|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> 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 := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_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," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> 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 := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_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(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__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;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> 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 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> 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)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> 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,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> 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 := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
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 := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0) - cos(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - cos(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> 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," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
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, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> 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 := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__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 := float_abs(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 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__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 := float_abs(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 max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> 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 := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_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 / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
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/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #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 add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(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] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(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] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(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] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(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] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_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] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> 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,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> 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_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 400;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=50;
> max_terms:=400;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(400),[]);
> array_norms:= Array(0..(400),[]);
> array_fact_1:= Array(0..(400),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(400),[]);
> array_x:= Array(0..(400),[]);
> array_tmp0:= Array(0..(400),[]);
> array_tmp1_g:= Array(0..(400),[]);
> array_tmp1:= Array(0..(400),[]);
> array_tmp2:= Array(0..(400),[]);
> array_m1:= Array(0..(400),[]);
> array_y_higher := Array(0..(2) ,(0..400+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..400+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..400+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..400+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(400) ,(0..400+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 400) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 400) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 400) do # do number 2
> array_y_higher[ord,term] := c(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 <= 400) do # do number 2
> array_y_higher_work[ord,term] := c(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 <= 400) do # do number 2
> array_y_higher_work2[ord,term] := c(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 <= 400) do # do number 2
> array_y_set_initial[ord,term] := c(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] := c(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] := c(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 <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(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 <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=400) do # do number 1
> term := 1;
> while (term <= 400) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_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 Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> 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_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> 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;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> array_y_set_initial[1,41] := false;
> array_y_set_initial[1,42] := false;
> array_y_set_initial[1,43] := false;
> array_y_set_initial[1,44] := false;
> array_y_set_initial[1,45] := false;
> array_y_set_initial[1,46] := false;
> array_y_set_initial[1,47] := false;
> array_y_set_initial[1,48] := false;
> array_y_set_initial[1,49] := false;
> array_y_set_initial[1,50] := false;
> array_y_set_initial[1,51] := false;
> array_y_set_initial[1,52] := false;
> array_y_set_initial[1,53] := false;
> array_y_set_initial[1,54] := false;
> array_y_set_initial[1,55] := false;
> array_y_set_initial[1,56] := false;
> array_y_set_initial[1,57] := false;
> array_y_set_initial[1,58] := false;
> array_y_set_initial[1,59] := false;
> array_y_set_initial[1,60] := false;
> array_y_set_initial[1,61] := false;
> array_y_set_initial[1,62] := false;
> array_y_set_initial[1,63] := false;
> array_y_set_initial[1,64] := false;
> array_y_set_initial[1,65] := false;
> array_y_set_initial[1,66] := false;
> array_y_set_initial[1,67] := false;
> array_y_set_initial[1,68] := false;
> array_y_set_initial[1,69] := false;
> array_y_set_initial[1,70] := false;
> array_y_set_initial[1,71] := false;
> array_y_set_initial[1,72] := false;
> array_y_set_initial[1,73] := false;
> array_y_set_initial[1,74] := false;
> array_y_set_initial[1,75] := false;
> array_y_set_initial[1,76] := false;
> array_y_set_initial[1,77] := false;
> array_y_set_initial[1,78] := false;
> array_y_set_initial[1,79] := false;
> array_y_set_initial[1,80] := false;
> array_y_set_initial[1,81] := false;
> array_y_set_initial[1,82] := false;
> array_y_set_initial[1,83] := false;
> array_y_set_initial[1,84] := false;
> array_y_set_initial[1,85] := false;
> array_y_set_initial[1,86] := false;
> array_y_set_initial[1,87] := false;
> array_y_set_initial[1,88] := false;
> array_y_set_initial[1,89] := false;
> array_y_set_initial[1,90] := false;
> array_y_set_initial[1,91] := false;
> array_y_set_initial[1,92] := false;
> array_y_set_initial[1,93] := false;
> array_y_set_initial[1,94] := false;
> array_y_set_initial[1,95] := false;
> array_y_set_initial[1,96] := false;
> array_y_set_initial[1,97] := false;
> array_y_set_initial[1,98] := false;
> array_y_set_initial[1,99] := false;
> array_y_set_initial[1,100] := false;
> array_y_set_initial[1,101] := false;
> array_y_set_initial[1,102] := false;
> array_y_set_initial[1,103] := false;
> array_y_set_initial[1,104] := false;
> array_y_set_initial[1,105] := false;
> array_y_set_initial[1,106] := false;
> array_y_set_initial[1,107] := false;
> array_y_set_initial[1,108] := false;
> array_y_set_initial[1,109] := false;
> array_y_set_initial[1,110] := false;
> array_y_set_initial[1,111] := false;
> array_y_set_initial[1,112] := false;
> array_y_set_initial[1,113] := false;
> array_y_set_initial[1,114] := false;
> array_y_set_initial[1,115] := false;
> array_y_set_initial[1,116] := false;
> array_y_set_initial[1,117] := false;
> array_y_set_initial[1,118] := false;
> array_y_set_initial[1,119] := false;
> array_y_set_initial[1,120] := false;
> array_y_set_initial[1,121] := false;
> array_y_set_initial[1,122] := false;
> array_y_set_initial[1,123] := false;
> array_y_set_initial[1,124] := false;
> array_y_set_initial[1,125] := false;
> array_y_set_initial[1,126] := false;
> array_y_set_initial[1,127] := false;
> array_y_set_initial[1,128] := false;
> array_y_set_initial[1,129] := false;
> array_y_set_initial[1,130] := false;
> array_y_set_initial[1,131] := false;
> array_y_set_initial[1,132] := false;
> array_y_set_initial[1,133] := false;
> array_y_set_initial[1,134] := false;
> array_y_set_initial[1,135] := false;
> array_y_set_initial[1,136] := false;
> array_y_set_initial[1,137] := false;
> array_y_set_initial[1,138] := false;
> array_y_set_initial[1,139] := false;
> array_y_set_initial[1,140] := false;
> array_y_set_initial[1,141] := false;
> array_y_set_initial[1,142] := false;
> array_y_set_initial[1,143] := false;
> array_y_set_initial[1,144] := false;
> array_y_set_initial[1,145] := false;
> array_y_set_initial[1,146] := false;
> array_y_set_initial[1,147] := false;
> array_y_set_initial[1,148] := false;
> array_y_set_initial[1,149] := false;
> array_y_set_initial[1,150] := false;
> array_y_set_initial[1,151] := false;
> array_y_set_initial[1,152] := false;
> array_y_set_initial[1,153] := false;
> array_y_set_initial[1,154] := false;
