#BEGIN OUTFILE1 # Begin Function number 3 display_poles := proc() global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; local rad_given; if (glob_type_given_pole = 4) then # if number 1 rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); elif (glob_type_given_pole = 3) then # if number 2 omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); else omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); fi;# end if 2; if (array_poles[1,1] <> glob_large_float) then # if number 2 omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); else omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); fi;# end if 2; if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); else omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); fi;# end if 2; if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); else omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); fi;# end if 2 ; end; # End Function number 3 # Begin Function number 4 check_sign := proc( x0 ,xf) local ret; if (xf > x0) then # if number 2 ret := 1.0; else ret := -1.0; fi;# end if 2; ret;; end; # End Function number 4 # Begin Function number 5 est_size_answer := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local min_size; min_size := glob_large_float; if (omniabs(array_y[1]) < min_size) then # if number 2 min_size := omniabs(array_y[1]); omniout_float(ALWAYS,"min_size",32,min_size,32,""); fi;# end if 2; if (min_size < 1.0) then # if number 2 min_size := 1.0; omniout_float(ALWAYS,"min_size",32,min_size,32,""); fi;# end if 2; min_size; end; # End Function number 5 # Begin Function number 6 test_suggested_h := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; max_estimated_step_error := 0.0; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); if (est_tmp >= max_estimated_step_error) then # if number 2 max_estimated_step_error := est_tmp; fi;# end if 2; omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); max_estimated_step_error; end; # End Function number 6 # Begin Function number 7 reached_interval := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local ret; if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 ret := true; else ret := false; fi;# end if 2; return(ret); end; # End Function number 7 # Begin Function number 8 display_alot := proc(iter) global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; #TOP DISPLAY ALOT if (reached_interval()) then # if number 2 if (iter >= 0) then # if number 3 ind_var := array_x[1]; omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); if (omniabs(analytic_val_y) <> 0.0) then # if number 4 relerr := abserr*100.0/omniabs(analytic_val_y); if (relerr > 0.0000000000000000000000000000000001) then # if number 5 glob_good_digits := -trunc(log10(relerr)) + 3; else glob_good_digits := Digits; fi;# end if 5; else relerr := -1.0 ; glob_good_digits := -1; fi;# end if 4; if (glob_iter = 1) then # if number 4 array_1st_rel_error[1] := relerr; else array_last_rel_error[1] := relerr; fi;# end if 4; omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") ; omniout_float(ALWAYS,"h ",4,glob_h,20," "); fi;# end if 3; #BOTTOM DISPLAY ALOT fi;# end if 2; end; # End Function number 8 # Begin Function number 9 adjust_for_pole := proc(h_param) global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local hnew, sz2, tmp; #TOP ADJUST FOR POLE hnew := h_param; glob_normmax := glob_small_float; if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 tmp := omniabs(array_y_higher[1,1]); if (tmp < glob_normmax) then # if number 3 glob_normmax := tmp; fi;# end if 3 fi;# end if 2; if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 sz2 := array_pole[1]/10.0; if (sz2 < hnew) then # if number 3 omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); omniout_str(INFO,"Reached Optimal"); return(hnew); fi;# end if 3 fi;# end if 2; if ( not glob_reached_optimal_h) then # if number 2 glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1]; fi;# end if 2; hnew := sz2; ;#END block return(hnew); #BOTTOM ADJUST FOR POLE end; # End Function number 9 # Begin Function number 10 prog_report := proc(x_start,x_end) global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; #TOP PROGRESS REPORT clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO,"Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO,"Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 omniout_str_noeol(INFO,"Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO,"Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO,"Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)); fi;# end if 