#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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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 sin 1 $eq_no = 1
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
#emit pre mult CONST - LINEAR $eq_no = 1 i = 1
array_tmp2[1] := array_const_2D0[1] * array_x[1];
#emit pre add LINEAR - CONST $eq_no = 1 i = 1
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
#emit pre expt FULL - LINEAR $eq_no = 1 i = 1
array_tmp4[1] := expt(array_tmp1[1] , array_tmp3[1] ) ;
array_tmp4_a1[1] := ln(array_tmp1[1] ) ;
array_tmp4_a1[2] := array_tmp1[2] / array_tmp1[1];
#emit pre sin 1 $eq_no = 1
array_tmp5[1] := sin(array_x[1]);
array_tmp5_g[1] := cos(array_x[1]);
#emit pre ln 1 FULL $eq_no = 1
array_tmp6[1] := ln(array_tmp5[1]);
#emit pre mult CONST FULL $eq_no = 1 i = 1
array_tmp7[1] := array_const_2D0[1] * array_tmp6[1];
#emit pre mult CONST - LINEAR $eq_no = 1 i = 1
array_tmp8[1] := array_const_2D0[1] * array_x[1];
#emit pre add LINEAR - CONST $eq_no = 1 i = 1
array_tmp9[1] := array_tmp8[1] + array_const_1D0[1];
#emit pre cos 1 $eq_no = 1
array_tmp10[1] := cos(array_x[1]);
array_tmp10_g[1] := sin(array_x[1]);
#emit pre mult LINEAR - FULL $eq_no = 1 i = 1
array_tmp11[1] := array_tmp9[1] * array_tmp10[1];
#emit pre sin 1 $eq_no = 1
array_tmp12[1] := sin(array_x[1]);
array_tmp12_g[1] := cos(array_x[1]);
#emit pre div FULL - FULL $eq_no = 1 i = 1
array_tmp13[1] := (array_tmp11[1] / (array_tmp12[1]));
#emit pre add FULL FULL $eq_no = 1 i = 1
array_tmp14[1] := array_tmp7[1] + array_tmp13[1];
# emit pre mult FULL FULL $eq_no = 1 i = 1
array_tmp15[1] := (array_tmp4[1] * (array_tmp14[1]));
#emit pre add CONST FULL $eq_no = 1 i = 1
array_tmp16[1] := array_const_0D0[1] + array_tmp15[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_tmp16[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 sin ID_LINEAR iii = 2 $eq_no = 1
array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
#emit pre mult CONST - LINEAR $eq_no = 1 i = 2
array_tmp2[2] := array_const_2D0[1] * array_x[2];
#emit pre add LINEAR - CONST $eq_no = 1 i = 2
array_tmp3[2] := array_tmp2[2];
#emit pre expt FULL - LINEAR $eq_no = 1 i = 2
array_tmp4_a2[1] := (array_tmp4_a1[1] * array_tmp3[2] + array_tmp4_a1[2] * array_tmp3[1]) / glob_h;
array_tmp4[2] := array_tmp4[1] * array_tmp4_a2[1] * glob_h;
#emit pre sin ID_LINEAR iii = 2 $eq_no = 1
array_tmp5[2] := array_tmp5_g[1] * array_x[2] / 1;
array_tmp5_g[2] := -array_tmp5[1] * array_x[2] / 1;
#emit pre ln 2 FULL $eq_no = 1
array_tmp6[2] := array_tmp5[2] / array_tmp5[1];
#emit pre mult CONST FULL $eq_no = 1 i = 2
array_tmp7[2] := array_const_2D0[1] * array_tmp6[2];
#emit pre mult CONST - LINEAR $eq_no = 1 i = 2
array_tmp8[2] := array_const_2D0[1] * array_x[2];
#emit pre add LINEAR - CONST $eq_no = 1 i = 2
array_tmp9[2] := array_tmp8[2];
#emit pre cos ID_LINEAR iii = 2 $eq_no = 1
array_tmp10[2] := -array_tmp10_g[1] * array_x[2] / 1;
array_tmp10_g[2] := array_tmp10[1] * array_x[2] / 1;
#emit pre mult LINEAR FULL $eq_no = 1 i = 2
array_tmp11[2] := array_tmp10[1] * array_tmp9[2] + array_tmp10[2] * array_tmp9[1];