> array_y_set_initial[1,155] := false;
> array_y_set_initial[1,156] := false;
> array_y_set_initial[1,157] := false;
> array_y_set_initial[1,158] := false;
> array_y_set_initial[1,159] := false;
> array_y_set_initial[1,160] := false;
> array_y_set_initial[1,161] := false;
> array_y_set_initial[1,162] := false;
> array_y_set_initial[1,163] := false;
> array_y_set_initial[1,164] := false;
> array_y_set_initial[1,165] := false;
> array_y_set_initial[1,166] := false;
> array_y_set_initial[1,167] := false;
> array_y_set_initial[1,168] := false;
> array_y_set_initial[1,169] := false;
> array_y_set_initial[1,170] := false;
> array_y_set_initial[1,171] := false;
> array_y_set_initial[1,172] := false;
> array_y_set_initial[1,173] := false;
> array_y_set_initial[1,174] := false;
> array_y_set_initial[1,175] := false;
> array_y_set_initial[1,176] := false;
> array_y_set_initial[1,177] := false;
> array_y_set_initial[1,178] := false;
> array_y_set_initial[1,179] := false;
> array_y_set_initial[1,180] := false;
> array_y_set_initial[1,181] := false;
> array_y_set_initial[1,182] := false;
> array_y_set_initial[1,183] := false;
> array_y_set_initial[1,184] := false;
> array_y_set_initial[1,185] := false;
> array_y_set_initial[1,186] := false;
> array_y_set_initial[1,187] := false;
> array_y_set_initial[1,188] := false;
> array_y_set_initial[1,189] := false;
> array_y_set_initial[1,190] := false;
> array_y_set_initial[1,191] := false;
> array_y_set_initial[1,192] := false;
> array_y_set_initial[1,193] := false;
> array_y_set_initial[1,194] := false;
> array_y_set_initial[1,195] := false;
> array_y_set_initial[1,196] := false;
> array_y_set_initial[1,197] := false;
> array_y_set_initial[1,198] := false;
> array_y_set_initial[1,199] := false;
> array_y_set_initial[1,200] := false;
> array_y_set_initial[1,201] := false;
> array_y_set_initial[1,202] := false;
> array_y_set_initial[1,203] := false;
> array_y_set_initial[1,204] := false;
> array_y_set_initial[1,205] := false;
> array_y_set_initial[1,206] := false;
> array_y_set_initial[1,207] := false;
> array_y_set_initial[1,208] := false;
> array_y_set_initial[1,209] := false;
> array_y_set_initial[1,210] := false;
> array_y_set_initial[1,211] := false;
> array_y_set_initial[1,212] := false;
> array_y_set_initial[1,213] := false;
> array_y_set_initial[1,214] := false;
> array_y_set_initial[1,215] := false;
> array_y_set_initial[1,216] := false;
> array_y_set_initial[1,217] := false;
> array_y_set_initial[1,218] := false;
> array_y_set_initial[1,219] := false;
> array_y_set_initial[1,220] := false;
> array_y_set_initial[1,221] := false;
> array_y_set_initial[1,222] := false;
> array_y_set_initial[1,223] := false;
> array_y_set_initial[1,224] := false;
> array_y_set_initial[1,225] := false;
> array_y_set_initial[1,226] := false;
> array_y_set_initial[1,227] := false;
> array_y_set_initial[1,228] := false;
> array_y_set_initial[1,229] := false;
> array_y_set_initial[1,230] := false;
> array_y_set_initial[1,231] := false;
> array_y_set_initial[1,232] := false;
> array_y_set_initial[1,233] := false;
> array_y_set_initial[1,234] := false;
> array_y_set_initial[1,235] := false;
> array_y_set_initial[1,236] := false;
> array_y_set_initial[1,237] := false;
> array_y_set_initial[1,238] := false;
> array_y_set_initial[1,239] := false;
> array_y_set_initial[1,240] := false;
> array_y_set_initial[1,241] := false;
> array_y_set_initial[1,242] := false;
> array_y_set_initial[1,243] := false;
> array_y_set_initial[1,244] := false;
> array_y_set_initial[1,245] := false;
> array_y_set_initial[1,246] := false;
> array_y_set_initial[1,247] := false;
> array_y_set_initial[1,248] := false;
> array_y_set_initial[1,249] := false;
> array_y_set_initial[1,250] := false;
> array_y_set_initial[1,251] := false;
> array_y_set_initial[1,252] := false;
> array_y_set_initial[1,253] := false;
> array_y_set_initial[1,254] := false;
> array_y_set_initial[1,255] := false;
> array_y_set_initial[1,256] := false;
> array_y_set_initial[1,257] := false;
> array_y_set_initial[1,258] := false;
> array_y_set_initial[1,259] := false;
> array_y_set_initial[1,260] := false;
> array_y_set_initial[1,261] := false;
> array_y_set_initial[1,262] := false;
> array_y_set_initial[1,263] := false;
> array_y_set_initial[1,264] := false;
> array_y_set_initial[1,265] := false;
> array_y_set_initial[1,266] := false;
> array_y_set_initial[1,267] := false;
> array_y_set_initial[1,268] := false;
> array_y_set_initial[1,269] := false;
> array_y_set_initial[1,270] := false;
> array_y_set_initial[1,271] := false;
> array_y_set_initial[1,272] := false;
> array_y_set_initial[1,273] := false;
> array_y_set_initial[1,274] := false;
> array_y_set_initial[1,275] := false;
> array_y_set_initial[1,276] := false;
> array_y_set_initial[1,277] := false;
> array_y_set_initial[1,278] := false;
> array_y_set_initial[1,279] := false;
> array_y_set_initial[1,280] := false;
> array_y_set_initial[1,281] := false;
> array_y_set_initial[1,282] := false;
> array_y_set_initial[1,283] := false;
> array_y_set_initial[1,284] := false;
> array_y_set_initial[1,285] := false;
> array_y_set_initial[1,286] := false;
> array_y_set_initial[1,287] := false;
> array_y_set_initial[1,288] := false;
> array_y_set_initial[1,289] := false;
> array_y_set_initial[1,290] := false;
> array_y_set_initial[1,291] := false;
> array_y_set_initial[1,292] := false;
> array_y_set_initial[1,293] := false;
> array_y_set_initial[1,294] := false;
> array_y_set_initial[1,295] := false;
> array_y_set_initial[1,296] := false;
> array_y_set_initial[1,297] := false;
> array_y_set_initial[1,298] := false;
> array_y_set_initial[1,299] := false;
> array_y_set_initial[1,300] := false;
> array_y_set_initial[1,301] := false;
> array_y_set_initial[1,302] := false;
> array_y_set_initial[1,303] := false;
> array_y_set_initial[1,304] := false;
> array_y_set_initial[1,305] := false;
> array_y_set_initial[1,306] := false;
> array_y_set_initial[1,307] := false;
> array_y_set_initial[1,308] := false;
> array_y_set_initial[1,309] := false;
> array_y_set_initial[1,310] := false;
> array_y_set_initial[1,311] := false;
> array_y_set_initial[1,312] := false;
> array_y_set_initial[1,313] := false;
> array_y_set_initial[1,314] := false;
> array_y_set_initial[1,315] := false;
> array_y_set_initial[1,316] := false;
> array_y_set_initial[1,317] := false;
> array_y_set_initial[1,318] := false;
> array_y_set_initial[1,319] := false;
> array_y_set_initial[1,320] := false;
> array_y_set_initial[1,321] := false;
> array_y_set_initial[1,322] := false;
> array_y_set_initial[1,323] := false;
> array_y_set_initial[1,324] := false;
> array_y_set_initial[1,325] := false;
> array_y_set_initial[1,326] := false;
> array_y_set_initial[1,327] := false;
> array_y_set_initial[1,328] := false;
> array_y_set_initial[1,329] := false;
> array_y_set_initial[1,330] := false;
> array_y_set_initial[1,331] := false;
> array_y_set_initial[1,332] := false;
> array_y_set_initial[1,333] := false;
> array_y_set_initial[1,334] := false;
> array_y_set_initial[1,335] := false;
> array_y_set_initial[1,336] := false;
> array_y_set_initial[1,337] := false;
> array_y_set_initial[1,338] := false;
> array_y_set_initial[1,339] := false;
> array_y_set_initial[1,340] := false;
> array_y_set_initial[1,341] := false;
> array_y_set_initial[1,342] := false;
> array_y_set_initial[1,343] := false;
> array_y_set_initial[1,344] := false;
> array_y_set_initial[1,345] := false;
> array_y_set_initial[1,346] := false;
> array_y_set_initial[1,347] := false;
> array_y_set_initial[1,348] := false;
> array_y_set_initial[1,349] := false;
> array_y_set_initial[1,350] := false;
> array_y_set_initial[1,351] := false;
> array_y_set_initial[1,352] := false;
> array_y_set_initial[1,353] := false;
> array_y_set_initial[1,354] := false;
> array_y_set_initial[1,355] := false;
> array_y_set_initial[1,356] := false;
> array_y_set_initial[1,357] := false;
> array_y_set_initial[1,358] := false;
> array_y_set_initial[1,359] := false;
> array_y_set_initial[1,360] := false;
> array_y_set_initial[1,361] := false;
> array_y_set_initial[1,362] := false;
> array_y_set_initial[1,363] := false;
> array_y_set_initial[1,364] := false;
> array_y_set_initial[1,365] := false;
> array_y_set_initial[1,366] := false;
> array_y_set_initial[1,367] := false;
> array_y_set_initial[1,368] := false;
> array_y_set_initial[1,369] := false;
> array_y_set_initial[1,370] := false;
> array_y_set_initial[1,371] := false;
> array_y_set_initial[1,372] := false;
> array_y_set_initial[1,373] := false;
> array_y_set_initial[1,374] := false;
> array_y_set_initial[1,375] := false;
> array_y_set_initial[1,376] := false;
> array_y_set_initial[1,377] := false;
> array_y_set_initial[1,378] := false;
> array_y_set_initial[1,379] := false;
> array_y_set_initial[1,380] := false;
> array_y_set_initial[1,381] := false;
> array_y_set_initial[1,382] := false;
> array_y_set_initial[1,383] := false;
> array_y_set_initial[1,384] := false;
> array_y_set_initial[1,385] := false;
> array_y_set_initial[1,386] := false;
> array_y_set_initial[1,387] := false;
> array_y_set_initial[1,388] := false;
> array_y_set_initial[1,389] := false;
> array_y_set_initial[1,390] := false;
> array_y_set_initial[1,391] := false;
> array_y_set_initial[1,392] := false;
> array_y_set_initial[1,393] := false;
> array_y_set_initial[1,394] := false;
> array_y_set_initial[1,395] := false;
> array_y_set_initial[1,396] := false;
> array_y_set_initial[1,397] := false;
> array_y_set_initial[1,398] := false;
> array_y_set_initial[1,399] := false;
