104.14 bytes used=2688556692, alloc=5110872, time=104.30 bytes used=2692557404, alloc=5110872, time=104.46 bytes used=2696558228, alloc=5110872, time=104.61 bytes used=2700558916, alloc=5110872, time=104.77 bytes used=2704559832, alloc=5110872, time=104.92 bytes used=2708560520, alloc=5110872, time=105.08 bytes used=2712561268, alloc=5110872, time=105.23 bytes used=2716562368, alloc=5110872, time=105.38 bytes used=2720563068, alloc=5110872, time=105.54 bytes used=2724564020, alloc=5110872, time=105.70 bytes used=2728564944, alloc=5110872, time=105.85 bytes used=2732565656, alloc=5110872, time=106.00 bytes used=2736566368, alloc=5110872, time=106.16 bytes used=2740567288, alloc=5110872, time=106.32 bytes used=2744568000, alloc=5110872, time=106.47 bytes used=2748568688, alloc=5110872, time=106.63 bytes used=2752569512, alloc=5110872, time=106.78 bytes used=2756570300, alloc=5110872, time=106.94 bytes used=2760571032, alloc=5110872, time=107.10 bytes used=2764571692, alloc=5110872, time=107.25 bytes used=2768572580, alloc=5110872, time=107.41 bytes used=2772573548, alloc=5110872, time=107.57 bytes used=2776574252, alloc=5110872, time=107.72 bytes used=2780575092, alloc=5110872, time=107.88 bytes used=2784575932, alloc=5110872, time=108.03 bytes used=2788576676, alloc=5110872, time=108.19 bytes used=2792577556, alloc=5110872, time=108.34 bytes used=2796578344, alloc=5110872, time=108.50 bytes used=2800579012, alloc=5110872, time=108.65 bytes used=2804579712, alloc=5110872, time=108.81 bytes used=2808580496, alloc=5110872, time=108.96 bytes used=2812581256, alloc=5110872, time=109.12 bytes used=2816582268, alloc=5110872, time=109.28 bytes used=2820583132, alloc=5110872, time=109.43 bytes used=2824583876, alloc=5110872, time=109.58 bytes used=2828584612, alloc=5110872, time=109.74 bytes used=2832585388, alloc=5110872, time=109.89 bytes used=2836586076, alloc=5110872, time=110.05 bytes used=2840587424, alloc=5110872, time=110.21 bytes used=2844588100, alloc=5110872, time=110.36 bytes used=2848588764, alloc=5110872, time=110.52 bytes used=2852589420, alloc=5110872, time=110.68 bytes used=2856590092, alloc=5110872, time=110.83 bytes used=2860591040, alloc=5110872, time=110.99 bytes used=2864592020, alloc=5110872, time=111.14 bytes used=2868592704, alloc=5110872, time=111.30 bytes used=2872593704, alloc=5110872, time=111.45 bytes used=2876594428, alloc=5110872, time=111.61 TOP MAIN SOLVE Loop bytes used=2880595168, alloc=5110872, time=111.76 t[1] = 0.56 x2[1] (analytic) = 1.0007843335598132448746773988584 x2[1] (numeric) = 1.0007864613822716859333729492599 absolute error = 2.1278224584410586955504014534794e-06 relative error = 0.00021261548438436726140398743334008 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.0010281763149278667941020454403 x1[1] (numeric) = 2.001024244817015825879615747072 absolute error = 3.9314979120409144862983683441894e-06 relative error = 0.00019647389070158517615518525991681 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.621e+04 Order of pole (six term test) = 1.383e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 5.694e+27 Order of pole (six term test) = 4.276e+53 bytes used=2884595964, alloc=5110872, time=111.92 bytes used=2888596744, alloc=5110872, time=112.07 bytes used=2892597464, alloc=5110872, time=112.23 bytes used=2896598224, alloc=5110872, time=112.38 bytes