|\^/| 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_y2 := proc(x)
> return(sin(c(x)));
> end;
exact_soln_y2 := proc(x) return sin(c(x)) end proc
> exact_soln_y2p := proc(x)
> return( cos(c(x)));
> end;
exact_soln_y2p := proc(x) return cos(c(x)) end proc
> exact_soln_y2pp := proc(x)
> return( neg( sin(c(x))));
> end;
exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y1 := proc(x)
> return( cos(c(x)));
> end;
exact_soln_y1 := proc(x) return 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
> ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3
> rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 4
> glob_least_given_sing := rad_given;
> fi;# end if 4;
> elif
> (glob_type_given_pole = 3) then # if number 4
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> elif
> (glob_type_given_pole = 5) then # if number 5
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 5;
> if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," ");
> if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
> glob_least_ratio_sing := array_rad_test_poles[2,1];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
> glob_least_3_sing := array_rad_test_poles[2,2];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
> glob_least_6_sing := array_rad_test_poles[2,3];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> 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;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
(array_x[1] - array_given_rad_poles[2, 1])
+ array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ");
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 2")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_rad_test_poles[2, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_rad_test_poles[2, 1], 4, " ");
if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if array_rad_test_poles[2, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if array_rad_test_poles[2, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
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 5
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 5;
> 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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[1]) < min_size then
min_size := float_abs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y1[1]) < min_size then
min_size := float_abs(array_y1[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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := 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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 5
> if (iter >= 0) then # if number 6
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_float(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 7;
> 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," ");
> ;
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_float(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[2] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 7;
> array_est_rel_error[2] := 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 6;
> #BOTTOM DISPLAY ALOT
> fi;# end if 5;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2(ind_var));
omniout_float(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y2[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)*35*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, " ");
closed_form_val_y := evalf(exact_soln_y1(ind_var));
omniout_float(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y1[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[2]*100.0*
sqrt(glob_iter)*35*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[2] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
array_est_rel_error[2] := 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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 5
> 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 5;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 - 3 - 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_y2_higher[1,last_no-1],array_y2_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[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_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 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[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := 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_y1_higher[1,last_no-1],array_y1_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[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> 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 - 3 - 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_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> 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 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #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[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := 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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> 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 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> 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 - 3 - 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_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> 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 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #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[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := 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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> 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 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> 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 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_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 17;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 17
> display_poles();
> fi;# end if 17
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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 - 13;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_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_y2_higher[1, last_no - 1],
array_y2_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[2, 1] := glob_larger_float;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 1],
array_y1_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[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 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 - 13;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_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[2, 2] := glob_larger_float;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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 - 13;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_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;
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[2, 3] := glob_larger_float;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(array_x[1]);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[1] := neg(array_tmp1[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[3,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[4,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[1] := neg(array_y2[1]);
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
> array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[2] := neg(array_tmp1[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[3,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[4,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[2] := neg(array_y2[2]);
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
> array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[3] := neg(array_tmp1[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[3,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[4,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[3] := neg(array_y2[3]);
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
> array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[4] := neg(array_tmp1[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,7]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[3,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[4,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[4] := neg(array_y2[4]);
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
> array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[5] := neg(array_tmp1[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,8]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7));
> if (8 <= ATS_MAX_TERMS) then # if number 3
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y2_higher[2,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[3,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[4,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[5] := neg(array_y2[5]);
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_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 cos LINEAR $eq_no = 1
> array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit neg FULL $eq_no = 1
> array_tmp2[kkk] := neg(array_tmp1[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y2[kkk + order_d] := c(temporary);
> array_y2_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_y2_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;
> #emit neg FULL $eq_no = 2
> array_tmp5[kkk] := neg(array_y2[kkk]);
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_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_y1_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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := neg(array_tmp1[1]);
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y2_set_initial[1, 4] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[3, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[4, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp5[1] := neg(array_y2[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_tmp1_g[1])*array_x[2]/c(1);
array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
array_tmp2[2] := neg(array_tmp1[2]);
array_tmp3[2] := array_tmp2[2];
if not array_y2_set_initial[1, 5] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[3, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[4, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp5[2] := neg(array_y2[2]);
if not array_y1_set_initial[2, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_tmp1_g[2])*array_x[2]/c(2);
array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
array_tmp2[3] := neg(array_tmp1[3]);
array_tmp3[3] := array_tmp2[3];
if not array_y2_set_initial[1, 6] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[3, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[4, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp5[3] := neg(array_y2[3]);
if not array_y1_set_initial[2, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_tmp1_g[3])*array_x[2]/c(3);
array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
array_tmp2[4] := neg(array_tmp1[4]);
array_tmp3[4] := array_tmp2[4];
if not array_y2_set_initial[1, 7] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 6));
if 7 <= ATS_MAX_TERMS then
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[3, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[4, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp5[4] := neg(array_y2[4]);
if not array_y1_set_initial[2, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_tmp1_g[4])*array_x[2]/c(4);
array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
array_tmp2[5] := neg(array_tmp1[5]);
array_tmp3[5] := array_tmp2[5];
if not array_y2_set_initial[1, 8] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 7));
if 8 <= ATS_MAX_TERMS then
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary
end if;
temporary := c(temporary)*c(7)/c(glob_h);
array_y2_higher[2, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[3, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[4, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp5[5] := neg(array_y2[5]);
if not array_y1_set_initial[2, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp2[kkk] := neg(array_tmp1[kkk]);
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 3;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y2[kkk + order_d] := c(temporary);
array_y2_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_y2_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp5[kkk] := neg(array_y2[kkk]);
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_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_y1_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_3,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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_y2_init:= Array(0..(40),[]);
> array_y1_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y2:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_y1:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y2_higher := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=4) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_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 <=4) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_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 <=4) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_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 <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_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 <= 40) do # do number 2
