|\^/| 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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_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 (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 (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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1[1]) < min_size then min_size := omniabs(array_x1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; 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 min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_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; > 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; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_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; 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; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_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[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_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[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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_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[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_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[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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_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 (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 (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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_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_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_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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_x1_higher[1,n]) = 0.0) or (omniabs(array_x1_higher[1,n+1]) = 0.0)) then # if number 3 > 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 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 - 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 5 > 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 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 - 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[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 - 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[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 - 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[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 - 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[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_x1[term] := array_x1[term]* ratio; > array_x1_higher[1,term] := array_x1_higher[1,term]* ratio; > array_t[term] := array_t[term]* ratio; > 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; > 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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_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[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 - 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[2, 1] := rad_c end if 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[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 - 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[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 - 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[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no 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[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_x1[term] := array_x1[term]*ratio; array_x1_higher[1, term] := array_x1_higher[1, term]*ratio; array_t[term] := array_t[term]*ratio; 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; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_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 > ; > 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 > #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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1[iii]) then array_norms[iii] := omniabs(array_x1[iii]) end if; 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 end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_4D0[1] * array_x2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre diff $eq_no = 1 i = 1 order_d = 1 > array_tmp3[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_2D0[1] * array_tmp3[1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp2[1] - array_tmp4[1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_2D0[1] * array_x1[1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_x1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp9[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp10[1] := array_const_3D0[1] * array_tmp9[1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[1] := array_const_2D0[1] * array_x2[1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp12[1] := array_tmp10[1] - array_tmp11[1]; > #emit pre diff $eq_no = 2 i = 1 order_d = 2 > array_tmp13[1] := array_x1_higher[3,1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp14[1] := array_tmp12[1] - array_tmp13[1]; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp15[1] := array_x1_higher[2,1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp16[1] := array_tmp14[1] - array_tmp15[1]; > #emit pre add FULL FULL $eq_no = 2 i = 1 > array_tmp17[1] := array_tmp16[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_x2_set_initial[2,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_const_4D0[1] * array_x2[2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp3[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_const_2D0[1] * array_tmp3[2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp2[2] - array_tmp4[2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_const_2D0[1] * array_x1[2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_x1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp9[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp10[2] := array_const_3D0[1] * array_tmp9[2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp11[2] := array_const_2D0[1] * array_x2[2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp12[2] := array_tmp10[2] - array_tmp11[2]; > #emit pre diff $eq_no = 2 i = 2 order_d = 2 > array_tmp13[2] := array_x1_higher[3,2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp14[2] := array_tmp12[2] - array_tmp13[2]; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp15[2] := array_x1_higher[2,2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp16[2] := array_tmp14[2] - array_tmp15[2]; > #emit pre add FULL FULL $eq_no = 2 i = 2 > array_tmp17[2] := array_tmp16[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_x2_set_initial[2,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_const_4D0[1] * array_x2[3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp3[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_const_2D0[1] * array_tmp3[3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp2[3] - array_tmp4[3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_const_2D0[1] * array_x1[3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_x1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp9[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp10[3] := array_const_3D0[1] * array_tmp9[3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp11[3] := array_const_2D0[1] * array_x2[3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp12[3] := array_tmp10[3] - array_tmp11[3]; > #emit pre diff $eq_no = 2 i = 3 order_d = 2 > array_tmp13[3] := array_x1_higher[3,3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp14[3] := array_tmp12[3] - array_tmp13[3]; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp15[3] := array_x1_higher[2,3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp16[3] := array_tmp14[3] - array_tmp15[3]; > #emit pre add FULL FULL $eq_no = 2 i = 3 > array_tmp17[3] := array_tmp16[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_x2_set_initial[2,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_const_4D0[1] * array_x2[4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp3[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_const_2D0[1] * array_tmp3[4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp2[4] - array_tmp4[4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_const_2D0[1] * array_x1[4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_x1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp9[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp10[4] := array_const_3D0[1] * array_tmp9[4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp11[4] := array_const_2D0[1] * array_x2[4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp12[4] := array_tmp10[4] - array_tmp11[4]; > #emit pre diff $eq_no = 2 i = 4 order_d = 2 > array_tmp13[4] := array_x1_higher[3,4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp14[4] := array_tmp12[4] - array_tmp13[4]; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp15[4] := array_x1_higher[2,4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp16[4] := array_tmp14[4] - array_tmp15[4]; > #emit pre add FULL FULL $eq_no = 2 i = 4 > array_tmp17[4] := array_tmp16[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_x2_set_initial[2,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_const_4D0[1] * array_x2[5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp3[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_const_2D0[1] * array_tmp3[5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp2[5] - array_tmp4[5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_const_2D0[1] * array_x1[5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_x1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp9[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp10[5] := array_const_3D0[1] * array_tmp9[5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp11[5] := array_const_2D0[1] * array_x2[5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp12[5] := array_tmp10[5] - array_tmp11[5]; > #emit pre diff $eq_no = 2 i = 5 order_d = 2 > array_tmp13[5] := array_x1_higher[3,5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp14[5] := array_tmp12[5] - array_tmp13[5]; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp15[5] := array_x1_higher[2,5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp16[5] := array_tmp14[5] - array_tmp15[5]; > #emit pre add FULL FULL $eq_no = 2 i = 5 > array_tmp17[5] := array_tmp16[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_x2_set_initial[2,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit diff $eq_no = 1 > array_tmp3[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := array_const_2D0[1] * array_tmp3[kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp7[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; > #emit diff $eq_no = 2 > array_tmp9[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp10[kkk] := array_const_3D0[1] * array_tmp9[kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk]; > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x1_higher[3,kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk]; > #emit diff $eq_no = 2 > array_tmp15[kkk] := array_x1_higher[2,kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk]; > #emit FULL - FULL add $eq_no = 2 > array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; > #emit assign $eq_no = 2 > order_d := 2; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_x2_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_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; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_4D0[1]*array_x2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_x2_higher[2, 1]; array_tmp4[1] := array_const_2D0[1]*array_tmp3[1]; array_tmp5[1] := array_tmp2[1] - array_tmp4[1]; array_tmp6[1] := array_const_2D0[1]*array_x1[1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; if not array_x1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp7[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_tmp9[1] := array_x2_higher[2, 1]; array_tmp10[1] := array_const_3D0[1]*array_tmp9[1]; array_tmp11[1] := array_const_2D0[1]*array_x2[1]; array_tmp12[1] := array_tmp10[1] - array_tmp11[1]; array_tmp13[1] := array_x1_higher[3, 1]; array_tmp14[1] := array_tmp12[1] - array_tmp13[1]; array_tmp15[1] := array_x1_higher[2, 1]; array_tmp16[1] := array_tmp14[1] - array_tmp15[1]; array_tmp17[1] := array_tmp16[1] + array_x1[1]; if not array_x2_set_initial[2, 3] then if 1 <= glob_max_terms then temporary := array_tmp17[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_tmp1[2] := array_const_4D0[1]*array_x2[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_x2_higher[2, 2]; array_tmp4[2] := array_const_2D0[1]*array_tmp3[2]; array_tmp5[2] := array_tmp2[2] - array_tmp4[2]; array_tmp6[2] := array_const_2D0[1]*array_x1[2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; if not array_x1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp7[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_tmp9[2] := array_x2_higher[2, 2]; array_tmp10[2] := array_const_3D0[1]*array_tmp9[2]; array_tmp11[2] := array_const_2D0[1]*array_x2[2]; array_tmp12[2] := array_tmp10[2] - array_tmp11[2]; array_tmp13[2] := array_x1_higher[3, 2]; array_tmp14[2] := array_tmp12[2] - array_tmp13[2]; array_tmp15[2] := array_x1_higher[2, 2]; array_tmp16[2] := array_tmp14[2] - array_tmp15[2]; array_tmp17[2] := array_tmp16[2] + array_x1[2]; if not array_x2_set_initial[2, 4] then if 2 <= glob_max_terms then temporary := array_tmp17[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_tmp1[3] := array_const_4D0[1]*array_x2[3]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_x2_higher[2, 3]; array_tmp4[3] := array_const_2D0[1]*array_tmp3[3]; array_tmp5[3] := array_tmp2[3] - array_tmp4[3]; array_tmp6[3] := array_const_2D0[1]*array_x1[3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; if not array_x1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp7[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_tmp9[3] := array_x2_higher[2, 3]; array_tmp10[3] := array_const_3D0[1]*array_tmp9[3]; array_tmp11[3] := array_const_2D0[1]*array_x2[3]; array_tmp12[3] := array_tmp10[3] - array_tmp11[3]; array_tmp13[3] := array_x1_higher[3, 3]; array_tmp14[3] := array_tmp12[3] - array_tmp13[3]; array_tmp15[3] := array_x1_higher[2, 3]; array_tmp16[3] := array_tmp14[3] - array_tmp15[3]; array_tmp17[3] := array_tmp16[3] + array_x1[3]; if not array_x2_set_initial[2, 5] then if 3 <= glob_max_terms then temporary := array_tmp17[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_tmp1[4] := array_const_4D0[1]*array_x2[4]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_x2_higher[2, 4]; array_tmp4[4] := array_const_2D0[1]*array_tmp3[4]; array_tmp5[4] := array_tmp2[4] - array_tmp4[4]; array_tmp6[4] := array_const_2D0[1]*array_x1[4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; if not array_x1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp7[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_tmp9[4] := array_x2_higher[2, 4]; array_tmp10[4] := array_const_3D0[1]*array_tmp9[4]; array_tmp11[4] := array_const_2D0[1]*array_x2[4]; array_tmp12[4] := array_tmp10[4] - array_tmp11[4]; array_tmp13[4] := array_x1_higher[3, 4]; array_tmp14[4] := array_tmp12[4] - array_tmp13[4]; array_tmp15[4] := array_x1_higher[2, 4]; array_tmp16[4] := array_tmp14[4] - array_tmp15[4]; array_tmp17[4] := array_tmp16[4] + array_x1[4]; if not array_x2_set_initial[2, 6] then if 4 <= glob_max_terms then temporary := array_tmp17[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_tmp1[5] := array_const_4D0[1]*array_x2[5]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_x2_higher[2, 5]; array_tmp4[5] := array_const_2D0[1]*array_tmp3[5]; array_tmp5[5] := array_tmp2[5] - array_tmp4[5]; array_tmp6[5] := array_const_2D0[1]*array_x1[5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; if not array_x1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp7[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; array_tmp9[5] := array_x2_higher[2, 5]; array_tmp10[5] := array_const_3D0[1]*array_tmp9[5]; array_tmp11[5] := array_const_2D0[1]*array_x2[5]; array_tmp12[5] := array_tmp10[5] - array_tmp11[5]; array_tmp13[5] := array_x1_higher[3, 5]; array_tmp14[5] := array_tmp12[5] - array_tmp13[5]; array_tmp15[5] := array_x1_higher[2, 5]; array_tmp16[5] := array_tmp14[5] - array_tmp15[5]; array_tmp17[5] := array_tmp16[5] + array_x1[5]; if not array_x2_set_initial[2, 7] then if 5 <= glob_max_terms then temporary := array_tmp17[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; while kkk <= glob_max_terms do array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk]; array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_x2_higher[2, kkk]; array_tmp4[kkk] := array_const_2D0[1]*array_tmp3[kkk]; array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_x1_set_initial[1, kkk + order_d] then temporary := array_tmp7[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; array_tmp9[kkk] := array_x2_higher[2, kkk]; array_tmp10[kkk] := array_const_3D0[1]*array_tmp9[kkk]; array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk]; array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk]; array_tmp13[kkk] := array_x1_higher[3, kkk]; array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk]; array_tmp15[kkk] := array_x1_higher[2, kkk]; array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk]; array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d < glob_max_terms then if not array_x2_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_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; 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_1, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > 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_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_sm_hpostode.ode#################"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > 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,"!"); > 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_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := 0.0001;"); > 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_x1_init:= Array(0..(max_terms + 1),[]); > array_x2_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_x1:= Array(0..(max_terms + 1),[]); > array_t:= Array(0..(max_terms + 1),[]); > array_x2:= 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_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_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_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_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 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_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_x1[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_x2[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_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 <= 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 <= 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_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_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_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_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_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_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_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_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_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_3D0[1] := 3.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > ## 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_look_poles := true; > glob_max_h := 0.0001; > #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_x1_set_initial[1,1] := true; > array_x1_set_initial[1,2] := false; > array_x1_set_initial[1,3] := false; > array_x1_set_initial[1,4] := false; > array_x1_set_initial[1,5] := false; > array_x1_set_initial[1,6] := false; > array_x1_set_initial[1,7] := false; > array_x1_set_initial[1,8] := false; > array_x1_set_initial[1,9] := false; > array_x1_set_initial[1,10] := false; > array_x1_set_initial[1,11] := false; > array_x1_set_initial[1,12] := false; > array_x1_set_initial[1,13] := false; > array_x1_set_initial[1,14] := false; > array_x1_set_initial[1,15] := false; > array_x1_set_initial[1,16] := false; > array_x1_set_initial[1,17] := false; > array_x1_set_initial[1,18] := false; > array_x1_set_initial[1,19] := false; > array_x1_set_initial[1,20] := false; > array_x1_set_initial[1,21] := false; > array_x1_set_initial[1,22] := false; > array_x1_set_initial[1,23] := false; > array_x1_set_initial[1,24] := false; > array_x1_set_initial[1,25] := false; > array_x1_set_initial[1,26] := false; > array_x1_set_initial[1,27] := false; > array_x1_set_initial[1,28] := false; > array_x1_set_initial[1,29] := false; > array_x1_set_initial[1,30] := false; > array_x2_set_initial[2,1] := true; > array_x2_set_initial[2,2] := true; > array_x2_set_initial[2,3] := false; > array_x2_set_initial[2,4] := false; > array_x2_set_initial[2,5] := false; > array_x2_set_initial[2,6] := false; > array_x2_set_initial[2,7] := false; > array_x2_set_initial[2,8] := false; > array_x2_set_initial[2,9] := false; > array_x2_set_initial[2,10] := false; > array_x2_set_initial[2,11] := false; > array_x2_set_initial[2,12] := false; > array_x2_set_initial[2,13] := false; > array_x2_set_initial[2,14] := false; > array_x2_set_initial[2,15] := false; > array_x2_set_initial[2,16] := false; > array_x2_set_initial[2,17] := false; > array_x2_set_initial[2,18] := false; > array_x2_set_initial[2,19] := false; > array_x2_set_initial[2,20] := false; > array_x2_set_initial[2,21] := false; > array_x2_set_initial[2,22] := false; > array_x2_set_initial[2,23] := false; > array_x2_set_initial[2,24] := false; > array_x2_set_initial[2,25] := false; > array_x2_set_initial[2,26] := false; > array_x2_set_initial[2,27] := false; > array_x2_set_initial[2,28] := false; > array_x2_set_initial[2,29] := false; > array_x2_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_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 > ; > 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 > ; > 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_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 > ; > 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 > ; > 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_x1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =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_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 > #Jump Series array_x2; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =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_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 > ; > 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > 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_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,"2013-05-26T03:33:37-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6_sm_h") > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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_sm_h diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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_1, array_const_0D0, array_const_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, 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_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_sm_hpostode.ode#################"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); 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, "!"); 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_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := 0.0001;"); 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_x1_init := Array(0 .. max_terms + 1, []); array_x2_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_x1 := Array(0 .. max_terms + 1, []); array_t := Array(0 .. max_terms + 1, []); array_x2 := 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_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_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_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_x1_init[term] := 0.; term := term + 1 end do; 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_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_x1[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_x2[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_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 <= 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 <= 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_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[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_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[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_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_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_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_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_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; 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_look_poles := true; glob_max_h := 0.0001; 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_x1_set_initial[1, 1] := true; array_x1_set_initial[1, 2] := false; array_x1_set_initial[1, 3] := false; array_x1_set_initial[1, 4] := false; array_x1_set_initial[1, 5] := false; array_x1_set_initial[1, 6] := false; array_x1_set_initial[1, 7] := false; array_x1_set_initial[1, 8] := false; array_x1_set_initial[1, 9] := false; array_x1_set_initial[1, 10] := false; array_x1_set_initial[1, 11] := false; array_x1_set_initial[1, 12] := false; array_x1_set_initial[1, 13] := false; array_x1_set_initial[1, 14] := false; array_x1_set_initial[1, 15] := false; array_x1_set_initial[1, 16] := false; array_x1_set_initial[1, 17] := false; array_x1_set_initial[1, 18] := false; array_x1_set_initial[1, 19] := false; array_x1_set_initial[1, 20] := false; array_x1_set_initial[1, 21] := false; array_x1_set_initial[1, 22] := false; array_x1_set_initial[1, 23] := false; array_x1_set_initial[1, 24] := false; array_x1_set_initial[1, 25] := false; array_x1_set_initial[1, 26] := false; array_x1_set_initial[1, 27] := false; array_x1_set_initial[1, 28] := false; array_x1_set_initial[1, 29] := false; array_x1_set_initial[1, 30] := false; array_x2_set_initial[2, 1] := true; array_x2_set_initial[2, 2] := true; array_x2_set_initial[2, 3] := false; array_x2_set_initial[2, 4] := false; array_x2_set_initial[2, 5] := false; array_x2_set_initial[2, 6] := false; array_x2_set_initial[2, 7] := false; array_x2_set_initial[2, 8] := false; array_x2_set_initial[2, 9] := false; array_x2_set_initial[2, 10] := false; array_x2_set_initial[2, 11] := false; array_x2_set_initial[2, 12] := false; array_x2_set_initial[2, 13] := false; array_x2_set_initial[2, 14] := false; array_x2_set_initial[2, 15] := false; array_x2_set_initial[2, 16] := false; array_x2_set_initial[2, 17] := false; array_x2_set_initial[2, 18] := false; array_x2_set_initial[2, 19] := false; array_x2_set_initial[2, 20] := false; array_x2_set_initial[2, 21] := false; array_x2_set_initial[2, 22] := false; array_x2_set_initial[2, 23] := false; array_x2_set_initial[2, 24] := false; array_x2_set_initial[2, 25] := false; array_x2_set_initial[2, 26] := false; array_x2_set_initial[2, 27] := false; array_x2_set_initial[2, 28] := false; array_x2_set_initial[2, 29] := false; array_x2_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_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; 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; 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_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; 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; 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 := 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; 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 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; 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_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, "2013-05-26T03:33:37-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6_sm_h"); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 *\ diff (x2,t ,1) - 2.0 * 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_sm_h diffeq.mxt"); logitem_str(html_log_file, "mtest6_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 (x2,t,2) = 3.0 * diff(x2,t,1\ ) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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_sm_hpostode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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_look_poles := true; glob_max_h := 0.0001; #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=3276200, 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=8000760, alloc=4717728, 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=12001432, alloc=4717728, time=0.42 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=16002312, alloc=4783252, time=0.57 bytes used=20003148, alloc=4783252, time=0.71 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=24003976, alloc=4783252, time=0.86 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=28004824, alloc=4783252, time=1.00 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=32005548, alloc=4783252, time=1.15 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=36006884, alloc=4783252, time=1.29 bytes used=40007812, alloc=4783252, time=1.44 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=44008496, alloc=4783252, time=1.59 t[1] = 0.5 x1[1] (analytic) = 2.001091755187482740162486839163 x1[1] (numeric) = 2.001091755187482740162486839163 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.0001 x2[1] (analytic) = 1.0007256155636055990741531973548 x2[1] (numeric) = 1.0007256155636055990741531973548 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 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.800e+27 Order of pole (six term test) = 1.274e+54 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.573e+04 Order of pole (six term test) = 1.303e+07 bytes used=48009200, alloc=4783252, time=1.73 bytes used=52009900, alloc=4848776, time=1.88 bytes used=56010780, alloc=4848776, time=2.02 bytes used=60011780, alloc=4848776, time=2.17 bytes used=64012744, alloc=4848776, time=2.32 bytes used=68013508, alloc=4848776, time=2.47 bytes used=72014228, alloc=4848776, time=2.62 bytes used=76015032, alloc=4848776, time=2.76 bytes used=80015704, alloc=4848776, time=2.91 bytes used=84016460, alloc=4848776, time=3.06 bytes used=88017304, alloc=4848776, time=3.21 bytes used=92018240, alloc=4848776, time=3.36 bytes used=96019516, alloc=4848776, time=3.51 bytes used=100020276, alloc=4848776, time=3.66 bytes used=104021084, alloc=4848776, time=3.81 bytes used=108021796, alloc=4848776, time=3.96 bytes used=112022788, alloc=4848776, time=4.11 bytes used=116023492, alloc=4848776, time=4.26 bytes used=120024188, alloc=4848776, time=4.41 bytes used=124025268, alloc=4848776, time=4.56 bytes used=128026112, alloc=4848776, time=4.71 bytes used=132026920, alloc=4848776, time=4.85 bytes used=136027660, alloc=4848776, time=5.00 bytes used=140028508, alloc=4848776, time=5.15 bytes used=144029932, alloc=4848776, time=5.30 bytes used=148030972, alloc=4848776, time=5.45 bytes used=152031680, alloc=4848776, time=5.60 bytes used=156032364, alloc=4848776, time=5.75 bytes used=160033164, alloc=4848776, time=5.90 bytes used=164033888, alloc=4848776, time=6.05 bytes used=168034824, alloc=4848776, time=6.20 bytes used=172035820, alloc=4848776, time=6.35 bytes used=176036648, alloc=4848776, time=6.50 bytes used=180037324, alloc=4848776, time=6.65 bytes used=184038132, alloc=4848776, time=6.80 bytes used=188038976, alloc=4914300, time=6.95 bytes used=192039840, alloc=4914300, time=7.10 bytes used=196040592, alloc=4914300, time=7.25 bytes used=200041348, alloc=4914300, time=7.40 bytes used=204042012, alloc=4914300, time=7.55 bytes used=208042808, alloc=4914300, time=7.70 bytes used=212043952, alloc=4914300, time=7.85 bytes used=216044676, alloc=4914300, time=8.00 bytes used=220045816, alloc=4914300, time=8.15 bytes used=224046520, alloc=4914300, time=8.30 bytes used=228047316, alloc=4914300, time=8.45 bytes used=232048028, alloc=4914300, time=8.60 bytes used=236048820, alloc=4914300, time=8.75 bytes used=240049552, alloc=4914300, time=8.91 bytes used=244050272, alloc=4914300, time=9.06 bytes used=248051028, alloc=4914300, time=9.21 bytes used=252051800, alloc=4914300, time=9.36 bytes used=256052496, alloc=4914300, time=9.51 bytes used=260053592, alloc=4914300, time=9.66 bytes used=264054732, alloc=4914300, time=9.81 bytes used=268055556, alloc=4914300, time=9.96 bytes used=272056708, alloc=4914300, time=10.12 bytes used=276057376, alloc=4914300, time=10.27 bytes used=280058088, alloc=4914300, time=10.42 bytes used=284059180, alloc=4914300, time=10.57 bytes used=288060332, alloc=4914300, time=10.72 bytes used=292061668, alloc=4914300, time=10.87 bytes used=296062424, alloc=4914300, time=11.02 bytes used=300063096, alloc=4914300, time=11.17 bytes used=304063848, alloc=4914300, time=11.32 bytes used=308064672, alloc=4914300, time=11.47 bytes used=312065376, alloc=4914300, time=11.62 bytes used=316066216, alloc=4914300, time=11.77 bytes used=320066956, alloc=4914300, time=11.92 bytes used=324068148, alloc=4914300, time=12.07 bytes used=328069044, alloc=4914300, time=12.22 bytes used=332069960, alloc=4914300, time=12.38 bytes used=336070724, alloc=4914300, time=12.52 bytes used=340071392, alloc=4914300, time=12.67 bytes used=344072132, alloc=4914300, time=12.82 bytes used=348072880, alloc=4914300, time=12.97 bytes used=352073648, alloc=4914300, time=13.12 bytes used=356074404, alloc=4914300, time=13.27 bytes used=360075080, alloc=4914300, time=13.42 bytes used=364075984, alloc=4914300, time=13.57 bytes used=368077076, alloc=4914300, time=13.72 bytes used=372077816, alloc=4914300, time=13.88 bytes used=376078544, alloc=4914300, time=14.03 