used=2900598900, alloc=5110872, time=112.54 bytes used=2904599884, alloc=5110872, time=112.69 bytes used=2908600756, alloc=5110872, time=112.85 bytes used=2912601636, alloc=5110872, time=113.00 bytes used=2916602804, alloc=5110872, time=113.16 bytes used=2920603576, alloc=5110872, time=113.31 bytes used=2924604400, alloc=5110872, time=113.47 bytes used=2928605084, alloc=5110872, time=113.62 bytes used=2932605772, alloc=5110872, time=113.78 bytes used=2936606792, alloc=5110872, time=113.93 bytes used=2940608012, alloc=5110872, time=114.09 bytes used=2944608776, alloc=5110872, time=114.24 bytes used=2948609492, alloc=5110872, time=114.40 bytes used=2952610264, alloc=5110872, time=114.55 bytes used=2956610964, alloc=5110872, time=114.71 bytes used=2960612052, alloc=5110872, time=114.87 bytes used=2964612740, alloc=5110872, time=115.02 bytes used=2968613468, alloc=5110872, time=115.18 bytes used=2972614152, alloc=5110872, time=115.33 bytes used=2976614928, alloc=5110872, time=115.49 bytes used=2980615676, alloc=5110872, time=115.65 bytes used=2984616356, alloc=5110872, time=115.80 bytes used=2988617052, alloc=5110872, time=115.96 bytes used=2992617848, alloc=5110872, time=116.11 bytes used=2996618648, alloc=5110872, time=116.27 bytes used=3000619320, alloc=5110872, time=116.42 bytes used=3004620084, alloc=5110872, time=116.58 bytes used=3008620800, alloc=5110872, time=116.73 bytes used=3012621808, alloc=5110872, time=116.89 bytes used=3016622492, alloc=5110872, time=117.04 bytes used=3020623248, alloc=5110872, time=117.20 bytes used=3024623920, alloc=5110872, time=117.35 bytes used=3028624780, alloc=5110872, time=117.51 bytes used=3032625644, alloc=5110872, time=117.67 bytes used=3036626496, alloc=5110872, time=117.82 bytes used=3040627180, alloc=5110872, time=117.98 bytes used=3044627920, alloc=5110872, time=118.13 bytes used=3048628600, alloc=5110872, time=118.29 bytes used=3052629396, alloc=5110872, time=118.44 bytes used=3056630092, alloc=5110872, time=118.60 bytes used=3060630780, alloc=5110872, time=118.75 bytes used=3064631568, alloc=5110872, time=118.91 bytes used=3068632328, alloc=5110872, time=119.06 bytes used=3072633012, alloc=5110872, time=119.22 bytes used=3076633916, alloc=5110872, time=119.37 bytes used=3080634720, alloc=5110872, time=119.52 bytes used=3084635408, alloc=5110872, time=119.68 bytes used=3088636100, alloc=5110872, time=119.84 bytes used=3092636972, alloc=5110872, time=119.99 bytes used=3096637904, alloc=5110872, time=120.15 bytes used=3100638736, alloc=5110872, time=120.31 bytes used=3104639444, alloc=5110872, time=120.46 bytes used=3108640128, alloc=5110872, time=120.61 bytes used=3112640860, alloc=5110872, time=120.77 bytes used=3116641528, alloc=5110872, time=120.92 bytes used=3120642276, alloc=5110872, time=121.07 bytes used=3124643164, alloc=5110872, time=121.23 bytes used=3128644072, alloc=5110872, time=121.39 bytes used=3132644748, alloc=5110872, time=121.54 bytes used=3136645672, alloc=5110872, time=121.70 bytes used=3140646648, alloc=5110872, time=121.85 bytes used=3144647860, alloc=5110872, time=122.01 bytes used=3148648596, alloc=5110872, time=122.16 bytes used=3152649340, alloc=5110872, time=122.32 bytes used=3156650124, alloc=5110872, time=122.47 bytes used=3160650968, alloc=5110872, time=122.63 bytes used=3164651680, alloc=5110872, time=122.79 bytes used=3168652712, alloc=5110872, time=122.94 