> array_y1_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 <= 40) do # do number 2
> array_y1_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 <= 40) do # do number 2
> array_y1_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 <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_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 <=3) 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 <=3) 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 <=3) 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 <=3) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) 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_y2);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y1);
> 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_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_3);
> array_const_3[1] := c(3);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> 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_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y2_set_initial[1,31] := false;
> array_y2_set_initial[1,32] := false;
> array_y2_set_initial[1,33] := false;
> array_y2_set_initial[1,34] := false;
> array_y2_set_initial[1,35] := false;
> array_y2_set_initial[1,36] := false;
> array_y2_set_initial[1,37] := false;
> array_y2_set_initial[1,38] := false;
> array_y2_set_initial[1,39] := false;
> array_y2_set_initial[1,40] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> array_y1_set_initial[2,31] := false;
> array_y1_set_initial[2,32] := false;
> array_y1_set_initial[2,33] := false;
> array_y1_set_initial[2,34] := false;
> array_y1_set_initial[2,35] := false;
> array_y1_set_initial[2,36] := false;
> array_y1_set_initial[2,37] := false;
> array_y1_set_initial[2,38] := false;
> array_y1_set_initial[2,39] := false;
> array_y1_set_initial[2,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest4postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(5.0);");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> 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,"#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(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> 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,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return( neg( sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> 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(0.1);
> x_end := c(5.0);
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> glob_look_poles := true;
> 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(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> 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 17
> #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 18
> glob_display_interval := c(display_max);
> fi;# end if 18;
> 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 := 3;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 4) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
> 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 19;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 19;
> if (glob_look_poles) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if ( not found_h) then # if number 19
> 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 20
> 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 20;
> fi;# end if 19;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 19
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 19;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
> 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 19;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 18;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 18
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 18;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 18
> 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 := 3;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_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 19
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_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 19
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> 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 19
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 19;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> if (glob_subiter_method = 1 ) then # if number 19
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 20
> subiter := 1;
> while (subiter <= 4) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 20;
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 20
> check_for_pole();
> fi;# end if 20;
> if (reached_interval()) then # if number 20
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 20;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2;
> order_diff := 4;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,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 := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,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 := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 4;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 := 4;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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 := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_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 20
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 20;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 20;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 20
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-01T22:13:06-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest4")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 3 ) = neg ( cos ( 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 21
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_min_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> 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 21
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 22
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 23
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 24
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 25
> 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 26
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 26;
> if (glob_least_ratio_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_3_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_6_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> 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 26
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 26;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"mtest4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest4 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 26
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_min_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 31
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_ratio_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_3_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_6_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 31
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 31;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 30;
> if (glob_html_log) then # if number 30
> fclose(html_log_file);
> fi;# end if 30
> ;
> ;;
> fi;# end if 29
> #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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y2_init := Array(0 .. 40, []);
array_y1_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y2 := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_y1 := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y2_higher := Array(0 .. 4, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 4, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 4, 0 .. 41, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
array_y1_higher := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= 40 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= 40 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= 40 do
array_y2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y2_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 <= 40 do
array_y1_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 <= 40 do
array_y1_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 <= 40 do
array_y1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y1_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y2);
zero_ats_ar(array_x);
zero_ats_ar(array_y1);
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_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_3);
array_const_3[1] := c(3);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
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_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y2_set_initial[1, 31] := false;
array_y2_set_initial[1, 32] := false;
array_y2_set_initial[1, 33] := false;
array_y2_set_initial[1, 34] := false;
array_y2_set_initial[1, 35] := false;
array_y2_set_initial[1, 36] := false;
array_y2_set_initial[1, 37] := false;
array_y2_set_initial[1, 38] := false;
array_y2_set_initial[1, 39] := false;
array_y2_set_initial[1, 40] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
array_y1_set_initial[2, 31] := false;
array_y1_set_initial[2, 32] := false;
array_y1_set_initial[2, 33] := false;
array_y1_set_initial[2, 34] := false;
array_y1_set_initial[2, 35] := false;
array_y1_set_initial[2, 36] := false;
array_y1_set_initial[2, 37] := false;
array_y1_set_initial[2, 38] := false;
array_y1_set_initial[2, 39] := false;
array_y1_set_initial[2, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest4postode.ode#################");
omniout_str(ALWAYS,
"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(5.0);");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
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, "#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(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
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, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return( cos(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return( neg( sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return( cos(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
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(0.1);
x_end := c(5.0);
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
glob_look_poles := true;
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(1.000001);
glob_lower_ratio_limit := c(0.999999);
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 := 3;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] :=
array_y2_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;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] :=
array_y1_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 4 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 4 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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 := 3;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 4 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 4 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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 := 4;
ord := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, 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 := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, 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 := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, 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 := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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 := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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 := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_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 := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_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 := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_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 ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
omniout_str(INFO,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
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, "2015-05-01T22:13:06-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest4");
logitem_str(html_log_file, "diff ( y2 , x , 3 ) = n\
eg ( cos ( 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,
"mtest4 diffeq.mxt");
logitem_str(html_log_file, "mtest4 maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
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");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest4postode.ode#################
diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ;
diff ( y1 , x , 1 ) = neg ( y2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0);
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
glob_look_poles := true;
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(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y2 := proc(x)
return(sin(c(x)));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)));
end;
exact_soln_y2pp := proc(x)
return( neg( sin(c(x))));
end;
exact_soln_y1 := proc(x)
