#BEGIN OUTFILE1
# Begin Function number 3
display_alot := proc(iter)
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
glob_last;
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
#TOP DISPLAY ALOT
if (iter >= 0) then # if number 1
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 2
relerr := abserr*100.0/omniabs(analytic_val_y);
if (relerr <> 0.0) then # if number 3
glob_good_digits := -trunc(log10(relerr/100.0));
else
glob_good_digits := Digits;
fi;# end if 3
;
else
relerr := -1.0 ;
glob_good_digits := -1;
fi;# end if 2
;
if (glob_iter = 1) then # if number 2
array_1st_rel_error[1] := relerr;
else
array_last_rel_error[1] := relerr;
fi;# end if 2
;
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," ");
#BOTTOM DISPLAY ALOT
fi;# end if 1
;
# End Function number 3
end;
# Begin Function number 4
adjust_for_pole := proc(h_param)
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
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 1
tmp := omniabs(array_y_higher[1,1]);
if (tmp < glob_normmax) then # if number 2
glob_normmax := tmp;
fi;# end if 2
fi;# end if 1
;
if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
sz2 := array_pole[1]/10.0;
if (sz2 < hnew) then # if number 2
omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
omniout_str(INFO,"Reached Optimal");
return(hnew);
fi;# end if 2
fi;# end if 1
;
if ( not glob_reached_optimal_h) then # if number 1
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 1
;
hnew := sz2;
;#END block
return(hnew);
#BOTTOM ADJUST FOR POLE
# End Function number 4
end;
# Begin Function number 5
prog_report := proc(x_start,x_end)
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
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));
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 1
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));
fi;# end if 1
;
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 Function number 5
end;
# Begin Function number 6
check_for_pole := proc()
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
glob_last;
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
#TOP CHECK FOR POLE
#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]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
m := m - 1;
od;# end do number 2
;
if (m > 10) then # if number 1
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-1)*rm0-convfloat(m-2)*rm1;
if (omniabs(hdrc) > glob_small_float) then # if number 2
rcs := glob_h/hdrc;
ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1,1] := rcs;
array_real_pole[1,2] := ord_no;
else
array_real_pole[1,1] := glob_large_float;
array_real_pole[1,2] := glob_large_float;
fi;# end if 2
else
array_real_pole[1,1] := glob_large_float;
array_real_pole[1,2] := glob_large_float;
fi;# end if 1
;
#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 2
if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
cnt := cnt + 1;
else
cnt := 0;
fi;# end if 1
;
n := n - 1;
od;# end do number 2
;
m := n + cnt;
if (m <= 10) then # if number 1
array_complex_pole[1,1] := glob_large_float;
array_complex_pole[1,2] := glob_large_float;
elif ((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) then # if number 2
array_complex_pole[1,1] := glob_large_float;
array_complex_pole[1,2] := 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
array_complex_pole[1,1] := glob_large_float;
array_complex_pole[1,2] := glob_large_float;
else
if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
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) > glob_small_float) then # if number 5
if (rcs > 0.0) then # if number 6
rad_c := sqrt(rcs) * glob_h;
else
rad_c := glob_large_float;
fi;# end if 6
else
rad_c := glob_large_float;
ord_no := glob_large_float;
fi;# end if 5
else
rad_c := glob_large_float;
ord_no := glob_large_float;
fi;# end if 4
fi;# end if 3
;
array_complex_pole[1,1] := rad_c;
array_complex_pole[1,2] := ord_no;
fi;# end if 2
;
#BOTTOM RADII COMPLEX EQ = 1
found := false;
#TOP WHICH RADII EQ = 1
if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
array_poles[1,1] := array_complex_pole[1,1];
array_poles[1,2] := array_complex_pole[1,2];