bytes used=380079196, alloc=4914300, time=14.18 bytes used=384079956, alloc=4914300, time=14.32 bytes used=388080816, alloc=4914300, time=14.47 bytes used=392081492, alloc=4914300, time=14.63 bytes used=396082672, alloc=4914300, time=14.78 bytes used=400083432, alloc=4914300, time=14.93 bytes used=404084104, alloc=4914300, time=15.07 bytes used=408084980, alloc=4914300, time=15.22 bytes used=412085688, alloc=4914300, time=15.37 bytes used=416086560, alloc=4914300, time=15.53 bytes used=420087428, alloc=4914300, time=15.68 bytes used=424088264, alloc=4914300, time=15.83 bytes used=428089308, alloc=4914300, time=15.98 bytes used=432090724, alloc=4914300, time=16.14 bytes used=436091444, alloc=4914300, time=16.29 bytes used=440092236, alloc=4914300, time=16.44 bytes used=444093024, alloc=4914300, time=16.59 bytes used=448093740, alloc=4914300, time=16.74 bytes used=452094580, alloc=4914300, time=16.89 bytes used=456095316, alloc=4914300, time=17.04 bytes used=460096148, alloc=4914300, time=17.19 bytes used=464096856, alloc=4914300, time=17.34 bytes used=468097544, alloc=4914300, time=17.49 bytes used=472098264, alloc=4914300, time=17.64 bytes used=476099392, alloc=4914300, time=17.80 bytes used=480100296, alloc=4914300, time=17.95 bytes used=484101072, alloc=4914300, time=18.10 bytes used=488101768, alloc=4914300, time=18.25 bytes used=492102860, alloc=4914300, time=18.40 bytes used=496103552, alloc=4914300, time=18.55 bytes used=500104832, alloc=4914300, time=18.70 bytes used=504105580, alloc=4914300, time=18.85 bytes used=508106452, alloc=4914300, time=19.00 bytes used=512107272, alloc=4914300, time=19.15 TOP MAIN SOLVE Loop bytes used=516108012, alloc=4914300, time=19.30 bytes used=520108832, alloc=4914300, time=19.46 t[1] = 0.51 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.435e+27 Order of pole (six term test) = -1.340e+54 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.581e+04 Order of pole (six term test) = 1.316e+07 bytes used=524109596, alloc=4914300, time=19.61 bytes used=528110420, alloc=4914300, time=19.75 bytes used=532111160, alloc=4914300, time=19.91 bytes used=536112388, alloc=4914300, time=20.06 bytes used=540113288, alloc=4914300, time=20.21 bytes used=544114032, alloc=4914300, time=20.36 bytes used=548114844, alloc=4914300, time=20.51 bytes used=552115628, alloc=4914300, time=20.66 bytes used=556116364, alloc=4914300, time=20.82 bytes used=560117176, alloc=4914300, time=20.97 bytes used=564117956, alloc=4914300, time=21.12 bytes used=568118776, alloc=4914300, time=21.26 bytes used=572119504, alloc=4914300, time=21.41 bytes used=576120264, alloc=4914300, time=21.57 bytes used=580120984, alloc=4914300, time=21.71 bytes used=584121920, alloc=4914300, time=21.87 bytes used=588122932, alloc=4914300, time=22.02 bytes used=592123684, alloc=4914300, time=22.17 bytes used=596124380, alloc=4914300, time=22.33 bytes used=600125152, alloc=4914300, time=22.48 bytes used=604125940, alloc=4914300, time=22.63 bytes used=608127148, alloc=4914300, time=22.78 bytes used=612127968, alloc=4914300, time=22.93 bytes used=616128632, alloc=4914300, time=23.08 bytes used=620129272, alloc=4914300, time=23.23 bytes used=624129968, alloc=4914300, time=23.38 bytes used=628130676, alloc=4914300, time=23.54 bytes used=632131416, alloc=4914300, time=23.69 bytes used=636132124, alloc=4914300, time=23.84 bytes used=640133052, alloc=4914300, time=23.99 bytes used=644133828, alloc=4914300, time=24.14 bytes used=648134788, alloc=4914300, time=24.29 bytes used=652135556, alloc=4914300, time=24.44 bytes used=656136256, alloc=4914300, time=24.59 bytes used=660137076, alloc=4914300, time=24.74 bytes used=664137812, alloc=4914300, time=24.89 bytes used=668138512, alloc=4914300, time=25.05 bytes used=672139284, alloc=4914300, time=25.20 bytes used=676140028, alloc=4914300, time=25.35 bytes used=680140880, alloc=4914300, time=25.50 bytes used=684141824, alloc=4914300, time=25.65 bytes used=688142744, alloc=4914300, time=25.80 bytes used=692143448, alloc=4914300, time=25.95 bytes used=696144260, alloc=4914300, time=26.10 bytes used=700145724, alloc=4914300, time=26.25 bytes used=704146436, alloc=4914300, time=26.40 bytes used=708147332, alloc=4914300, time=26.55 bytes used=712148064, alloc=4914300, time=26.70 bytes used=716148720, alloc=4914300, time=26.85 bytes used=720149636, alloc=4914300, time=27.01 bytes used=724150316, alloc=4914300, time=27.16 bytes used=728151152, alloc=4914300, time=27.31 bytes used=732151832, alloc=4914300, time=27.46 bytes used=736152536, alloc=4914300, time=27.61 bytes used=740153208, alloc=4914300, time=27.76 bytes used=744154292, alloc=4914300, time=27.92 bytes used=748155092, alloc=4914300, time=28.07 bytes used=752155792, alloc=4914300, time=28.22 bytes used=756156524, alloc=4914300, time=28.37 bytes used=760157476, alloc=4914300, time=28.52 bytes used=764158144, alloc=4914300, time=28.67 bytes used=768158860, alloc=4914300, time=28.83 bytes used=772159540, alloc=4914300, time=28.98 bytes used=776160376, alloc=4914300, time=29.13 bytes used=780161436, alloc=4914300, time=29.28 bytes used=784162104, alloc=4914300, time=29.43 bytes used=788162784, alloc=4914300, time=29.58 bytes used=792164048, alloc=4914300, time=29.73 bytes used=796164924, alloc=4914300, time=29.88 bytes used=800165600, alloc=4914300, time=30.03 bytes used=804167084, alloc=4914300, time=30.18 bytes used=808167968, alloc=4914300, time=30.34 bytes used=812168692, alloc=4914300, time=30.49 bytes used=816169356, alloc=4914300, time=30.64 bytes used=820170048, alloc=4914300, time=30.79 bytes used=824170708, alloc=4914300, time=30.94 bytes used=828171464, alloc=4914300, time=31.09 bytes used=832172344, alloc=4914300, time=31.25 bytes used=836173152, alloc=4914300, time=31.40 bytes used=840173852, alloc=4914300, time=31.55 bytes used=844175160, alloc=4914300, time=31.70 bytes used=848175944, alloc=4914300, time=31.85 bytes used=852176788, alloc=4914300, time=32.00 bytes used=856177536, alloc=4914300, time=32.15 bytes used=860178252, alloc=4914300, time=32.30 bytes used=864178976, alloc=4914300, time=32.45 bytes used=868179740, alloc=4914300, time=32.60 bytes used=872180848, alloc=4914300, time=32.75 bytes used=876181792, alloc=4914300, time=32.91 bytes used=880182552, alloc=4914300, time=33.06 bytes used=884183248, alloc=4914300, time=33.21 bytes used=888184472, alloc=4914300, time=33.36 bytes used=892185332, alloc=4914300, time=33.51 bytes used=896186332, alloc=4914300, time=33.66 bytes used=900187188, alloc=4914300, time=33.82 bytes used=904187888, alloc=4914300, time=33.97 bytes used=908188760, alloc=4914300, time=34.12 bytes used=912189936, alloc=4914300, time=34.27 bytes used=916190600, alloc=4914300, time=34.42 bytes used=920191356, alloc=4914300, time=34.57 bytes used=924192152, alloc=4914300, time=34.73 bytes used=928193044, alloc=4914300, time=34.88 bytes used=932193832, alloc=4914300, time=35.03 bytes used=936194644, alloc=4914300, time=35.18 bytes used=940195424, alloc=4914300, time=35.33 bytes used=944196084, alloc=4914300, time=35.48 bytes used=948197312, alloc=4914300, time=35.63 bytes used=952198100, alloc=4914300, time=35.78 bytes used=956198892, alloc=4914300, time=35.93 bytes used=960199820, alloc=4914300, time=36.08 bytes used=964200476, alloc=4914300, time=36.23 bytes used=968201540, alloc=4914300, time=36.39 bytes used=972202308, alloc=4914300, time=36.54 bytes used=976203252, alloc=4914300, time=36.69 bytes used=980204012, alloc=4914300, time=36.84 bytes used=984204896, alloc=4914300, time=36.99 bytes used=988205824, alloc=4914300, time=37.13 TOP MAIN SOLVE Loop bytes used=992206812, alloc=4914300, time=37.29 t[1] = 0.52 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.209e+27 Order of pole (six term test) = -7.376e+53 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.589e+04 Order of pole (six term test) = 1.329e+07 bytes used=996207636, alloc=4914300, time=37.44 bytes used=1000208372, alloc=4914300, time=37.59 bytes used=1004209280, alloc=4914300, time=37.74 bytes used=1008210000, alloc=4914300, time=37.89 bytes used=1012210796, alloc=4914300, time=38.04 bytes used=1016211576, alloc=4914300, time=38.20 bytes used=1020212232, alloc=4914300, time=38.35 bytes used=1024213060, alloc=4914300, time=38.50 bytes used=1028213856, alloc=4914300, time=38.65 bytes used=1032214848, alloc=4914300, time=38.80 bytes used=1036215516, alloc=4914300, time=38.95 bytes used=1040216516, alloc=4914300, time=39.10 bytes used=1044217216, alloc=4914300, time=39.25 bytes used=1048218052, alloc=4914300, time=39.41 bytes used=1052219008, alloc=4914300, time=39.56 bytes used=1056219888, alloc=4914300, time=39.71 bytes used=1060221092, alloc=4914300, time=39.86 bytes used=1064221820, alloc=4914300, time=40.01 bytes used=1068222544, alloc=4914300, time=40.16 bytes used=1072223292, alloc=4914300, time=40.32 bytes used=1076224084, alloc=4914300, time=40.47 bytes used=1080224828, alloc=4914300, time=40.62 bytes used=1084225728, alloc=4914300, time=40.77 bytes used=1088226436, alloc=4914300, time=40.92 bytes used=1092227428, alloc=4914300, time=41.07 bytes used=1096228096, alloc=4914300, time=41.22 bytes used=1100228956, alloc=4914300, time=41.37 bytes used=1104229740, alloc=4914300, time=41.53 bytes used=1108230412, alloc=4914300, time=41.68 bytes used=1112231112, alloc=4914300, time=41.83 bytes used=1116231876, alloc=4914300, time=41.98 bytes used=1120232968, alloc=4914300, time=42.13 bytes used=1124233680, alloc=4914300, time=42.28 bytes used=1128234520, alloc=4914300, time=42.43 bytes used=1132235344, alloc=4914300, time=42.58 bytes used=1136236108, alloc=4914300, time=42.74 bytes used=1140236812, alloc=4914300, time=42.89 bytes used=1144237580, alloc=4914300, time=43.04 bytes used=1148238272, alloc=4914300, time=43.19 bytes used=1152238980, alloc=4914300, time=43.34 bytes used=1156239676, alloc=4914300, time=43.49 bytes used=1160240384, alloc=4914300, time=43.64 bytes used=1164241080, alloc=4914300, time=43.79 bytes used=1168241932, alloc=4914300, time=43.95 bytes used=1172242708, alloc=4914300, time=44.10 bytes used=1176243576, alloc=4914300, time=44.25 bytes used=1180244324, alloc=4914300, time=44.40 bytes used=1184245120, alloc=4914300, time=44.55 bytes used=1188245900, alloc=4914300, time=44.70 bytes used=1192246588, alloc=4914300, time=44.85 bytes used=1196247492, alloc=4914300, time=45.00 bytes used=1200248320, alloc=4914300, time=45.16 bytes used=1204249284, alloc=4914300, time=45.31 bytes used=1208250080, alloc=4914300, time=45.46 bytes used=1212251084, alloc=4914300, time=45.61 bytes used=1216251752, alloc=4914300, time=45.77 bytes used=1220252700, alloc=4914300, time=45.92 bytes used=1224253496, alloc=4914300, time=46.07 bytes used=1228254396, alloc=4914300, time=46.22 bytes used=1232255192, alloc=4914300, time=46.37 bytes used=1236256760, alloc=4914300, time=46.52 bytes used=1240257860, alloc=4914300, time=46.67 bytes used=1244258552, alloc=4914300, time=46.82 bytes used=1248259476, alloc=4914300, time=46.98 bytes used=1252260408, alloc=4914300, time=47.13 bytes used=1256261700, alloc=4914300, time=47.28 bytes used=1260262484, alloc=4914300, time=47.43 bytes used=1264263500, alloc=4914300, time=47.58 bytes used=1268264356, alloc=4914300, time=47.73 bytes used=1272265068, alloc=4914300, time=47.88 bytes used=1276265888, alloc=4914300, time=48.03 bytes