return( cos(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y2[1] (closed_form) = 0.099833416646828152306814198410622
y2[1] (numeric) = 0.099833416646828152306814198410622
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.99500416527802576609556198780387
y1[1] (numeric) = 0.99500416527802576609556198780387
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
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) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09933
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 2
memory used=42.4MB, alloc=40.3MB, time=0.59
memory used=83.6MB, alloc=40.3MB, time=1.03
TOP MAIN SOLVE Loop
memory used=124.8MB, alloc=40.3MB, time=1.47
x[1] = 0.11
y2[1] (closed_form) = 0.10977830083717480866494949008345
y2[1] (numeric) = 0.10977830083717480866494949008347
absolute error = 2e-32
relative error = 1.8218536675717332517910891446314e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.99395609795669685035783961141985
y1[1] (numeric) = 0.99395609795669685035783961141984
absolute error = 1e-32
relative error = 1.0060806529138739295356804682092e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
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) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1091
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 2
memory used=166.0MB, alloc=40.3MB, time=1.92
memory used=207.2MB, alloc=40.3MB, time=2.36
TOP MAIN SOLVE Loop
x[1] = 0.12
y2[1] (closed_form) = 0.11971220728891935996735061427097
y2[1] (numeric) = 0.119712207288919359967350614271
absolute error = 3e-32
relative error = 2.5060100953277485493704713765586e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.99280863585386625224809816785763
y1[1] (numeric) = 0.99280863585386625224809816785762
absolute error = 1e-32
relative error = 1.0072434544648665414102250278741e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
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) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1189
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 2
memory used=248.4MB, alloc=40.3MB, time=2.80
memory used=289.5MB, alloc=40.3MB, time=3.23
memory used=330.6MB, alloc=40.3MB, time=3.67
TOP MAIN SOLVE Loop
x[1] = 0.13
y2[1] (closed_form) = 0.12963414261969485954120581070831
y2[1] (numeric) = 0.12963414261969485954120581070834
absolute error = 3e-32
relative error = 2.3142051464027043651080784631679e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.99156189371478803959451217115181
y1[1] (numeric) = 0.99156189371478803959451217115181
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
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) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1285
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 2
memory used=371.8MB, alloc=40.3MB, time=4.11
memory used=413.0MB, alloc=40.3MB, time=4.55
memory used=454.2MB, alloc=40.3MB, time=5.00
TOP MAIN SOLVE Loop
x[1] = 0.14
y2[1] (closed_form) = 0.13954311464423648171798835170537
y2[1] (numeric) = 0.13954311464423648171798835170541
absolute error = 4e-32
relative error = 2.8664975768943904047348344728184e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9902159962126371718989482270114
y1[1] (numeric) = 0.99021599621263717189894822701139
absolute error = 1e-32
relative error = 1.0098806763623134088645046107846e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
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) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1382
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 2
memory used=495.5MB, alloc=40.3MB, time=5.44
memory used=536.7MB, alloc=40.3MB, time=5.87
TOP MAIN SOLVE Loop
memory used=577.8MB, alloc=40.3MB, time=6.31
x[1] = 0.15
y2[1] (closed_form) = 0.14943813247359922149772543868764
y2[1] (numeric) = 0.14943813247359922149772543868767
absolute error = 3e-32
relative error = 2.0075197343154705432671799057549e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.98877107793604228673498099865434
y1[1] (numeric) = 0.98877107793604228673498099865433
absolute error = 1e-32
relative error = 1.0113564426736640909001707623026e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1478
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 2
memory used=619.2MB, alloc=40.3MB, time=6.76
memory used=660.3MB, alloc=40.3MB, time=7.20
TOP MAIN SOLVE Loop
memory used=701.5MB, alloc=40.3MB, time=7.64
x[1] = 0.16
y2[1] (closed_form) = 0.15931820661424596331146315968599
y2[1] (numeric) = 0.15931820661424596331146315968603
absolute error = 4e-32
relative error = 2.5106986106648320739151935355573e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.98722728337562694904095252401834
y1[1] (numeric) = 0.98722728337562694904095252401834
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1573
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 2
memory used=742.7MB, alloc=40.3MB, time=8.08
memory used=783.9MB, alloc=40.3MB, time=8.53
TOP MAIN SOLVE Loop
x[1] = 0.17
y2[1] (closed_form) = 0.16918234906699601015762437667085
y2[1] (numeric) = 0.1691823490669960101576243766709
absolute error = 5e-32
relative error = 2.9553910485189006998222702989205e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9855847669095607091719299902125
y1[1] (numeric) = 0.98558476690956070917192999021251
absolute error = 1e-32
relative error = 1.0146260713176810517259565757587e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1667
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 2
memory used=825.1MB, alloc=40.3MB, time=8.97
memory used=866.2MB, alloc=40.3MB, time=9.42
memory used=907.5MB, alloc=40.3MB, time=9.86
TOP MAIN SOLVE Loop
x[1] = 0.18
y2[1] (closed_form) = 0.17902957342582417834180273969921
y2[1] (numeric) = 0.17902957342582417834180273969926
absolute error = 5e-32
relative error = 2.7928346721284056824311567640715e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.98384369278812141459271602461153
y1[1] (numeric) = 0.98384369278812141459271602461154
absolute error = 1e-32
relative error = 1.0164216199486862747130581631310e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1761
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 2
memory used=948.7MB, alloc=40.3MB, time=10.30
memory used=989.9MB, alloc=40.3MB, time=10.73
memory used=1031.1MB, alloc=40.3MB, time=11.19
TOP MAIN SOLVE Loop
x[1] = 0.19
y2[1] (closed_form) = 0.18885889497650057799285115298131
y2[1] (numeric) = 0.18885889497650057799285115298135
absolute error = 4e-32
relative error = 2.1179833761590704274770212663126e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.98200423511727031896787750418991
y1[1] (numeric) = 0.98200423511727031896787750418992
absolute error = 1e-32
relative error = 1.0183255471200494754242006144117e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1855
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 2
memory used=1072.3MB, alloc=40.3MB, time=11.62
memory used=1113.5MB, alloc=40.3MB, time=12.06
TOP MAIN SOLVE Loop
memory used=1154.6MB, alloc=40.3MB, time=12.50
x[1] = 0.2
y2[1] (closed_form) = 0.19866933079506121545941262711839
y2[1] (numeric) = 0.19866933079506121545941262711844
absolute error = 5e-32
relative error = 2.5167447738361721012130481837629e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.98006657784124163112419651674817
y1[1] (numeric) = 0.98006657784124163112419651674816
absolute error = 1e-32
relative error = 1.0203388449411926897924327768492e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1947
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 2
memory used=1195.9MB, alloc=40.3MB, time=12.95
memory used=1237.2MB, alloc=40.3MB, time=13.39
TOP MAIN SOLVE Loop
x[1] = 0.21
y2[1] (closed_form) = 0.20845989984609957060871242622764
y2[1] (numeric) = 0.2084598998460995706087124262277
absolute error = 6e-32
relative error = 2.8782514068315495085983108012333e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.97803091472414824491613856809935
y1[1] (numeric) = 0.97803091472414824491613856809934
absolute error = 1e-32
relative error = 1.0224625673331073524464086165795e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2039
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 2
memory used=1278.4MB, alloc=40.3MB, time=13.83
memory used=1319.7MB, alloc=40.3MB, time=14.28
memory used=1360.8MB, alloc=40.3MB, time=14.72
TOP MAIN SOLVE Loop
x[1] = 0.22
y2[1] (closed_form) = 0.21822962308086931995179100545701
y2[1] (numeric) = 0.21822962308086931995179100545707
absolute error = 6e-32
relative error = 2.7493975910761578254322454743429e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9758974493306054894060229810447
y1[1] (numeric) = 0.9758974493306054894060229810447
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.213
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 2
memory used=1402.1MB, alloc=40.3MB, time=15.16
memory used=1443.2MB, alloc=40.3MB, time=15.61
memory used=1484.4MB, alloc=40.3MB, time=16.05
TOP MAIN SOLVE Loop
x[1] = 0.23
y2[1] (closed_form) = 0.22797752353518839540461721236007
y2[1] (numeric) = 0.22797752353518839540461721236013
absolute error = 6e-32
relative error = 2.6318383965925914177221340142687e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9736663950053748369677306480716
y1[1] (numeric) = 0.97366639500537483696773064807161
absolute error = 1e-32
relative error = 1.0270458189064641551739991395066e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.222
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 2
memory used=1525.8MB, alloc=40.3MB, time=16.48
memory used=1567.0MB, alloc=40.3MB, time=16.92
memory used=1608.3MB, alloc=40.3MB, time=17.38
TOP MAIN SOLVE Loop
x[1] = 0.24
y2[1] (closed_form) = 0.23770262642713458836079208448982
y2[1] (numeric) = 0.23770262642713458836079208448987
absolute error = 5e-32
relative error = 2.1034685544514591305546015880043e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.97133797485202960492617524696338
y1[1] (numeric) = 0.97133797485202960492617524696339
absolute error = 1e-32
relative error = 1.0295077778178462266084903163054e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2309
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 2
memory used=1649.6MB, alloc=40.3MB, time=17.81
memory used=1690.8MB, alloc=40.3MB, time=18.25
TOP MAIN SOLVE Loop
memory used=1731.9MB, alloc=40.3MB, time=18.69
x[1] = 0.25
y2[1] (closed_form) = 0.24740395925452292959684870484939
y2[1] (numeric) = 0.24740395925452292959684870484943
absolute error = 4e-32
relative error = 1.6167890004884284291332797332231e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.96891242171064478414459544949419
y1[1] (numeric) = 0.96891242171064478414459544949419
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2397
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 2
memory used=1773.2MB, alloc=40.3MB, time=19.14
memory used=1814.4MB, alloc=40.3MB, time=19.58
TOP MAIN SOLVE Loop
x[1] = 0.26
y2[1] (closed_form) = 0.25708055189215509735338846436522
y2[1] (numeric) = 0.25708055189215509735338846436526
absolute error = 4e-32
relative error = 1.5559325552086079033359390319003e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.96638997813451322555821764645006
y1[1] (numeric) = 0.96638997813451322555821764645006
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2484
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 2
memory used=1855.7MB, alloc=40.3MB, time=20.02
memory used=1896.8MB, alloc=40.3MB, time=20.45
memory used=1938.0MB, alloc=40.3MB, time=20.91
TOP MAIN SOLVE Loop
x[1] = 0.27
y2[1] (closed_form) = 0.26673143668883112873228652102054
y2[1] (numeric) = 0.26673143668883112873228652102057
absolute error = 3e-32
relative error = 1.1247268178215527492773931171829e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9637708963658905130162327094922
y1[1] (numeric) = 0.96377089636589051301623270949219
absolute error = 1e-32
relative error = 1.0375909915631601514930305045560e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2571
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 2
memory used=1979.2MB, alloc=40.3MB, time=21.34
memory used=2020.4MB, alloc=40.3MB, time=21.78
memory used=2061.6MB, alloc=40.3MB, time=22.22
TOP MAIN SOLVE Loop
x[1] = 0.28
y2[1] (closed_form) = 0.27635564856411373331966955845785
y2[1] (numeric) = 0.27635564856411373331966955845788
absolute error = 3e-32
relative error = 1.0855576919043898016729914701780e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.96105543831077094792459005359648
y1[1] (numeric) = 0.96105543831077094792459005359646
absolute error = 2e-32
relative error = 2.0810454009972227513247622478529e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2656
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 2
memory used=2102.8MB, alloc=40.3MB, time=22.67
memory used=2144.0MB, alloc=40.3MB, time=23.11
TOP MAIN SOLVE Loop
memory used=2185.1MB, alloc=40.3MB, time=23.55
x[1] = 0.29
y2[1] (closed_form) = 0.28595222510483553268394020550437
y2[1] (numeric) = 0.2859522251048355326839402055044
absolute error = 3e-32
relative error = 1.0491263003462004376796670684356e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.95824387551269716807012477793186
y1[1] (numeric) = 0.95824387551269716807012477793186
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.274
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 2
memory used=2226.4MB, alloc=40.3MB, time=23.98