found := true;
array_type_pole[1] := 2;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"Complex estimate of poles used");
fi;# end if 3
;
fi;# end if 2
;
if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
array_poles[1,1] := array_real_pole[1,1];
array_poles[1,2] := array_real_pole[1,2];
found := true;
array_type_pole[1] := 1;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"Real estimate of pole used");
fi;# end if 3
;
fi;# end if 2
;
if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
array_poles[1,1] := glob_large_float;
array_poles[1,2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"NO POLE");
fi;# end if 3
;
fi;# end if 2
;
if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2
array_poles[1,1] := array_real_pole[1,1];
array_poles[1,2] := array_real_pole[1,2];
found := true;
array_type_pole[1] := 1;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"Real estimate of pole used");
fi;# end if 3
;
fi;# end if 2
;
if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
array_poles[1,1] := array_complex_pole[1,1];
array_poles[1,2] := array_complex_pole[1,2];
array_type_pole[1] := 2;
found := true;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"Complex estimate of poles used");
fi;# end if 3
;
fi;# end if 2
;
if ( not found ) then # if number 2
array_poles[1,1] := glob_large_float;
array_poles[1,2] := glob_large_float;
array_type_pole[1] := 3;
if (glob_display_flag) then # if number 3
omniout_str(ALWAYS,"NO POLE");
fi;# end if 3
;
fi;# end if 2
;
#BOTTOM WHICH RADII EQ = 1
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
#TOP WHICH RADIUS EQ = 1
if (array_pole[1] > array_poles[1,1]) then # if number 2
array_pole[1] := array_poles[1,1];
array_pole[2] := array_poles[1,2];
fi;# end if 2
;
#BOTTOM WHICH RADIUS EQ = 1
#BOTTOM CHECK FOR POLE
display_pole();
# End Function number 6
end;
# Begin Function number 7
get_norms := proc()
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
glob_last;
local iii;
if ( not glob_initial_pass) then # if number 2
iii := 1;
while (iii <= glob_max_terms) do # do number 2
array_norms[iii] := 0.0;
iii := iii + 1;
od;# end do number 2
;
#TOP GET NORMS
iii := 1;
while (iii <= glob_max_terms) do # do number 2
if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
array_norms[iii] := omniabs(array_y[iii]);
fi;# end if 3
;
iii := iii + 1;
od;# end do number 2
#BOTTOM GET NORMS
;
fi;# end if 2
;
# End Function number 7
end;
# Begin Function number 8
atomall := proc()
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
glob_last;
local kkk, order_d, adj2, temporary, term;
#TOP ATOMALL
#END OUTFILE1
#BEGIN ATOMHDR1
#emit pre mult CONST - LINEAR $eq_no = 1 i = 1
array_tmp1[1] := array_const_0D1[1] * array_x[1];
#emit pre add LINEAR - CONST $eq_no = 1 i = 1
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
#emit pre mult CONST - LINEAR $eq_no = 1 i = 1
array_tmp3[1] := array_const_0D2[1] * array_x[1];
#emit pre add LINEAR - CONST $eq_no = 1 i = 1
array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
#emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
array_tmp5[1] := array_tmp2[1] * array_tmp4[1];
#emit pre add CONST FULL $eq_no = 1 i = 1
array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1] * expt(glob_h , (1)) * factorial_3(0,1);
array_y[2] := temporary;
array_y_higher[1,2] := temporary;
temporary := temporary / glob_h * (2.0);
array_y_higher[2,1] := temporary
;
fi;# end if 2
;
fi;# end if 1
;
kkk := 2;
#END ATOMHDR1
#BEGIN ATOMHDR2
#emit pre mult CONST - LINEAR $eq_no = 1 i = 2
array_tmp1[2] := array_const_0D1[1] * array_x[2];
#emit pre add LINEAR - CONST $eq_no = 1 i = 2
array_tmp2[2] := array_tmp1[2];
#emit pre mult CONST - LINEAR $eq_no = 1 i = 2
array_tmp3[2] := array_const_0D2[1] * array_x[2];
#emit pre add LINEAR - CONST $eq_no = 1 i = 2
array_tmp4[2] := array_tmp3[2];
#emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
array_tmp5[2] := array_tmp2[1] * array_tmp4[2] + array_tmp2[2] * array_tmp4[1];
#emit pre add CONST FULL $eq_no = 1 i = 2
array_tmp6[2] := array_tmp5[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_tmp6[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 LINEAR - LINEAR $eq_no = 1 i = 3