#emit pre sin ID_LINEAR iii = 2 $eq_no = 1
array_tmp12[2] := array_tmp12_g[1] * array_x[2] / 1;
array_tmp12_g[2] := -array_tmp12[1] * array_x[2] / 1;
#emit pre div FULL - FULL $eq_no = 1 i = 2
array_tmp13[2] := ((array_tmp11[2] - ats(2,array_tmp12,array_tmp13,2))/array_tmp12[1]);
#emit pre add FULL FULL $eq_no = 1 i = 2
array_tmp14[2] := array_tmp7[2] + array_tmp13[2];
# emit pre mult FULL FULL $eq_no = 1 i = 2
array_tmp15[2] := ats(2,array_tmp4,array_tmp14,1);
#emit pre add CONST FULL $eq_no = 1 i = 2
array_tmp16[2] := array_tmp15[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_tmp16[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 sin ID_LINEAR iii = 3 $eq_no = 1
array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
#emit pre expt FULL - LINEAR $eq_no = 1 i = 3
array_tmp4_a1[3] := (array_tmp1[3] -att(2,array_tmp1,array_tmp4_a1,2))/ array_tmp1[1];
array_tmp4_a2[2] := (array_tmp4_a1[3] * array_tmp3[1] + array_tmp4_a1[2] * array_tmp3[2]) * 2 / glob_h;
array_tmp4[3] := ats(2,array_tmp4,array_tmp4_a2,1)*glob_h/2;
#emit pre sin ID_LINEAR iii = 3 $eq_no = 1
array_tmp5[3] := array_tmp5_g[2] * array_x[2] / 2;
array_tmp5_g[3] := -array_tmp5[2] * array_x[2] / 2;
#emit pre ln ID_FULL iii = 3 $eq_no = 1
#emit pre ln 3 $eq_no = 1
array_tmp6[3] := ( array_tmp5[3] - att(2,array_tmp5,array_tmp6,2) ) / array_tmp5[1];
#emit pre mult CONST FULL $eq_no = 1 i = 3
array_tmp7[3] := array_const_2D0[1] * array_tmp6[3];
#emit pre cos ID_LINEAR iii = 3 $eq_no = 1
array_tmp10[3] := -array_tmp10_g[2] * array_x[2] / 2;
array_tmp10_g[3] := array_tmp10[2] * array_x[2] / 2;
#emit pre mult LINEAR FULL $eq_no = 1 i = 3
array_tmp11[3] := array_tmp10[2] * array_tmp9[2] + array_tmp10[3] * array_tmp9[1];
#emit pre sin ID_LINEAR iii = 3 $eq_no = 1
array_tmp12[3] := array_tmp12_g[2] * array_x[2] / 2;
array_tmp12_g[3] := -array_tmp12[2] * array_x[2] / 2;
#emit pre div FULL - FULL $eq_no = 1 i = 3
array_tmp13[3] := ((array_tmp11[3] - ats(3,array_tmp12,array_tmp13,2))/array_tmp12[1]);
#emit pre add FULL FULL $eq_no = 1 i = 3
array_tmp14[3] := array_tmp7[3] + array_tmp13[3];
# emit pre mult FULL FULL $eq_no = 1 i = 3
array_tmp15[3] := ats(3,array_tmp4,array_tmp14,1);
#emit pre add CONST FULL $eq_no = 1 i = 3
array_tmp16[3] := array_tmp15[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_tmp16[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 sin ID_LINEAR iii = 4 $eq_no = 1
array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
#emit pre expt FULL - LINEAR $eq_no = 1 i = 4
array_tmp4_a1[4] := (array_tmp1[4] -att(3,array_tmp1,array_tmp4_a1,2))/ array_tmp1[1];
array_tmp4_a2[3] := (array_tmp4_a1[4] * array_tmp3[1] + array_tmp4_a1[3] * array_tmp3[2]) * 3 / glob_h;
array_tmp4[4] := ats(3,array_tmp4,array_tmp4_a2,1)*glob_h/3;
#emit pre sin ID_LINEAR iii = 4 $eq_no = 1
array_tmp5[4] := array_tmp5_g[3] * array_x[2] / 3;
array_tmp5_g[4] := -array_tmp5[3] * array_x[2] / 3;
#emit pre ln ID_FULL iii = 4 $eq_no = 1
#emit pre ln 4 $eq_no = 1
array_tmp6[4] := ( array_tmp5[4] - att(3,array_tmp5,array_tmp6,2) ) / array_tmp5[1];
#emit pre mult CONST FULL $eq_no = 1 i = 4
array_tmp7[4] := array_const_2D0[1] * array_tmp6[4];