memory used=2267.5MB, alloc=40.3MB, time=24.42
TOP MAIN SOLVE Loop
x[1] = 0.3
y2[1] (closed_form) = 0.29552020666133957510532074568503
y2[1] (numeric) = 0.29552020666133957510532074568505
absolute error = 2e-32
relative error = 6.7677267236482451699209531029548e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.95533648912560601964231022756805
y1[1] (numeric) = 0.95533648912560601964231022756806
absolute error = 1e-32
relative error = 1.0467516015380856009327908455870e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2823
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 2
memory used=2308.8MB, alloc=40.3MB, time=24.87
memory used=2350.0MB, alloc=40.3MB, time=25.33
memory used=2391.2MB, alloc=40.3MB, time=25.78
TOP MAIN SOLVE Loop
x[1] = 0.31
y2[1] (closed_form) = 0.30505863644344350156564332395896
y2[1] (numeric) = 0.30505863644344350156564332395898
absolute error = 2e-32
relative error = 6.5561166315997449231716170028411e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.95233356988571339784280543620221
y1[1] (numeric) = 0.95233356988571339784280543620223
absolute error = 2e-32
relative error = 2.1001044836002303327454476474836e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2905
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 2
memory used=2432.5MB, alloc=40.3MB, time=26.23
memory used=2473.6MB, alloc=40.3MB, time=26.67
memory used=2514.9MB, alloc=40.3MB, time=27.11
TOP MAIN SOLVE Loop
x[1] = 0.32
y2[1] (closed_form) = 0.31456656061611776666175754341715
y2[1] (numeric) = 0.31456656061611776666175754341717
absolute error = 2e-32
relative error = 6.3579548826892185779101948190767e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.94923541808244086757530727376609
y1[1] (numeric) = 0.94923541808244086757530727376611
absolute error = 2e-32
relative error = 2.1069588870168985639438319667824e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2986
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 2
memory used=2556.3MB, alloc=40.3MB, time=27.55
memory used=2597.4MB, alloc=40.3MB, time=28.00
memory used=2638.7MB, alloc=40.3MB, time=28.44
TOP MAIN SOLVE Loop
x[1] = 0.33
y2[1] (closed_form) = 0.32404302839486834670019569617022
y2[1] (numeric) = 0.32404302839486834670019569617025
absolute error = 3e-32
relative error = 9.2580297587649288830101937482670e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.94604234352838697152941057836621
y1[1] (numeric) = 0.94604234352838697152941057836622
absolute error = 1e-32
relative error = 1.0570351389033719013512246936692e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3066
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 2
memory used=2680.0MB, alloc=40.3MB, time=28.88
memory used=2721.2MB, alloc=40.3MB, time=29.31
TOP MAIN SOLVE Loop
memory used=2762.4MB, alloc=40.3MB, time=29.77
x[1] = 0.34
y2[1] (closed_form) = 0.33348709214081439678177148703079
y2[1] (numeric) = 0.33348709214081439678177148703082
absolute error = 3e-32
relative error = 8.9958504262985229685643473349653e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.94275466552834622850264406002658
y1[1] (numeric) = 0.94275466552834622850264406002659
absolute error = 1e-32
relative error = 1.0607213483685831202937827622284e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3144
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 2
memory used=2803.6MB, alloc=40.3MB, time=30.20
memory used=2844.8MB, alloc=40.3MB, time=30.66
TOP MAIN SOLVE Loop
x[1] = 0.35
y2[1] (closed_form) = 0.34289780745545134918963490691763
y2[1] (numeric) = 0.34289780745545134918963490691765
absolute error = 2e-32
relative error = 5.8326415524247302509246725756321e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.93937271284737892003503235730367
y1[1] (numeric) = 0.93937271284737892003503235730368
absolute error = 1e-32
relative error = 1.0645401833834950584242632965675e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3221
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 2
memory used=2886.0MB, alloc=40.3MB, time=31.09
memory used=2927.1MB, alloc=40.3MB, time=31.53
memory used=2968.3MB, alloc=40.3MB, time=31.97
TOP MAIN SOLVE Loop
x[1] = 0.36
y2[1] (closed_form) = 0.35227423327508997684991343592073
y2[1] (numeric) = 0.35227423327508997684991343592075
absolute error = 2e-32
relative error = 5.6773950833872244012328772236860e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.93589682367793485835091236812474
y1[1] (numeric) = 0.93589682367793485835091236812476
absolute error = 2e-32
relative error = 2.1369876992853746943292352547215e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3297
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 2
memory used=3009.5MB, alloc=40.3MB, time=32.41
memory used=3050.7MB, alloc=40.3MB, time=32.86
memory used=3091.9MB, alloc=40.3MB, time=33.30
TOP MAIN SOLVE Loop
x[1] = 0.37
y2[1] (closed_form) = 0.36161543196496197803729246912715
y2[1] (numeric) = 0.36161543196496197803729246912719
absolute error = 4e-32
relative error = 1.1061474833263123013366890623216e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.93232734560603442320381290449088
y1[1] (numeric) = 0.9323273456060344232038129044909
absolute error = 2e-32
relative error = 2.1451693007030203111482463335611e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3371
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 2
memory used=3133.2MB, alloc=40.3MB, time=33.73
memory used=3174.3MB, alloc=40.3MB, time=34.23
TOP MAIN SOLVE Loop
memory used=3215.5MB, alloc=40.3MB, time=34.67
x[1] = 0.38
y2[1] (closed_form) = 0.3709204694129826718454854663492
y2[1] (numeric) = 0.37092046941298267184548546634924
absolute error = 4e-32
relative error = 1.0783982901591774726685676408678e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.92866463557651024949253080772456
y1[1] (numeric) = 0.92866463557651024949253080772458
absolute error = 2e-32
relative error = 2.1536299794149157443180906061186e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3445
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 2
memory used=3256.8MB, alloc=40.3MB, time=35.13
memory used=3298.1MB, alloc=40.3MB, time=35.56
TOP MAIN SOLVE Loop
memory used=3339.3MB, alloc=40.3MB, time=36.00
x[1] = 0.39
y2[1] (closed_form) = 0.38018841512316142823118209784716
y2[1] (numeric) = 0.38018841512316142823118209784719
absolute error = 3e-32
relative error = 7.8908243404211956440396798999009e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9249090598573130414506767528811
y1[1] (numeric) = 0.92490905985731304145067675288112
absolute error = 2e-32
relative error = 2.1623747531552374206082103360578e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3516
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 2
memory used=3380.6MB, alloc=40.3MB, time=36.45
memory used=3421.8MB, alloc=40.3MB, time=36.89
TOP MAIN SOLVE Loop
x[1] = 0.4
y2[1] (closed_form) = 0.38941834230865049166631175679571
y2[1] (numeric) = 0.38941834230865049166631175679574
absolute error = 3e-32
relative error = 7.7037973666433492110340618900883e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.9210609940028850827985267320518
y1[1] (numeric) = 0.92106099400288508279852673205182
absolute error = 2e-32
relative error = 2.1714088567664774062278599103175e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3587
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 2
memory used=3463.2MB, alloc=40.3MB, time=37.33
memory used=3504.3MB, alloc=40.3MB, time=37.77
memory used=3545.6MB, alloc=40.3MB, time=38.20
TOP MAIN SOLVE Loop
x[1] = 0.41
y2[1] (closed_form) = 0.39860932798442289359379764005114
y2[1] (numeric) = 0.39860932798442289359379764005118
absolute error = 4e-32
relative error = 1.0034888095133374599884491128482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.91712082281660510547564205827702
y1[1] (numeric) = 0.91712082281660510547564205827703
absolute error = 1e-32
relative error = 1.0903688752032272686284200446165e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3656
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 2
memory used=3586.8MB, alloc=40.3MB, time=38.66
memory used=3628.0MB, alloc=40.3MB, time=39.09
memory used=3669.2MB, alloc=40.3MB, time=39.55
TOP MAIN SOLVE Loop
x[1] = 0.42
y2[1] (closed_form) = 0.40776045305957018597278715808634
y2[1] (numeric) = 0.40776045305957018597278715808638
absolute error = 4e-32
relative error = 9.8096810761970471765127527641685e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.91308894031230827243608878966567
y1[1] (numeric) = 0.91308894031230827243608878966567
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3723
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 2
memory used=3710.4MB, alloc=40.3MB, time=39.98
memory used=3751.7MB, alloc=40.3MB, time=40.42
TOP MAIN SOLVE Loop
memory used=3792.8MB, alloc=40.3MB, time=40.86
x[1] = 0.43
y2[1] (closed_form) = 0.41687080242921076621691867262457
y2[1] (numeric) = 0.4168708024292107662169186726246
absolute error = 3e-32
relative error = 7.1964742613736612050260047179132e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.90896574967488512247591047766345
y1[1] (numeric) = 0.90896574967488512247591047766343
absolute error = 2e-32
relative error = 2.2003029274924288586094653589129e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3789
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 2
memory used=3834.1MB, alloc=40.3MB, time=41.31
memory used=3875.3MB, alloc=40.3MB, time=41.75
TOP MAIN SOLVE Loop
x[1] = 0.44
y2[1] (closed_form) = 0.42593946506599960276972075077992
y2[1] (numeric) = 0.42593946506599960276972075077994
absolute error = 2e-32
relative error = 4.6955029153969066303347553414383e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.90475166321996341716553738899837
y1[1] (numeric) = 0.90475166321996341716553738899837
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3854
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 2
memory used=3916.5MB, alloc=40.3MB, time=42.19
memory used=3957.8MB, alloc=40.3MB, time=42.63
memory used=3998.9MB, alloc=40.3MB, time=43.08
TOP MAIN SOLVE Loop
x[1] = 0.45
y2[1] (closed_form) = 0.4349655341112302104208442462319
y2[1] (numeric) = 0.43496553411123021042084424623192
absolute error = 2e-32
relative error = 4.5980654630179415802165551129761e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.90044710235267692166884061148645
y1[1] (numeric) = 0.90044710235267692166884061148644
absolute error = 1e-32
relative error = 1.1105594069737272884444606710116e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3917
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 2
memory used=4040.2MB, alloc=40.3MB, time=43.64
memory used=4081.3MB, alloc=40.3MB, time=44.08
memory used=4122.5MB, alloc=40.3MB, time=44.55
TOP MAIN SOLVE Loop
x[1] = 0.46
y2[1] (closed_form) = 0.4439481069655197652415136439289
y2[1] (numeric) = 0.44394810696551976524151364392892
absolute error = 2e-32
relative error = 4.5050310354298560567933411674058e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.89605249752552524253638990350041
y1[1] (numeric) = 0.89605249752552524253638990350039
absolute error = 2e-32
relative error = 2.2320120813490923284652883710187e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3978
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4163.9MB, alloc=40.3MB, time=44.98
memory used=4205.1MB, alloc=40.3MB, time=45.44
memory used=4246.4MB, alloc=40.3MB, time=45.89
TOP MAIN SOLVE Loop
x[1] = 0.47
y2[1] (closed_form) = 0.45288628537906829070327480039641
y2[1] (numeric) = 0.45288628537906829070327480039644
absolute error = 3e-32
relative error = 6.6241793952514672404578861362144e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.89156828819532893645401927653339
y1[1] (numeric) = 0.89156828819532893645401927653339
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4038
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4038
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 2
memory used=4287.5MB, alloc=40.3MB, time=46.33
memory used=4328.7MB, alloc=40.3MB, time=46.77
TOP MAIN SOLVE Loop
memory used=4369.9MB, alloc=40.3MB, time=47.20
x[1] = 0.48
y2[1] (closed_form) = 0.46177917554148288913664294258864
y2[1] (numeric) = 0.46177917554148288913664294258869
absolute error = 5e-32
relative error = 1.0827686186015194819756811270705e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.88699492277928419439995483115874
y1[1] (numeric) = 0.88699492277928419439995483115873
absolute error = 1e-32
relative error = 1.1274021691878787428048684309357e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4096
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4096
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 2
memory used=4411.2MB, alloc=40.3MB, time=47.67
memory used=4452.4MB, alloc=40.3MB, time=48.11
TOP MAIN SOLVE Loop
x[1] = 0.49
y2[1] (closed_form) = 0.47062588817115803618135833718796
y2[1] (numeric) = 0.47062588817115803618135833718801
absolute error = 5e-32
relative error = 1.0624149936651150309747700341755e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.88233285861012149570546815913666
y1[1] (numeric) = 0.88233285861012149570546815913665
absolute error = 1e-32
relative error = 1.1333591288612230659188985538320e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4152
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4152