array_tmp5[3] := array_tmp2[2] * array_tmp4[2];
#emit pre add CONST FULL $eq_no = 1 i = 3
array_tmp6[3] := array_tmp5[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_tmp6[3] * expt(glob_h , (1)) * factorial_3(2,3);
array_y[4] := temporary;
array_y_higher[1,4] := temporary;
temporary := temporary / glob_h * (2.0);
array_y_higher[2,3] := temporary
;
fi;# end if 2
;
fi;# end if 1
;
kkk := 4;
#END ATOMHDR3
#BEGIN ATOMHDR4
#emit pre add CONST FULL $eq_no = 1 i = 4
array_tmp6[4] := array_tmp5[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_tmp6[4] * expt(glob_h , (1)) * factorial_3(3,4);
array_y[5] := temporary;
array_y_higher[1,5] := temporary;
temporary := temporary / glob_h * (2.0);
array_y_higher[2,4] := temporary
;
fi;# end if 2
;
fi;# end if 1
;
kkk := 5;
#END ATOMHDR4
#BEGIN ATOMHDR5
#emit pre add CONST FULL $eq_no = 1 i = 5
array_tmp6[5] := array_tmp5[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_tmp6[5] * expt(glob_h , (1)) * factorial_3(4,5);
array_y[6] := temporary;
array_y_higher[1,6] := temporary;
temporary := temporary / glob_h * (2.0);
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 LINEAR - LINEAR $eq_no = 1 i = 1
#emit NOT FULL - FULL add $eq_no = 1
array_tmp6[kkk] := array_tmp5[kkk];
#emit assign $eq_no = 1
order_d := 1;
if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
temporary := array_tmp6[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 := 2;
while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
temporary := temporary / glob_h * convfp(adj2);
array_y_higher[adj2,term] := temporary;
adj2 := adj2 + 1;
term := term - 1;
od;# end do number 2
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 Function number 8
end;
#BEGIN ATS LIBRARY BLOCK
omniout_str := proc(iolevel,str)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
printf("%s\n",str);
fi;
# End Function number 1
end;
omniout_str_noeol := proc(iolevel,str)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
printf("%s",str);
fi;
# End Function number 1
end;
omniout_labstr := proc(iolevel,label,str)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
print(label,str);
fi;
# End Function number 1
end;
omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
else
printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
fi;
fi;
# End Function number 1
end;
omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
if vallen = 5 then
printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
else
printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
fi;
fi;
# End Function number 1
end;
omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
global glob_iolevel;
if (glob_iolevel >= iolevel) then
print(prelabel,"[",elemnt,"]",value, postlabel);
fi;
# End Function number 1
end;
dump_series := proc(iolevel,dump_label,series_name,
array_series,numb)
global glob_iolevel;
local i;
if (glob_iolevel >= iolevel) then
i := 1;
while (i <= numb) do
print(dump_label,series_name
,i,array_series[i]);
i := i + 1;
od;
fi;
# End Function number 1
end;
dump_series_2 := proc(iolevel,dump_label,series_name2,
array_series2,numb,subnum,array_x)
global glob_iolevel;
local i,sub,ts_term;
if (glob_iolevel >= iolevel) then
sub := 1;
while (sub <= subnum) do
i := 1;
while (i <= numb) do
print(dump_label,series_name2,sub,i,array_series2[sub,i]);
od;
sub := sub + 1;
od;
fi;
# End Function number 1
end;
cs_info := proc(iolevel,str)
global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
if (glob_iolevel >= iolevel) then
print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
fi;
# End Function number 1
end;
# Begin Function number 2
logitem_time := proc(fd,secs_in)
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
secs := (secs_in);
fprintf(fd,"
");
if (secs >= 0.0) then # if number 1
sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
milliniums := convfloat(secs / sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int) * years_in_century;
years_int := floor(years);
days := (years - years_int) * days_in_year;
days_int := floor(days);