> array_y_set_initial[1,400] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 400;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> 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/sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"Digits:=50;");
> omniout_str(ALWAYS,"max_terms:=400;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_start := c(0.0);");
> omniout_str(ALWAYS,"x_end := c(1.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := false;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)));");
> omniout_str(ALWAYS,"");
> 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 := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.0);
> x_end := c(1.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := false;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_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 := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(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 , c(term_no - 1)) / c(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;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> 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 := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> 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 , c(term_no - 1)) / c(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;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> 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_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> 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 := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(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 := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_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 , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(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 := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_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 , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(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 := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_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 , c(calc_term - 1)) / c(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 := ATS_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 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-19T21:24:53-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
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,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, 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_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 400;
Digits := 50;
max_terms := 400;
glob_html_log := true;
array_y_init := Array(0 .. 400, []);
array_norms := Array(0 .. 400, []);
array_fact_1 := Array(0 .. 400, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 400, []);
array_x := Array(0 .. 400, []);
array_tmp0 := Array(0 .. 400, []);
array_tmp1_g := Array(0 .. 400, []);
array_tmp1 := Array(0 .. 400, []);
array_tmp2 := Array(0 .. 400, []);
array_m1 := Array(0 .. 400, []);
array_y_higher := Array(0 .. 2, 0 .. 401, []);
array_y_higher_work := Array(0 .. 2, 0 .. 401, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 401, []);
array_y_set_initial := Array(0 .. 2, 0 .. 401, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 400, 0 .. 401, []);
term := 1;
while term <= 400 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 400 do array_norms[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 400 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 400 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 400 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 400 do array_tmp0[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 400 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 400 do array_tmp1[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 400 do array_tmp2[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 400 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 400 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 400 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 400 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 400 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 400 do
term := 1;
while term <= 400 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
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_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
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;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
array_y_set_initial[1, 41] := false;
array_y_set_initial[1, 42] := false;
array_y_set_initial[1, 43] := false;
array_y_set_initial[1, 44] := false;
array_y_set_initial[1, 45] := false;
array_y_set_initial[1, 46] := false;
array_y_set_initial[1, 47] := false;
array_y_set_initial[1, 48] := false;
array_y_set_initial[1, 49] := false;
array_y_set_initial[1, 50] := false;
array_y_set_initial[1, 51] := false;
array_y_set_initial[1, 52] := false;
array_y_set_initial[1, 53] := false;
array_y_set_initial[1, 54] := false;
array_y_set_initial[1, 55] := false;
array_y_set_initial[1, 56] := false;
array_y_set_initial[1, 57] := false;
array_y_set_initial[1, 58] := false;
array_y_set_initial[1, 59] := false;
array_y_set_initial[1, 60] := false;
array_y_set_initial[1, 61] := false;
array_y_set_initial[1, 62] := false;
array_y_set_initial[1, 63] := false;
array_y_set_initial[1, 64] := false;
array_y_set_initial[1, 65] := false;
array_y_set_initial[1, 66] := false;
array_y_set_initial[1, 67] := false;
array_y_set_initial[1, 68] := false;
array_y_set_initial[1, 69] := false;
array_y_set_initial[1, 70] := false;
array_y_set_initial[1, 71] := false;
array_y_set_initial[1, 72] := false;
array_y_set_initial[1, 73] := false;
array_y_set_initial[1, 74] := false;
array_y_set_initial[1, 75] := false;
array_y_set_initial[1, 76] := false;
array_y_set_initial[1, 77] := false;
array_y_set_initial[1, 78] := false;
array_y_set_initial[1, 79] := false;
array_y_set_initial[1, 80] := false;
array_y_set_initial[1, 81] := false;
array_y_set_initial[1, 82] := false;
array_y_set_initial[1, 83] := false;
array_y_set_initial[1, 84] := false;
array_y_set_initial[1, 85] := false;
array_y_set_initial[1, 86] := false;
array_y_set_initial[1, 87] := false;
array_y_set_initial[1, 88] := false;
array_y_set_initial[1, 89] := false;
array_y_set_initial[1, 90] := false;
array_y_set_initial[1, 91] := false;
array_y_set_initial[1, 92] := false;
array_y_set_initial[1, 93] := false;
array_y_set_initial[1, 94] := false;
array_y_set_initial[1, 95] := false;
array_y_set_initial[1, 96] := false;
array_y_set_initial[1, 97] := false;
array_y_set_initial[1, 98] := false;
array_y_set_initial[1, 99] := false;
array_y_set_initial[1, 100] := false;
array_y_set_initial[1, 101] := false;
array_y_set_initial[1, 102] := false;
array_y_set_initial[1, 103] := false;
array_y_set_initial[1, 104] := false;
array_y_set_initial[1, 105] := false;
array_y_set_initial[1, 106] := false;
array_y_set_initial[1, 107] := false;
array_y_set_initial[1, 108] := false;
array_y_set_initial[1, 109] := false;
array_y_set_initial[1, 110] := false;
array_y_set_initial[1, 111] := false;
array_y_set_initial[1, 112] := false;
array_y_set_initial[1, 113] := false;
array_y_set_initial[1, 114] := false;
array_y_set_initial[1, 115] := false;
array_y_set_initial[1, 116] := false;
array_y_set_initial[1, 117] := false;
array_y_set_initial[1, 118] := false;
array_y_set_initial[1, 119] := false;
array_y_set_initial[1, 120] := false;
array_y_set_initial[1, 121] := false;
array_y_set_initial[1, 122] := false;
array_y_set_initial[1, 123] := false;
array_y_set_initial[1, 124] := false;
array_y_set_initial[1, 125] := false;
array_y_set_initial[1, 126] := false;
array_y_set_initial[1, 127] := false;
array_y_set_initial[1, 128] := false;
array_y_set_initial[1, 129] := false;
array_y_set_initial[1, 130] := false;
array_y_set_initial[1, 131] := false;
array_y_set_initial[1, 132] := false;
array_y_set_initial[1, 133] := false;
array_y_set_initial[1, 134] := false;
array_y_set_initial[1, 135] := false;
array_y_set_initial[1, 136] := false;
array_y_set_initial[1, 137] := false;
array_y_set_initial[1, 138] := false;
array_y_set_initial[1, 139] := false;
array_y_set_initial[1, 140] := false;
array_y_set_initial[1, 141] := false;
array_y_set_initial[1, 142] := false;
array_y_set_initial[1, 143] := false;
array_y_set_initial[1, 144] := false;
array_y_set_initial[1, 145] := false;
array_y_set_initial[1, 146] := false;
array_y_set_initial[1, 147] := false;
array_y_set_initial[1, 148] := false;
array_y_set_initial[1, 149] := false;
array_y_set_initial[1, 150] := false;
array_y_set_initial[1, 151] := false;
array_y_set_initial[1, 152] := false;
array_y_set_initial[1, 153] := false;
array_y_set_initial[1, 154] := false;
array_y_set_initial[1, 155] := false;
array_y_set_initial[1, 156] := false;
array_y_set_initial[1, 157] := false;
array_y_set_initial[1, 158] := false;
array_y_set_initial[1, 159] := false;
array_y_set_initial[1, 160] := false;
array_y_set_initial[1, 161] := false;
array_y_set_initial[1, 162] := false;
array_y_set_initial[1, 163] := false;
array_y_set_initial[1, 164] := false;
array_y_set_initial[1, 165] := false;
array_y_set_initial[1, 166] := false;
array_y_set_initial[1, 167] := false;
array_y_set_initial[1, 168] := false;
array_y_set_initial[1, 169] := false;
array_y_set_initial[1, 170] := false;
array_y_set_initial[1, 171] := false;
array_y_set_initial[1, 172] := false;
array_y_set_initial[1, 173] := false;
array_y_set_initial[1, 174] := false;
array_y_set_initial[1, 175] := false;
array_y_set_initial[1, 176] := false;