used=1280266668, alloc=4914300, time=48.19 bytes used=1284267396, alloc=4914300, time=48.34 bytes used=1288268104, alloc=4914300, time=48.49 bytes used=1292268860, alloc=4914300, time=48.64 bytes used=1296269692, alloc=4914300, time=48.79 bytes used=1300270444, alloc=4914300, time=48.94 bytes used=1304271204, alloc=4914300, time=49.10 bytes used=1308272196, alloc=4914300, time=49.25 bytes used=1312273160, alloc=4914300, time=49.40 bytes used=1316274168, alloc=4914300, time=49.55 bytes used=1320274932, alloc=4914300, time=49.70 bytes used=1324275652, alloc=4914300, time=49.86 bytes used=1328276356, alloc=4914300, time=50.01 bytes used=1332277060, alloc=4914300, time=50.16 bytes used=1336277728, alloc=4914300, time=50.31 bytes used=1340278540, alloc=4914300, time=50.46 bytes used=1344279324, alloc=4914300, time=50.61 bytes used=1348280128, alloc=4914300, time=50.76 bytes used=1352280944, alloc=4914300, time=50.92 bytes used=1356281664, alloc=4914300, time=51.07 bytes used=1360282380, alloc=4914300, time=51.22 bytes used=1364283052, alloc=4914300, time=51.37 bytes used=1368283992, alloc=4914300, time=51.53 bytes used=1372284800, alloc=4914300, time=51.68 bytes used=1376285772, alloc=4914300, time=51.84 bytes used=1380286612, alloc=4914300, time=51.99 bytes used=1384287320, alloc=4914300, time=52.14 bytes used=1388288020, alloc=4914300, time=52.29 bytes used=1392288888, alloc=4914300, time=52.44 bytes used=1396289900, alloc=4914300, time=52.59 bytes used=1400291052, alloc=4914300, time=52.74 bytes used=1404291732, alloc=4914300, time=52.90 bytes used=1408292488, alloc=4914300, time=53.04 bytes used=1412293192, alloc=4914300, time=53.20 bytes used=1416293888, alloc=4914300, time=53.35 bytes used=1420294736, alloc=4914300, time=53.50 bytes used=1424295536, alloc=4914300, time=53.65 bytes used=1428296248, alloc=4914300, time=53.80 bytes used=1432297072, alloc=4914300, time=53.95 bytes used=1436297896, alloc=4914300, time=54.10 bytes used=1440298676, alloc=4914300, time=54.25 bytes used=1444299608, alloc=4914300, time=54.40 bytes used=1448300592, alloc=4914300, time=54.56 bytes used=1452301308, alloc=4914300, time=54.71 bytes used=1456302500, alloc=4914300, time=54.86 bytes used=1460303372, alloc=4914300, time=55.01 bytes used=1464304072, alloc=4914300, time=55.16 TOP MAIN SOLVE Loop bytes used=1468304888, alloc=4914300, time=55.31 t[1] = 0.53 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.468e+27 Order of pole (six term test) = -1.023e+54 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.597e+04 Order of pole (six term test) = 1.342e+07 bytes used=1472305716, alloc=4914300, time=55.47 bytes used=1476306504, alloc=4914300, time=55.62 bytes used=1480307420, alloc=4914300, time=55.77 bytes used=1484308208, alloc=4914300, time=55.92 bytes used=1488308880, alloc=4914300, time=56.07 bytes used=1492310008, alloc=4914300, time=56.23 bytes used=1496310720, alloc=4914300, time=56.38 bytes used=1500311708, alloc=4914300, time=56.53 bytes used=1504312412, alloc=4914300, time=56.68 bytes used=1508313472, alloc=4914300, time=56.83 bytes used=1512314524, alloc=4914300, time=56.98 bytes used=1516315216, alloc=4914300, time=57.14 bytes used=1520316096, alloc=4914300, time=57.29 bytes used=1524317020, alloc=4914300, time=57.44 bytes used=1528318108, alloc=4914300, time=57.59 bytes used=1532318764, alloc=4914300, time=57.74 bytes used=1536319700, alloc=4914300, time=57.89 bytes used=1540320480, alloc=4914300, time=58.04 bytes used=1544321240, alloc=4914300, time=58.20 bytes used=1548322148, alloc=4914300, time=58.35 bytes used=1552322968, alloc=4914300, time=58.50 bytes used=1556323868, alloc=4914300, time=58.65 bytes used=1560324532, alloc=4914300, time=58.80 bytes used=1564325252, alloc=4914300, time=58.95 bytes used=1568326168, alloc=4914300, time=59.11 bytes used=1572326940, alloc=4914300, time=59.26 bytes used=1576328156, alloc=4914300, time=59.41 bytes used=1580329084, alloc=4914300, time=59.56 bytes used=1584329824, alloc=4914300, time=59.71 bytes used=1588330512, alloc=4914300, time=59.86 bytes used=1592331224, alloc=4914300, time=60.01 bytes used=1596331896, alloc=4914300, time=60.16 bytes used=1600332836, alloc=4914300, time=60.31 bytes used=1604333588, alloc=4914300, time=60.47 bytes used=1608334336, alloc=4914300, time=60.62 bytes used=1612335016, alloc=4914300, time=60.77 bytes used=1616335692, alloc=4914300, time=60.92 bytes used=1620336500, alloc=4914300, time=61.07 bytes used=1624337284, alloc=4914300, time=61.22 bytes used=1628337980, alloc=4914300, time=61.37 bytes used=1632338824, alloc=4914300, time=61.52 bytes used=1636339764, alloc=4914300, time=61.67 bytes used=1640340688, alloc=4914300, time=61.82 bytes used=1644341540, alloc=4914300, time=61.98 bytes used=1648342320, alloc=4914300, time=62.13 bytes used=1652343080, alloc=4914300, time=62.28 bytes used=1656343852, alloc=4914300, time=62.43 bytes used=1660344748, alloc=4914300, time=62.58 bytes used=1664345568, alloc=4914300, time=62.73 bytes used=1668346380, alloc=4914300, time=62.88 bytes used=1672347432, alloc=4914300, time=63.03 bytes used=1676348088, alloc=4914300, time=63.18 bytes used=1680348764, alloc=4914300, time=63.33 bytes used=1684349816, alloc=4914300, time=63.48 bytes used=1688350488, alloc=4914300, time=63.64 bytes used=1692351172, alloc=4914300, time=63.79 bytes used=1696351944, alloc=4914300, time=63.94 bytes used=1700352640, alloc=4914300, time=64.09 bytes used=1704353492, alloc=4914300, time=64.24 bytes used=1708354160, alloc=4914300, time=64.39 bytes used=1712354852, alloc=4914300, time=64.54 bytes used=1716355812, alloc=4914300, time=64.69 bytes used=1720356500, alloc=4914300, time=64.84 bytes used=1724357264, alloc=4914300, time=64.99 bytes used=1728357948, alloc=4914300, time=65.14 bytes used=1732358668, alloc=4914300, time=65.30 bytes used=1736359492, alloc=4914300, time=65.45 bytes used=1740360204, alloc=4914300, time=65.60 bytes used=1744360928, alloc=4914300, time=65.75 bytes used=1748361584, alloc=4914300, time=65.90 bytes used=1752362296, alloc=4914300, time=66.05 bytes used=1756363076, alloc=4914300, time=66.20 bytes used=1760363760, alloc=4914300, time=66.35 bytes used=1764364456, alloc=4914300, time=66.50 bytes used=1768365200, alloc=4914300, time=66.65 bytes used=1772365856, alloc=4914300, time=66.80 bytes used=1776366516, alloc=4914300, time=66.95 bytes used=1780367224, alloc=4914300, time=67.11 bytes used=1784367980, alloc=4914300, time=67.26 bytes used=1788368944, alloc=4914300, time=67.41 bytes used=1792370076, alloc=4914300, time=67.56 bytes used=1796370876, alloc=4914300, time=67.71 bytes used=1800371724, alloc=4914300, time=67.86 bytes used=1804372556, alloc=4914300, time=68.01 bytes used=1808373328, alloc=4914300, time=68.16 bytes used=1812374136, alloc=4914300, time=68.31 bytes used=1816374928, alloc=4914300, time=68.46 bytes used=1820375720, alloc=4914300, time=68.61 bytes used=1824376444, alloc=4914300, time=68.76 bytes used=1828377176, alloc=4914300, time=68.91 bytes used=1832378152, alloc=4914300, time=69.07 bytes used=1836379160, alloc=4914300, time=69.22 bytes used=1840379848, alloc=4914300, time=69.37 bytes used=1844380556, alloc=4914300, time=69.53 bytes used=1848381244, alloc=4914300, time=69.68 bytes used=1852382124, alloc=4914300, time=69.83 bytes used=1856383260, alloc=4914300, time=69.98 bytes used=1860384052, alloc=4914300, time=70.13 bytes used=1864384980, alloc=4914300, time=70.29 bytes used=1868385660, alloc=4914300, time=70.44 bytes used=1872386440, alloc=4914300, time=70.59 bytes used=1876387200, alloc=4914300, time=70.74 bytes used=1880388488, alloc=4914300, time=70.89 bytes used=1884389284, alloc=4914300, time=71.04 bytes used=1888390260, alloc=4914300, time=71.20 bytes used=1892391264, alloc=4914300, time=71.34 bytes used=1896392016, alloc=4914300, time=71.50 bytes used=1900392788, alloc=4914300, time=71.65 bytes used=1904393464, alloc=4914300, time=71.80 bytes used=1908394260, alloc=4914300, time=71.95 bytes used=1912395032, alloc=4914300, time=72.10 bytes used=1916395716, alloc=4914300, time=72.26 bytes used=1920396412, alloc=4914300, time=72.41 bytes used=1924397068, alloc=4914300, time=72.56 bytes used=1928397736, alloc=4914300, time=72.71 bytes used=1932398696, alloc=4914300, time=72.86 bytes used=1936399372, alloc=4914300, time=73.01 bytes used=1940400740, alloc=4914300, time=73.16 TOP MAIN SOLVE Loop bytes used=1944401532, alloc=4914300, time=73.31 t[1] = 0.54 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 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 = 5.080e+27 Order of pole (six term test) = -2.778e+52 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.605e+04 Order of pole (six term test) = 1.356e+07 bytes used=1948402252, alloc=4914300, time=73.46 bytes used=1952403148, alloc=4914300, time=73.61 bytes used=1956403836, alloc=4914300, time=73.77 bytes used=1960404572, alloc=4914300, time=73.92 bytes used=1964405284, alloc=4914300, time=74.07 bytes used=1968406172, alloc=4914300, time=74.22 bytes used=1972406912, alloc=4914300, time=74.37 bytes used=1976407628, alloc=4914300, time=74.53 bytes used=1980408404, alloc=4914300, time=74.67 bytes used=1984409852, alloc=4914300, time=74.83 bytes used=1988410668, alloc=4914300, time=74.98 bytes used=1992411360, alloc=4914300, time=75.13 bytes used=1996412256, alloc=4914300, time=75.28 bytes used=2000413120, alloc=4914300, time=75.44 bytes used=2004413804, alloc=4914300, time=75.59 bytes used=2008414500, alloc=4914300, time=75.74 bytes used=2012415236, alloc=4914300, time=75.89 bytes used=2016416012, alloc=4914300, time=76.04 bytes used=2020416760, alloc=4914300, time=76.19 bytes used=2024417528, alloc=4914300, time=76.34 bytes used=2028418224, alloc=4914300, time=76.49 bytes used=2032419144, alloc=4914300, time=76.64 bytes used=2036419928, alloc=4914300, time=76.80 bytes used=2040420672, alloc=4914300, time=76.95 bytes used=2044421520, alloc=4914300, time=77.10 bytes used=2048422252, alloc=4914300, time=77.25 bytes used=2052423052, alloc=4914300, time=77.40 bytes used=2056423752, alloc=4914300, time=77.55 bytes used=2060424428, alloc=4914300, time=77.70 bytes used=2064425092, alloc=4914300, time=77.85 bytes used=2068425776, alloc=4914300, time=78.00 bytes used=2072426452, alloc=4914300, time=78.15 bytes used=2076427132, alloc=4914300, time=78.30 bytes used=2080427860, alloc=4914300, time=78.45 bytes used=2084428520, alloc=4914300, time=78.60 bytes used=2088429184, alloc=4914300, time=78.75 bytes used=2092429848, alloc=4914300, time=78.91 bytes used=2096430520, alloc=4914300, time=79.06 bytes used=2100431272, alloc=4914300, time=79.21 bytes used=2104432168, alloc=4914300, time=79.36 bytes used=2108432920, alloc=4914300, time=79.51 bytes used=2112433752, alloc=4914300, time=79.66 bytes used=2116435200, alloc=4914300, time=79.81 bytes used=2120436076, alloc=4914300, time=79.96 bytes used=2124436744, alloc=4914300, time=80.12 bytes used=2128437552, alloc=4914300, time=80.27 bytes used=2132438336, alloc=4914300, time=80.42 bytes used=2136439064, alloc=4914300, time=80.57 bytes used=2140439736, alloc=4914300, time=80.72 bytes used=2144440460, alloc=4914300, time=80.87 bytes used=2148441256, alloc=4914300, time=81.02 bytes used=2152442108, alloc=4914300, time=81.17 bytes used=2156442948, alloc=4914300, time=81.32 bytes used=2160443864, alloc=4914300, time=81.48 bytes