hours := (days - days_int) * hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int) * min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int) * sec_in_minute;
sec_int := floor(seconds);
if (millinium_int > 0) then # if number 2
fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
elif (cent_int > 0) then # if number 3
fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
elif (years_int > 0) then # if number 4
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 5
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 6
fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
elif (minutes_int > 0) then # if number 7
fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
else
fprintf(fd,"%d Seconds",sec_int);
fi;# end if 7
else
fprintf(fd,"Unknown");
fi;# end if 6
fprintf(fd," | ");
# End Function number 2
end;
omniout_timestr := proc (secs_in)
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
secs := convfloat(secs_in);
if (secs >= 0.0) then # if number 6
sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
milliniums := convfloat(secs / sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int) * years_in_century;
years_int := floor(years);
days := (years - years_int) * days_in_year;
days_int := floor(days);
hours := (days - days_int) * hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int) * min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int) * sec_in_minute;
sec_int := floor(seconds);
if (millinium_int > 0) then # if number 7
printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
elif (cent_int > 0) then # if number 8
printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
elif (years_int > 0) then # if number 9
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 10
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 11
printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
elif (minutes_int > 0) then # if number 12
printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
else
printf(" = %d Seconds\n",sec_int);
fi;# end if 12
else
printf(" Unknown\n");
fi;# end if 11
# End Function number 2
end;
# Begin Function number 3
ats := proc(
mmm_ats,array_a,array_b,jjj_ats)
local iii_ats, lll_ats,ma_ats, ret_ats;
ret_ats := 0.0;
if (jjj_ats <= mmm_ats) then # if number 11
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 + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1;
od;# end do number 1
fi;# end if 11
;
ret_ats;
# End Function number 3
end;
# Begin Function number 4
att := proc(
mmm_att,array_aa,array_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 11
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 12
ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
fi;# end if 12
;
iii_att := iii_att + 1;
od;# end do number 1
;
ret_att := ret_att / convfp(mmm_att) ;
fi;# end if 11
;
ret_att;
# End Function number 4
end;
# Begin Function number 5
display_pole := proc()
global ALWAYS,glob_display_flag, glob_large_float, array_pole;
if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
fi;# end if 11
# End Function number 5
end;
# Begin Function number 6
logditto := proc(file)
fprintf(file,"");
fprintf(file,"ditto");
fprintf(file," | ");
# End Function number 6
end;
# Begin Function number 7
logitem_integer := proc(file,n)
fprintf(file,"");
fprintf(file,"%d",n);
fprintf(file," | ");
# End Function number 7
end;
# Begin Function number 8
logitem_str := proc(file,str)
fprintf(file,"");
fprintf(file,str);
fprintf(file," | ");
# End Function number 8
end;
# Begin Function number 9
logitem_good_digits := proc(file,rel_error)
global glob_small_float;
local good_digits;
fprintf(file,"");
if (rel_error <> -1.0) then # if number 11
if (rel_error <> 0.0) then # if number 12
good_digits := -trunc(log10(rel_error/100.0));
fprintf(file,"%d",good_digits);
else
good_digits := Digits;
fprintf(file,"%d",good_digits);
fi;# end if 12
;
else
fprintf(file,"Unknown");
fi;# end if 11
;
fprintf(file," | ");
# End Function number 9
end;
# Begin Function number 10
log_revs := proc(file,revs)
fprintf(file,revs);
# End Function number 10
end;
# Begin Function number 11
logitem_float := proc(file,x)
fprintf(file,"");
fprintf(file,"%g",x);
fprintf(file," | ");