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 2
memory used=4493.6MB, alloc=40.3MB, time=48.56
memory used=4534.8MB, alloc=40.3MB, time=49.00
memory used=4576.0MB, alloc=40.3MB, time=49.44
TOP MAIN SOLVE Loop
x[1] = 0.5
y2[1] (closed_form) = 0.47942553860420300027328793521557
y2[1] (numeric) = 0.47942553860420300027328793521563
absolute error = 6e-32
relative error = 1.2514977857600929114635010052756e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.87758256189037271611628158260383
y1[1] (numeric) = 0.87758256189037271611628158260385
absolute error = 2e-32
relative error = 2.2789878546490982446266555364099e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4207
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4207
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 2
memory used=4617.3MB, alloc=40.3MB, time=49.89
memory used=4658.5MB, alloc=40.3MB, time=50.33
memory used=4699.7MB, alloc=40.3MB, time=50.77
TOP MAIN SOLVE Loop
x[1] = 0.51
y2[1] (closed_form) = 0.48817724688290749450013023767457
y2[1] (numeric) = 0.48817724688290749450013023767463
absolute error = 6e-32
relative error = 1.2290617881744782017493327657050e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.87274450764575126310580847357551
y1[1] (numeric) = 0.87274450764575126310580847357552
absolute error = 1e-32
relative error = 1.1458107054692597333792993299734e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4261
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4261
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 2
memory used=4741.0MB, alloc=40.3MB, time=51.28
memory used=4782.2MB, alloc=40.3MB, time=51.75
TOP MAIN SOLVE Loop
memory used=4823.3MB, alloc=40.3MB, time=52.23
x[1] = 0.52
y2[1] (closed_form) = 0.49688013784373671433445894254775
y2[1] (numeric) = 0.49688013784373671433445894254781
absolute error = 6e-32
relative error = 1.2075346835229975266236197928669e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.86781917967764990038784757198851
y1[1] (numeric) = 0.86781917967764990038784757198854
absolute error = 3e-32
relative error = 3.4569413424514832526432563583826e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4312
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4312
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 2
memory used=4864.6MB, alloc=40.3MB, time=52.67
memory used=4905.8MB, alloc=40.3MB, time=53.11
TOP MAIN SOLVE Loop
x[1] = 0.53
y2[1] (closed_form) = 0.50553334120484696181366102246608
y2[1] (numeric) = 0.50553334120484696181366102246613
absolute error = 5e-32
relative error = 9.8905444853219918713510338381691e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.8628070705147610118066950185642
y1[1] (numeric) = 0.86280707051476101180669501856422
absolute error = 2e-32
relative error = 2.3180153111248567922165470502791e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4362
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4362
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 2
memory used=4947.0MB, alloc=40.3MB, time=53.55
memory used=4988.3MB, alloc=40.3MB, time=54.00
memory used=5029.5MB, alloc=40.3MB, time=54.44
TOP MAIN SOLVE Loop
x[1] = 0.54
y2[1] (closed_form) = 0.51413599165311310467728068295824
y2[1] (numeric) = 0.51413599165311310467728068295828
absolute error = 4e-32
relative error = 7.7800427609409513559610975078009e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.8577086813638241425379687789178
y1[1] (numeric) = 0.8577086813638241425379687789178
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.441
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.441
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 2
memory used=5070.8MB, alloc=40.3MB, time=54.87
memory used=5112.0MB, alloc=40.3MB, time=55.33
memory used=5153.1MB, alloc=40.3MB, time=55.77
TOP MAIN SOLVE Loop
x[1] = 0.55
y2[1] (closed_form) = 0.52268722893065916778837810775729
y2[1] (numeric) = 0.52268722893065916778837810775733
absolute error = 4e-32
relative error = 7.6527601567449981793694067295567e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.85252452205950574280498179761777
y1[1] (numeric) = 0.85252452205950574280498179761777
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4456
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4456
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 2
memory used=5194.4MB, alloc=40.3MB, time=56.20
memory used=5235.5MB, alloc=40.3MB, time=56.66
memory used=5276.8MB, alloc=40.3MB, time=57.09
TOP MAIN SOLVE Loop
x[1] = 0.56
y2[1] (closed_form) = 0.53118619792088340385186944111203
y2[1] (numeric) = 0.53118619792088340385186944111207
absolute error = 4e-32
relative error = 7.5303161408493015494038179548360e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.84725511101341612609452550386632
y1[1] (numeric) = 0.84725511101341612609452550386632
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4501
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4501
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 2
memory used=5318.1MB, alloc=40.3MB, time=57.53
memory used=5359.4MB, alloc=40.3MB, time=57.97
TOP MAIN SOLVE Loop
memory used=5400.6MB, alloc=40.3MB, time=58.42
x[1] = 0.57
y2[1] (closed_form) = 0.53963204873396924099446349307883
y2[1] (numeric) = 0.53963204873396924099446349307887
absolute error = 4e-32
relative error = 7.4124581914369246048334158139102e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.84190097516226874013375636391601
y1[1] (numeric) = 0.84190097516226874013375636391601
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4543
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4543
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 2
memory used=5441.9MB, alloc=40.3MB, time=58.86
memory used=5483.1MB, alloc=40.3MB, time=59.30
TOP MAIN SOLVE Loop
x[1] = 0.58
y2[1] (closed_form) = 0.54802393679187355618269605957646
y2[1] (numeric) = 0.54802393679187355618269605957649
absolute error = 3e-32
relative error = 5.4742134395843526372782926957189e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.83646264991518693465788732805002
y1[1] (numeric) = 0.83646264991518693465788732805001
absolute error = 1e-32
relative error = 1.1955106424672935751964175215789e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4584
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4584
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 2
memory used=5524.4MB, alloc=40.3MB, time=59.75
memory used=5565.7MB, alloc=40.3MB, time=60.20
memory used=5606.9MB, alloc=40.3MB, time=60.64
TOP MAIN SOLVE Loop
x[1] = 0.59
y2[1] (closed_form) = 0.55636102291278377572254337887577
y2[1] (numeric) = 0.55636102291278377572254337887579
absolute error = 2e-32
relative error = 3.5947881279122672250783008540811e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.83094067910016349524799652249068
y1[1] (numeric) = 0.83094067910016349524799652249068
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4623
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 2
memory used=5648.2MB, alloc=40.3MB, time=61.08
memory used=5689.4MB, alloc=40.3MB, time=61.53
memory used=5730.6MB, alloc=40.3MB, time=61.97
TOP MAIN SOLVE Loop
x[1] = 0.6
y2[1] (closed_form) = 0.56464247339503535720094544565866
y2[1] (numeric) = 0.56464247339503535720094544565868
absolute error = 2e-32
relative error = 3.5420643933754507467492242142109e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.82533561490967829724095249895538
y1[1] (numeric) = 0.82533561490967829724095249895538
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.466
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.466
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 2
memory used=5771.9MB, alloc=40.3MB, time=62.41
memory used=5813.2MB, alloc=40.3MB, time=62.86
TOP MAIN SOLVE Loop
memory used=5854.3MB, alloc=40.3MB, time=63.30
x[1] = 0.61
y2[1] (closed_form) = 0.57286746010048126119097603216272
y2[1] (numeric) = 0.57286746010048126119097603216273
absolute error = 1e-32
relative error = 1.7456044716252507362706331249149e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.81964801784547951790074657865482
y1[1] (numeric) = 0.81964801784547951790074657865482
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4695
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 2
memory used=5895.7MB, alloc=40.3MB, time=63.73
memory used=5936.9MB, alloc=40.3MB, time=64.19
TOP MAIN SOLVE Loop
x[1] = 0.62
y2[1] (closed_form) = 0.58103516053730507584296322758221
y2[1] (numeric) = 0.58103516053730507584296322758222
absolute error = 1e-32
relative error = 1.7210662416285829802640352190038e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.8138784566625339286839996543607
y1[1] (numeric) = 0.8138784566625339286839996543607
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4729
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4729
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 2
memory used=5978.3MB, alloc=40.3MB, time=64.62
memory used=6019.5MB, alloc=40.3MB, time=65.06
memory used=6060.8MB, alloc=40.3MB, time=65.50
TOP MAIN SOLVE Loop
x[1] = 0.63
y2[1] (closed_form) = 0.58914475794226951311811209079462
y2[1] (numeric) = 0.58914475794226951311811209079463
absolute error = 1e-32
relative error = 1.6973757069361725967914220639108e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.80802750831215187252370896577706
y1[1] (numeric) = 0.80802750831215187252370896577706
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.476
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 2
memory used=6102.2MB, alloc=40.3MB, time=65.95
memory used=6143.3MB, alloc=40.3MB, time=66.39
memory used=6184.6MB, alloc=40.3MB, time=66.83
TOP MAIN SOLVE Loop
x[1] = 0.64
y2[1] (closed_form) = 0.59719544136239205188354623920793
y2[1] (numeric) = 0.59719544136239205188354623920794
absolute error = 1e-32
relative error = 1.6744936929168164811188136616446e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.80209575788429261358611077926032
y1[1] (numeric) = 0.80209575788429261358611077926033
absolute error = 1e-32
relative error = 1.2467339344091835043765333244264e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.479
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 2
memory used=6225.9MB, alloc=40.3MB, time=67.26
memory used=6267.1MB, alloc=40.3MB, time=67.72
memory used=6308.3MB, alloc=40.3MB, time=68.16
TOP MAIN SOLVE Loop
x[1] = 0.65
y2[1] (closed_form) = 0.60518640573603956037252167860594
y2[1] (numeric) = 0.60518640573603956037252167860597
absolute error = 3e-32
relative error = 4.9571503450269033048518397165628e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.79608379854905582891760457067991
y1[1] (numeric) = 0.79608379854905582891760457067991
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 2
memory used=6349.6MB, alloc=40.3MB, time=68.59
memory used=6390.9MB, alloc=40.3MB, time=69.05
TOP MAIN SOLVE Loop
memory used=6432.2MB, alloc=40.3MB, time=69.48
x[1] = 0.66
y2[1] (closed_form) = 0.6131168519734337886151454793963
y2[1] (numeric) = 0.61311685197343378861514547939633
absolute error = 3e-32
relative error = 4.8930313860138186286772799436418e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.78999223149736509278381709123024
y1[1] (numeric) = 0.78999223149736509278381709123025
absolute error = 1e-32
relative error = 1.2658352324611882697842840177057e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4844
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4844
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 2
memory used=6473.5MB, alloc=40.3MB, time=69.92
memory used=6514.7MB, alloc=40.3MB, time=70.38
TOP MAIN SOLVE Loop
x[1] = 0.67
y2[1] (closed_form) = 0.62098598703655968035744391412659
y2[1] (numeric) = 0.62098598703655968035744391412663
absolute error = 4e-32
relative error = 6.4413691830448753775237599965938e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.78382166588084928530294214483812
y1[1] (numeric) = 0.78382166588084928530294214483812
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4867
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4867
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 2
memory used=6555.9MB, alloc=40.3MB, time=70.81
memory used=6597.2MB, alloc=40.3MB, time=71.25
memory used=6638.5MB, alloc=40.3MB, time=71.69
TOP MAIN SOLVE Loop
x[1] = 0.68
y2[1] (closed_form) = 0.62879302401846851370417818742025
y2[1] (numeric) = 0.62879302401846851370417818742027
absolute error = 2e-32
relative error = 3.1806968646351541844819338546206e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.77757271875092793718239408404432
y1[1] (numeric) = 0.77757271875092793718239408404432
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4889
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4889
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 2
memory used=6679.7MB, alloc=40.3MB, time=72.14
memory used=6721.0MB, alloc=40.3MB, time=72.58
memory used=6762.2MB, alloc=40.3MB, time=73.02
TOP MAIN SOLVE Loop
x[1] = 0.69
y2[1] (closed_form) = 0.63653718222196794023742920700872
y2[1] (numeric) = 0.63653718222196794023742920700874
absolute error = 2e-32
relative error = 3.1420002725034476796470444715189e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.77124601499710660197353931549777
y1[1] (numeric) = 0.77124601499710660197353931549777
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4909
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4909