bytes used=3172653372, alloc=5110872, time=123.10 bytes used=3176654220, alloc=5110872, time=123.25 bytes used=3180654936, alloc=5110872, time=123.41 bytes used=3184655620, alloc=5110872, time=123.56 bytes used=3188656312, alloc=5110872, time=123.72 bytes used=3192657256, alloc=5110872, time=123.88 bytes used=3196658048, alloc=5110872, time=124.03 bytes used=3200658764, alloc=5110872, time=124.19 bytes used=3204659712, alloc=5110872, time=124.35 bytes used=3208660556, alloc=5110872, time=124.50 bytes used=3212661440, alloc=5110872, time=124.66 bytes used=3216662136, alloc=5110872, time=124.81 bytes used=3220662812, alloc=5110872, time=124.97 bytes used=3224663468, alloc=5110872, time=125.12 bytes used=3228664324, alloc=5110872, time=125.27 bytes used=3232665012, alloc=5110872, time=125.43 bytes used=3236665872, alloc=5110872, time=125.58 bytes used=3240666652, alloc=5110872, time=125.74 bytes used=3244667328, alloc=5110872, time=125.89 bytes used=3248668252, alloc=5110872, time=126.05 bytes used=3252669072, alloc=5110872, time=126.20 bytes used=3256670016, alloc=5110872, time=126.36 bytes used=3260670808, alloc=5110872, time=126.51 bytes used=3264671504, alloc=5110872, time=126.67 bytes used=3268672428, alloc=5110872, time=126.83 bytes used=3272673132, alloc=5110872, time=126.98 bytes used=3276673920, alloc=5110872, time=127.13 bytes used=3280675260, alloc=5110872, time=127.29 bytes used=3284675916, alloc=5110872, time=127.44 bytes used=3288676824, alloc=5110872, time=127.59 bytes used=3292677552, alloc=5110872, time=127.75 bytes used=3296678424, alloc=5110872, time=127.90 bytes used=3300679096, alloc=5110872, time=128.06 bytes used=3304680576, alloc=5110872, time=128.22 bytes used=3308681476, alloc=5110872, time=128.37 bytes used=3312682392, alloc=5110872, time=128.53 bytes used=3316683324, alloc=5110872, time=128.68 bytes used=3320684188, alloc=5110872, time=128.84 bytes used=3324685708, alloc=5110872, time=128.99 bytes used=3328686652, alloc=5110872, time=129.15 bytes used=3332687368, alloc=5110872, time=129.30 bytes used=3336688636, alloc=5110872, time=129.46 bytes used=3340689624, alloc=5110872, time=129.61 bytes used=3344690928, alloc=5110872, time=129.77 bytes used=3348691796, alloc=5110872, time=129.92 TOP MAIN SOLVE Loop bytes used=3352692576, alloc=5110872, time=130.08 t[1] = 0.57 x2[1] (analytic) = 1.0007950113046470922804150240495 x2[1] (numeric) = 1.0007979458960522539118927636819 absolute error = 2.9345914051616314777396324331495e-06 relative error = 0.00029322602251344825362472727174762 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.0010179457896591667751322768074 x1[1] (numeric) = 2.0010125940044635105446594504287 absolute error = 5.3517851956562304728263787465749e-06 relative error = 0.00026745313338728015696063131242026 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.629e+04 Order of pole (six term test) = 1.397e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 3.898e+27 Order of pole (six term test) = -2.603e+54 bytes used=3356693260, alloc=5110872, time=130.23 bytes used=3360693984, alloc=5110872, time=130.39 bytes used=3364694776, alloc=5110872, time=130.54 bytes used=3368695548, alloc=5110872, time=130.69 bytes used=3372696348, alloc=5110872, time=130.85 bytes used=3376697020, alloc=5110872, time=131.00 bytes used=3380698152, alloc=5110872, time=131.16 