#emit pre cos ID_LINEAR iii = 4 $eq_no = 1
array_tmp10[4] := -array_tmp10_g[3] * array_x[2] / 3;
array_tmp10_g[4] := array_tmp10[3] * array_x[2] / 3;
#emit pre mult LINEAR FULL $eq_no = 1 i = 4
array_tmp11[4] := array_tmp10[3] * array_tmp9[2] + array_tmp10[4] * array_tmp9[1];
#emit pre sin ID_LINEAR iii = 4 $eq_no = 1
array_tmp12[4] := array_tmp12_g[3] * array_x[2] / 3;
array_tmp12_g[4] := -array_tmp12[3] * array_x[2] / 3;
#emit pre div FULL - FULL $eq_no = 1 i = 4
array_tmp13[4] := ((array_tmp11[4] - ats(4,array_tmp12,array_tmp13,2))/array_tmp12[1]);
#emit pre add FULL FULL $eq_no = 1 i = 4
array_tmp14[4] := array_tmp7[4] + array_tmp13[4];
# emit pre mult FULL FULL $eq_no = 1 i = 4
array_tmp15[4] := ats(4,array_tmp4,array_tmp14,1);
#emit pre add CONST FULL $eq_no = 1 i = 4
array_tmp16[4] := array_tmp15[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_tmp16[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 sin ID_LINEAR iii = 5 $eq_no = 1
array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
#emit pre expt FULL - LINEAR $eq_no = 1 i = 5
array_tmp4_a1[5] := (array_tmp1[5] -att(4,array_tmp1,array_tmp4_a1,2))/ array_tmp1[1];
array_tmp4_a2[4] := (array_tmp4_a1[5] * array_tmp3[1] + array_tmp4_a1[4] * array_tmp3[2]) * 4 / glob_h;
array_tmp4[5] := ats(4,array_tmp4,array_tmp4_a2,1)*glob_h/4;
#emit pre sin ID_LINEAR iii = 5 $eq_no = 1
array_tmp5[5] := array_tmp5_g[4] * array_x[2] / 4;
array_tmp5_g[5] := -array_tmp5[4] * array_x[2] / 4;
#emit pre ln ID_FULL iii = 5 $eq_no = 1
#emit pre ln 5 $eq_no = 1
array_tmp6[5] := ( array_tmp5[5] - att(4,array_tmp5,array_tmp6,2) ) / array_tmp5[1];
#emit pre mult CONST FULL $eq_no = 1 i = 5
array_tmp7[5] := array_const_2D0[1] * array_tmp6[5];
#emit pre cos ID_LINEAR iii = 5 $eq_no = 1
array_tmp10[5] := -array_tmp10_g[4] * array_x[2] / 4;
array_tmp10_g[5] := array_tmp10[4] * array_x[2] / 4;
#emit pre mult LINEAR FULL $eq_no = 1 i = 5
array_tmp11[5] := array_tmp10[4] * array_tmp9[2] + array_tmp10[5] * array_tmp9[1];
#emit pre sin ID_LINEAR iii = 5 $eq_no = 1
array_tmp12[5] := array_tmp12_g[4] * array_x[2] / 4;
array_tmp12_g[5] := -array_tmp12[4] * array_x[2] / 4;
#emit pre div FULL - FULL $eq_no = 1 i = 5
array_tmp13[5] := ((array_tmp11[5] - ats(5,array_tmp12,array_tmp13,2))/array_tmp12[1]);
#emit pre add FULL FULL $eq_no = 1 i = 5
array_tmp14[5] := array_tmp7[5] + array_tmp13[5];
# emit pre mult FULL FULL $eq_no = 1 i = 5
array_tmp15[5] := ats(5,array_tmp4,array_tmp14,1);
#emit pre add CONST FULL $eq_no = 1 i = 5
array_tmp16[5] := array_tmp15[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_tmp16[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 sin LINEAR $eq_no = 1
array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
#emit expt FULL LINEAR $eq_no = 1 i = 1
array_tmp4_a1[kkk] := (array_tmp1[kkk] - att(kkk-1,array_tmp1,array_tmp4_a1,2))/array_tmp1[1];
array_tmp4_a2[kkk-1] := (array_tmp4_a1[kkk] * array_tmp3[1] + array_tmp4_a1[kkk-1] * array_tmp3[2]) * (kkk-1)/glob_h;
array_tmp4[kkk] := ats(kkk-1,array_tmp4,array_tmp4_a2,1) * glob_h/(kkk-1);
#emit sin LINEAR $eq_no = 1