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 2
memory used=6803.6MB, alloc=40.3MB, time=73.45
memory used=6844.8MB, alloc=40.3MB, time=73.89
TOP MAIN SOLVE Loop
memory used=6886.0MB, alloc=40.3MB, time=74.33
x[1] = 0.7
y2[1] (closed_form) = 0.64421768723769105367261435139872
y2[1] (numeric) = 0.64421768723769105367261435139875
absolute error = 3e-32
relative error = 4.6568109808713117359699209228648e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.76484218728448842625585999019186
y1[1] (numeric) = 0.76484218728448842625585999019187
absolute error = 1e-32
relative error = 1.3074592597335938698746728353053e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4927
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4927
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 2
memory used=6927.4MB, alloc=40.3MB, time=74.78
memory used=6968.6MB, alloc=40.3MB, time=75.22
TOP MAIN SOLVE Loop
x[1] = 0.71
y2[1] (closed_form) = 0.65183377102153668121012797285284
y2[1] (numeric) = 0.65183377102153668121012797285286
absolute error = 2e-32
relative error = 3.0682669246572677397779021813019e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.75836187599050816654145794413955
y1[1] (numeric) = 0.75836187599050816654145794413957
absolute error = 2e-32
relative error = 2.6372633742799492530594693858876e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4943
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4943
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 2
memory used=7009.8MB, alloc=40.3MB, time=75.66
memory used=7050.9MB, alloc=40.3MB, time=76.09
memory used=7092.2MB, alloc=40.3MB, time=76.55
TOP MAIN SOLVE Loop
x[1] = 0.72
y2[1] (closed_form) = 0.65938467197147315361800383264817
y2[1] (numeric) = 0.65938467197147315361800383264818
absolute error = 1e-32
relative error = 1.5165654321477203357119039156049e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.75180572914089497944548696225195
y1[1] (numeric) = 0.75180572914089497944548696225197
absolute error = 2e-32
relative error = 2.6602617171931426982201891539493e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4957
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4957
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 2
memory used=7133.6MB, alloc=40.3MB, time=76.98
memory used=7174.7MB, alloc=40.3MB, time=77.42
memory used=7216.0MB, alloc=40.3MB, time=77.86
TOP MAIN SOLVE Loop
x[1] = 0.73
y2[1] (closed_form) = 0.66686963500369787373259413076153
y2[1] (numeric) = 0.66686963500369787373259413076155
absolute error = 2e-32
relative error = 2.9990869204727094153192585309935e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.74517440234487038879013215855033
y1[1] (numeric) = 0.74517440234487038879013215855035
absolute error = 2e-32
relative error = 2.6839354568628756191548285450706e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4969
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4969
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 2
memory used=7257.3MB, alloc=40.3MB, time=78.31
memory used=7298.4MB, alloc=40.3MB, time=78.75
memory used=7339.7MB, alloc=40.3MB, time=79.19
TOP MAIN SOLVE Loop
x[1] = 0.74
y2[1] (closed_form) = 0.67428791162814506748388115760817
y2[1] (numeric) = 0.6742879116281450674838811576082
absolute error = 3e-32
relative error = 4.4491380436528334605194900702897e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.73846855872958790979142456069883
y1[1] (numeric) = 0.73846855872958790979142456069885
absolute error = 2e-32
relative error = 2.7083075865012678425941625899104e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4979
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4979
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 2
memory used=7381.0MB, alloc=40.3MB, time=79.63
memory used=7422.2MB, alloc=40.3MB, time=80.06
TOP MAIN SOLVE Loop
memory used=7463.3MB, alloc=40.3MB, time=80.50
x[1] = 0.75
y2[1] (closed_form) = 0.68163876002333416673324195277989
y2[1] (numeric) = 0.68163876002333416673324195277992
absolute error = 3e-32
relative error = 4.4011581734250303509177349886343e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.73168886887382088631183875300008
y1[1] (numeric) = 0.73168886887382088631183875300011
absolute error = 3e-32
relative error = 4.1001033740166784056452059804705e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4987
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 2
memory used=7504.6MB, alloc=40.3MB, time=80.94
memory used=7545.8MB, alloc=40.3MB, time=81.39
TOP MAIN SOLVE Loop
x[1] = 0.76
y2[1] (closed_form) = 0.68892144511055133914775563876973
y2[1] (numeric) = 0.68892144511055133914775563876975
absolute error = 2e-32
relative error = 2.9030886092957371454415397095206e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.72483601074090517233968836666701
y1[1] (numeric) = 0.72483601074090517233968836666702
absolute error = 1e-32
relative error = 1.3796224044909559951870120177153e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4994
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 2
memory used=7587.1MB, alloc=40.3MB, time=81.83
memory used=7628.4MB, alloc=40.3MB, time=82.27
memory used=7669.5MB, alloc=40.3MB, time=82.70
TOP MAIN SOLVE Loop
x[1] = 0.77
y2[1] (closed_form) = 0.69613523862735674701988373445221
y2[1] (numeric) = 0.69613523862735674701988373445225
absolute error = 4e-32
relative error = 5.7460099389412059849812174760497e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.71791066961094336337129056532434
y1[1] (numeric) = 0.71791066961094336337129056532436
absolute error = 2e-32
relative error = 2.7858619249716097277693846674882e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4998
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 2
memory used=7710.8MB, alloc=40.3MB, time=83.14
memory used=7752.1MB, alloc=40.3MB, time=83.59
memory used=7793.2MB, alloc=40.3MB, time=84.03
TOP MAIN SOLVE Loop
x[1] = 0.78
y2[1] (closed_form) = 0.70327941920041018436789732511792
y2[1] (numeric) = 0.70327941920041018436789732511795
absolute error = 3e-32
relative error = 4.2657298338274055159561119486760e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.71091353801227735721626502376456
y1[1] (numeric) = 0.71091353801227735721626502376458
absolute error = 2e-32
relative error = 2.8132816342083224421967142135470e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 2
memory used=7834.6MB, alloc=40.3MB, time=84.47
memory used=7875.8MB, alloc=40.3MB, time=84.91
TOP MAIN SOLVE Loop
memory used=7917.0MB, alloc=40.3MB, time=85.34
x[1] = 0.79
y2[1] (closed_form) = 0.7103532724176078098140288749692
y2[1] (numeric) = 0.71035327241760780981402887496923
absolute error = 3e-32
relative error = 4.2232507633699440444242117090390e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.70384531565223609691278086108495
y1[1] (numeric) = 0.70384531565223609691278086108496
absolute error = 1e-32
relative error = 1.4207667192802507471305291751001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 2
memory used=7958.4MB, alloc=40.3MB, time=85.80
memory used=7999.5MB, alloc=40.3MB, time=86.23
TOP MAIN SOLVE Loop
x[1] = 0.8
y2[1] (closed_form) = 0.71735609089952276162717461058139
y2[1] (numeric) = 0.71735609089952276162717461058141
absolute error = 2e-32
relative error = 2.7880156387772723490049644522139e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.69670670934716542092074998164232
y1[1] (numeric) = 0.69670670934716542092074998164232
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8040.9MB, alloc=40.3MB, time=86.67
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4998
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 2
memory used=8082.2MB, alloc=40.3MB, time=87.11
memory used=8123.4MB, alloc=40.3MB, time=87.56
TOP MAIN SOLVE Loop
x[1] = 0.81
y2[1] (closed_form) = 0.72428717437014251092817685251454
y2[1] (numeric) = 0.72428717437014251092817685251457
absolute error = 3e-32
relative error = 4.1420034844726774493234715007737e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.6894984329517470175496392406801
y1[1] (numeric) = 0.68949843295174701754963924068009
absolute error = 1e-32
relative error = 1.4503296196323374815898349922412e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4994
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 2
memory used=8164.7MB, alloc=40.3MB, time=88.00
memory used=8206.0MB, alloc=40.3MB, time=88.44
memory used=8247.3MB, alloc=40.3MB, time=88.88
TOP MAIN SOLVE Loop
x[1] = 0.82
y2[1] (closed_form) = 0.73114582972689587938131336468772
y2[1] (numeric) = 0.73114582972689587938131336468776
absolute error = 4e-32
relative error = 5.4708648225404167679977161808652e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.68222120728761355166655797843693
y1[1] (numeric) = 0.68222120728761355166655797843691
absolute error = 2e-32
relative error = 2.9316004525154433989688989109211e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4988
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4988
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 2
memory used=8288.6MB, alloc=40.3MB, time=89.31
memory used=8329.8MB, alloc=40.3MB, time=89.75
memory used=8371.2MB, alloc=40.3MB, time=90.19
TOP MAIN SOLVE Loop
x[1] = 0.83
y2[1] (closed_form) = 0.73793137110996271872858022613808
y2[1] (numeric) = 0.73793137110996271872858022613811
absolute error = 3e-32
relative error = 4.0654187061969418647964719051794e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.67487576007126710211246291786445
y1[1] (numeric) = 0.67487576007126710211246291786442
absolute error = 3e-32
relative error = 4.4452626357230536977994424954309e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.498
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.498
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 2
memory used=8412.6MB, alloc=40.3MB, time=90.64
memory used=8453.8MB, alloc=40.3MB, time=91.08
TOP MAIN SOLVE Loop
memory used=8495.1MB, alloc=40.3MB, time=91.52
x[1] = 0.84
y2[1] (closed_form) = 0.74464311997085932125657267062965
y2[1] (numeric) = 0.74464311997085932125657267062967
absolute error = 2e-32
relative error = 2.6858503709512115049324626494095e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.66746282584130811792267103687086
y1[1] (numeric) = 0.66746282584130811792267103687083
absolute error = 3e-32
relative error = 4.4946323358437667727440878712148e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.497
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.497
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 2
memory used=8536.5MB, alloc=40.3MB, time=91.95
memory used=8577.7MB, alloc=40.3MB, time=92.41
TOP MAIN SOLVE Loop
x[1] = 0.85
y2[1] (closed_form) = 0.75128040514029270271207152423547
y2[1] (numeric) = 0.7512804051402927027120715242355
absolute error = 3e-32
relative error = 3.9931828109369970737227756632712e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.65998314588498217039541602946147
y1[1] (numeric) = 0.65998314588498217039541602946144
absolute error = 3e-32
relative error = 4.5455706235910782901110646614476e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4958
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4958
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 2
memory used=8619.0MB, alloc=40.3MB, time=92.84
memory used=8660.2MB, alloc=40.3MB, time=93.28
memory used=8701.4MB, alloc=40.3MB, time=93.72
TOP MAIN SOLVE Loop
x[1] = 0.86
y2[1] (closed_form) = 0.75784256289527697229458872952865
y2[1] (numeric) = 0.75784256289527697229458872952867
absolute error = 2e-32
relative error = 2.6390705641540635661109487598376e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.65243746816405184627203066422386
y1[1] (numeric) = 0.65243746816405184627203066422385
absolute error = 1e-32
relative error = 1.5327139362703728856785609726008e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4944
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4944
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 2
memory used=8742.6MB, alloc=40.3MB, time=94.16
memory used=8784.0MB, alloc=40.3MB, time=94.59
memory used=8825.2MB, alloc=40.3MB, time=95.05
TOP MAIN SOLVE Loop
x[1] = 0.87
y2[1] (closed_form) = 0.76432893702550507814480282372285
y2[1] (numeric) = 0.76432893702550507814480282372289
absolute error = 4e-32
relative error = 5.2333488976180461258752970927359e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.64482654724000119477766380548283
y1[1] (numeric) = 0.64482654724000119477766380548281
absolute error = 2e-32
relative error = 3.1016092754872421034948142280779e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4929
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4929
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 2
memory used=8866.5MB, alloc=40.3MB, time=95.48
memory used=8907.6MB, alloc=40.3MB, time=95.92
TOP MAIN SOLVE Loop
memory used=8948.8MB, alloc=40.3MB, time=96.36
x[1] = 0.88
y2[1] (closed_form) = 0.77073887889896929120964513075599
y2[1] (numeric) = 0.77073887889896929120964513075603
absolute error = 4e-32
relative error = 5.1898251269147818752636115922543e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.63715114419858020801549860572209
y1[1] (numeric) = 0.63715114419858020801549860572209
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4911
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4911