2; omniout_str_noeol(INFO,"Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); #BOTTOM PROGRESS REPORT end; # End Function number 10 # Begin Function number 11 check_for_pole := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; #TOP CHECK FOR POLE array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1,1] := glob_large_float; array_poles[1,2] := glob_large_float; #TOP radius ratio test in Henrici1 found_sing := 1; n := glob_max_terms - 1 - 10; cnt := 0; while ((cnt < 5) and (found_sing = 1)) do # do number 1 if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 found_sing := 0; else tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); tmp_ratio := tmp_rad / prev_tmp_rad; if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 if (tmp_rad < rad_c) then # if number 4 rad_c := tmp_rad; fi;# end if 4; elif (cnt = 0) then # if number 4 if (tmp_rad < rad_c) then # if number 5 rad_c := tmp_rad; fi;# end if 5; elif (cnt > 0) then # if number 5 found_sing := 0; fi;# end if 5 fi;# end if 4; prev_tmp_rad := tmp_rad;; cnt := cnt + 1; n := n + 1; od;# end do number 1; if (found_sing = 1) then # if number 4 if (rad_c < array_pole[1]) then # if number 5 array_pole[1] := rad_c; array_poles[1,1] := rad_c; fi;# end if 5; fi;# end if 4; #BOTTOM radius ratio test in Henrici1 #IN RADII REAL EQ = 1 #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 #Applies to pole of arbitrary r_order on the real axis, #Due to Prof. George Corliss. n := glob_max_terms; m := n - 1 - 1; while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 m := m - 1; od;# end do number 1; if (m > 10) then # if number 4 rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; if (omniabs(hdrc) > 0.0) then # if number 5 rcs := glob_h/hdrc; ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; array_real_poles[1,1] := rcs; array_real_poles[1,2] := ord_no; else array_real_poles[1,1] := glob_large_float; array_real_poles[1,2] := glob_large_float; fi;# end if 5 else array_real_poles[1,1] := glob_large_float; array_real_poles[1,2] := glob_large_float; fi;# end if 4; #BOTTOM RADII REAL EQ = 1 #TOP RADII COMPLEX EQ = 1 #Computes radius of convergence for complex conjugate pair of poles. #from 6 adjacent Taylor series terms #Also computes r_order of poles. #Due to Manuel Prieto. #With a correction by Dennis J. Darland n := glob_max_terms - 1 - 1; cnt := 0; while ((cnt < 5) and (n >= 10)) do # do number 1 if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 cnt := cnt + 1; else cnt := 0; fi;# end if 4; n := n - 1; od;# end do number 1; m := n + cnt; if (m <= 10) then # if number 4 rad_c := glob_large_float; ord_no := glob_large_float; else rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 rad_c := glob_large_float; ord_no := glob_large_float; else if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; if (omniabs(rcs) <> 0.0) then # if number 7 if (rcs > 0.0) then # if number 8 rad_c := sqrt(rcs) * omniabs(glob_h); else rad_c := glob_large_float; fi;# end if 8 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 7 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 6 fi;# end if 5; array_complex_poles[1,1] := rad_c; array_complex_poles[1,2] := ord_no; fi;# end if 4; #BOTTOM RADII COMPLEX EQ = 1 #START ADJUST ALL SERIES if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 h_new := array_pole[1] * glob_ratio_of_radius; term := 1; ratio := 1.0; while (term <= glob_max_terms) do # do number 1 array_y[term] := array_y[term]* ratio; array_y_higher[1,term] := array_y_higher[1,term]* ratio; array_x[term] := array_x[term]* ratio; ratio := ratio * h_new / omniabs(glob_h); term := term + 1; od;# end do number 1; glob_h := h_new; fi;# end if 4; #BOTTOM ADJUST ALL SERIES ; if (reached_interval()) then # if number 4 display_poles(); fi;# end if 4 end; # End Function number 11 # Begin Function number 12 get_norms := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local iii; if ( not glob_initial_pass) then # if number 4 iii := 1; while (iii <= glob_max_terms) do # do number 1 array_norms[iii] := 0.0; iii := iii + 1; od;# end do number 1; #TOP GET NORMS iii := 1; while (iii <= glob_max_terms) do # do number 1 if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 array_norms[iii] := omniabs(array_y[iii]); fi;# end if 5; iii := iii + 1; od;# end do number 1 #BOTTOM GET NORMS ; fi;# end if 4; end; # End Function number 12 # Begin Function number 13 atomall := proc() global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; local kkk, order_d, adj2, adj3 , temporary, term; #TOP ATOMALL #END OUTFILE1 #BEGIN ATOMHDR1 # emit pre mult FULL FULL $eq_no = 1 i = 