# End Function number 11
end;
# Begin Function number 12
logitem_pole := proc(file,pole)
fprintf(file,"");
if (pole = 0) then # if number 11
fprintf(file,"NA");
elif (pole = 1) then # if number 12
fprintf(file,"Real");
elif (pole = 2) then # if number 13
fprintf(file,"Complex");
else
fprintf(file,"No Pole");
fi;# end if 13
fprintf(file," | ");
# End Function number 12
end;
# Begin Function number 13
logstart := proc(file)
fprintf(file,"");
# End Function number 13
end;
# Begin Function number 14
logend := proc(file)
fprintf(file,"
\n");
# End Function number 14
end;
# Begin Function number 15
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 13
omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
glob_max_terms := 30;
fi;# end if 13
;
if (glob_max_iter < 2) then # if number 13
omniout_str(ALWAYS,"Illegal max_iter");
errflag := true;
fi;# end if 13
;
if (errflag) then # if number 13
quit;
fi;# end if 13
# End Function number 15
end;
# Begin Function number 16
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 13
sec_left := 0.0;
else
if (sub2 > 0.0) then # if number 14
rrr := (sub1/sub2);
sec_left := rrr * ms2 - ms2;
else
sec_left := 0.0;
fi;# end if 14
fi;# end if 13
;
sec_left;
# End Function number 16
end;
# Begin Function number 17
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 13
rrr := (100.0*sub2)/sub1;
else
rrr := 0.0;
fi;# end if 13
;
rrr;
# End Function number 17
end;
# Begin Function number 18
factorial_2 := proc(nnn)
local ret;
ret := nnn!;
# End Function number 18
end;
# Begin Function number 19
factorial_1 := proc(nnn)
global glob_max_terms,array_fact_1;
local ret;
if (nnn <= glob_max_terms) then # if number 13
if (array_fact_1[nnn] = 0) then # if number 14
ret := factorial_2(nnn);
array_fact_1[nnn] := ret;
else
ret := array_fact_1[nnn];
fi;# end if 14
;
else
ret := factorial_2(nnn);
fi;# end if 13
;
ret;
# End Function number 19
end;
# Begin Function number 20
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 13
if (array_fact_2[mmm,nnn] = 0) then # if number 14
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm,nnn] := ret;
else
ret := array_fact_2[mmm,nnn];
fi;# end if 14
;
else
ret := factorial_2(mmm)/factorial_2(nnn);
fi;# end if 13
;
ret;
# End Function number 20
end;
# Begin Function number 21
convfp := proc(mmm)
(mmm);
# End Function number 21
end;
# Begin Function number 22
convfloat := proc(mmm)
(mmm);
# End Function number 22
end;
elapsed_time_seconds := proc()
time();
end;
omniabs := proc(x)
abs(x);
end;
expt := proc(x,y)
(x^y);
end;
#END ATS LIBRARY BLOCK
#BEGIN USER DEF BLOCK
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * 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, log10norm, max_terms, opt_iter, tmp,subiter;
global
INFO,
DEBUGL,
ALWAYS,
glob_iolevel,
glob_max_terms,
DEBUGMASSIVE,
#Top Generate Globals Decl
glob_curr_iter_when_opt,
glob_warned2,
glob_no_eqs,
glob_abserr,
glob_last_good_h,
glob_log10normmin,
MAX_UNCHANGED,
glob_disp_incr,
sec_in_minute,
glob_log10abserr,
glob_iter,
glob_start,
glob_orig_start_sec,
glob_warned,
glob_relerr,
glob_optimal_done,
glob_clock_sec,
glob_normmax,
glob_hmin_init,
glob_almost_1,
glob_max_opt_iter,
glob_current_iter,
glob_unchanged_h_cnt,
glob_small_float,
glob_max_trunc_err,
glob_log10_abserr,
years_in_century,
glob_optimal_expect_sec,
glob_max_rel_trunc_err,
glob_max_iter,
glob_h,
centuries_in_millinium,
min_in_hour,
djd_debug2,
glob_good_digits,
glob_subiter_method,
glob_percent_done,
glob_max_sec,
glob_smallish_float,
glob_optimal_clock_start_sec,
glob_log10_relerr,
glob_large_float,
glob_reached_optimal_h,
hours_in_day,
djd_debug,
glob_dump_analytic,
days_in_year,
glob_display_flag,
glob_log10relerr,
glob_max_hours,
glob_hmax,
glob_not_yet_start_msg,
glob_optimal_start,
glob_look_poles,
glob_hmin,
glob_initial_pass,
glob_clock_start_sec,
glob_dump,
glob_max_minutes,
glob_not_yet_finished,
glob_html_log,
#Bottom Generate Globals Decl
#BEGIN CONST
array_const_0D3,
array_const_0D2,
array_const_0D1,
array_const_0D0,
array_const_1,
#END CONST
array_norms,
array_y,
array_x,
array_fact_1,
array_tmp0,
array_tmp1,
array_tmp2,
array_tmp3,
array_tmp4,