array_y_set_initial[1, 177] := false;
array_y_set_initial[1, 178] := false;
array_y_set_initial[1, 179] := false;
array_y_set_initial[1, 180] := false;
array_y_set_initial[1, 181] := false;
array_y_set_initial[1, 182] := false;
array_y_set_initial[1, 183] := false;
array_y_set_initial[1, 184] := false;
array_y_set_initial[1, 185] := false;
array_y_set_initial[1, 186] := false;
array_y_set_initial[1, 187] := false;
array_y_set_initial[1, 188] := false;
array_y_set_initial[1, 189] := false;
array_y_set_initial[1, 190] := false;
array_y_set_initial[1, 191] := false;
array_y_set_initial[1, 192] := false;
array_y_set_initial[1, 193] := false;
array_y_set_initial[1, 194] := false;
array_y_set_initial[1, 195] := false;
array_y_set_initial[1, 196] := false;
array_y_set_initial[1, 197] := false;
array_y_set_initial[1, 198] := false;
array_y_set_initial[1, 199] := false;
array_y_set_initial[1, 200] := false;
array_y_set_initial[1, 201] := false;
array_y_set_initial[1, 202] := false;
array_y_set_initial[1, 203] := false;
array_y_set_initial[1, 204] := false;
array_y_set_initial[1, 205] := false;
array_y_set_initial[1, 206] := false;
array_y_set_initial[1, 207] := false;
array_y_set_initial[1, 208] := false;
array_y_set_initial[1, 209] := false;
array_y_set_initial[1, 210] := false;
array_y_set_initial[1, 211] := false;
array_y_set_initial[1, 212] := false;
array_y_set_initial[1, 213] := false;
array_y_set_initial[1, 214] := false;
array_y_set_initial[1, 215] := false;
array_y_set_initial[1, 216] := false;
array_y_set_initial[1, 217] := false;
array_y_set_initial[1, 218] := false;
array_y_set_initial[1, 219] := false;
array_y_set_initial[1, 220] := false;
array_y_set_initial[1, 221] := false;
array_y_set_initial[1, 222] := false;
array_y_set_initial[1, 223] := false;
array_y_set_initial[1, 224] := false;
array_y_set_initial[1, 225] := false;
array_y_set_initial[1, 226] := false;
array_y_set_initial[1, 227] := false;
array_y_set_initial[1, 228] := false;
array_y_set_initial[1, 229] := false;
array_y_set_initial[1, 230] := false;
array_y_set_initial[1, 231] := false;
array_y_set_initial[1, 232] := false;
array_y_set_initial[1, 233] := false;
array_y_set_initial[1, 234] := false;
array_y_set_initial[1, 235] := false;
array_y_set_initial[1, 236] := false;
array_y_set_initial[1, 237] := false;
array_y_set_initial[1, 238] := false;
array_y_set_initial[1, 239] := false;
array_y_set_initial[1, 240] := false;
array_y_set_initial[1, 241] := false;
array_y_set_initial[1, 242] := false;
array_y_set_initial[1, 243] := false;
array_y_set_initial[1, 244] := false;
array_y_set_initial[1, 245] := false;
array_y_set_initial[1, 246] := false;
array_y_set_initial[1, 247] := false;
array_y_set_initial[1, 248] := false;
array_y_set_initial[1, 249] := false;
array_y_set_initial[1, 250] := false;
array_y_set_initial[1, 251] := false;
array_y_set_initial[1, 252] := false;
array_y_set_initial[1, 253] := false;
array_y_set_initial[1, 254] := false;
array_y_set_initial[1, 255] := false;
array_y_set_initial[1, 256] := false;
array_y_set_initial[1, 257] := false;
array_y_set_initial[1, 258] := false;
array_y_set_initial[1, 259] := false;
array_y_set_initial[1, 260] := false;
array_y_set_initial[1, 261] := false;
array_y_set_initial[1, 262] := false;
array_y_set_initial[1, 263] := false;
array_y_set_initial[1, 264] := false;
array_y_set_initial[1, 265] := false;
array_y_set_initial[1, 266] := false;
array_y_set_initial[1, 267] := false;
array_y_set_initial[1, 268] := false;
array_y_set_initial[1, 269] := false;
array_y_set_initial[1, 270] := false;
array_y_set_initial[1, 271] := false;
array_y_set_initial[1, 272] := false;
array_y_set_initial[1, 273] := false;
array_y_set_initial[1, 274] := false;
array_y_set_initial[1, 275] := false;
array_y_set_initial[1, 276] := false;
array_y_set_initial[1, 277] := false;
array_y_set_initial[1, 278] := false;
array_y_set_initial[1, 279] := false;
array_y_set_initial[1, 280] := false;
array_y_set_initial[1, 281] := false;
array_y_set_initial[1, 282] := false;
array_y_set_initial[1, 283] := false;
array_y_set_initial[1, 284] := false;
array_y_set_initial[1, 285] := false;
array_y_set_initial[1, 286] := false;
array_y_set_initial[1, 287] := false;
array_y_set_initial[1, 288] := false;
array_y_set_initial[1, 289] := false;
array_y_set_initial[1, 290] := false;
array_y_set_initial[1, 291] := false;
array_y_set_initial[1, 292] := false;
array_y_set_initial[1, 293] := false;
array_y_set_initial[1, 294] := false;
array_y_set_initial[1, 295] := false;
array_y_set_initial[1, 296] := false;
array_y_set_initial[1, 297] := false;
array_y_set_initial[1, 298] := false;
array_y_set_initial[1, 299] := false;
array_y_set_initial[1, 300] := false;
array_y_set_initial[1, 301] := false;
array_y_set_initial[1, 302] := false;
array_y_set_initial[1, 303] := false;
array_y_set_initial[1, 304] := false;
array_y_set_initial[1, 305] := false;
array_y_set_initial[1, 306] := false;
array_y_set_initial[1, 307] := false;
array_y_set_initial[1, 308] := false;
array_y_set_initial[1, 309] := false;
array_y_set_initial[1, 310] := false;
array_y_set_initial[1, 311] := false;
array_y_set_initial[1, 312] := false;
array_y_set_initial[1, 313] := false;
array_y_set_initial[1, 314] := false;
array_y_set_initial[1, 315] := false;
array_y_set_initial[1, 316] := false;
array_y_set_initial[1, 317] := false;
array_y_set_initial[1, 318] := false;
array_y_set_initial[1, 319] := false;
array_y_set_initial[1, 320] := false;
array_y_set_initial[1, 321] := false;
array_y_set_initial[1, 322] := false;
array_y_set_initial[1, 323] := false;
array_y_set_initial[1, 324] := false;
array_y_set_initial[1, 325] := false;
array_y_set_initial[1, 326] := false;
array_y_set_initial[1, 327] := false;
array_y_set_initial[1, 328] := false;
array_y_set_initial[1, 329] := false;
array_y_set_initial[1, 330] := false;
array_y_set_initial[1, 331] := false;
array_y_set_initial[1, 332] := false;
array_y_set_initial[1, 333] := false;
array_y_set_initial[1, 334] := false;
array_y_set_initial[1, 335] := false;
array_y_set_initial[1, 336] := false;
array_y_set_initial[1, 337] := false;
array_y_set_initial[1, 338] := false;
array_y_set_initial[1, 339] := false;
array_y_set_initial[1, 340] := false;
array_y_set_initial[1, 341] := false;
array_y_set_initial[1, 342] := false;
array_y_set_initial[1, 343] := false;
array_y_set_initial[1, 344] := false;
array_y_set_initial[1, 345] := false;
array_y_set_initial[1, 346] := false;
array_y_set_initial[1, 347] := false;
array_y_set_initial[1, 348] := false;
array_y_set_initial[1, 349] := false;
array_y_set_initial[1, 350] := false;
array_y_set_initial[1, 351] := false;
array_y_set_initial[1, 352] := false;
array_y_set_initial[1, 353] := false;
array_y_set_initial[1, 354] := false;
array_y_set_initial[1, 355] := false;
array_y_set_initial[1, 356] := false;
array_y_set_initial[1, 357] := false;
array_y_set_initial[1, 358] := false;
array_y_set_initial[1, 359] := false;
array_y_set_initial[1, 360] := false;
array_y_set_initial[1, 361] := false;
array_y_set_initial[1, 362] := false;
array_y_set_initial[1, 363] := false;
array_y_set_initial[1, 364] := false;
array_y_set_initial[1, 365] := false;
array_y_set_initial[1, 366] := false;
array_y_set_initial[1, 367] := false;
array_y_set_initial[1, 368] := false;
array_y_set_initial[1, 369] := false;
array_y_set_initial[1, 370] := false;
array_y_set_initial[1, 371] := false;
array_y_set_initial[1, 372] := false;
array_y_set_initial[1, 373] := false;
array_y_set_initial[1, 374] := false;
array_y_set_initial[1, 375] := false;
array_y_set_initial[1, 376] := false;
array_y_set_initial[1, 377] := false;
array_y_set_initial[1, 378] := false;
array_y_set_initial[1, 379] := false;
array_y_set_initial[1, 380] := false;
array_y_set_initial[1, 381] := false;
array_y_set_initial[1, 382] := false;
array_y_set_initial[1, 383] := false;
array_y_set_initial[1, 384] := false;
array_y_set_initial[1, 385] := false;
array_y_set_initial[1, 386] := false;
array_y_set_initial[1, 387] := false;
array_y_set_initial[1, 388] := false;
array_y_set_initial[1, 389] := false;
array_y_set_initial[1, 390] := false;
array_y_set_initial[1, 391] := false;
array_y_set_initial[1, 392] := false;
array_y_set_initial[1, 393] := false;
array_y_set_initial[1, 394] := false;
array_y_set_initial[1, 395] := false;
array_y_set_initial[1, 396] := false;
array_y_set_initial[1, 397] := false;
array_y_set_initial[1, 398] := false;
array_y_set_initial[1, 399] := false;
array_y_set_initial[1, 400] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 400;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "Digits:=50;");
omniout_str(ALWAYS, "max_terms:=400;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_start := c(0.0);");
omniout_str(ALWAYS, "x_end := c(1.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := false;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(2.0) - cos(c(x)));");
omniout_str(ALWAYS, "");
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 := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.);
x_end := c(1.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_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 := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
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 := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = sin ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-19T21:24:53-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sin");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 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_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"sin diffeq.mxt");