1 array_tmp1[1] := (array_y[1] * (array_y[1])); #emit pre add CONST FULL $eq_no = 1 i = 1 array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 if ( not array_y_set_initial[1,2]) then # if number 1 if (1 <= glob_max_terms) then # if number 2 temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); array_y[2] := temporary; array_y_higher[1,2] := temporary; temporary := temporary / glob_h * (1.0); array_y_higher[2,1] := temporary; fi;# end if 2; fi;# end if 1; kkk := 2; #END ATOMHDR1 #BEGIN ATOMHDR2 # emit pre mult FULL FULL $eq_no = 1 i = 2 array_tmp1[2] := ats(2,array_y,array_y,1); #emit pre add CONST FULL $eq_no = 1 i = 2 array_tmp2[2] := array_tmp1[2]; #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 if ( not array_y_set_initial[1,3]) then # if number 1 if (2 <= glob_max_terms) then # if number 2 temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); array_y[3] := temporary; array_y_higher[1,3] := temporary; temporary := temporary / glob_h * (2.0); array_y_higher[2,2] := temporary; fi;# end if 2; fi;# end if 1; kkk := 3; #END ATOMHDR2 #BEGIN ATOMHDR3 # emit pre mult FULL FULL $eq_no = 1 i = 3 array_tmp1[3] := ats(3,array_y,array_y,1); #emit pre add CONST FULL $eq_no = 1 i = 3 array_tmp2[3] := array_tmp1[3]; #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 if ( not array_y_set_initial[1,4]) then # if number 1 if (3 <= glob_max_terms) then # if number 2 temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); array_y[4] := temporary; array_y_higher[1,4] := temporary; temporary := temporary / glob_h * (3.0); array_y_higher[2,3] := temporary; fi;# end if 2; fi;# end if 1; kkk := 4; #END ATOMHDR3 #BEGIN ATOMHDR4 # emit pre mult FULL FULL $eq_no = 1 i = 4 array_tmp1[4] := ats(4,array_y,array_y,1); #emit pre add CONST FULL $eq_no = 1 i = 4 array_tmp2[4] := array_tmp1[4]; #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 if ( not array_y_set_initial[1,5]) then # if number 1 if (4 <= glob_max_terms) then # if number 2 temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); array_y[5] := temporary; array_y_higher[1,5] := temporary; temporary := temporary / glob_h * (4.0); array_y_higher[2,4] := temporary; fi;# end if 2; fi;# end if 1; kkk := 5; #END ATOMHDR4 #BEGIN ATOMHDR5 # emit pre mult FULL FULL $eq_no = 1 i = 5 array_tmp1[5] := ats(5,array_y,array_y,1); #emit pre add CONST FULL $eq_no = 1 i = 5 array_tmp2[5] := array_tmp1[5]; #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 if ( not array_y_set_initial[1,6]) then # if number 1 if (5 <= glob_max_terms) then # if number 2 temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); array_y[6] := temporary; array_y_higher[1,6] := temporary; temporary := temporary / glob_h * (5.0); array_y_higher[2,5] := temporary; fi;# end if 2; fi;# end if 1; kkk := 6; #END ATOMHDR5 #BEGIN OUTFILE3 #Top Atomall While Loop-- outfile3 while (kkk <= glob_max_terms) do # do number 1 #END OUTFILE3 #BEGIN OUTFILE4 #emit mult FULL FULL $eq_no = 1 array_tmp1[kkk] := ats(kkk,array_y,array_y,1); #emit NOT FULL - FULL add $eq_no = 1 array_tmp2[kkk] := array_tmp1[kkk]; #emit assign $eq_no = 1 order_d := 1; if (kkk + order_d < glob_max_terms) then # if number 1 if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); array_y[kkk + order_d] := temporary; array_y_higher[1,kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while (term >= 1) do # do number 1 if (adj3 <= order_d + 1) then # if number 3 if (adj2 > 0) then # if number 4 temporary := temporary / glob_h * convfp(adj2); else temporary := temporary; fi;# end if 4; array_y_higher[adj3,term] := temporary; fi;# end if 3; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1; od;# end do number 1 fi;# end if 2 fi;# end if 1; kkk := kkk + 1; od;# end do number 1; #BOTTOM ATOMALL #END OUTFILE4 #BEGIN OUTFILE5 #BOTTOM ATOMALL ??? end; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # 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; # End Function number 15 # Begin Function number 16 logditto := proc(file) fprintf(file,""); fprintf(file,"ditto"); fprintf(file,""); end; # End Function number 16 # Begin Function number 17 logitem_integer := proc(file,n) fprintf(file,""); fprintf(file,"%d",n); fprintf(file,""); end; # End Function number 17 # Begin Function number 18 logitem_str := proc(file,str) fprintf(file,""); fprintf(file,str); fprintf(file,""); end; # 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; # End Function number 19 # Begin Function number 20 log_revs := proc(file,revs) fprintf(file,revs); end; # End Function number 20 # Begin Function number 21 logitem_float := proc(file,x) fprintf(file,""); fprintf(file,"%g",x); fprintf(file,""); end; # 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; # End Function number 22 # Begin Function number 23 logstart := proc(file) fprintf(file,""); end; # End Function number 23 # Begin Function number 24 logend := proc(file) fprintf(file,"\n"); end; # 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; # 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; # 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; # End Function number 27 # Begin Function number 28 factorial_2 := proc(nnn) nnn!; end; # 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; # 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; # End Function number 30 # Begin Function number 31 convfp := proc(mmm) (mmm); end; # End Function number 31 # Begin Function number 32 convfloat := proc(mmm) (mmm); end; # End Function number 32 # Begin Function number 33 elapsed_time_seconds := proc() time(); end; # End Function number 33 # Begin Function number 34 omniabs := proc(x) abs(x); end; # End Function number 34 # Begin Function number 35 expt := proc(x,y) (x^y); end; # 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; # End Function number 36 #END ATS LIBRARY BLOCK #BEGIN USER DEF BLOCK #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0/(1.0 - 2.0*x)); end; #END USER DEF BLOCK #END USER DEF BLOCK #END OUTFILE5 # Begin Function number 2 main := proc() #BEGIN OUTFIEMAIN local d1,d2,d3,d4,est_err_2,niii,done_once, term,ord,order_diff,term_no,html_log_file,iiif,jjjf, rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, x_start,x_end ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, #Top Generate Globals Decl MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.0; glob_ratio_of_radius := 0.1; glob_percent_done := 0.0; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.0; glob_clock_start_sec := 0.0; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.000001; glob_type_given_pole := 0; glob_large_float := 9.0e100; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.0; glob_next_display := 0.0; glob_dump_analytic := false; glob_abserr := 0.1e-10; glob_relerr := 0.1e-10; glob_max_hours := 0.0; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1e-10; glob_max_trunc_err := 0.1e-10; glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.0; glob_optimal_start := 0.0; glob_small_float := 0.0; glob_smallish_float := 0.0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.0; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.0; glob_max_minutes := 0.0; #Write Set Defaults glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.0; glob_max_minutes := 15.0; omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS,"##############temp/nonlinear2postode.ode#################"); omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS,"Digits:=32;"); omniout_str(ALWAYS,"max_terms:=30;"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS,"## problem from Boyce DePrima -"); omniout_str(ALWAYS,"## _Elementary Differential Equations and Boundary Value Problems_"); omniout_str(ALWAYS,"## page 23"); omniout_str(ALWAYS,"## Singularity at x = 0.5 (which depends on init condition)"); omniout_str(ALWAYS,"##"); omniout_str(ALWAYS,"x_start := 0.0;"); omniout_str(ALWAYS,"x_end := 0.2 ;"); omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS,"glob_look_poles := true;"); omniout_str(ALWAYS,"glob_max_iter := 1000000;"); omniout_str(ALWAYS,"glob_max_h := 0.001;"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"## Not Given = 0"); omniout_str(ALWAYS,"## No Pole = 3"); omniout_str(ALWAYS,"## Pole = 4"); omniout_str(ALWAYS,"glob_type_given_pole := 4;"); omniout_str(ALWAYS,"## Real Part"); omniout_str(ALWAYS,"array_given_rad_poles[1,1] := 0.5;"); omniout_str(ALWAYS,"## Imag Part"); omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 0.0;"); omniout_str(ALWAYS,"## Order"); omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 0.0;"); omniout_str(ALWAYS,"## Not Used"); omniout_str(ALWAYS,"array_given_ord_poles[1,2] := 0.0;"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,""); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); omniout_str(ALWAYS,"glob_display_interval:=0.01;"); omniout_str(ALWAYS,"glob_look_poles:=true;"); omniout_str(ALWAYS,"glob_max_iter:=10000000;"); omniout_str(ALWAYS,"glob_max_minutes:=3;"); omniout_str(ALWAYS,"glob_subiter_method:=3;"); omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS,"exact_soln_y := proc(x)"); omniout_str(ALWAYS,"return(2.0/(1.0 - 2.0*x));"); omniout_str(ALWAYS,"end;"); omniout_str(ALWAYS,"#END USER DEF BLOCK"); omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.0; glob_smallish_float := 0.0; glob_large_float := 1.0e100; glob_almost_1 := 0.99; #BEGIN FIRST INPUT BLOCK #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; #END FIRST INPUT BLOCK #START OF INITS AFTER INPUT BLOCK glob_max_terms := max_terms; glob_html_log := true; #END OF INITS AFTER INPUT BLOCK array_y_init:= Array(0..