used=2164444584, alloc=4914300, time=81.63 bytes used=2168445364, alloc=4914300, time=81.78 bytes used=2172446336, alloc=4914300, time=81.93 bytes used=2176447032, alloc=4914300, time=82.08 bytes used=2180447828, alloc=4914300, time=82.23 bytes used=2184448536, alloc=4914300, time=82.39 bytes used=2188449360, alloc=4914300, time=82.54 bytes used=2192450268, alloc=4914300, time=82.69 bytes used=2196451572, alloc=4914300, time=82.84 bytes used=2200452228, alloc=4914300, time=82.99 bytes used=2204453056, alloc=4914300, time=83.14 bytes used=2208453732, alloc=4914300, time=83.29 bytes used=2212454532, alloc=4914300, time=83.44 bytes used=2216455484, alloc=4914300, time=83.60 bytes used=2220456180, alloc=4914300, time=83.75 bytes used=2224456912, alloc=4914300, time=83.90 bytes used=2228457720, alloc=4914300, time=84.05 bytes used=2232458408, alloc=4914300, time=84.20 bytes used=2236459272, alloc=4914300, time=84.35 bytes used=2240460028, alloc=4914300, time=84.51 bytes used=2244461016, alloc=4914300, time=84.66 bytes used=2248461868, alloc=4914300, time=84.81 bytes used=2252462608, alloc=4914300, time=84.96 bytes used=2256463372, alloc=4914300, time=85.11 bytes used=2260464032, alloc=4914300, time=85.26 bytes used=2264464724, alloc=4914300, time=85.41 bytes used=2268465380, alloc=4914300, time=85.56 bytes used=2272466540, alloc=4914300, time=85.71 bytes used=2276467568, alloc=4914300, time=85.87 bytes used=2280468340, alloc=4914300, time=86.02 bytes used=2284469092, alloc=4914300, time=86.17 bytes used=2288469900, alloc=4914300, time=86.32 bytes used=2292471252, alloc=4914300, time=86.47 bytes used=2296471976, alloc=4914300, time=86.62 bytes used=2300472708, alloc=4914300, time=86.77 bytes used=2304473368, alloc=4914300, time=86.92 bytes used=2308474244, alloc=4914300, time=87.08 bytes used=2312475744, alloc=4914300, time=87.23 bytes used=2316476572, alloc=4914300, time=87.39 bytes used=2320477328, alloc=4914300, time=87.54 bytes used=2324478156, alloc=4914300, time=87.69 bytes used=2328478992, alloc=4914300, time=87.84 bytes used=2332479680, alloc=4914300, time=87.99 bytes used=2336480600, alloc=4914300, time=88.14 bytes used=2340481324, alloc=4914300, time=88.29 bytes used=2344482048, alloc=4914300, time=88.44 bytes used=2348482804, alloc=4914300, time=88.60 bytes used=2352483792, alloc=4914300, time=88.75 bytes used=2356484476, alloc=4914300, time=88.90 bytes used=2360485220, alloc=4914300, time=89.05 bytes used=2364486000, alloc=4914300, time=89.20 bytes used=2368486780, alloc=4914300, time=89.35 bytes used=2372487500, alloc=4914300, time=89.50 bytes used=2376488200, alloc=4914300, time=89.65 bytes used=2380489128, alloc=4914300, time=89.81 bytes used=2384489972, alloc=4914300, time=89.96 bytes used=2388491364, alloc=4914300, time=90.11 bytes used=2392492044, alloc=4914300, time=90.26 bytes used=2396492912, alloc=4914300, time=90.41 bytes used=2400493656, alloc=4914300, time=90.56 bytes used=2404494340, alloc=4914300, time=90.71 bytes used=2408495256, alloc=4914300, time=90.86 bytes used=2412495980, alloc=4914300, time=91.01 bytes used=2416496788, alloc=4914300, time=91.17 TOP MAIN SOLVE Loop bytes used=2420497484, alloc=4914300, time=91.32 t[1] = 0.55 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.594e+27 Order of pole (six term test) = 1.677e+54 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.613e+04 Order of pole (six term test) = 1.369e+07 bytes used=2424498172, alloc=4914300, time=91.47 bytes used=2428498916, alloc=4914300, time=91.62 bytes used=2432499768, alloc=4914300, time=91.77 bytes used=2436500576, alloc=4914300, time=91.92 bytes used=2440501404, alloc=4914300, time=92.07 bytes used=2444502220, alloc=4914300, time=92.22 bytes used=2448502880, alloc=4914300, time=92.38 bytes used=2452503560, alloc=4914300, time=92.52 bytes used=2456504972, alloc=4914300, time=92.67 bytes used=2460506128, alloc=4914300, time=92.83 bytes used=2464507084, alloc=4914300, time=92.98 bytes used=2468507916, alloc=4914300, time=93.13 bytes used=2472508600, alloc=4914300, time=93.28 bytes used=2476509288, alloc=4914300, time=93.43 bytes used=2480510120, alloc=4914300, time=93.58 bytes used=2484512228, alloc=4914300, time=93.73 bytes used=2488512896, alloc=4914300, time=93.89 bytes used=2492513680, alloc=4914300, time=94.04 bytes used=2496514568, alloc=4914300, time=94.19 bytes used=2500515444, alloc=4914300, time=94.34 bytes used=2504516264, alloc=4914300, time=94.49 bytes used=2508517136, alloc=4914300, time=94.65 bytes used=2512518588, alloc=4914300, time=94.80 bytes used=2516519460, alloc=4914300, time=94.95 bytes used=2520520456, alloc=4914300, time=95.10 bytes used=2524521644, alloc=4914300, time=95.25 bytes used=2528522432, alloc=4914300, time=95.40 bytes used=2532523228, alloc=4914300, time=95.55 bytes used=2536524020, alloc=4914300, time=95.71 bytes used=2540524872, alloc=4914300, time=95.86 bytes used=2544525728, alloc=4914300, time=96.01 bytes used=2548526408, alloc=4914300, time=96.16 bytes used=2552527144, alloc=4914300, time=96.31 bytes used=2556527824, alloc=4914300, time=96.46 bytes used=2560528656, alloc=4914300, time=96.61 bytes used=2564529352, alloc=4914300, time=96.76 bytes used=2568530200, alloc=4914300, time=96.91 bytes used=2572530904, alloc=4914300, time=97.06 bytes used=2576531668, alloc=4914300, time=97.22 bytes used=2580532612, alloc=4914300, time=97.36 bytes used=2584533368, alloc=4914300, time=97.52 bytes used=2588534036, alloc=4914300, time=97.67 bytes used=2592534744, alloc=4914300, time=97.82 bytes used=2596535564, alloc=4914300, time=97.97 bytes used=2600536292, alloc=4914300, time=98.12 bytes used=2604537076, alloc=4914300, time=98.27 bytes used=2608537880, alloc=4914300, time=98.42 bytes used=2612538572, alloc=4914300, time=98.57 bytes used=2616539228, alloc=4914300, time=98.72 bytes used=2620539896, alloc=4914300, time=98.87 bytes used=2624540700, alloc=4914300, time=99.02 bytes used=2628541716, alloc=4914300, time=99.18 bytes used=2632542428, alloc=4914300, time=99.33 bytes used=2636543180, alloc=4914300, time=99.48 bytes used=2640544032, alloc=4914300, time=99.64 bytes used=2644545460, alloc=4914300, time=99.79 bytes used=2648546236, alloc=4914300, time=99.94 bytes used=2652547224, alloc=4914300, time=100.09 bytes used=2656548192, alloc=4914300, time=100.24 bytes used=2660548868, alloc=4914300, time=100.39 bytes used=2664549636, alloc=4914300, time=100.55 bytes used=2668550428, alloc=4914300, time=100.70 bytes used=2672551156, alloc=4914300, time=100.85 bytes used=2676551852, alloc=4914300, time=101.00 bytes used=2680552624, alloc=4914300, time=101.15 bytes used=2684553300, alloc=4914300, time=101.30 bytes used=2688553968, alloc=4914300, time=101.45 bytes used=2692554928, alloc=4914300, time=101.60 bytes used=2696555704, alloc=4914300, time=101.76 bytes used=2700556548, alloc=4914300, time=101.91 bytes used=2704557392, alloc=4914300, time=102.06 bytes used=2708558120, alloc=4914300, time=102.21 bytes used=2712559412, alloc=4914300, time=102.36 bytes used=2716560248, alloc=4914300, time=102.51 bytes used=2720561104, alloc=4914300, time=102.66 bytes used=2724561796, alloc=4914300, time=102.81 bytes used=2728562712, alloc=4914300, time=102.96 bytes used=2732563440, alloc=4914300, time=103.11 bytes used=2736564156, alloc=4914300, time=103.27 bytes used=2740565120, alloc=4914300, time=103.42 bytes used=2744565900, alloc=4914300, time=103.57 bytes used=2748566556, alloc=4914300, time=103.72 bytes used=2752567456, alloc=4914300, time=103.87 bytes used=2756568160, alloc=4914300, time=104.02 bytes used=2760569052, alloc=4914300, time=104.17 bytes used=2764570032, alloc=4914300, time=104.32 bytes used=2768570780, alloc=4914300, time=104.48 bytes used=2772571720, alloc=4914300, time=104.63 bytes used=2776572684, alloc=4914300, time=104.78 bytes used=2780573416, alloc=4914300, time=104.93 bytes used=2784574096, alloc=4914300, time=105.08 bytes used=2788575228, alloc=4914300, time=105.24 bytes used=2792575912, alloc=4914300, time=105.38 bytes used=2796576636, alloc=4914300, time=105.54 bytes used=2800577404, alloc=4914300, time=105.69 bytes used=2804578200, alloc=4914300, time=105.84 bytes used=2808579104, alloc=4914300, time=105.99 bytes used=2812579880, alloc=4914300, time=106.14 bytes used=2816580652, alloc=4914300, time=106.29 bytes used=2820581416, alloc=4914300, time=106.44 bytes used=2824582092, alloc=4914300, time=106.59 bytes used=2828582984, alloc=4914300, time=106.75 bytes used=2832583656, alloc=4914300, time=106.90 bytes used=2836584508, alloc=4914300, time=107.05 bytes used=2840585296, alloc=4914300, time=107.20 bytes used=2844586084, alloc=4914300, time=107.35 bytes used=2848587028, alloc=4914300, time=107.50 bytes used=2852587804, alloc=4914300, time=107.65 bytes used=2856589044, alloc=4914300, time=107.80 bytes used=2860589852, alloc=4914300, time=107.95 bytes used=2864590520, alloc=4914300, time=108.11 bytes used=2868591228, alloc=4914300, time=108.26 bytes used=2872591984, alloc=4914300, time=108.41 bytes used=2876592972, alloc=4914300, time=108.56 bytes used=2880593720, alloc=4914300, time=108.71 bytes used=2884594744, alloc=4914300, time=108.86 bytes used=2888595544, alloc=4914300, time=109.01 bytes used=2892596344, alloc=4914300, time=109.17 TOP MAIN SOLVE Loop bytes used=2896597128, alloc=4914300, time=109.32 t[1] = 0.56 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 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 = 5.694e+27 Order of pole (six term test) = 4.276e+53 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.621e+04 Order of pole (six term test) = 1.383e+07 bytes used=2900597816, alloc=4914300, time=109.47 bytes used=2904598552, alloc=4914300, time=109.62 bytes used=2908599288, alloc=4914300, time=109.77 bytes used=2912600620, alloc=4914300, time=109.92 bytes used=2916602032, alloc=4914300, time=110.07 bytes used=2920602736, alloc=4914300, time=110.22 bytes used=2924603476, alloc=4914300, time=110.37 bytes used=2928604192, alloc=4914300, time=110.52 bytes used=2932605084, alloc=4914300, time=110.68 bytes used=2936606284, alloc=4914300, time=110.83 bytes used=2940607248, alloc=4914300, time=110.98 bytes used=2944608400, alloc=4914300, time=111.13 bytes used=2948609208, alloc=4914300, time=111.28 bytes used=2952609868, alloc=4914300, time=111.43 bytes used=2956610816, alloc=4914300, time=111.58 bytes used=2960611504, alloc=4914300, time=111.73 bytes used=2964612208, alloc=4914300, time=111.89 bytes used=2968612892, alloc=4914300, time=112.04 bytes used=2972613704, alloc=4914300, time=112.19 bytes used=2976614756, alloc=4914300, time=112.34 bytes used=2980615524, alloc=4914300, time=112.49 bytes used=2984616392, alloc=4914300, time=112.64 bytes used=2988617168, alloc=4914300, time=112.79 bytes used=2992617920, alloc=4914300, time=112.94 bytes used=2996618788, alloc=4914300, time=113.10 bytes used=3000619464, alloc=4914300, time=113.25 bytes used=3004620224, alloc=4914300, time=113.39 bytes used=3008621036, alloc=4914300, time=113.54 bytes used=3012622500, alloc=4914300, time=113.70 bytes used=3016623188, alloc=4914300, time=113.85 bytes used=3020623980, alloc=4914300, time=114.00 bytes used=3024624844, alloc=4914300, time=114.15 bytes used=3028625540, alloc=4914300, time=114.30 bytes used=3032626396, alloc=4914300, time=114.45 bytes used=3036627084, alloc=4914300, time=114.60 bytes