array_tmp5,
array_tmp6,
array_last_rel_error,
array_type_pole,
array_y_init,
array_1st_rel_error,
array_m1,
array_pole,
array_poles,
array_y_higher_work2,
array_fact_2,
array_real_pole,
array_y_set_initial,
array_complex_pole,
array_y_higher_work,
array_y_higher,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
DEBUGL := 3;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_no_eqs := 0;
glob_abserr := 0.1e-10;
glob_last_good_h := 0.1;
glob_log10normmin := 0.1;
MAX_UNCHANGED := 10;
glob_disp_incr := 0.1;
sec_in_minute := 60;
glob_log10abserr := 0.0;
glob_iter := 0;
glob_start := 0;
glob_orig_start_sec := 0.0;
glob_warned := false;
glob_relerr := 0.1e-10;
glob_optimal_done := false;
glob_clock_sec := 0.0;
glob_normmax := 0.0;
glob_hmin_init := 0.001;
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_current_iter := 0;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1e-50;
glob_max_trunc_err := 0.1e-10;
glob_log10_abserr := 0.1e-10;
years_in_century := 100;
glob_optimal_expect_sec := 0.1;
glob_max_rel_trunc_err := 0.1e-10;
glob_max_iter := 1000;
glob_h := 0.1;
centuries_in_millinium := 10;
min_in_hour := 60;
djd_debug2 := true;
glob_good_digits := 0;
glob_subiter_method := 3;
glob_percent_done := 0.0;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1e-100;
glob_optimal_clock_start_sec := 0.0;
glob_log10_relerr := 0.1e-10;
glob_large_float := 9.0e100;
glob_reached_optimal_h := false;
hours_in_day := 24;
djd_debug := true;
glob_dump_analytic := false;
days_in_year := 365;
glob_display_flag := true;
glob_log10relerr := 0.0;
glob_max_hours := 0.0;
glob_hmax := 1.0;
glob_not_yet_start_msg := true;
glob_optimal_start := 0.0;
glob_look_poles := false;
glob_hmin := 0.00000000001;
glob_initial_pass := true;
glob_clock_start_sec := 0.0;
glob_dump := false;
glob_max_minutes := 0.0;
glob_not_yet_finished := true;
glob_html_log := true;
#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/mult_lin_linpostode.ode#################");
omniout_str(ALWAYS,"diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);");
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 := 5.0 ;");
omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS,"glob_h := 0.05;");
omniout_str(ALWAYS,"glob_look_poles := true;");
omniout_str(ALWAYS,"glob_max_iter := 1000000;");
omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS,"glob_h := 0.00001 ;");
omniout_str(ALWAYS,"glob_look_poles := true;");
omniout_str(ALWAYS,"glob_max_iter := 100;");
omniout_str(ALWAYS,"glob_max_minutes := 1;");
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(0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * 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 := 1.0e-200;
glob_smallish_float := 1.0e-64;
glob_large_float := 1.0e100;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
#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_norms:= Array(0..(max_terms + 1),[]);
array_y:= Array(0..(max_terms + 1),[]);
array_x:= Array(0..(max_terms + 1),[]);
array_fact_1:= Array(0..(max_terms + 1),[]);
array_tmp0:= Array(0..(max_terms + 1),[]);
array_tmp1:= Array(0..(max_terms + 1),[]);
array_tmp2:= Array(0..(max_terms + 1),[]);
array_tmp3:= Array(0..(max_terms + 1),[]);
array_tmp4:= Array(0..(max_terms + 1),[]);
array_tmp5:= Array(0..(max_terms + 1),[]);
array_tmp6:= Array(0..(max_terms + 1),[]);
array_last_rel_error:= Array(0..(max_terms + 1),[]);
array_type_pole:= Array(0..(max_terms + 1),[]);
array_y_init:= Array(0..(max_terms + 1),[]);
array_1st_rel_error:= Array(0..(max_terms + 1),[]);
array_m1:= Array(0..(max_terms + 1),[]);
array_pole:= Array(0..(max_terms + 1),[]);
array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
term := 1;
while (term <= max_terms) do # do number 2