array_tmp5[kkk] := array_tmp5_g[kkk - 1] * array_x[2] / (kkk - 1);
array_tmp5_g[kkk] := -array_tmp5[kkk - 1] * array_x[2] / (kkk - 1);
#emit ln FULL $eq_no = 1
array_tmp6[kkk] := (array_tmp5[kkk] - att(kkk-1,array_tmp5,array_tmp6,2))/array_tmp5[1];
#emit mult CONST FULL $eq_no = 1 i = 1
array_tmp7[kkk] := array_const_2D0[1] * array_tmp6[kkk];
#emit cos LINEAR $eq_no = 1
array_tmp10[kkk] := -array_tmp10_g[kkk - 1] * array_x[2] / (kkk - 1);
array_tmp10_g[kkk] := array_tmp10[kkk - 1] * array_x[2] / (kkk - 1);
#emit mult LINEAR FULL $eq_no = 1 i = 1
array_tmp11[kkk] := array_tmp10[kkk-1] * array_tmp9[2] + array_tmp10[kkk] * array_tmp9[1];
#emit sin LINEAR $eq_no = 1
array_tmp12[kkk] := array_tmp12_g[kkk - 1] * array_x[2] / (kkk - 1);
array_tmp12_g[kkk] := -array_tmp12[kkk - 1] * array_x[2] / (kkk - 1);
#emit div FULL FULL $eq_no = 1
array_tmp13[kkk] := ((array_tmp11[kkk] - ats(kkk,array_tmp12,array_tmp13,2))/array_tmp12[1]);
#emit FULL - FULL add $eq_no = 1
array_tmp14[kkk] := array_tmp7[kkk] + array_tmp13[kkk];
#emit mult FULL FULL $eq_no = 1
array_tmp15[kkk] := ats(kkk,array_tmp4,array_tmp14,1);
#emit NOT FULL - FULL add $eq_no = 1
array_tmp16[kkk] := array_tmp15[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_tmp16[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(expt(sin(x),2.0*x+1.0));
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,
array_const_2D0,
array_const_1D0,
#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_g,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4_c1,
array_tmp4_a1,
array_tmp4_a2,
array_tmp4,
array_tmp5_g,
array_tmp5,
array_tmp6,
array_tmp7,
array_tmp8,
array_tmp9,
array_tmp10_g,
array_tmp10,
array_tmp11,
array_tmp12_g,
array_tmp12,
array_tmp13,
array_tmp14,
array_tmp15,
array_tmp16,
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/expt_sin_lin_newpostode.ode#################");
omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ;");
omniout_str(ALWAYS,"!");
omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS,"Digits:=32;");
omniout_str(ALWAYS,"max_terms:=30;");
omniout_str(ALWAYS,"!");
omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS,"x_start := 0.1;");
omniout_str(ALWAYS,"x_end := 0.11 ;");
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 := 0.0001;");
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:=0.1;");
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(expt(sin(x),2.0*x+1.0));");
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_g:= 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_c1:= Array(0..(max_terms + 1),[]);
array_tmp4_a1:= Array(0..(max_terms + 1),[]);
array_tmp4_a2:= Array(0..(max_terms + 1),[]);
array_tmp4:= Array(0..(max_terms + 1),[]);
array_tmp5_g:= 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_g:= Array(0..(max_terms + 1),[]);
array_tmp10:= Array(0..(max_terms + 1),[]);
array_tmp11:= Array(0..(max_terms + 1),[]);
array_tmp12_g:= 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_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_g[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_c1[term] := 0.0;
term := term + 1;
od;# end do number 1;
term := 1;