logitem_str(html_log_file,
"sin maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=4.5MB, alloc=41.6MB, time=0.03
memory used=19.1MB, alloc=45.6MB, time=0.20
##############ECHO OF PROBLEM#################
##############temp/sinpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=50;
max_terms:=400;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.0);
x_end := c(1.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(2.0) - cos(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 50
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=52.3MB, alloc=53.6MB, time=0.61
memory used=88.0MB, alloc=53.6MB, time=1.00
memory used=123.9MB, alloc=53.6MB, time=1.39
memory used=159.7MB, alloc=53.6MB, time=1.78
memory used=195.5MB, alloc=53.6MB, time=2.17
memory used=231.3MB, alloc=53.6MB, time=2.56
memory used=267.1MB, alloc=53.6MB, time=2.95
memory used=302.9MB, alloc=53.6MB, time=3.34
memory used=338.6MB, alloc=53.6MB, time=3.73
TOP MAIN SOLVE Loop
x[1] = 0.0099999940000011999998857142920635
y[1] (closed_form) = 1.0000499995233357522136337445359
y[1] (numeric) = 1.0000499995233357522136337445359
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009999
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=374.5MB, alloc=53.6MB, time=4.14
memory used=410.3MB, alloc=53.6MB, time=4.53
memory used=446.2MB, alloc=53.6MB, time=4.92
memory used=481.9MB, alloc=53.6MB, time=5.30
memory used=517.8MB, alloc=53.6MB, time=5.69
memory used=553.5MB, alloc=53.6MB, time=6.08
memory used=589.2MB, alloc=53.6MB, time=6.47
memory used=624.9MB, alloc=53.6MB, time=6.86
memory used=660.7MB, alloc=53.6MB, time=7.25
memory used=696.5MB, alloc=53.6MB, time=7.64
TOP MAIN SOLVE Loop
x[1] = 0.019999987333335866666425396838801
y[1] (closed_form) = 1.0001999930801059076745157721168
y[1] (numeric) = 1.0001999930801059076745157721168
absolute error = 1e-49
relative error = 9.9980004690912861239074294346793e-48 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01999
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=732.3MB, alloc=53.6MB, time=8.03
memory used=768.1MB, alloc=53.6MB, time=8.44
memory used=804.0MB, alloc=53.6MB, time=8.83
memory used=839.7MB, alloc=53.6MB, time=9.23
memory used=875.5MB, alloc=53.6MB, time=9.63
memory used=911.3MB, alloc=53.6MB, time=10.05
memory used=947.2MB, alloc=53.6MB, time=10.45
memory used=982.9MB, alloc=53.6MB, time=10.84
memory used=1018.8MB, alloc=53.6MB, time=11.25
memory used=1054.6MB, alloc=53.6MB, time=11.70
TOP MAIN SOLVE Loop
x[1] = 0.029999980666670533332965079385538
y[1] (closed_form) = 1.0004499656710997826002354327863
y[1] (numeric) = 1.0004499656710997826002354327863
absolute error = 1e-49
relative error = 9.9955023670694221419454716383141e-48 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02998
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=1090.5MB, alloc=53.6MB, time=12.19
memory used=1126.3MB, alloc=53.6MB, time=12.64
memory used=1162.1MB, alloc=53.6MB, time=13.05
memory used=1198.0MB, alloc=53.6MB, time=13.45
memory used=1233.8MB, alloc=53.6MB, time=13.89
memory used=1269.6MB, alloc=53.6MB, time=14.36
memory used=1305.3MB, alloc=53.6MB, time=14.83
memory used=1341.1MB, alloc=53.6MB, time=15.22
memory used=1377.0MB, alloc=53.6MB, time=15.61
memory used=1412.9MB, alloc=53.6MB, time=16.00
TOP MAIN SOLVE Loop
x[1] = 0.039999974000005199999504761932275
y[1] (closed_form) = 1.0007998922992999165069601390862
y[1] (numeric) = 1.0007998922992999165069601390862
absolute error = 1e-49
relative error = 9.9920074701700637258273983949607e-48 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03996
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=1448.7MB, alloc=53.6MB, time=16.39
memory used=1484.5MB, alloc=53.6MB, time=16.78
memory used=1520.3MB, alloc=53.6MB, time=17.17
memory used=1556.1MB, alloc=53.6MB, time=17.56
memory used=1591.9MB, alloc=53.6MB, time=17.95
memory used=1627.8MB, alloc=53.6MB, time=18.36
memory used=1663.6MB, alloc=53.6MB, time=18.75
memory used=1699.5MB, alloc=53.6MB, time=19.14
memory used=1735.3MB, alloc=53.6MB, time=19.53
memory used=1771.1MB, alloc=53.6MB, time=19.92
TOP MAIN SOLVE Loop
x[1] = 0.049999967333339866666044444479012
y[1] (closed_form) = 1.0012497379723817500140490996986
y[1] (numeric) = 1.0012497379723817500140490996986
absolute error = 3e-49
relative error = 2.9962554657694715246710936119866e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04992
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=1807.0MB, alloc=53.6MB, time=20.31
memory used=1843.0MB, alloc=53.6MB, time=20.70
memory used=1878.8MB, alloc=53.6MB, time=21.09
memory used=1914.8MB, alloc=53.6MB, time=21.48
memory used=1950.6MB, alloc=53.6MB, time=21.87
memory used=1986.5MB, alloc=53.6MB, time=22.26
memory used=2022.3MB, alloc=53.6MB, time=22.66
memory used=2058.1MB, alloc=53.6MB, time=23.05
memory used=2093.8MB, alloc=53.6MB, time=23.44
memory used=2129.7MB, alloc=53.6MB, time=23.83
TOP MAIN SOLVE Loop
x[1] = 0.05999996066667453333258412702575
y[1] (closed_form) = 1.0017994577062128234742550921001
y[1] (numeric) = 1.0017994577062128234742550921001
absolute error = 3e-49
relative error = 2.9946113235766777641295310366353e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05986
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=2165.6MB, alloc=53.6MB, time=24.22
memory used=2201.4MB, alloc=53.6MB, time=24.61
memory used=2237.2MB, alloc=53.6MB, time=25.00
memory used=2273.0MB, alloc=53.6MB, time=25.41
memory used=2308.9MB, alloc=53.6MB, time=25.80
memory used=2344.7MB, alloc=53.6MB, time=26.19
memory used=2380.5MB, alloc=53.6MB, time=26.59
memory used=2416.3MB, alloc=53.6MB, time=26.98
memory used=2452.2MB, alloc=53.6MB, time=27.39
memory used=2488.0MB, alloc=53.6MB, time=27.80
TOP MAIN SOLVE Loop
x[1] = 0.069999954000009199999123809572487
y[1] (closed_form) = 1.0024489965293511467352559283147
y[1] (numeric) = 1.0024489965293511467352559283147
absolute error = 2e-49
relative error = 1.9951139728049407220197090388112e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06977
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=2523.9MB, alloc=53.6MB, time=28.19
memory used=2559.7MB, alloc=53.6MB, time=28.59
memory used=2595.7MB, alloc=53.6MB, time=28.98
memory used=2631.6MB, alloc=53.6MB, time=29.39
memory used=2667.4MB, alloc=53.6MB, time=29.77
memory used=2703.4MB, alloc=53.6MB, time=30.17
memory used=2739.2MB, alloc=53.6MB, time=30.55
memory used=2775.0MB, alloc=53.6MB, time=30.94
memory used=2811.0MB, alloc=53.6MB, time=31.33
memory used=2846.7MB, alloc=53.6MB, time=31.72
TOP MAIN SOLVE Loop
x[1] = 0.079999947333343866665663492119224
y[1] (closed_form) = 1.0031982894885422901998878619116
y[1] (numeric) = 1.0031982894885422901998878619116
absolute error = 2e-49
relative error = 1.9936238139118581133808789595284e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07966
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=2882.7MB, alloc=53.6MB, time=32.11
memory used=2918.6MB, alloc=53.6MB, time=32.50
memory used=2954.4MB, alloc=53.6MB, time=32.89
memory used=2990.1MB, alloc=53.6MB, time=33.28
memory used=3026.1MB, alloc=53.6MB, time=33.67
memory used=3061.9MB, alloc=53.6MB, time=34.06
memory used=3097.8MB, alloc=53.6MB, time=34.45
memory used=3133.7MB, alloc=53.6MB, time=34.84
memory used=3169.6MB, alloc=53.6MB, time=35.23
memory used=3205.5MB, alloc=53.6MB, time=35.63
TOP MAIN SOLVE Loop
x[1] = 0.089999940666678533332203174665961
y[1] (closed_form) = 1.0040472616552146474812887397204
y[1] (numeric) = 1.0040472616552146474812887397204
absolute error = 3e-49
relative error = 2.9879071579303670495345689037409e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08951
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=3241.4MB, alloc=53.6MB, time=36.02
memory used=3277.2MB, alloc=53.6MB, time=36.39
memory used=3313.0MB, alloc=53.6MB, time=36.78
memory used=3348.9MB, alloc=53.6MB, time=37.17
memory used=3384.7MB, alloc=53.6MB, time=37.58
memory used=3420.5MB, alloc=53.6MB, time=37.97
memory used=3456.4MB, alloc=53.6MB, time=38.36
memory used=3492.2MB, alloc=53.6MB, time=38.72
memory used=3528.1MB, alloc=53.6MB, time=39.11
memory used=3563.9MB, alloc=53.6MB, time=39.50
TOP MAIN SOLVE Loop
x[1] = 0.099999934000013199998742857212698
y[1] (closed_form) = 1.0049958281329722201329641049132
y[1] (numeric) = 1.0049958281329722201329641049132
absolute error = 3e-49
relative error = 2.9850870182946335095505217805471e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09933
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=3599.8MB, alloc=53.6MB, time=39.89
memory used=3635.7MB, alloc=53.6MB, time=40.28
memory used=3671.5MB, alloc=53.6MB, time=40.67
memory used=3707.3MB, alloc=53.6MB, time=41.06
memory used=3743.2MB, alloc=53.6MB, time=41.45
memory used=3779.1MB, alloc=53.6MB, time=41.83
memory used=3815.0MB, alloc=53.6MB, time=42.22
memory used=3850.8MB, alloc=53.6MB, time=42.61
memory used=3886.8MB, alloc=53.6MB, time=43.00
memory used=3922.6MB, alloc=53.6MB, time=43.39
TOP MAIN SOLVE Loop
x[1] = 0.10999992733334786666528253975944
y[1] (closed_form) = 1.0060438940660841751825462320824
y[1] (numeric) = 1.0060438940660841751825462320824
absolute error = 2e-49
relative error = 1.9879848302808005136756777925530e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1091
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=3958.5MB, alloc=53.6MB, time=43.78
memory used=3994.3MB, alloc=53.6MB, time=44.17
memory used=4030.1MB, alloc=53.6MB, time=44.56
memory used=4065.9MB, alloc=53.6MB, time=44.95
memory used=4101.8MB, alloc=53.6MB, time=45.34
memory used=4137.6MB, alloc=53.6MB, time=45.72