array_norms[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_y[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_x[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_fact_1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp0[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp2[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp3[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp4[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp5[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_tmp6[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_last_rel_error[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_type_pole[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_y_init[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_1st_rel_error[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_m1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
term := 1;
while (term <= max_terms) do # do number 2
array_pole[term] := 0.0;
term := term + 1;
od;# end do number 2
;
ord := 1;
while (ord <=1) do # do number 2
term := 1;
while (term <= 3) do # do number 3
array_poles[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=2) do # do number 2
term := 1;
while (term <= max_terms) do # do number 3
array_y_higher_work2[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=max_terms) do # do number 2
term := 1;
while (term <= max_terms) do # do number 3
array_fact_2[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=1) do # do number 2
term := 1;
while (term <= 3) do # do number 3
array_real_pole[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=2) do # do number 2
term := 1;
while (term <= max_terms) do # do number 3
array_y_set_initial[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=1) do # do number 2
term := 1;
while (term <= 3) do # do number 3
array_complex_pole[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=2) do # do number 2
term := 1;
while (term <= max_terms) do # do number 3
array_y_higher_work[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
ord := 1;
while (ord <=2) do # do number 2
term := 1;
while (term <= max_terms) do # do number 3
array_y_higher[ord,term] := 0.0;
term := term + 1;
od;# end do number 3
;
ord := ord + 1;
od;# end do number 2
;
#BEGIN ARRAYS DEFINED AND INITIALIZATED
array_x := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_x[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_y := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_y[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp6 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp6[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp5 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp5[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp4 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp4[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp3 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp3[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp2 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp2[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_tmp0 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_tmp0[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_0D3 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_const_0D3[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_0D3[1] := 0.3;
array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_const_0D2[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_0D2[1] := 0.2;
array_const_0D1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_const_0D1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_0D1[1] := 0.1;
array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_const_0D0[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_0D0[1] := 0.0;
array_const_1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms + 1) do # do number 2
array_const_1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_const_1[1] := 1;
array_m1 := Array(1..(max_terms+1 + 1),[]);
term := 1;
while (term <= max_terms) do # do number 2
array_m1[term] := 0.0;
term := term + 1;
od;# end do number 2
;
array_m1[1] := -1.0;
#END ARRAYS DEFINED AND INITIALIZATED
#Initing Factorial Tables
iiif := 0;
while (iiif <= glob_max_terms) do # do number 2
jjjf := 0;
while (jjjf <= glob_max_terms) do # do number 3
array_fact_1[iiif] := 0;
array_fact_2[iiif,jjjf] := 0;
jjjf := jjjf + 1;
od;# end do number 3
;
iiif := iiif + 1;
od;# end do number 2
;
#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 := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