(max_terms + 1),[]); array_norms:= Array(0..(max_terms + 1),[]); array_fact_1:= Array(0..(max_terms + 1),[]); array_pole:= Array(0..(4 + 1),[]); array_real_pole:= Array(0..(4 + 1),[]); array_complex_pole:= Array(0..(4 + 1),[]); array_1st_rel_error:= Array(0..(2 + 1),[]); array_last_rel_error:= Array(0..(2 + 1),[]); array_type_pole:= Array(0..(2 + 1),[]); array_type_real_pole:= Array(0..(2 + 1),[]); array_type_complex_pole:= Array(0..(2 + 1),[]); array_y:= Array(0..(max_terms + 1),[]); array_x:= Array(0..(max_terms + 1),[]); array_tmp0:= Array(0..(max_terms + 1),[]); array_tmp1:= Array(0..(max_terms + 1),[]); array_tmp2:= Array(0..(max_terms + 1),[]); array_m1:= Array(0..(max_terms + 1),[]); array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); term := 1; while (term <= max_terms) do # do number 1 array_y_init[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_norms[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_fact_1[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 4) do # do number 1 array_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 4) do # do number 1 array_real_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 4) do # do number 1 array_complex_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_1st_rel_error[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_last_rel_error[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_real_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_complex_pole[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_y[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_x[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_tmp0[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_tmp1[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_tmp2[term] := 0.0; term := term + 1; od;# end do number 1; term := 1; while (term <= max_terms) do # do number 1 array_m1[term] := 0.0; term := term + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= max_terms) do # do number 2 array_y_higher[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= max_terms) do # do number 2 array_y_higher_work[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= max_terms) do # do number 2 array_y_higher_work2[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= max_terms) do # do number 2 array_y_set_initial[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_poles[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_given_rad_poles[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_given_ord_poles[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_real_poles[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_complex_poles[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=max_terms) do # do number 1 term := 1; while (term <= max_terms) do # do number 2 array_fact_2[ord,term] := 0.0; term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; #BEGIN ARRAYS DEFINED AND INITIALIZATED array_y := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_y[term] := 0.0; term := term + 1; od;# end do number 1; array_x := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_x[term] := 0.0; term := term + 1; od;# end do number 1; array_tmp0 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_tmp0[term] := 0.0; term := term + 1; od;# end do number 1; array_tmp1 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_tmp1[term] := 0.0; term := term + 1; od;# end do number 1; array_tmp2 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_tmp2[term] := 0.0; term := term + 1; od;# end do number 1; array_m1 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_m1[term] := 0.0; term := term + 1; od;# end do number 1; array_const_1 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_const_1[term] := 0.0; term := term + 1; od;# end do number 1; array_const_1[1] := 1; array_const_0D0 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms + 1) do # do number 1 array_const_0D0[term] := 0.0; term := term + 1; od;# end do number 1; array_const_0D0[1] := 0.0; array_m1 := Array(1..