used=3040628288, alloc=4914300, time=114.75 bytes used=3044629128, alloc=4914300, time=114.91 bytes used=3048629852, alloc=4914300, time=115.06 bytes used=3052630592, alloc=4914300, time=115.21 bytes used=3056631472, alloc=4914300, time=115.36 bytes used=3060632448, alloc=4914300, time=115.51 bytes used=3064633104, alloc=4914300, time=115.66 bytes used=3068633896, alloc=4914300, time=115.81 bytes used=3072634752, alloc=4914300, time=115.96 bytes used=3076635476, alloc=4914300, time=116.11 bytes used=3080636196, alloc=4914300, time=116.26 bytes used=3084637136, alloc=4914300, time=116.41 bytes used=3088637936, alloc=4914300, time=116.57 bytes used=3092638880, alloc=4914300, time=116.72 bytes used=3096639720, alloc=4914300, time=116.87 bytes used=3100640680, alloc=4914300, time=117.02 bytes used=3104641612, alloc=4914300, time=117.18 bytes used=3108642576, alloc=4914300, time=117.33 bytes used=3112643628, alloc=4914300, time=117.48 bytes used=3116644348, alloc=4914300, time=117.63 bytes used=3120645164, alloc=4914300, time=117.78 bytes used=3124645920, alloc=4914300, time=117.93 bytes used=3128646644, alloc=4914300, time=118.08 bytes used=3132647476, alloc=4914300, time=118.23 bytes used=3136648604, alloc=4914300, time=118.38 bytes used=3140649328, alloc=4914300, time=118.54 bytes used=3144650184, alloc=4914300, time=118.69 bytes used=3148650992, alloc=4914300, time=118.84 bytes used=3152651728, alloc=4914300, time=118.99 bytes used=3156653324, alloc=4914300, time=119.14 bytes used=3160653984, alloc=4914300, time=119.29 bytes used=3164654720, alloc=4914300, time=119.44 bytes used=3168655440, alloc=4914300, time=119.59 bytes used=3172656248, alloc=4914300, time=119.74 bytes used=3176657376, alloc=4914300, time=119.89 bytes used=3180658160, alloc=4914300, time=120.04 bytes used=3184658916, alloc=4914300, time=120.19 bytes used=3188659816, alloc=4914300, time=120.34 bytes used=3192660680, alloc=4914300, time=120.50 bytes used=3196661688, alloc=4914300, time=120.65 bytes used=3200662908, alloc=4914300, time=120.80 bytes used=3204663676, alloc=4914300, time=120.95 bytes used=3208664340, alloc=4914300, time=121.10 bytes used=3212665192, alloc=4914300, time=121.25 bytes used=3216666016, alloc=4914300, time=121.40 bytes used=3220667512, alloc=4914300, time=121.56 bytes used=3224668364, alloc=4914300, time=121.71 bytes used=3228669124, alloc=4914300, time=121.86 bytes used=3232669896, alloc=4914300, time=122.01 bytes used=3236670968, alloc=4914300, time=122.16 bytes used=3240671852, alloc=4914300, time=122.31 bytes used=3244673248, alloc=4914300, time=122.46 bytes used=3248674040, alloc=4914300, time=122.62 bytes used=3252674700, alloc=4914300, time=122.77 bytes used=3256675420, alloc=4914300, time=122.92 bytes used=3260676148, alloc=4914300, time=123.07 bytes used=3264676816, alloc=4914300, time=123.22 bytes used=3268677820, alloc=4914300, time=123.38 bytes used=3272678604, alloc=4914300, time=123.53 bytes used=3276679368, alloc=4914300, time=123.68 bytes used=3280680184, alloc=4914300, time=123.83 bytes used=3284680988, alloc=4914300, time=123.98 bytes used=3288681876, alloc=4914300, time=124.13 bytes used=3292682792, alloc=4914300, time=124.28 bytes used=3296683668, alloc=4914300, time=124.43 bytes used=3300685192, alloc=4914300, time=124.58 bytes used=3304686028, alloc=4914300, time=124.73 bytes used=3308686792, alloc=4914300, time=124.88 bytes used=3312687604, alloc=4914300, time=125.03 bytes used=3316688368, alloc=4914300, time=125.18 bytes used=3320689176, alloc=4914300, time=125.33 bytes used=3324689880, alloc=4914300, time=125.48 bytes used=3328690700, alloc=4914300, time=125.64 bytes used=3332691532, alloc=4914300, time=125.79 bytes used=3336692356, alloc=4914300, time=125.94 bytes used=3340693056, alloc=4914300, time=126.09 bytes used=3344693816, alloc=4914300, time=126.24 bytes used=3348694500, alloc=4914300, time=126.39 bytes used=3352695388, alloc=4914300, time=126.54 bytes used=3356696452, alloc=4914300, time=126.70 bytes used=3360697120, alloc=4914300, time=126.85 bytes used=3364697880, alloc=4914300, time=127.00 bytes used=3368698844, alloc=4914300, time=127.15 TOP MAIN SOLVE Loop bytes used=3372699524, alloc=4914300, time=127.30 t[1] = 0.57 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.898e+27 Order of pole (six term test) = -2.603e+54 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.629e+04 Order of pole (six term test) = 1.397e+07 bytes used=3376700288, alloc=4914300, time=127.46 bytes used=3380701148, alloc=4914300, time=127.61 bytes used=3384701828, alloc=4914300, time=127.76 bytes used=3388703212, alloc=4914300, time=127.91 bytes used=3392703892, alloc=4914300, time=128.06 bytes used=3396704752, alloc=4914300, time=128.21 bytes used=3400705568, alloc=4914300, time=128.36 bytes used=3404706376, alloc=4914300, time=128.52 bytes used=3408707280, alloc=4914300, time=128.67 bytes used=3412708272, alloc=4914300, time=128.82 bytes used=3416708984, alloc=4914300, time=128.98 bytes used=3420709792, alloc=4914300, time=129.13 bytes used=3424710512, alloc=4914300, time=129.28 bytes used=3428711780, alloc=4914300, time=129.43 bytes used=3432712656, alloc=4914300, time=129.58 bytes used=3436713436, alloc=4914300, time=129.73 bytes used=3440714800, alloc=4914300, time=129.88 bytes used=3444715644, alloc=4914300, time=130.03 bytes used=3448716352, alloc=4914300, time=130.19 bytes used=3452716992, alloc=4914300, time=130.34 bytes used=3456717704, alloc=4914300, time=130.49 bytes used=3460718644, alloc=4914300, time=130.64 bytes used=3464719640, alloc=4914300, time=130.79 bytes used=3468720380, alloc=4914300, time=130.94 bytes used=3472721292, alloc=4914300, time=131.09 bytes used=3476722028, alloc=4914300, time=131.24 bytes used=3480722880, alloc=4914300, time=131.40 bytes used=3484723600, alloc=4914300, time=131.55 bytes used=3488724440, alloc=4914300, time=131.70 bytes used=3492725592, alloc=4914300, time=131.85 bytes used=3496726396, alloc=4914300, time=132.00 bytes used=3500727060, alloc=4914300, time=132.15 bytes used=3504727988, alloc=4914300, time=132.30 bytes used=3508728988, alloc=4914300, time=132.45 bytes used=3512729744, alloc=4914300, time=132.61 bytes used=3516730456, alloc=4914300, time=132.76 bytes used=3520731284, alloc=4914300, time=132.91 bytes used=3524732036, alloc=4914300, time=133.06 bytes used=3528732836, alloc=4914300, time=133.21 bytes used=3532733764, alloc=4914300, time=133.36 bytes used=3536734620, alloc=4914300, time=133.51 bytes used=3540735336, alloc=4914300, time=133.66 bytes used=3544736056, alloc=4914300, time=133.81 bytes used=3548736748, alloc=4914300, time=133.97 bytes used=3552737572, alloc=4914300, time=134.12 bytes used=3556738336, alloc=4914300, time=134.27 bytes used=3560739064, alloc=4914300, time=134.42 bytes used=3564739864, alloc=4914300, time=134.57 bytes used=3568740604, alloc=4914300, time=134.72 bytes used=3572741348, alloc=4914300, time=134.87 bytes used=3576742456, alloc=4914300, time=135.02 bytes used=3580743264, alloc=4914300, time=135.18 bytes used=3584743952, alloc=4914300, time=135.33 bytes used=3588744608, alloc=4914300, time=135.47 bytes used=3592745668, alloc=4914300, time=135.62 bytes used=3596746600, alloc=4914300, time=135.78 bytes used=3600747460, alloc=4914300, time=135.93 bytes used=3604748488, alloc=4914300, time=136.08 bytes used=3608749476, alloc=4914300, time=136.23 bytes used=3612750208, alloc=4914300, time=136.38 bytes used=3616751076, alloc=4914300, time=136.53 bytes used=3620751936, alloc=4914300, time=136.68 bytes used=3624752984, alloc=4914300, time=136.83 bytes used=3628753676, alloc=4914300, time=136.98 bytes used=3632754488, alloc=4914300, time=137.13 bytes used=3636755372, alloc=4914300, time=137.29 bytes used=3640756160, alloc=4914300, time=137.44 bytes used=3644756936, alloc=4914300, time=137.59 bytes used=3648757656, alloc=4914300, time=137.74 bytes used=3652758536, alloc=4914300, time=137.89 bytes used=3656759436, alloc=4914300, time=138.04 bytes used=3660760160, alloc=4914300, time=138.19 bytes used=3664760844, alloc=4914300, time=138.34 bytes used=3668761748, alloc=4914300, time=138.49 bytes used=3672763408, alloc=4914300, time=138.64 bytes used=3676764156, alloc=4914300, time=138.79 bytes used=3680764844, alloc=4914300, time=138.94 bytes used=3684765608, alloc=4914300, time=139.09 bytes used=3688766568, alloc=4914300, time=139.25 bytes used=3692767268, alloc=4914300, time=139.40 bytes used=3696767988, alloc=4914300, time=139.55 bytes used=3700768708, alloc=4914300, time=139.70 bytes used=3704769604, alloc=4914300, time=139.85 bytes used=3708770432, alloc=4914300, time=140.00 bytes used=3712771332, alloc=4914300, time=140.15 bytes used=3716772004, alloc=4914300, time=140.30 bytes used=3720773084, alloc=4914300, time=140.45 bytes used=3724773808, alloc=4914300, time=140.60 bytes used=3728774672, alloc=4914300, time=140.75 bytes used=3732775472, alloc=4914300, time=140.91 bytes used=3736776644, alloc=4914300, time=141.06 bytes used=3740777356, alloc=4914300, time=141.21 bytes used=3744778192, alloc=4914300, time=141.36 bytes used=3748779112, alloc=4914300, time=141.51 bytes used=3752779856, alloc=4914300, time=141.66 bytes used=3756780948, alloc=4914300, time=141.81 bytes used=3760781648, alloc=4914300, time=141.97 bytes used=3764782392, alloc=4914300, time=142.12 bytes used=3768783096, alloc=4914300, time=142.27 bytes used=3772783948, alloc=4914300, time=142.42 bytes used=3776784604, alloc=4914300, time=142.57 bytes used=3780785348, alloc=4914300, time=142.72 bytes used=3784786112, alloc=4914300, time=142.87 bytes used=3788786820, alloc=4914300, time=143.02 bytes used=3792787936, alloc=4914300, time=143.17 bytes used=3796788816, alloc=4914300, time=143.33 bytes used=3800789652, alloc=4914300, time=143.48 bytes used=3804790424, alloc=4914300, time=143.63 bytes used=3808791160, alloc=4914300, time=143.78 bytes used=3812792084, alloc=4914300, time=143.93 bytes used=3816792808, alloc=4914300, time=144.08 bytes used=3820793900, alloc=4914300, time=144.23 bytes used=3824794664, alloc=4914300, time=144.38 bytes used=3828795428, alloc=4914300, time=144.53 bytes used=3832796380, alloc=4914300, time=144.68 bytes used=3836797084, alloc=4914300, time=144.83 bytes used=3840797788, alloc=4914300, time=144.99 bytes used=3844798468, alloc=4914300, time=145.13 TOP MAIN SOLVE Loop bytes used=3848799340, alloc=4914300, time=145.29 t[1] = 0.58 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.637e+04 Order of pole (six term test) = 1.411e+07 bytes used=3852800088, alloc=4914300, time=145.44 bytes used=3856800748, alloc=4914300, time=145.59 bytes used=3860801408, alloc=4914300, time=145.74 bytes used=3864802112, alloc=4914300, time=145.89 bytes used=3868802772, alloc=4914300, time=146.04 bytes used=3872803484, alloc=4914300, time=146.20 bytes used=3876804240, alloc=4914300, time=146.35 bytes used=3880804904, alloc=4914300, time=146.50 bytes used=3884805608, alloc=4914300, time=146.65 bytes used=3888806288, alloc=4914300, time=146.80 bytes used=3892807068, alloc=4914300, time=146.95 bytes used=3896807760, alloc=4914300, time=147.10 bytes used=3900808604, alloc=4914300, time=147.25 bytes used=3904809544, alloc=4914300, time=147.41 bytes used=3908810324, alloc=4914300, time=147.56 bytes used=3912811020, alloc=4914300, time=147.71 bytes used=3916811752, alloc=4914300, time=147.86 