#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);
glob_abserr := expt(10.0 , (glob_log10_abserr));
glob_relerr := expt(10.0 , (glob_log10_relerr));
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;
if (glob_html_log) then # if number 2
html_log_file := fopen("html/entry.html",WRITE,TEXT);
fi;# end if 2
;
#BEGIN SOLUTION CODE
omniout_str(ALWAYS,"START of Soultion");
#Start Series -- INITIALIZE FOR SOLUTION
array_x[1] := x_start;
array_x[2] := glob_h;
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
;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
tmp := omniabs(array_y_higher[1,1]);
log10norm := (log10(tmp));
if (log10norm < glob_log10normmin) then # if number 3
glob_log10normmin := log10norm;
fi;# end if 3
fi;# end if 2
;
display_alot(current_iter)
;
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 (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
#left paren 0001C
omniout_str(INFO," ");
omniout_str(INFO,"TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if (glob_look_poles) then # if number 2
#left paren 0004C
check_for_pole();
fi;# end if 2
;#was right paren 0004C
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
#Jump Series array_y
order_diff := 1;
#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 3
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 3
;
#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 3
temp_sum := temp_sum + array_y_higher_work[ord,iii];
iii := iii - 1;
od;# end do number 3
;
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 3
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 3
;
#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 3
temp_sum := temp_sum + array_y_higher_work[ord,iii];
iii := iii - 1;
od;# end do number 3
;
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 3
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 3
;
#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 3
temp_sum := temp_sum + array_y_higher_work[ord,iii];
iii := iii - 1;
od;# end do number 3
;
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 3
array_y[term_no] := array_y_higher_work2[1,term_no];
ord := 1;
while (ord <= order_diff) do # do number 4
array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
ord := ord + 1;
od;# end do number 4
;
term_no := term_no - 1;
od;# end do number 3
;
#END PART 2 HEVE MOVED TERMS to REGULAR Array
display_alot(current_iter)
;
od;# end do number 2
;#right paren 0001C
omniout_str(ALWAYS,"Finished!");
if (glob_iter >= glob_max_iter) then # if number 2
omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
fi;# end if 2
;
if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
fi;# end if 2
;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,"diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);");
omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
;
prog_report(x_start,x_end);
if (glob_html_log) then # if number 2
logstart(html_log_file);
logitem_str(html_log_file,"2012-09-02T22:13:37-05:00")
;
logitem_str(html_log_file,"Maple")
;
logitem_str(html_log_file,"mult_lin_lin")
;
logitem_str(html_log_file,"diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);")
;
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_pole(html_log_file,array_type_pole[1])
;
if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 3
logitem_float(html_log_file,array_pole[1])
;
logitem_float(html_log_file,array_pole[2])
;
0;
else
logitem_str(html_log_file,"NA")
;
logitem_str(html_log_file,"NA")
;
0;
fi;# end if 3
;
logitem_time(html_log_file,convfloat(glob_clock_sec))
;
if (glob_percent_done < 100.0) then # if number 3
logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
;
0;
else
logitem_str(html_log_file,"Done")
;
0;
fi;# end if 3
;
log_revs(html_log_file," 126 | ")
;
logitem_str(html_log_file,"mult_lin_lin diffeq.mxt")
;
logitem_str(html_log_file,"mult_lin_lin maple results")
;
logitem_str(html_log_file,"c c++ Maple and Maxima")
;
logend(html_log_file)
;
;
fi;# end if 2
;
if (glob_html_log) then # if number 2
fclose(html_log_file);
fi;# end if 2
;
;;
#END OUTFILEMAIN
# End Function number 8
end;
main();