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 2
memory used=8990.1MB, alloc=40.3MB, time=96.80
memory used=9031.3MB, alloc=40.3MB, time=97.23
TOP MAIN SOLVE Loop
x[1] = 0.89
y2[1] (closed_form) = 0.77707174752682386549033371297318
y2[1] (numeric) = 0.77707174752682386549033371297325
absolute error = 7e-32
relative error = 9.0081772014988434081936613612776e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.62941202657369688020355305738025
y1[1] (numeric) = 0.62941202657369688020355305738025
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=9072.7MB, alloc=40.3MB, time=97.69
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4891
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4891
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 2
memory used=9113.9MB, alloc=40.3MB, time=98.13
memory used=9155.1MB, alloc=40.3MB, time=98.56
TOP MAIN SOLVE Loop
x[1] = 0.9
y2[1] (closed_form) = 0.78332690962748338846138231571355
y2[1] (numeric) = 0.78332690962748338846138231571362
absolute error = 7e-32
relative error = 8.9362434942122684721095195656241e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.62160996827066445648471615140713
y1[1] (numeric) = 0.62160996827066445648471615140713
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4869
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4869
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 2
memory used=9196.4MB, alloc=40.3MB, time=99.00
memory used=9237.6MB, alloc=40.3MB, time=99.44
memory used=9279.0MB, alloc=40.3MB, time=99.89
TOP MAIN SOLVE Loop
x[1] = 0.91
y2[1] (closed_form) = 0.78950373968995041187895751787155
y2[1] (numeric) = 0.78950373968995041187895751787163
absolute error = 8e-32
relative error = 1.0132947569243581063081589588558e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.61374574948881154652117822617468
y1[1] (numeric) = 0.61374574948881154652117822617467
absolute error = 1e-32
relative error = 1.6293391861905347267678537725338e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4846
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4846
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 2
memory used=9320.2MB, alloc=40.3MB, time=100.33
memory used=9361.3MB, alloc=40.3MB, time=100.77
memory used=9402.5MB, alloc=40.3MB, time=101.22
TOP MAIN SOLVE Loop
x[1] = 0.92
y2[1] (closed_form) = 0.79560162003636603026827610248162
y2[1] (numeric) = 0.7956016200363660302682761024817
absolute error = 8e-32
relative error = 1.0055283697932049520820357089439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.60582015664346284179740470667438
y1[1] (numeric) = 0.60582015664346284179740470667438
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.482
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.482
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 2
memory used=9443.9MB, alloc=40.3MB, time=101.67
memory used=9485.2MB, alloc=40.3MB, time=102.11
TOP MAIN SOLVE Loop
memory used=9526.3MB, alloc=40.3MB, time=102.55
x[1] = 0.93
y2[1] (closed_form) = 0.80161994088377715208431921591065
y2[1] (numeric) = 0.80161994088377715208431921591074
absolute error = 9e-32
relative error = 1.1227265616767965087693065789178e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.59783398228729823849490708443298
y1[1] (numeric) = 0.59783398228729823849490708443299
absolute error = 1e-32
relative error = 1.6727051817530083924888988545676e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4792
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4792
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 2
memory used=9567.7MB, alloc=40.3MB, time=102.98
memory used=9608.9MB, alloc=40.3MB, time=103.44
TOP MAIN SOLVE Loop
x[1] = 0.94
y2[1] (closed_form) = 0.80755810040511428687021979863415
y2[1] (numeric) = 0.80755810040511428687021979863423
absolute error = 8e-32
relative error = 9.9064079674103604444523412160134e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.58978802503109822996098981522402
y1[1] (numeric) = 0.58978802503109822996098981522403
absolute error = 1e-32
relative error = 1.6955244215873528317788450478026e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4763
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 2
memory used=9650.1MB, alloc=40.3MB, time=103.88
memory used=9691.4MB, alloc=40.3MB, time=104.31
memory used=9732.6MB, alloc=40.3MB, time=104.75
TOP MAIN SOLVE Loop
x[1] = 0.95
y2[1] (closed_form) = 0.81341550478937375068542210210256
y2[1] (numeric) = 0.81341550478937375068542210210263
absolute error = 7e-32
relative error = 8.6056879402767024629462614977729e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.58168308946388349416618097376046
y1[1] (numeric) = 0.58168308946388349416618097376047
absolute error = 1e-32
relative error = 1.7191491692180088054618740078576e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4732
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 2
memory used=9774.0MB, alloc=40.3MB, time=105.20
memory used=9815.2MB, alloc=40.3MB, time=105.64
memory used=9856.5MB, alloc=40.3MB, time=106.08
TOP MAIN SOLVE Loop
x[1] = 0.96
y2[1] (closed_form) = 0.81919156830099827163322214643043
y2[1] (numeric) = 0.81919156830099827163322214643052
absolute error = 9e-32
relative error = 1.0986441204059244157379011799345e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.57351998607245666212505080035186
y1[1] (numeric) = 0.57351998607245666212505080035187
absolute error = 1e-32
relative error = 1.7436183991566481011479254485116e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4698
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4698
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 2
memory used=9897.8MB, alloc=40.3MB, time=106.52
memory used=9939.0MB, alloc=40.3MB, time=106.97
TOP MAIN SOLVE Loop
memory used=9980.1MB, alloc=40.3MB, time=107.41
x[1] = 0.97
y2[1] (closed_form) = 0.82488571333845005747662003785634
y2[1] (numeric) = 0.82488571333845005747662003785643
absolute error = 9e-32
relative error = 1.0910602347051810325796937774813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.56529953116035431303652775484986
y1[1] (numeric) = 0.56529953116035431303652775484988
absolute error = 2e-32
relative error = 3.5379473885193704095866285017291e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4663
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 2
memory used=10021.4MB, alloc=40.3MB, time=107.84
memory used=10062.6MB, alloc=40.3MB, time=108.28
TOP MAIN SOLVE Loop
memory used=10103.8MB, alloc=40.3MB, time=108.73
x[1] = 0.98
y2[1] (closed_form) = 0.83049737049197046808453328771915
y2[1] (numeric) = 0.83049737049197046808453328771923
absolute error = 8e-32
relative error = 9.6327818536751727491818872618845e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.55702254676621730087665826735994
y1[1] (numeric) = 0.55702254676621730087665826735997
absolute error = 3e-32
relative error = 5.3857783987675849159909778565776e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4626
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4626
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 2
memory used=10145.2MB, alloc=40.3MB, time=109.17
memory used=10186.5MB, alloc=40.3MB, time=109.61
TOP MAIN SOLVE Loop
x[1] = 0.99
y2[1] (closed_form) = 0.83602597860052051678925941154711
y2[1] (numeric) = 0.8360259786005205167892594115472
absolute error = 9e-32
relative error = 1.0765215711437219355903634507875e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.54868986058158757534312640865361
y1[1] (numeric) = 0.54868986058158757534312640865363
absolute error = 2e-32
relative error = 3.6450463981238623642542740957079e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4587
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4587
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 2
memory used=10227.9MB, alloc=40.3MB, time=110.06
memory used=10269.1MB, alloc=40.3MB, time=110.50
memory used=10310.4MB, alloc=40.3MB, time=110.94
TOP MAIN SOLVE Loop
x[1] = 1
y2[1] (closed_form) = 0.8414709848078965066525023216303
y2[1] (numeric) = 0.84147098480789650665250232163038
absolute error = 8e-32
relative error = 9.5071608462249697300927956189964e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.54030230586813971740093660744298
y1[1] (numeric) = 0.54030230586813971740093660744299
absolute error = 1e-32
relative error = 1.8508157176809256179117532413986e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4546
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4546
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 2
memory used=10351.7MB, alloc=40.3MB, time=111.39
memory used=10393.0MB, alloc=40.3MB, time=111.83
memory used=10434.2MB, alloc=40.3MB, time=112.27
TOP MAIN SOLVE Loop
x[1] = 1.01
y2[1] (closed_form) = 0.84683184461801519012309878478201
y2[1] (numeric) = 0.8468318446180151901230987847821
absolute error = 9e-32
relative error = 1.0627847851021328137197078576002e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.53186072137435546620673135577918
y1[1] (numeric) = 0.53186072137435546620673135577919
absolute error = 1e-32
relative error = 1.8801914858761304160058742988838e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4504
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4504
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 2
memory used=10475.4MB, alloc=40.3MB, time=112.70
memory used=10516.8MB, alloc=40.3MB, time=113.16
TOP MAIN SOLVE Loop
memory used=10558.0MB, alloc=40.3MB, time=113.59
x[1] = 1.02
y2[1] (closed_form) = 0.85210802194936292361654998545538
y2[1] (numeric) = 0.85210802194936292361654998545548
absolute error = 1.0e-31
relative error = 1.1735601288112572819824797672248e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.52336595125164956988961380803381
y1[1] (numeric) = 0.52336595125164956988961380803383
absolute error = 2e-32
relative error = 3.8214178725553772908756845559987e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.446
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 2
memory used=10599.2MB, alloc=40.3MB, time=114.05
memory used=10640.5MB, alloc=40.3MB, time=114.48
TOP MAIN SOLVE Loop
x[1] = 1.03
y2[1] (closed_form) = 0.85729898918860337214627438529442
y2[1] (numeric) = 0.85729898918860337214627438529452
absolute error = 1.0e-31
relative error = 1.1664541923074667312790368212473e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.51481884496995534753350229983735
y1[1] (numeric) = 0.51481884496995534753350229983736
absolute error = 1e-32
relative error = 1.9424308371197244332449996487096e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4414
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4414
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 2
memory used=10681.8MB, alloc=40.3MB, time=114.92
memory used=10723.0MB, alloc=40.3MB, time=115.36
memory used=10764.2MB, alloc=40.3MB, time=115.80
TOP MAIN SOLVE Loop
x[1] = 1.04
y2[1] (closed_form) = 0.86240422724333840328079169211617
y2[1] (numeric) = 0.86240422724333840328079169211625
absolute error = 8e-32
relative error = 9.2763923775882623203232111975617e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.50622025723277840373447342099217
y1[1] (numeric) = 0.50622025723277840373447342099219
absolute error = 2e-32
relative error = 3.9508494008771513524566758570049e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4366
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4366
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 2
memory used=10805.6MB, alloc=40.3MB, time=116.23
memory used=10846.9MB, alloc=40.3MB, time=116.69
memory used=10888.0MB, alloc=40.3MB, time=117.13
TOP MAIN SOLVE Loop
x[1] = 1.05
y2[1] (closed_form) = 0.86742322559401689438140948500027
y2[1] (numeric) = 0.86742322559401689438140948500035
absolute error = 8e-32
relative error = 9.2227182348288513446157392090060e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.4975710478917269902908495728121
y1[1] (numeric) = 0.49757104789172699029084957281211
absolute error = 1e-32
relative error = 2.0097632373047619814603684257021e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4316
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4316
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 2
memory used=10929.4MB, alloc=40.3MB, time=117.56
memory used=10970.6MB, alloc=40.3MB, time=118.00
TOP MAIN SOLVE Loop
memory used=11011.7MB, alloc=40.3MB, time=118.45
x[1] = 1.06
y2[1] (closed_form) = 0.87235548234498626228294592199742
y2[1] (numeric) = 0.8723554823449862622829459219975
absolute error = 8e-32
relative error = 9.1705734209351574322086407674450e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.48887208186052756191863753995641
y1[1] (numeric) = 0.48887208186052756191863753995641
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4265
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4265
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 2
memory used=11053.2MB, alloc=40.3MB, time=118.89
memory used=11094.1MB, alloc=40.3MB, time=119.33
TOP MAIN SOLVE Loop
memory used=11135.1MB, alloc=40.3MB, time=119.76
x[1] = 1.07
y2[1] (closed_form) = 0.87720050427468161030706325777682
y2[1] (numeric) = 0.87720050427468161030706325777689
absolute error = 7e-32
relative error = 7.9799315730991184489344042478960e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.48012422902853412436509306817592
y1[1] (numeric) = 0.48012422902853412436509306817592