while (term <= max_terms) do # do number 1
array_tmp4_a1[term] := 0.0;
term := term + 1;
od;# end do number 1;
term := 1;
while (term <= max_terms) do # do number 1
array_tmp4_a2[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_g[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_g[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_g[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_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_g := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp1_g[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_c1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp4_c1[term] := 0.0;
term := term + 1;
od;# end do number 1;
array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp4_a1[term] := 0.0;
term := term + 1;
od;# end do number 1;
array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp4_a2[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_g := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp5_g[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_g := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp10_g[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_g := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_tmp12_g[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_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_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_1D0 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 1
array_const_1D0[term] := 0.0;
term := term + 1;
od;# end do number 1;
array_const_1D0[1] := 1.0;
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
x_start := 0.1;
x_end := 0.11 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_max_h := 0.0001;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.1;
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 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ;");
omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
;
prog_report(x_start,x_end);
if (glob_html_log) then # if number 6
logstart(html_log_file);
logitem_str(html_log_file,"2013-05-26T20:17:11-05:00")
;
logitem_str(html_log_file,"Maple")
;
logitem_str(html_log_file,"expt_sin_lin_new")
;
logitem_str(html_log_file,"diff ( y , x , 1 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ;")
;
logitem_float(html_log_file,x_start)
;
logitem_float(html_log_file,x_end)
;
logitem_float(html_log_file,array_x[1])
;
logitem_float(html_log_file,glob_h)
;
logitem_integer(html_log_file,Digits)
;
;
logitem_good_digits(html_log_file,array_last_rel_error[1])
;
logitem_integer(html_log_file,glob_max_terms)
;
logitem_float(html_log_file,array_1st_rel_error[1])
;
logitem_float(html_log_file,array_last_rel_error[1])
;
logitem_integer(html_log_file,glob_iter)
;
logitem_time(html_log_file,convfloat(glob_clock_sec))
;
if (glob_percent_done < 100.0) then # if number 7
logitem_time(html_log_file,convfloat(glob_total_exp_sec))
;
0;
else
logitem_str(html_log_file,"Done")
;
0;
fi;# end if 7;
log_revs(html_log_file," 190 | ")
;
logitem_str(html_log_file,"expt_sin_lin_new diffeq.mxt")
;
logitem_str(html_log_file,"expt_sin_lin_new 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();