bytes used=3920812544, alloc=4914300, time=148.01 bytes used=3924813332, alloc=4914300, time=148.16 bytes used=3928814496, alloc=4914300, time=148.31 bytes used=3932815860, alloc=4914300, time=148.47 bytes used=3936816744, alloc=4914300, time=148.62 bytes used=3940817580, alloc=4914300, time=148.77 bytes used=3944818472, alloc=4914300, time=148.92 bytes used=3948819296, alloc=4914300, time=149.07 bytes used=3952820268, alloc=4914300, time=149.23 bytes used=3956821020, alloc=4914300, time=149.38 bytes used=3960821696, alloc=4914300, time=149.53 bytes used=3964822472, alloc=4914300, time=149.68 bytes used=3968823244, alloc=4914300, time=149.83 bytes used=3972824284, alloc=4914300, time=149.98 bytes used=3976825096, alloc=4914300, time=150.13 bytes used=3980825852, alloc=4914300, time=150.28 bytes used=3984826572, alloc=4914300, time=150.44 bytes used=3988827344, alloc=4914300, time=150.59 bytes used=3992828056, alloc=4914300, time=150.74 bytes used=3996828764, alloc=4914300, time=150.89 bytes used=4000829712, alloc=4914300, time=151.04 bytes used=4004830460, alloc=4914300, time=151.19 bytes used=4008831212, alloc=4914300, time=151.34 bytes used=4012832208, alloc=4914300, time=151.49 bytes used=4016832920, alloc=4914300, time=151.64 bytes used=4020833756, alloc=4914300, time=151.79 bytes used=4024834548, alloc=4914300, time=151.94 bytes used=4028835552, alloc=4914300, time=152.10 bytes used=4032836484, alloc=4914300, time=152.25 bytes used=4036837228, alloc=4914300, time=152.40 bytes used=4040837940, alloc=4914300, time=152.55 bytes used=4044838872, alloc=4914300, time=152.70 bytes used=4048839872, alloc=4914300, time=152.86 bytes used=4052840744, alloc=4914300, time=153.01 bytes used=4056841568, alloc=4914300, time=153.16 bytes used=4060842284, alloc=4914300, time=153.31 bytes used=4064843436, alloc=4914300, time=153.46 bytes used=4068844348, alloc=4914300, time=153.61 bytes used=4072845272, alloc=4914300, time=153.76 bytes used=4076846072, alloc=4914300, time=153.91 bytes used=4080846736, alloc=4914300, time=154.06 bytes used=4084847580, alloc=4914300, time=154.21 bytes used=4088848320, alloc=4914300, time=154.37 bytes used=4092849144, alloc=4914300, time=154.52 bytes used=4096849900, alloc=4914300, time=154.67 bytes used=4100850572, alloc=4914300, time=154.82 bytes used=4104851432, alloc=4914300, time=154.97 bytes used=4108852132, alloc=4914300, time=155.12 bytes used=4112852920, alloc=4914300, time=155.27 bytes used=4116853720, alloc=4914300, time=155.42 bytes used=4120854412, alloc=4914300, time=155.57 bytes used=4124855320, alloc=4914300, time=155.72 bytes used=4128856132, alloc=4914300, time=155.88 bytes used=4132856976, alloc=4914300, time=156.03 bytes used=4136857920, alloc=4914300, time=156.17 bytes used=4140858716, alloc=4914300, time=156.32 bytes used=4144859564, alloc=4914300, time=156.47 bytes used=4148860420, alloc=4914300, time=156.62 bytes used=4152861216, alloc=4914300, time=156.78 bytes used=4156862020, alloc=4914300, time=156.93 bytes used=4160862816, alloc=4914300, time=157.08 bytes used=4164863556, alloc=4914300, time=157.23 bytes used=4168864252, alloc=4914300, time=157.38 bytes used=4172864972, alloc=4914300, time=157.53 bytes used=4176865836, alloc=4914300, time=157.68 bytes used=4180866536, alloc=4914300, time=157.83 bytes used=4184867384, alloc=4914300, time=157.98 bytes used=4188868160, alloc=4914300, time=158.13 bytes used=4192869148, alloc=4914300, time=158.28 bytes used=4196870072, alloc=4914300, time=158.44 bytes used=4200871160, alloc=4914300, time=158.59 bytes used=4204872064, alloc=4914300, time=158.75 bytes used=4208872808, alloc=4914300, time=158.90 bytes used=4212873588, alloc=4914300, time=159.05 bytes used=4216874320, alloc=4914300, time=159.20 bytes used=4220875044, alloc=4914300, time=159.35 bytes used=4224875932, alloc=4914300, time=159.50 bytes used=4228876640, alloc=4914300, time=159.65 bytes used=4232877296, alloc=4914300, time=159.80 bytes used=4236878000, alloc=4914300, time=159.95 bytes used=4240878692, alloc=4914300, time=160.10 bytes used=4244880204, alloc=4914300, time=160.26 bytes used=4248880968, alloc=4914300, time=160.41 bytes used=4252882248, alloc=4914300, time=160.56 bytes used=4256883444, alloc=4914300, time=160.71 bytes used=4260884192, alloc=4914300, time=160.86 bytes used=4264885844, alloc=4914300, time=161.01 bytes used=4268886604, alloc=4914300, time=161.16 bytes used=4272887428, alloc=4914300, time=161.31 bytes used=4276888184, alloc=4914300, time=161.46 bytes used=4280889464, alloc=4914300, time=161.61 bytes used=4284890328, alloc=4914300, time=161.76 bytes used=4288891052, alloc=4914300, time=161.91 bytes used=4292892416, alloc=4914300, time=162.06 bytes used=4296893140, alloc=4914300, time=162.21 bytes used=4300894140, alloc=4914300, time=162.36 bytes used=4304894916, alloc=4914300, time=162.52 bytes used=4308895600, alloc=4914300, time=162.67 bytes used=4312896380, alloc=4914300, time=162.82 bytes used=4316897124, alloc=4914300, time=162.97 bytes used=4320897884, alloc=4914300, time=163.12 TOP MAIN SOLVE Loop bytes used=4324898948, alloc=4914300, time=163.27 t[1] = 0.59 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 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.646e+04 Order of pole (six term test) = 1.425e+07 bytes used=4328899868, alloc=4914300, time=163.42 bytes used=4332900760, alloc=4914300, time=163.57 bytes used=4336901616, alloc=4914300, time=163.72 bytes used=4340902628, alloc=4914300, time=163.88 bytes used=4344903424, alloc=4914300, time=164.03 bytes used=4348904368, alloc=4914300, time=164.18 bytes used=4352905080, alloc=4914300, time=164.33 bytes used=4356905768, alloc=4914300, time=164.49 bytes used=4360906772, alloc=4914300, time=164.64 bytes used=4364907480, alloc=4914300, time=164.79 bytes used=4368908540, alloc=4914300, time=164.94 bytes used=4372909364, alloc=4914300, time=165.09 bytes used=4376910116, alloc=4914300, time=165.25 bytes used=4380910956, alloc=4914300, time=165.40 bytes used=4384911680, alloc=4914300, time=165.55 bytes used=4388912404, alloc=4914300, time=165.70 bytes used=4392913096, alloc=4914300, time=165.85 bytes used=4396913812, alloc=4914300, time=166.00 bytes used=4400914644, alloc=4914300, time=166.15 bytes used=4404915472, alloc=4914300, time=166.31 bytes used=4408916276, alloc=4914300, time=166.46 bytes used=4412917228, alloc=4914300, time=166.61 bytes used=4416917996, alloc=4914300, time=166.76 bytes used=4420918824, alloc=4914300, time=166.91 bytes used=4424919544, alloc=4914300, time=167.06 bytes used=4428920248, alloc=4914300, time=167.21 bytes used=4432920928, alloc=4914300, time=167.37 bytes used=4436921652, alloc=4914300, time=167.52 bytes used=4440922984, alloc=4914300, time=167.67 bytes used=4444923772, alloc=4914300, time=167.82 bytes used=4448924664, alloc=4914300, time=167.97 bytes used=4452925788, alloc=4914300, time=168.12 bytes used=4456926644, alloc=4914300, time=168.28 bytes used=4460927324, alloc=4914300, time=168.43 bytes used=4464928316, alloc=4914300, time=168.58 bytes used=4468929084, alloc=4914300, time=168.73 bytes used=4472929900, alloc=4914300, time=168.88 bytes used=4476930776, alloc=4914300, time=169.03 bytes used=4480931500, alloc=4914300, time=169.18 bytes used=4484932284, alloc=4914300, time=169.34 bytes used=4488933040, alloc=4914300, time=169.49 bytes used=4492933912, alloc=4914300, time=169.64 bytes used=4496934688, alloc=4914300, time=169.79 bytes used=4500935388, alloc=4914300, time=169.94 bytes used=4504936584, alloc=4914300, time=170.09 bytes used=4508937336, alloc=4914300, time=170.25 bytes used=4512938072, alloc=4914300, time=170.40 bytes used=4516939080, alloc=4914300, time=170.55 bytes used=4520939860, alloc=4914300, time=170.70 bytes used=4524940620, alloc=4914300, time=170.85 bytes used=4528941660, alloc=4914300, time=171.01 bytes used=4532942472, alloc=4914300, time=171.16 bytes used=4536943400, alloc=4914300, time=171.31 bytes used=4540944140, alloc=4914300, time=171.46 bytes used=4544944880, alloc=4914300, time=171.61 bytes used=4548945608, alloc=4914300, time=171.76 bytes used=4552946388, alloc=4914300, time=171.91 bytes used=4556947092, alloc=4914300, time=172.06 bytes used=4560947952, alloc=4914300, time=172.21 bytes used=4564948776, alloc=4914300, time=172.36 bytes used=4568950180, alloc=4914300, time=172.51 bytes used=4572950916, alloc=4914300, time=172.66 bytes used=4576951820, alloc=4914300, time=172.81 bytes used=4580952888, alloc=4914300, time=172.97 bytes used=4584953568, alloc=4914300, time=173.12 bytes used=4588954304, alloc=4914300, time=173.27 bytes used=4592955128, alloc=4914300, time=173.42 bytes used=4596955824, alloc=4914300, time=173.57 bytes used=4600956588, alloc=4914300, time=173.72 bytes used=4604957264, alloc=4914300, time=173.87 bytes used=4608958036, alloc=4914300, time=174.02 bytes used=4612958880, alloc=4914300, time=174.17 bytes used=4616959920, alloc=4914300, time=174.33 bytes used=4620960824, alloc=4914300, time=174.48 bytes used=4624962016, alloc=4914300, time=174.63 bytes used=4628962836, alloc=4914300, time=174.78 bytes used=4632963508, alloc=4914300, time=174.93 bytes used=4636964264, alloc=4914300, time=175.08 bytes used=4640965104, alloc=4914300, time=175.23 bytes used=4644965852, alloc=4914300, time=175.38 bytes used=4648966624, alloc=4914300, time=175.53 bytes used=4652967756, alloc=4914300, time=175.68 bytes used=4656968504, alloc=4914300, time=175.84 bytes used=4660969264, alloc=4914300, time=175.99 bytes used=4664969960, alloc=4914300, time=176.13 bytes used=4668970788, alloc=4914300, time=176.28 bytes used=4672971600, alloc=4914300, time=176.44 bytes used=4676972448, alloc=4914300, time=176.59 bytes used=4680973128, alloc=4914300, time=176.74 bytes used=4684974124, alloc=4914300, time=176.89 bytes used=4688974932, alloc=4914300, time=177.04 bytes used=4692975656, alloc=4914300, time=177.19 bytes used=4696976344, alloc=4914300, time=177.34 bytes used=4700977116, alloc=4914300, time=177.49 bytes used=4704978276, alloc=4914300, time=177.64 bytes used=4708979232, alloc=4914300, time=177.79 bytes used=4712980008, alloc=4914300, time=177.94 bytes used=4716980992, alloc=4914300, time=178.09 bytes used=4720981928, alloc=4914300, time=178.24 bytes used=4724982632, alloc=4914300, time=178.39 bytes used=4728983500, alloc=4914300, time=178.54 bytes used=4732984236, alloc=4914300, time=178.70 bytes used=4736985108, alloc=4914300, time=178.85 bytes used=4740985864, alloc=4914300, time=179.00 bytes used=4744986796, alloc=4914300, time=179.15 bytes used=4748987732, alloc=4914300, time=179.30 bytes used=4752988540, alloc=4914300, time=179.45 bytes used=4756989536, alloc=4914300, time=179.61 bytes used=4760990332, alloc=4914300, time=179.75 bytes used=4764991216, alloc=4914300, time=179.91 bytes used=4768991980, alloc=4914300, time=180.06 bytes used=4772992812, alloc=4914300, time=180.21 bytes used=4776993516, alloc=4914300, time=180.36 Finished! Maximum Time Reached before Solution Completed! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 996 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 58 Seconds Expected Time Remaining = 6 Minutes 2 Seconds Optimized Time Remaining = 5 Minutes 59 Seconds Expected Total Time = 8 Minutes 59 Seconds Time to Timeout Unknown Percent Done = 33.23 % > quit bytes used=4778265476, alloc=4914300, time=180.41