bytes used=3384698908, alloc=5110872, time=131.31 bytes used=3388700032, alloc=5110872, time=131.47 bytes used=3392700884, alloc=5110872, time=131.62 bytes used=3396701676, alloc=5110872, time=131.78 bytes used=3400702404, alloc=5110872, time=131.93 bytes used=3404703092, alloc=5110872, time=132.08 bytes used=3408704264, alloc=5110872, time=132.24 bytes used=3412705028, alloc=5110872, time=132.40 bytes used=3416705760, alloc=5110872, time=132.55 bytes used=3420706424, alloc=5110872, time=132.71 bytes used=3424707320, alloc=5110872, time=132.87 bytes used=3428707988, alloc=5110872, time=133.02 bytes used=3432708752, alloc=5110872, time=133.17 bytes used=3436709540, alloc=5110872, time=133.33 bytes used=3440710308, alloc=5110872, time=133.48 bytes used=3444711248, alloc=5110872, time=133.64 bytes used=3448712312, alloc=5110872, time=133.79 bytes used=3452712968, alloc=5110872, time=133.95 bytes used=3456714376, alloc=5110872, time=134.11 bytes used=3460715424, alloc=5110872, time=134.27 bytes used=3464716088, alloc=5110872, time=134.42 bytes used=3468717408, alloc=5110872, time=134.58 bytes used=3472718296, alloc=5110872, time=134.73 bytes used=3476719252, alloc=5110872, time=134.88 bytes used=3480720088, alloc=5110872, time=135.04 bytes used=3484720924, alloc=5110872, time=135.19 bytes used=3488722244, alloc=5110872, time=135.34 bytes used=3492722984, alloc=5110872, time=135.50 bytes used=3496723764, alloc=5110872, time=135.65 bytes used=3500724884, alloc=5110872, time=135.81 bytes used=3504725608, alloc=5110872, time=135.96 bytes used=3508726560, alloc=5110872, time=136.12 bytes used=3512727288, alloc=5110872, time=136.28 bytes used=3516728032, alloc=5110872, time=136.43 bytes used=3520728820, alloc=5110872, time=136.58 bytes used=3524729976, alloc=5110872, time=136.74 bytes used=3528730808, alloc=5110872, time=136.89 bytes used=3532731616, alloc=5110872, time=137.05 bytes used=3536732320, alloc=5110872, time=137.20 bytes used=3540733072, alloc=5110872, time=137.36 bytes used=3544733812, alloc=5110872, time=137.51 bytes used=3548734640, alloc=5110872, time=137.66 bytes used=3552735680, alloc=5110872, time=137.82 bytes used=3556736584, alloc=5110872, time=137.97 bytes used=3560737304, alloc=5110872, time=138.13 bytes used=3564737984, alloc=5110872, time=138.28 bytes used=3568738848, alloc=5110872, time=138.44 bytes used=3572739564, alloc=5110872, time=138.59 bytes used=3576740344, alloc=5110872, time=138.75 bytes used=3580741032, alloc=5110872, time=138.90 bytes used=3584741696, alloc=5110872, time=139.06 bytes used=3588742380, alloc=5110872, time=139.21 bytes used=3592743172, alloc=5110872, time=139.37 bytes used=3596743864, alloc=5110872, time=139.52 bytes used=3600744616, alloc=5110872, time=139.68 bytes used=3604745396, alloc=5110872, time=139.84 bytes used=3608746124, alloc=5110872, time=139.99 bytes used=3612746856, alloc=5110872, time=140.15 bytes used=3616747988, alloc=5110872, time=140.30 bytes used=3620748728, alloc=5110872, time=140.46 bytes used=3624749564, alloc=5110872, time=140.61 bytes used=3628750332, alloc=5110872, time=140.77 bytes used=3632751036, alloc=5110872, time=140.92 bytes used=3636751788, alloc=5110872, time=141.08 bytes used=3640752684, alloc=5110872, time=141.23 bytes used=3644753388, alloc=5110872, time=141.39 bytes used=3648754060, alloc=5110872, time=141.54 bytes