memory used=4173.5MB, alloc=53.6MB, time=46.11
memory used=4209.4MB, alloc=53.6MB, time=46.50
memory used=4245.3MB, alloc=53.6MB, time=46.89
memory used=4281.2MB, alloc=53.6MB, time=47.28
TOP MAIN SOLVE Loop
x[1] = 0.11999992066668253333182222230617
y[1] (closed_form) = 1.0071913546489703265216992476449
y[1] (numeric) = 1.0071913546489703265216992476449
absolute error = 4e-49
relative error = 3.9714399667321343070509721644874e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=4317.2MB, alloc=53.6MB, time=47.67
memory used=4353.1MB, alloc=53.6MB, time=48.06
memory used=4388.9MB, alloc=53.6MB, time=48.45
memory used=4424.8MB, alloc=53.6MB, time=48.84
memory used=4460.6MB, alloc=53.6MB, time=49.23
memory used=4496.5MB, alloc=53.6MB, time=49.63
memory used=4532.3MB, alloc=53.6MB, time=50.01
memory used=4568.0MB, alloc=53.6MB, time=50.41
memory used=4603.8MB, alloc=53.6MB, time=50.78
memory used=4639.6MB, alloc=53.6MB, time=51.17
TOP MAIN SOLVE Loop
x[1] = 0.12999991400001719999836190485291
y[1] (closed_form) = 1.008438095136681591613200595634
y[1] (numeric) = 1.008438095136681591613200595634
absolute error = 5e-49
relative error = 4.9581625526773762457110336301590e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1285
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=4675.4MB, alloc=53.6MB, time=51.58
memory used=4711.3MB, alloc=53.6MB, time=51.95
memory used=4747.2MB, alloc=53.6MB, time=52.34
memory used=4783.0MB, alloc=53.6MB, time=52.73
memory used=4818.9MB, alloc=53.6MB, time=53.13
memory used=4854.8MB, alloc=53.6MB, time=53.52
memory used=4890.5MB, alloc=53.6MB, time=53.91
memory used=4926.4MB, alloc=53.6MB, time=54.30
memory used=4962.3MB, alloc=53.6MB, time=54.69
memory used=4998.1MB, alloc=53.6MB, time=55.06
TOP MAIN SOLVE Loop
x[1] = 0.13999990733335186666490158739965
y[1] (closed_form) = 1.0097839908563743754796591957367
y[1] (numeric) = 1.0097839908563743754796591957367
absolute error = 7e-49
relative error = 6.9321756567594841756476059929717e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1382
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=5034.0MB, alloc=53.6MB, time=55.45
memory used=5070.0MB, alloc=53.6MB, time=55.84
memory used=5105.9MB, alloc=53.6MB, time=56.23
memory used=5141.8MB, alloc=53.6MB, time=56.63
memory used=5177.6MB, alloc=53.6MB, time=57.01
memory used=5213.3MB, alloc=53.6MB, time=57.41
memory used=5249.1MB, alloc=53.6MB, time=57.80
memory used=5284.9MB, alloc=53.6MB, time=58.19
memory used=5320.7MB, alloc=53.6MB, time=58.58
memory used=5356.5MB, alloc=53.6MB, time=58.97
TOP MAIN SOLVE Loop
x[1] = 0.14999990066668653333144126994638
y[1] (closed_form) = 1.0112289072197777345465632680932
y[1] (numeric) = 1.0112289072197777345465632680932
absolute error = 1.0e-48
relative error = 9.8889578102484240548288225361752e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1478
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=5392.5MB, alloc=53.6MB, time=59.36
memory used=5428.3MB, alloc=53.6MB, time=59.75
memory used=5464.1MB, alloc=53.6MB, time=60.14
memory used=5500.1MB, alloc=53.6MB, time=60.53
memory used=5536.0MB, alloc=53.6MB, time=60.92
memory used=5571.9MB, alloc=53.6MB, time=61.31
memory used=5607.7MB, alloc=53.6MB, time=61.70
memory used=5643.5MB, alloc=53.6MB, time=62.09
memory used=5679.3MB, alloc=53.6MB, time=62.47
memory used=5715.2MB, alloc=53.6MB, time=62.86
TOP MAIN SOLVE Loop
x[1] = 0.15999989400002119999798095249312
y[1] (closed_form) = 1.012772699736652073635325048572
y[1] (numeric) = 1.012772699736652073635325048572
absolute error = 7e-49
relative error = 6.9117186924767885086947196891945e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1573
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=5751.1MB, alloc=53.6MB, time=63.25
memory used=5787.0MB, alloc=53.6MB, time=63.64
memory used=5822.8MB, alloc=53.6MB, time=64.03
memory used=5858.7MB, alloc=53.6MB, time=64.42
memory used=5894.5MB, alloc=53.6MB, time=64.81
memory used=5930.4MB, alloc=53.6MB, time=65.20
memory used=5966.3MB, alloc=53.6MB, time=65.59
memory used=6002.1MB, alloc=53.6MB, time=65.98
memory used=6038.0MB, alloc=53.6MB, time=66.38
memory used=6073.9MB, alloc=53.6MB, time=66.77
TOP MAIN SOLVE Loop
x[1] = 0.16999988733335586666452063503986
y[1] (closed_form) = 1.0144152140292380302496330955551
y[1] (numeric) = 1.0144152140292380302496330955551
absolute error = 7e-49
relative error = 6.9005274203214406547201283276457e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1667
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=6109.8MB, alloc=53.6MB, time=67.16
memory used=6145.7MB, alloc=53.6MB, time=67.55
memory used=6181.5MB, alloc=53.6MB, time=67.92
memory used=6217.4MB, alloc=53.6MB, time=68.31
memory used=6253.4MB, alloc=53.6MB, time=68.70
memory used=6289.3MB, alloc=53.6MB, time=69.09
memory used=6325.2MB, alloc=53.6MB, time=69.48
memory used=6361.0MB, alloc=53.6MB, time=69.88
memory used=6396.8MB, alloc=53.6MB, time=70.27
TOP MAIN SOLVE Loop
x[1] = 0.1799998806666905333310603175866
y[1] (closed_form) = 1.016156285847694101280650734545
y[1] (numeric) = 1.016156285847694101280650734545
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1761
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=6432.8MB, alloc=53.6MB, time=70.66
memory used=6468.7MB, alloc=53.6MB, time=71.05
memory used=6504.4MB, alloc=53.6MB, time=71.44
memory used=6540.3MB, alloc=53.6MB, time=71.83
memory used=6576.2MB, alloc=53.6MB, time=72.22
memory used=6612.0MB, alloc=53.6MB, time=72.61
memory used=6647.9MB, alloc=53.6MB, time=72.98
memory used=6683.8MB, alloc=53.6MB, time=73.38
memory used=6719.6MB, alloc=53.6MB, time=73.77
memory used=6755.5MB, alloc=53.6MB, time=74.16
TOP MAIN SOLVE Loop
x[1] = 0.18999987400002519999760000013333
y[1] (closed_form) = 1.0179957410865214683833130816079
y[1] (numeric) = 1.0179957410865214683833130816079
absolute error = 5e-49
relative error = 4.9116119038606470220478229463355e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1855
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=6791.5MB, alloc=53.6MB, time=74.55
memory used=6827.3MB, alloc=53.6MB, time=74.94
memory used=6863.2MB, alloc=53.6MB, time=75.33
memory used=6899.1MB, alloc=53.6MB, time=75.72
memory used=6934.9MB, alloc=53.6MB, time=76.11
memory used=6970.7MB, alloc=53.6MB, time=76.50
memory used=7006.6MB, alloc=53.6MB, time=76.89
memory used=7042.4MB, alloc=53.6MB, time=77.28
memory used=7078.2MB, alloc=53.6MB, time=77.67
memory used=7114.1MB, alloc=53.6MB, time=78.06
TOP MAIN SOLVE Loop
x[1] = 0.19999986733335986666413968268007
y[1] (closed_form) = 1.0199333958019743795570622638594
y[1] (numeric) = 1.0199333958019743795570622638594
absolute error = 3e-49
relative error = 2.9413685367573416817922378305134e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1947
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=7150.0MB, alloc=53.6MB, time=78.45
memory used=7185.8MB, alloc=53.6MB, time=78.84
memory used=7221.7MB, alloc=53.6MB, time=79.23
memory used=7257.6MB, alloc=53.6MB, time=79.61
memory used=7293.5MB, alloc=53.6MB, time=80.00
memory used=7329.4MB, alloc=53.6MB, time=80.39
memory used=7365.3MB, alloc=53.6MB, time=80.78
memory used=7401.2MB, alloc=53.6MB, time=81.17
memory used=7437.2MB, alloc=53.6MB, time=81.56
memory used=7473.0MB, alloc=53.6MB, time=81.95
TOP MAIN SOLVE Loop
x[1] = 0.20999986066669453333067936522681
y[1] (closed_form) = 1.0219690562304543459096927107067
y[1] (numeric) = 1.0219690562304543459096927107067
absolute error = 9e-49
relative error = 8.8065288720155702532981857779203e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2039
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=7509.0MB, alloc=53.6MB, time=82.34
memory used=7544.9MB, alloc=53.6MB, time=82.73
memory used=7580.8MB, alloc=53.6MB, time=83.13
memory used=7616.7MB, alloc=53.6MB, time=83.52
memory used=7652.6MB, alloc=53.6MB, time=83.91
memory used=7688.4MB, alloc=53.6MB, time=84.30
memory used=7724.2MB, alloc=53.6MB, time=84.69
memory used=7760.2MB, alloc=53.6MB, time=85.06
memory used=7796.0MB, alloc=53.6MB, time=85.45
memory used=7831.8MB, alloc=53.6MB, time=85.84
TOP MAIN SOLVE Loop
x[1] = 0.21999985400002919999721904777354
y[1] (closed_form) = 1.0241025188078863142024110949127
y[1] (numeric) = 1.0241025188078863142024110949127
absolute error = 8e-49
relative error = 7.8117179218663145602328308614264e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.213
Order of pole (three term test) = 392
NO COMPLEX POLE (six term test) for Equation 1
memory used=7867.8MB, alloc=53.6MB, time=86.23
memory used=7903.7MB, alloc=53.6MB, time=86.63
memory used=7939.6MB, alloc=53.6MB, time=87.01
memory used=7975.4MB, alloc=53.6MB, time=87.41
memory used=8011.3MB, alloc=53.6MB, time=87.80
memory used=8047.1MB, alloc=53.6MB, time=88.19
memory used=8083.1MB, alloc=53.6MB, time=88.58
memory used=8119.0MB, alloc=53.6MB, time=88.95
memory used=8154.9MB, alloc=53.6MB, time=89.34
memory used=8190.8MB, alloc=53.6MB, time=89.73
TOP MAIN SOLVE Loop
x[1] = 0.22999984733336386666375873032028
y[1] (closed_form) = 1.0263335701900748775775866193551
y[1] (numeric) = 1.0263335701900748775775866193551
absolute error = 1.0e-48
relative error = 9.7434209407649215425129411773620e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.222
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8226.7MB, alloc=53.6MB, time=90.14
memory used=8262.5MB, alloc=53.6MB, time=90.53
memory used=8298.4MB, alloc=53.6MB, time=90.91
memory used=8334.3MB, alloc=53.6MB, time=91.30
memory used=8370.1MB, alloc=53.6MB, time=91.69
memory used=8406.1MB, alloc=53.6MB, time=92.08
memory used=8441.9MB, alloc=53.6MB, time=92.47