(max_terms+1 + 1),[]); term := 1; while (term <= max_terms) do # do number 1 array_m1[term] := 0.0; term := term + 1; od;# end do number 1; array_m1[1] := -1.0; #END ARRAYS DEFINED AND INITIALIZATED #Initing Factorial Tables iiif := 0; while (iiif <= glob_max_terms) do # do number 1 jjjf := 0; while (jjjf <= glob_max_terms) do # do number 2 array_fact_1[iiif] := 0; array_fact_2[iiif,jjjf] := 0; jjjf := jjjf + 1; od;# end do number 2; iiif := iiif + 1; od;# end do number 1; #Done Initing Factorial Tables #TOP SECOND INPUT BLOCK #BEGIN SECOND INPUT BLOCK #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## problem from Boyce DePrima - ## _Elementary Differential Equations and Boundary Value Problems_ ## page 23 ## Singularity at x = 0.5 (which depends on init condition) ## x_start := 0.0; x_end := 0.2 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.001; ## Not Given = 0 ## No Pole = 3 ## Pole = 4 glob_type_given_pole := 4; ## Real Part array_given_rad_poles[1,1] := 0.5; ## Imag Part array_given_rad_poles[1,2] := 0.0; ## Order array_given_ord_poles[1,1] := 0.0; ## Not Used array_given_ord_poles[1,2] := 0.0; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK #END SECOND INPUT BLOCK #BEGIN INITS AFTER SECOND INPUT BLOCK glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); if (glob_h > 0.0) then # if number 1 glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval); else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval); fi;# end if 1; chk_data(); #AFTER INITS AFTER SECOND INPUT BLOCK array_y_set_initial[1,1] := true; array_y_set_initial[1,2] := false; array_y_set_initial[1,3] := false; array_y_set_initial[1,4] := false; array_y_set_initial[1,5] := false; array_y_set_initial[1,6] := false; array_y_set_initial[1,7] := false; array_y_set_initial[1,8] := false; array_y_set_initial[1,9] := false; array_y_set_initial[1,10] := false; array_y_set_initial[1,11] := false; array_y_set_initial[1,12] := false; array_y_set_initial[1,13] := false; array_y_set_initial[1,14] := false; array_y_set_initial[1,15] := false; array_y_set_initial[1,16] := false; array_y_set_initial[1,17] := false; array_y_set_initial[1,18] := false; array_y_set_initial[1,19] := false; array_y_set_initial[1,20] := false; array_y_set_initial[1,21] := false; array_y_set_initial[1,22] := false; array_y_set_initial[1,23] := false; array_y_set_initial[1,24] := false; array_y_set_initial[1,25] := false; array_y_set_initial[1,26] := false; array_y_set_initial[1,27] := false; array_y_set_initial[1,28] := false; array_y_set_initial[1,29] := false; array_y_set_initial[1,30] := false; #BEGIN OPTIMIZE CODE omniout_str(ALWAYS,"START of Optimize"); #Start Series -- INITIALIZE FOR OPTIMIZE glob_check_sign := check_sign(x_start,x_end); glob_h := check_sign(x_start,x_end); found_h := false; glob_h := glob_min_h; if (glob_max_h < glob_h) then # if number 4 glob_h := glob_max_h; fi;# end if 4; if (glob_display_interval < glob_h) then # if number 4 glob_h := glob_display_interval; fi;# end if 4; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); estimated_step_error := 0.0; while ((opt_iter <= 100) and ( not found_h)) do # do number 1 omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; #Start Series array_y term_no := 1; while (term_no <= order_diff) do # do number 2 array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); term_no := term_no + 1; od;# end do number 2; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 2 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 3 it := term_no + r_order - 1; array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); term_no := term_no + 1; od;# end do number 3; r_order := r_order + 1; od;# end do number 2 ; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 found_h := true; glob_h := glob_max_h; best_h := glob_h; elif ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 glob_h := glob_h/2.0; best_h := glob_h; found_h := true; else glob_h := glob_h*2.0; best_h := glob_h; fi;# end if 5; omniout_float(ALWAYS,"best_h",32,best_h,32,""); opt_iter := opt_iter + 1; od;# end do number 1; if (( not found_h) and (opt_iter = 1)) then # if number 5 omniout_str(ALWAYS,"Beginning glob_h too large."); found_h := false; fi;# end if 5; if (opt_iter > 100) then # if number 5 glob_h := glob_max_h; found_h := false; fi;# end if 5; if (glob_display_interval < glob_h) then # if number 5 glob_h := glob_display_interval; fi;# end if 5; #END OPTIMIZE CODE if (glob_html_log) then # if number 5 html_log_file := fopen("entry.html",WRITE,TEXT); fi;# end if 5; #BEGIN SOLUTION CODE if (found_h) then # if number 5 omniout_str(ALWAYS,"START of Soultion"); #Start Series -- INITIALIZE FOR SOLUTION array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; #Start Series array_y term_no := 1; while (term_no <= order_diff) do # do number 1 array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); term_no := term_no + 1; od;# end do number 1; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 1 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 2 it := term_no + r_order - 1; array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); term_no := term_no + 1; od;# end do number 2; r_order := r_order + 1; od;# end do number 1 ; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL," "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 #left paren 0001C if (reached_interval()) then # if number 6 omniout_str(INFO," "); omniout_str(INFO,"TOP MAIN SOLVE Loop"); fi;# end if 6; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if (glob_look_poles) then # if number 6 #left paren 0004C check_for_pole(); fi;# end if 6;#was right paren 0004C if (reached_interval()) then # if number 6 glob_next_display := glob_next_display + glob_display_interval; fi;# end if 6; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; #Jump Series array_y; order_diff := 2; #START PART 1 SUM AND ADJUST #START SUM AND ADJUST EQ =1 #sum_and_adjust array_y #BEFORE ADJUST SUBSERIES EQ =1 ord := 2; calc_term := 1; #adjust_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := 0.0; ord := 2; calc_term := 1; #sum_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 temp_sum := temp_sum + array_y_higher_work[ord,iii]; iii := iii - 1; od;# end do number 2; array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); #AFTER SUM SUBSERIES EQ =1 #BEFORE ADJUST SUBSERIES EQ =1 ord := 1; calc_term := 2; #adjust_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := 0.0; ord := 1; calc_term := 2; #sum_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 temp_sum := temp_sum + array_y_higher_work[ord,iii]; iii := iii - 1; od;# end do number 2; array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); #AFTER SUM SUBSERIES EQ =1 #BEFORE ADJUST SUBSERIES EQ =1 ord := 1; calc_term := 1; #adjust_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := 0.0; ord := 1; calc_term := 1; #sum_subseriesarray_y iii := glob_max_terms; while (iii >= calc_term) do # do number 2 temp_sum := temp_sum + array_y_higher_work[ord,iii]; iii := iii - 1; od;# end do number 2; array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); #AFTER SUM SUBSERIES EQ =1 #END SUM AND ADJUST EQ =1 #END PART 1 #START PART 2 MOVE TERMS to REGULAR Array term_no := glob_max_terms; while (term_no >= 1) do # do number 2 array_y[term_no] := array_y_higher_work2[1,term_no]; ord := 1; while (ord <= order_diff) do # do number 3 array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; ord := ord + 1; od;# end do number 3; term_no := term_no - 1; od;# end do number 2; #END PART 2 HEVE MOVED TERMS to REGULAR Array ; od;# end do number 1;#right paren 0001C omniout_str(ALWAYS,"Finished!"); if (glob_iter >= glob_max_iter) then # if number 6 omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); fi;# end if 6; if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); fi;# end if 6; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO,"diff ( y , x , 1 ) = y * y;"); omniout_int(INFO,"Iterations ",32,glob_iter,4," ") ; prog_report(x_start,x_end); if (glob_html_log) then # if number 6 logstart(html_log_file); logitem_str(html_log_file,"2013-05-26T04:35:12-05:00") ; logitem_str(html_log_file,"Maple") ; logitem_str(html_log_file,"nonlinear2") ; logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") ; logitem_float(html_log_file,x_start) ; logitem_float(html_log_file,x_end) ; logitem_float(html_log_file,array_x[1]) ; logitem_float(html_log_file,glob_h) ; logitem_integer(html_log_file,Digits) ; ; logitem_good_digits(html_log_file,array_last_rel_error[1]) ; logitem_integer(html_log_file,glob_max_terms) ; logitem_float(html_log_file,array_1st_rel_error[1]) ; logitem_float(html_log_file,array_last_rel_error[1]) ; logitem_integer(html_log_file,glob_iter) ; logitem_time(html_log_file,convfloat(glob_clock_sec)) ; if (glob_percent_done < 100.0) then # if number 7 logitem_time(html_log_file,convfloat(glob_total_exp_sec)) ; 0; else logitem_str(html_log_file,"Done") ; 0; fi;# end if 7; log_revs(html_log_file," 189 ") ; logitem_str(html_log_file,"nonlinear2 diffeq.mxt") ; logitem_str(html_log_file,"nonlinear2 maple results") ; logitem_str(html_log_file,"All Tests - All Languages") ; logend(html_log_file) ; ; fi;# end if 6; if (glob_html_log) then # if number 6 fclose(html_log_file); fi;# end if 6 ; ;; fi;# end if 5 #END OUTFILEMAIN end; # End Function number 13 main();