used=3652754976, alloc=5110872, time=141.70 bytes used=3656755844, alloc=5110872, time=141.85 bytes used=3660756600, alloc=5110872, time=142.01 bytes used=3664757704, alloc=5110872, time=142.16 bytes used=3668758692, alloc=5110872, time=142.32 bytes used=3672759460, alloc=5110872, time=142.48 bytes used=3676760296, alloc=5110872, time=142.63 bytes used=3680761004, alloc=5110872, time=142.79 bytes used=3684761796, alloc=5110872, time=142.94 bytes used=3688762464, alloc=5110872, time=143.10 bytes used=3692763268, alloc=5110872, time=143.25 bytes used=3696763928, alloc=5110872, time=143.40 bytes used=3700764588, alloc=5110872, time=143.56 bytes used=3704766440, alloc=5110872, time=143.72 bytes used=3708767268, alloc=5110872, time=143.87 bytes used=3712768156, alloc=5110872, time=144.03 bytes used=3716768876, alloc=5110872, time=144.18 bytes used=3720769692, alloc=5110872, time=144.34 bytes used=3724770720, alloc=5110872, time=144.49 bytes used=3728771856, alloc=5110872, time=144.65 bytes used=3732772700, alloc=5110872, time=144.80 bytes used=3736773484, alloc=5110872, time=144.96 bytes used=3740774168, alloc=5110872, time=145.11 bytes used=3744774932, alloc=5110872, time=145.27 bytes used=3748775804, alloc=5110872, time=145.42 bytes used=3752776672, alloc=5110872, time=145.58 bytes used=3756777836, alloc=5110872, time=145.74 bytes used=3760778764, alloc=5110872, time=145.89 bytes used=3764779560, alloc=5110872, time=146.05 bytes used=3768780260, alloc=5110872, time=146.20 bytes used=3772781492, alloc=5110872, time=146.36 bytes used=3776782168, alloc=5110872, time=146.51 bytes used=3780782984, alloc=5110872, time=146.67 bytes used=3784783728, alloc=5110872, time=146.83 bytes used=3788784472, alloc=5110872, time=146.98 bytes used=3792785136, alloc=5110872, time=147.14 bytes used=3796785984, alloc=5110872, time=147.30 bytes used=3800786860, alloc=5110872, time=147.45 bytes used=3804787592, alloc=5110872, time=147.60 bytes used=3808788260, alloc=5110872, time=147.76 bytes used=3812789000, alloc=5110872, time=147.92 bytes used=3816789716, alloc=5110872, time=148.07 bytes used=3820790940, alloc=5110872, time=148.22 TOP MAIN SOLVE Loop bytes used=3824791864, alloc=5110872, time=148.38 t[1] = 0.58 x2[1] (analytic) = 1.0008059561651928575442831532282 x2[1] (numeric) = 1.0008098398165204554447851228428 absolute error = 3.8836513275979005019696146127510e-06 relative error = 0.0003880523795520722987602762480083 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.0010078170598177236585215698858 x1[1] (numeric) = 2.0010008260992983781180888658058 absolute error = 6.9909605193455404327040800148479e-06 relative error = 0.00034937197444924094819204359349945 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.637e+04 Order of pole (six term test) = 1.411e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=3828793068, alloc=5110872, time=148.53 bytes used=3832793888, alloc=5110872, time=148.69 bytes used=3836794640, alloc=5110872, time=148.85 bytes used=3840795316, alloc=5110872, time=149.00 bytes used=3844796024, alloc=5110872, time=149.16 bytes used=3848796728, alloc=5110872, time=149.31 bytes used=3852797516, alloc=5110872, time=149.47 bytes used=3856798300, alloc=5110872, time=149.62 bytes used=3860799112, alloc=5110872, time=149.78 bytes used=3864799828, alloc=5110872, time=149.93 bytes used=3868800796, alloc=5110872, time=150.09 bytes