memory used=8477.8MB, alloc=53.6MB, time=92.86
memory used=8513.8MB, alloc=53.6MB, time=93.25
memory used=8549.7MB, alloc=53.6MB, time=93.64
TOP MAIN SOLVE Loop
x[1] = 0.23999984066669853333029841286702
y[1] (closed_form) = 1.0286619872740384888677964415954
y[1] (numeric) = 1.0286619872740384888677964415954
absolute error = 8e-49
relative error = 7.7770930577497632083395189430262e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2309
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8585.6MB, alloc=53.6MB, time=94.03
memory used=8621.6MB, alloc=53.6MB, time=94.42
memory used=8657.4MB, alloc=53.6MB, time=94.81
memory used=8693.3MB, alloc=53.6MB, time=95.20
memory used=8729.2MB, alloc=53.6MB, time=95.59
memory used=8765.1MB, alloc=53.6MB, time=95.98
memory used=8800.9MB, alloc=53.6MB, time=96.38
memory used=8836.8MB, alloc=53.6MB, time=96.75
memory used=8872.5MB, alloc=53.6MB, time=97.14
memory used=8908.4MB, alloc=53.6MB, time=97.53
TOP MAIN SOLVE Loop
x[1] = 0.24999983400003319999683809541376
y[1] (closed_form) = 1.031087537220319543085458296391
y[1] (numeric) = 1.031087537220319543085458296391
absolute error = 1.0e-48
relative error = 9.6984975950332250415387027483859e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2397
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8944.4MB, alloc=53.6MB, time=97.92
memory used=8980.3MB, alloc=53.6MB, time=98.31
memory used=9016.1MB, alloc=53.6MB, time=98.70
memory used=9052.0MB, alloc=53.6MB, time=99.09
memory used=9087.9MB, alloc=53.6MB, time=99.48
memory used=9123.8MB, alloc=53.6MB, time=99.87
memory used=9159.8MB, alloc=53.6MB, time=100.26
memory used=9195.7MB, alloc=53.6MB, time=100.66
memory used=9231.6MB, alloc=53.6MB, time=101.05
memory used=9267.4MB, alloc=53.6MB, time=101.44
TOP MAIN SOLVE Loop
x[1] = 0.25999982733336786666337777796049
y[1] (closed_form) = 1.0336099774762680981063676528272
y[1] (numeric) = 1.0336099774762680981063676528272
absolute error = 1.2e-48
relative error = 1.1609795049869787578679491087167e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2484
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9303.3MB, alloc=53.6MB, time=101.83
memory used=9339.2MB, alloc=53.6MB, time=102.22
memory used=9375.1MB, alloc=53.6MB, time=102.61
memory used=9411.1MB, alloc=53.6MB, time=102.98
memory used=9447.0MB, alloc=53.6MB, time=103.38
memory used=9482.8MB, alloc=53.6MB, time=103.77
memory used=9518.8MB, alloc=53.6MB, time=104.16
memory used=9554.7MB, alloc=53.6MB, time=104.55
memory used=9590.6MB, alloc=53.6MB, time=104.95
memory used=9626.4MB, alloc=53.6MB, time=105.34
TOP MAIN SOLVE Loop
x[1] = 0.26999982066670253332991746050723
y[1] (closed_form) = 1.0362290558002969051975785309381
y[1] (numeric) = 1.0362290558002969051975785309381
absolute error = 9e-49
relative error = 8.6853383907954120870049477802152e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9662.4MB, alloc=53.6MB, time=105.73
memory used=9698.3MB, alloc=53.6MB, time=106.12
memory used=9734.2MB, alloc=53.6MB, time=106.52
memory used=9770.1MB, alloc=53.6MB, time=106.89
memory used=9806.0MB, alloc=53.6MB, time=107.28
memory used=9841.8MB, alloc=53.6MB, time=107.67
memory used=9877.6MB, alloc=53.6MB, time=108.06
memory used=9913.6MB, alloc=53.6MB, time=108.45
memory used=9949.5MB, alloc=53.6MB, time=108.84
memory used=9985.4MB, alloc=53.6MB, time=109.23
TOP MAIN SOLVE Loop
x[1] = 0.27999981400003719999645714305397
y[1] (closed_form) = 1.0389445102871053239100215962469
y[1] (numeric) = 1.0389445102871053239100215962469
absolute error = 1.1e-48
relative error = 1.0587668437614848192197172039584e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2656
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10021.4MB, alloc=53.6MB, time=109.63
memory used=10057.3MB, alloc=53.6MB, time=110.02
memory used=10093.3MB, alloc=53.6MB, time=110.41
memory used=10129.2MB, alloc=53.6MB, time=110.80
memory used=10165.1MB, alloc=53.6MB, time=111.19
memory used=10201.0MB, alloc=53.6MB, time=111.58
memory used=10236.9MB, alloc=53.6MB, time=111.97
memory used=10272.8MB, alloc=53.6MB, time=112.36
memory used=10308.6MB, alloc=53.6MB, time=112.75
memory used=10344.5MB, alloc=53.6MB, time=113.16
TOP MAIN SOLVE Loop
x[1] = 0.28999980733337186666299682560071
y[1] (closed_form) = 1.0417560693938695989687532602328
y[1] (numeric) = 1.0417560693938695989687532602328
absolute error = 1.0e-48
relative error = 9.5991761351756294353855576130917e-47 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.274
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10380.3MB, alloc=53.6MB, time=113.55
memory used=10416.2MB, alloc=53.6MB, time=113.94
memory used=10452.1MB, alloc=53.6MB, time=114.33
memory used=10487.9MB, alloc=53.6MB, time=114.72
memory used=10523.7MB, alloc=53.6MB, time=115.11
memory used=10559.7MB, alloc=53.6MB, time=115.50
memory used=10595.6MB, alloc=53.6MB, time=115.89
memory used=10631.4MB, alloc=53.6MB, time=116.28
memory used=10667.4MB, alloc=53.6MB, time=116.67
memory used=10703.3MB, alloc=53.6MB, time=117.06
TOP MAIN SOLVE Loop
x[1] = 0.29999980066670653332953650814744
y[1] (closed_form) = 1.0446634519673968801584638966606
y[1] (numeric) = 1.0446634519673968801584638966606
absolute error = 1.4e-48
relative error = 1.3401445196186425907222266218952e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2823
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10739.3MB, alloc=53.6MB, time=117.45
memory used=10775.2MB, alloc=53.6MB, time=117.84
memory used=10811.0MB, alloc=53.6MB, time=118.23
memory used=10846.8MB, alloc=53.6MB, time=118.62
memory used=10882.8MB, alloc=53.6MB, time=119.02
memory used=10918.6MB, alloc=53.6MB, time=119.41
memory used=10954.6MB, alloc=53.6MB, time=119.80
memory used=10990.5MB, alloc=53.6MB, time=120.19
memory used=11026.3MB, alloc=53.6MB, time=120.58
memory used=11062.2MB, alloc=53.6MB, time=120.97
TOP MAIN SOLVE Loop
x[1] = 0.30999979400004119999607619069418
y[1] (closed_form) = 1.0476663672722402698285053711416
y[1] (numeric) = 1.0476663672722402698285053711416
absolute error = 1.2e-48
relative error = 1.1454028090301148611820556053879e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2905
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11098.1MB, alloc=53.6MB, time=121.36
memory used=11134.0MB, alloc=53.6MB, time=121.75
memory used=11169.9MB, alloc=53.6MB, time=122.14
memory used=11205.8MB, alloc=53.6MB, time=122.52
memory used=11241.7MB, alloc=53.6MB, time=122.91
memory used=11277.6MB, alloc=53.6MB, time=123.30
memory used=11313.5MB, alloc=53.6MB, time=123.69
memory used=11349.4MB, alloc=53.6MB, time=124.08
memory used=11385.2MB, alloc=53.6MB, time=124.47
memory used=11421.1MB, alloc=53.6MB, time=124.86
TOP MAIN SOLVE Loop
x[1] = 0.31999978733337586666261587324092
y[1] (closed_form) = 1.0507645150197720865398651178533
y[1] (numeric) = 1.0507645150197720865398651178533
absolute error = 1.6e-48
relative error = 1.5227008308040294141442511672558e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2986
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11457.1MB, alloc=53.6MB, time=125.25
memory used=11493.0MB, alloc=53.6MB, time=125.64
memory used=11528.9MB, alloc=53.6MB, time=126.03
memory used=11564.9MB, alloc=53.6MB, time=126.42
memory used=11600.8MB, alloc=53.6MB, time=126.81
memory used=11636.6MB, alloc=53.6MB, time=127.20
memory used=11672.5MB, alloc=53.6MB, time=127.59
memory used=11708.4MB, alloc=53.6MB, time=127.98
memory used=11744.4MB, alloc=53.6MB, time=128.38
TOP MAIN SOLVE Loop
memory used=11780.3MB, alloc=53.6MB, time=128.77
x[1] = 0.32999978066671053332915555578765
y[1] (closed_form) = 1.0539575853982124375558260734341
y[1] (numeric) = 1.0539575853982124375558260734341
absolute error = 1.3e-48
relative error = 1.2334462202374361906084012351590e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3066
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11816.2MB, alloc=53.6MB, time=129.17
memory used=11852.3MB, alloc=53.6MB, time=129.56
memory used=11888.2MB, alloc=53.6MB, time=129.95
memory used=11924.0MB, alloc=53.6MB, time=130.34
memory used=11960.0MB, alloc=53.6MB, time=130.73
memory used=11995.8MB, alloc=53.6MB, time=131.11
memory used=12031.6MB, alloc=53.6MB, time=131.50
memory used=12067.6MB, alloc=53.6MB, time=131.89
memory used=12103.5MB, alloc=53.6MB, time=132.28
TOP MAIN SOLVE Loop
x[1] = 0.33999977400004519999569523833439
y[1] (closed_form) = 1.0572452591036100973480908698594
y[1] (numeric) = 1.0572452591036100973480908698594
absolute error = 1.4e-48
relative error = 1.3241960537964445182328243563969e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3144
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12139.5MB, alloc=53.6MB, time=132.67
memory used=12175.4MB, alloc=53.6MB, time=133.06
memory used=12211.2MB, alloc=53.6MB, time=133.45
memory used=12247.2MB, alloc=53.6MB, time=133.84
memory used=12283.2MB, alloc=53.6MB, time=134.23
memory used=12319.1MB, alloc=53.6MB, time=134.62
memory used=12355.0MB, alloc=53.6MB, time=135.01
memory used=12390.9MB, alloc=53.6MB, time=135.41
memory used=12426.8MB, alloc=53.6MB, time=135.80
memory used=12462.7MB, alloc=53.6MB, time=136.19
TOP MAIN SOLVE Loop
x[1] = 0.34999976733337986666223492088113
y[1] (closed_form) = 1.0606272073717725940604676993263
y[1] (numeric) = 1.0606272073717725940604676993263
absolute error = 2.0e-48
relative error = 1.8856766883776130457140937885136e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3221
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12498.7MB, alloc=53.6MB, time=136.58
memory used=12534.5MB, alloc=53.6MB, time=136.95
memory used=12570.5MB, alloc=53.6MB, time=137.34