used=3872801560, alloc=5110872, time=150.24 bytes used=3876802324, alloc=5110872, time=150.40 bytes used=3880803200, alloc=5110872, time=150.55 bytes used=3884803928, alloc=5110872, time=150.71 bytes used=3888804972, alloc=5110872, time=150.87 bytes used=3892806176, alloc=5110872, time=151.02 bytes used=3896806936, alloc=5110872, time=151.18 bytes used=3900808252, alloc=5110872, time=151.33 bytes used=3904809036, alloc=5110872, time=151.49 bytes used=3908809828, alloc=5110872, time=151.64 bytes used=3912810524, alloc=5110872, time=151.79 bytes used=3916811200, alloc=5110872, time=151.95 bytes used=3920812288, alloc=5110872, time=152.11 bytes used=3924813260, alloc=5110872, time=152.26 bytes used=3928814072, alloc=5110872, time=152.42 bytes used=3932814836, alloc=5110872, time=152.57 bytes used=3936815568, alloc=5110872, time=152.73 bytes used=3940816868, alloc=5110872, time=152.89 bytes used=3944817644, alloc=5110872, time=153.04 bytes used=3948818372, alloc=5110872, time=153.20 bytes used=3952819092, alloc=5110872, time=153.35 bytes used=3956819964, alloc=5110872, time=153.50 bytes used=3960821336, alloc=5110872, time=153.66 bytes used=3964822372, alloc=5110872, time=153.82 bytes used=3968823336, alloc=5110872, time=153.97 bytes used=3972824084, alloc=5110872, time=154.13 bytes used=3976824908, alloc=5110872, time=154.28 bytes used=3980825688, alloc=5110872, time=154.44 bytes used=3984826476, alloc=5110872, time=154.59 bytes used=3988827220, alloc=5110872, time=154.75 bytes used=3992828220, alloc=5110872, time=154.90 bytes used=3996828960, alloc=5110872, time=155.06 bytes used=4000830092, alloc=5110872, time=155.21 bytes used=4004831128, alloc=5110872, time=155.37 bytes used=4008831952, alloc=5110872, time=155.53 bytes used=4012832916, alloc=5110872, time=155.68 bytes used=4016833640, alloc=5110872, time=155.84 bytes used=4020834464, alloc=5110872, time=155.99 bytes used=4024835300, alloc=5110872, time=156.15 bytes used=4028836032, alloc=5110872, time=156.30 bytes used=4032836776, alloc=5110872, time=156.46 bytes used=4036837520, alloc=5110872, time=156.61 bytes used=4040838800, alloc=5110872, time=156.77 bytes used=4044839508, alloc=5110872, time=156.93 bytes used=4048840280, alloc=5110872, time=157.08 bytes used=4052841000, alloc=5110872, time=157.23 bytes used=4056842268, alloc=5110872, time=157.39 bytes used=4060842960, alloc=5110872, time=157.54 bytes used=4064843724, alloc=5110872, time=157.70 bytes used=4068844492, alloc=5110872, time=157.86 bytes used=4072845248, alloc=5110872, time=158.01 bytes used=4076845908, alloc=5110872, time=158.16 bytes used=4080846624, alloc=5110872, time=158.38 bytes used=4084847292, alloc=5110872, time=158.75 bytes used=4088848032, alloc=5110872, time=159.12 bytes used=4092849376, alloc=5110872, time=159.49 bytes used=4096850360, alloc=5110872, time=159.86 bytes used=4100851136, alloc=5110872, time=160.23 bytes used=4104851916, alloc=5110872, time=160.60 bytes used=4108852560, alloc=5110872, time=160.97 bytes used=4112853308, alloc=5110872, time=161.33 bytes used=4116853968, alloc=5110872, time=161.70 bytes used=4120854668, alloc=5110872, time=162.07 bytes used=4124855784, alloc=5110872, time=162.44 bytes used=4128856536, alloc=5110872, time=162.81 bytes used=4132857364, alloc=5110872, time=163.17 bytes used=4136858432, alloc=5110872, time=163.54 bytes used=4140859184, alloc=5110872, time=163.91 bytes used=4144859964, alloc=5110872, time=164.28 bytes used=4148860764, alloc=5110872, time=164.65 bytes used=4152861556, alloc=5110872, time=165.02 bytes used=4156862324, alloc=5110872, time=165.38 bytes used=4160863028, alloc=5110872, time=165.75 bytes used=4164863768, alloc=5110872, time=166.12 bytes used=4168864616, alloc=5110872, time=166.49 bytes used=4172865464, alloc=5110872, time=166.86 bytes used=4176866480, alloc=5110872, time=167.22 bytes used=4180867220, alloc=5110872, time=167.59 bytes used=4184868048, alloc=5110872, time=167.96 bytes used=4188868772, alloc=5110872, time=168.33 bytes used=4192869700, alloc=5110872, time=168.70 bytes used=4196870396, alloc=5110872, time=169.07 bytes used=4200871624, alloc=5110872, time=169.44 bytes used=4204872868, alloc=5110872, time=169.82 bytes used=4208873660, alloc=5110872, time=170.19 bytes used=4212875120, alloc=5110872, time=170.56 bytes used=4216876280, alloc=5110872, time=170.93 bytes used=4220877252, alloc=5110872, time=171.30 bytes used=4224878000, alloc=5110872, time=171.67 bytes used=4228878728, alloc=5110872, time=172.04 bytes used=4232879528, alloc=5110872, time=172.41 bytes used=4236880364, alloc=5110872, time=172.77 bytes used=4240881420, alloc=5110872, time=173.14 bytes used=4244882284, alloc=5110872, time=173.51 bytes used=4248882960, alloc=5110872, time=173.88 bytes used=4252883652, alloc=5110872, time=174.25 bytes used=4256884360, alloc=5110872, time=174.62 bytes used=4260885104, alloc=5110872, time=174.99 bytes used=4264885844, alloc=5110872, time=175.36 bytes used=4268886516, alloc=5110872, time=175.74 bytes used=4272887248, alloc=5110872, time=176.11 bytes used=4276888144, alloc=5110872, time=176.48 bytes used=4280889064, alloc=5110872, time=176.85 bytes used=4284889764, alloc=5110872, time=177.22 bytes used=4288890572, alloc=5110872, time=177.58 bytes used=4292891800, alloc=5110872, time=177.95 TOP MAIN SOLVE Loop bytes used=4296892852, alloc=5110872, time=178.32 bytes used=4300893576, alloc=5110872, time=178.69 t[1] = 0.59 x2[1] (analytic) = 1.0008171730259982862801800140618 x2[1] (numeric) = 1.0008221531971810411539313473588 absolute error = 4.9801711827548737513332970283374e-06 relative error = 0.00049761048441017344064260472066758 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.000997789112522112663621650095 x1[1] (numeric) = 2.0009889399247201054663350419579 absolute error = 8.8491878020071972866081370839074e-06 relative error = 0.00044223875959063245578125737433036 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9 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 = 1.646e+04 Order of pole (six term test) = 1.425e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=4304894284, alloc=5110872, time=179.06 bytes used=4308895292, alloc=5110872, time=179.43 bytes used=4312896008, alloc=5110872, time=179.80 bytes used=4316896828, alloc=5110872, time=180.17 bytes used=4320897800, alloc=5110872, time=180.54 bytes used=4324898580, alloc=5110872, time=180.91 Finished! Maximum Time Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 906 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 6 Minutes 57 Seconds Optimized Time Remaining = 6 Minutes 54 Seconds Expected Total Time = 9 Minutes 54 Seconds Time to Timeout Unknown Percent Done = 30.23 % > quit bytes used=4325110996, alloc=5110872, time=180.92