memory used=12606.4MB, alloc=53.6MB, time=137.73
memory used=12642.2MB, alloc=53.6MB, time=138.13
memory used=12678.1MB, alloc=53.6MB, time=138.52
memory used=12714.1MB, alloc=53.6MB, time=138.91
memory used=12750.0MB, alloc=53.6MB, time=139.30
memory used=12785.9MB, alloc=53.6MB, time=139.69
memory used=12821.7MB, alloc=53.6MB, time=140.08
TOP MAIN SOLVE Loop
x[1] = 0.35999976066671453332877460342787
y[1] (closed_form) = 1.0641030920111423109523370708884
y[1] (numeric) = 1.0641030920111423109523370708884
absolute error = 2.3e-48
relative error = 2.1614447108249888544875158521224e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3297
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12857.6MB, alloc=53.6MB, time=140.47
memory used=12893.5MB, alloc=53.6MB, time=140.86
memory used=12929.4MB, alloc=53.6MB, time=141.25
memory used=12965.3MB, alloc=53.6MB, time=141.64
memory used=13001.2MB, alloc=53.6MB, time=142.03
memory used=13037.1MB, alloc=53.6MB, time=142.42
memory used=13072.9MB, alloc=53.6MB, time=142.81
memory used=13108.8MB, alloc=53.6MB, time=143.20
memory used=13144.7MB, alloc=53.6MB, time=143.59
memory used=13180.7MB, alloc=53.6MB, time=143.98
TOP MAIN SOLVE Loop
x[1] = 0.3699997540000491999953142859746
y[1] (closed_form) = 1.0676725654366153152435351768446
y[1] (numeric) = 1.0676725654366153152435351768446
absolute error = 2.3e-48
relative error = 2.1542185071126513468233137625205e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3371
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13216.7MB, alloc=53.6MB, time=144.37
memory used=13252.5MB, alloc=53.6MB, time=144.76
memory used=13288.4MB, alloc=53.6MB, time=145.16
memory used=13324.2MB, alloc=53.6MB, time=145.55
memory used=13360.2MB, alloc=53.6MB, time=145.94
memory used=13396.0MB, alloc=53.6MB, time=146.33
memory used=13431.8MB, alloc=53.6MB, time=146.72
memory used=13467.7MB, alloc=53.6MB, time=147.11
memory used=13503.6MB, alloc=53.6MB, time=147.48
memory used=13539.5MB, alloc=53.6MB, time=147.88
TOP MAIN SOLVE Loop
x[1] = 0.37999974733338386666185396852134
y[1] (closed_form) = 1.0713352707042995325104607435943
y[1] (numeric) = 1.0713352707042995325104607435943
absolute error = 2.4e-48
relative error = 2.2401950777017092455496689636656e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3445
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13575.5MB, alloc=53.6MB, time=148.27
memory used=13611.3MB, alloc=53.6MB, time=148.66
memory used=13647.1MB, alloc=53.6MB, time=149.05
memory used=13683.0MB, alloc=53.6MB, time=149.44
memory used=13719.0MB, alloc=53.6MB, time=149.83
memory used=13755.0MB, alloc=53.6MB, time=150.22
memory used=13790.9MB, alloc=53.6MB, time=150.61
memory used=13826.8MB, alloc=53.6MB, time=151.00
memory used=13862.7MB, alloc=53.6MB, time=151.39
memory used=13898.6MB, alloc=53.6MB, time=151.78
TOP MAIN SOLVE Loop
x[1] = 0.38999974066671853332839365106808
y[1] (closed_form) = 1.0750908415472087908495651485973
y[1] (numeric) = 1.0750908415472087908495651485973
absolute error = 2.9e-48
relative error = 2.6974464742221104797408428656021e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3516
Order of pole (three term test) = 392.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13934.5MB, alloc=53.6MB, time=152.16
memory used=13970.4MB, alloc=53.6MB, time=152.55
memory used=14006.2MB, alloc=53.6MB, time=152.94
memory used=14042.1MB, alloc=53.6MB, time=153.33
memory used=14078.1MB, alloc=53.6MB, time=153.72
memory used=14114.0MB, alloc=53.6MB, time=154.11
memory used=14149.8MB, alloc=53.6MB, time=154.50
memory used=14185.7MB, alloc=53.6MB, time=154.89
memory used=14221.7MB, alloc=53.6MB, time=155.28
memory used=14257.7MB, alloc=53.6MB, time=155.67
TOP MAIN SOLVE Loop
x[1] = 0.39999973400005319999493333361481
y[1] (closed_form) = 1.078938902411889165438313516108
y[1] (numeric) = 1.078938902411889165438313516108
absolute error = 3.4e-48
relative error = 3.1512442385750927724737941702499e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=14293.6MB, alloc=53.6MB, time=156.06
memory used=14329.5MB, alloc=53.6MB, time=156.45
memory used=14365.4MB, alloc=53.6MB, time=156.84
memory used=14401.3MB, alloc=53.6MB, time=157.23
memory used=14437.3MB, alloc=53.6MB, time=157.63
memory used=14473.2MB, alloc=53.6MB, time=158.01
memory used=14509.1MB, alloc=53.6MB, time=158.41
memory used=14545.2MB, alloc=53.6MB, time=158.80
memory used=14581.0MB, alloc=53.6MB, time=159.19
memory used=14616.9MB, alloc=53.6MB, time=159.56
TOP MAIN SOLVE Loop
x[1] = 0.40999972733338786666147301616155
y[1] (closed_form) = 1.0828790684959739608945659762499
y[1] (numeric) = 1.0828790684959739608945659762499
absolute error = 3.5e-48
relative error = 3.2321245297142916007432849287467e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3656
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=14653.0MB, alloc=53.6MB, time=159.97
memory used=14689.0MB, alloc=53.6MB, time=160.34
memory used=14725.0MB, alloc=53.6MB, time=160.73
memory used=14760.9MB, alloc=53.6MB, time=161.13
memory used=14796.8MB, alloc=53.6MB, time=161.52
memory used=14832.6MB, alloc=53.6MB, time=161.91
memory used=14868.6MB, alloc=53.6MB, time=162.30
memory used=14904.4MB, alloc=53.6MB, time=162.69
memory used=14940.3MB, alloc=53.6MB, time=163.08
memory used=14976.2MB, alloc=53.6MB, time=163.47
TOP MAIN SOLVE Loop
x[1] = 0.41999972066672253332801269870829
y[1] (closed_form) = 1.086910945786663575972446108472
y[1] (numeric) = 1.086910945786663575972446108472
absolute error = 3.7e-48
relative error = 3.4041427352836941969897130147856e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3723
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=15012.1MB, alloc=53.6MB, time=163.86
memory used=15047.9MB, alloc=53.6MB, time=164.25
memory used=15083.9MB, alloc=53.6MB, time=164.64
memory used=15119.8MB, alloc=53.6MB, time=165.05
memory used=15155.7MB, alloc=53.6MB, time=165.44
memory used=15191.7MB, alloc=53.6MB, time=165.83
memory used=15227.5MB, alloc=53.6MB, time=166.22
memory used=15263.5MB, alloc=53.6MB, time=166.61
memory used=15299.4MB, alloc=53.6MB, time=167.00
memory used=15335.2MB, alloc=53.6MB, time=167.39
TOP MAIN SOLVE Loop
x[1] = 0.42999971400005719999455238125503
y[1] (closed_form) = 1.0910341311001264026454239899484
y[1] (numeric) = 1.0910341311001264026454239899484
absolute error = 3.0e-48
relative error = 2.7496848306431982277729537511471e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3789
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=15371.1MB, alloc=53.6MB, time=167.78
memory used=15407.0MB, alloc=53.6MB, time=168.17
memory used=15442.9MB, alloc=53.6MB, time=168.56
memory used=15478.9MB, alloc=53.6MB, time=168.95
memory used=15514.8MB, alloc=53.6MB, time=169.34
memory used=15550.7MB, alloc=53.6MB, time=169.73
memory used=15586.6MB, alloc=53.6MB, time=170.12
memory used=15622.6MB, alloc=53.6MB, time=170.51
memory used=15658.5MB, alloc=53.6MB, time=170.91
memory used=15694.4MB, alloc=53.6MB, time=171.30
TOP MAIN SOLVE Loop
x[1] = 0.43999970733339186666109206380176
y[1] (closed_form) = 1.0952482121218168195247928765898
y[1] (numeric) = 1.0952482121218168195247928765898
absolute error = 3.2e-48
relative error = 2.9217121421277301471449745696092e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3854
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=15730.4MB, alloc=53.6MB, time=171.69
memory used=15766.3MB, alloc=53.6MB, time=172.08
memory used=15802.2MB, alloc=53.6MB, time=172.47
memory used=15838.2MB, alloc=53.6MB, time=172.86
memory used=15874.0MB, alloc=53.6MB, time=173.23
memory used=15909.8MB, alloc=53.6MB, time=173.62
memory used=15945.8MB, alloc=53.6MB, time=174.01
memory used=15981.6MB, alloc=53.6MB, time=174.41
memory used=16017.6MB, alloc=53.6MB, time=174.80
memory used=16053.5MB, alloc=53.6MB, time=175.19
TOP MAIN SOLVE Loop
x[1] = 0.4499997006667265333276317463485
y[1] (closed_form) = 1.0995527674477062478531715248481
y[1] (numeric) = 1.0995527674477062478531715248481
absolute error = 3.7e-48
relative error = 3.3650044904970590334119804214321e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3917
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=16089.5MB, alloc=53.6MB, time=175.58
memory used=16125.4MB, alloc=53.6MB, time=175.97
memory used=16161.3MB, alloc=53.6MB, time=176.36
memory used=16197.2MB, alloc=53.6MB, time=176.75
memory used=16233.1MB, alloc=53.6MB, time=177.14
memory used=16269.0MB, alloc=53.6MB, time=177.53
memory used=16304.9MB, alloc=53.6MB, time=177.92
memory used=16340.7MB, alloc=53.6MB, time=178.31
memory used=16376.6MB, alloc=53.6MB, time=178.70
memory used=16412.5MB, alloc=53.6MB, time=179.09
TOP MAIN SOLVE Loop
x[1] = 0.45999969400006119999417142889524
y[1] (closed_form) = 1.1039473666264231470072892824559
y[1] (numeric) = 1.1039473666264231470072892824559
absolute error = 4.4e-48
relative error = 3.9856972651205791057295938409597e-46 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 50
h = 9.9999933333346666665396825467372e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3978
Order of pole (three term test) = 392.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=16448.6MB, alloc=53.6MB, time=179.48
memory used=16484.4MB, alloc=53.6MB, time=179.88
memory used=16520.3MB, alloc=53.6MB, time=180.26
Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( x ) ;
Iterations = 4628
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 3 Minutes 28 Seconds
Optimized Time Remaining = 3 Minutes 28 Seconds
Expected Total Time = 6 Minutes 28 Seconds
Time to Timeout 0.0 Seconds
Percent Done = 46.38 %
> quit
memory used=16545.8MB, alloc=53.6MB, time=180.53