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4212
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4212
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 2
memory used=11176.1MB, alloc=40.3MB, time=120.20
memory used=11217.0MB, alloc=40.3MB, time=120.64
TOP MAIN SOLVE Loop
x[1] = 1.08
y2[1] (closed_form) = 0.88195780688494747373533498762476
y2[1] (numeric) = 0.88195780688494747373533498762484
absolute error = 8e-32
relative error = 9.0707287100907881108618287765710e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.47132836417374002391352478852603
y1[1] (numeric) = 0.47132836417374002391352478852604
absolute error = 1e-32
relative error = 2.1216631037112423847777714573716e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4157
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4157
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 2
memory used=11258.0MB, alloc=40.3MB, time=121.09
memory used=11298.8MB, alloc=40.3MB, time=121.52
memory used=11339.8MB, alloc=40.3MB, time=121.95
TOP MAIN SOLVE Loop
x[1] = 1.09
y2[1] (closed_form) = 0.88662691444948723160860062863605
y2[1] (numeric) = 0.88662691444948723160860062863613
absolute error = 8e-32
relative error = 9.0229609203407221123488899107590e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.46248536687530087702789707387514
y1[1] (numeric) = 0.46248536687530087702789707387515
absolute error = 1e-32
relative error = 2.1622305733829374458118142722034e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4101
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4101
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 2
memory used=11380.8MB, alloc=40.3MB, time=122.39
memory used=11421.8MB, alloc=40.3MB, time=122.83
memory used=11462.7MB, alloc=40.3MB, time=123.27
TOP MAIN SOLVE Loop
x[1] = 1.1
y2[1] (closed_form) = 0.8912073600614353399518025778717
y2[1] (numeric) = 0.89120736006143533995180257787179
absolute error = 9e-32
relative error = 1.0098659866744800444678674852928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.45359612142557738777137005178472
y1[1] (numeric) = 0.45359612142557738777137005178472
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4042
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4042
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 2
memory used=11503.8MB, alloc=40.3MB, time=123.70
memory used=11544.7MB, alloc=40.3MB, time=124.14
TOP MAIN SOLVE Loop
memory used=11585.7MB, alloc=40.3MB, time=124.58
x[1] = 1.11
y2[1] (closed_form) = 0.89569868568004762924062595933937
y2[1] (numeric) = 0.89569868568004762924062595933946
absolute error = 9e-32
relative error = 1.0048021889377750437995502497241e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.44466151674170684864373751193357
y1[1] (numeric) = 0.44466151674170684864373751193357
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3983
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3983
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 2
memory used=11626.8MB, alloc=40.3MB, time=125.01
memory used=11667.7MB, alloc=40.3MB, time=125.45
TOP MAIN SOLVE Loop
memory used=11708.7MB, alloc=40.3MB, time=125.91
x[1] = 1.12
y2[1] (closed_form) = 0.90010044217650499711910324733915
y2[1] (numeric) = 0.90010044217650499711910324733923
absolute error = 8e-32
relative error = 8.8878969780921869267196205739329e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.43568244627671216761398879396113
y1[1] (numeric) = 0.43568244627671216761398879396112
absolute error = 1e-32
relative error = 2.2952496905621863932273286161367e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3922
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3922
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 2
memory used=11749.7MB, alloc=40.3MB, time=126.34
memory used=11790.7MB, alloc=40.3MB, time=126.78
TOP MAIN SOLVE Loop
x[1] = 1.13
y2[1] (closed_form) = 0.9044121893788259160370815224114
y2[1] (numeric) = 0.90441218937882591603708152241149
absolute error = 9e-32
relative error = 9.9512148395317811475587861626794e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.42665980793015731037121583565354
y1[1] (numeric) = 0.42665980793015731037121583565353
absolute error = 1e-32
relative error = 2.3437876767705676070253513391040e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3859
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3859
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 2
memory used=11831.7MB, alloc=40.3MB, time=127.22
memory used=11872.6MB, alloc=40.3MB, time=127.66
memory used=11913.7MB, alloc=40.3MB, time=128.09
TOP MAIN SOLVE Loop
x[1] = 1.14
y2[1] (closed_form) = 0.9086334961158832645942155781022
y2[1] (numeric) = 0.90863349611588326459421557810229
absolute error = 9e-32
relative error = 9.9049837348855320529025029946894e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.41759450395835809217518674082258
y1[1] (numeric) = 0.41759450395835809217518674082257
absolute error = 1e-32
relative error = 2.3946675315911689408191841299543e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3794
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3794
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 2
memory used=11954.8MB, alloc=40.3MB, time=128.53
memory used=11995.7MB, alloc=40.3MB, time=128.98
memory used=12036.6MB, alloc=40.3MB, time=129.41
TOP MAIN SOLVE Loop
x[1] = 1.15
y2[1] (closed_form) = 0.91276394026052108094403304975368
y2[1] (numeric) = 0.91276394026052108094403304975376
absolute error = 8e-32
relative error = 8.7645881340542879304444600032112e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.40848744088415729815257671880992
y1[1] (numeric) = 0.40848744088415729815257671880992
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3729
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3729
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 2
memory used=12077.7MB, alloc=40.3MB, time=129.86
memory used=12118.4MB, alloc=40.3MB, time=130.28
TOP MAIN SOLVE Loop
memory used=12159.4MB, alloc=40.3MB, time=130.72
x[1] = 1.16
y2[1] (closed_form) = 0.91680310877176692661866166687433
y2[1] (numeric) = 0.91680310877176692661866166687443
absolute error = 1.0e-31
relative error = 1.0907467376934304006864358212757e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.39933952940627315445163962339401
y1[1] (numeric) = 0.39933952940627315445163962339402
absolute error = 1e-32
relative error = 2.5041347684432143166386845864530e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3661
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3661
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 2
memory used=12200.5MB, alloc=40.3MB, time=131.17
memory used=12241.4MB, alloc=40.3MB, time=131.61
TOP MAIN SOLVE Loop
memory used=12282.4MB, alloc=40.3MB, time=132.05
x[1] = 1.17
y2[1] (closed_form) = 0.92075059773613563957301300896203
y2[1] (numeric) = 0.92075059773613563957301300896213
absolute error = 1.0e-31
relative error = 1.0860704326000071520742710060653e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.3901516843082302153326619350505
y1[1] (numeric) = 0.39015168430823021533266193505051
absolute error = 1e-32
relative error = 2.5631056848391647153358290323670e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3592
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3592
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 2
memory used=12323.4MB, alloc=40.3MB, time=132.48
memory used=12364.4MB, alloc=40.3MB, time=132.91
TOP MAIN SOLVE Loop
x[1] = 1.18
y2[1] (closed_form) = 0.92460601240802034610753802587476
y2[1] (numeric) = 0.92460601240802034610753802587487
absolute error = 1.1e-31
relative error = 1.1896959193842878227035551928199e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.38092482436688177302959946671276
y1[1] (numeric) = 0.38092482436688177302959946671278
absolute error = 2e-32
relative error = 5.2503797916665345836180073297707e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3522
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3522
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 2
memory used=12405.5MB, alloc=40.3MB, time=133.34
memory used=12446.4MB, alloc=40.3MB, time=133.78
memory used=12487.3MB, alloc=40.3MB, time=134.22
TOP MAIN SOLVE Loop
x[1] = 1.19
y2[1] (closed_form) = 0.92836896724916669260202111160267
y2[1] (numeric) = 0.92836896724916669260202111160279
absolute error = 1.2e-31
relative error = 1.2925895224133765598050553158072e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.37165987226053293806567955835047
y1[1] (numeric) = 0.37165987226053293806567955835049
absolute error = 2e-32
relative error = 5.3812642937088548613935325903777e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.345
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.345
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 2
memory used=12528.5MB, alloc=40.3MB, time=134.66
memory used=12569.4MB, alloc=40.3MB, time=135.09
memory used=12610.3MB, alloc=40.3MB, time=135.53
TOP MAIN SOLVE Loop
x[1] = 1.2
y2[1] (closed_form) = 0.93203908596722634967013443549483
y2[1] (numeric) = 0.93203908596722634967013443549494
absolute error = 1.1e-31
relative error = 1.1802080154808869515756286146788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.36235775447667357763837335562308
y1[1] (numeric) = 0.36235775447667357763837335562311
absolute error = 3e-32
relative error = 8.2791108039972193706502988177133e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3377
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3377
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 2
memory used=12651.4MB, alloc=40.3MB, time=135.97
memory used=12692.3MB, alloc=40.3MB, time=136.41
memory used=12733.2MB, alloc=40.3MB, time=136.84
TOP MAIN SOLVE Loop
x[1] = 1.21
y2[1] (closed_form) = 0.93561600155338593341646488854361
y2[1] (numeric) = 0.93561600155338593341646488854372
absolute error = 1.1e-31
relative error = 1.1756960100871408312350079741769e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.35301940121933033870301071366479
y1[1] (numeric) = 0.35301940121933033870301071366483
absolute error = 4e-32
relative error = 1.1330822006337286180955577608168e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3303
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3303
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 2
memory used=12774.4MB, alloc=40.3MB, time=137.28
memory used=12815.2MB, alloc=40.3MB, time=137.72
TOP MAIN SOLVE Loop
memory used=12856.2MB, alloc=40.3MB, time=138.16
x[1] = 1.22
y2[1] (closed_form) = 0.93909935631906758093524527188837
y2[1] (numeric) = 0.93909935631906758093524527188848
absolute error = 1.1e-31
relative error = 1.1713350590629783758899019479540e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.3436457463160470204755229744352
y1[1] (numeric) = 0.34364574631604702047552297443524
absolute error = 4e-32
relative error = 1.1639893823452847975735699500606e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3227
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3227
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 2
memory used=12897.1MB, alloc=40.3MB, time=138.61
memory used=12938.1MB, alloc=40.3MB, time=139.05
TOP MAIN SOLVE Loop
x[1] = 1.23
y2[1] (closed_form) = 0.94248880193169751002382356538924
y2[1] (numeric) = 0.94248880193169751002382356538934
absolute error = 1.0e-31
relative error = 1.0610205637991976337809176067095e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.33423772712450259823954724549766
y1[1] (numeric) = 0.3342377271245025982395472454977
absolute error = 4e-32
relative error = 1.1967529920732172255226357687978e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.315
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.315
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 2
memory used=12979.2MB, alloc=40.3MB, time=139.48
memory used=13020.1MB, alloc=40.3MB, time=139.92
memory used=13061.1MB, alloc=40.3MB, time=140.36
TOP MAIN SOLVE Loop
x[1] = 1.24
y2[1] (closed_form) = 0.94578399944953898628470596308179
y2[1] (numeric) = 0.94578399944953898628470596308188
absolute error = 9e-32
relative error = 9.5159148444445456168653298709188e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.32479628443877623657769341569738
y1[1] (numeric) = 0.32479628443877623657769341569743
absolute error = 5e-32
relative error = 1.5394264773193533328532731450800e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3072
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3072
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 2
memory used=13102.1MB, alloc=40.3MB, time=140.80
memory used=13143.1MB, alloc=40.3MB, time=141.23
memory used=13184.0MB, alloc=40.3MB, time=141.67
TOP MAIN SOLVE Loop
x[1] = 1.25
y2[1] (closed_form) = 0.94898461935558621434849084703605
y2[1] (numeric) = 0.94898461935558621434849084703615
absolute error = 1.0e-31
relative error = 1.0537578582454329877253077296853e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.31532236239526866544753855243804
y1[1] (numeric) = 0.3153223623952686654475385524381
absolute error = 6e-32
relative error = 1.9028146162620620165087579727933e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2992
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2992
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 2
memory used=13225.1MB, alloc=40.3MB, time=142.11
memory used=13266.0MB, alloc=40.3MB, time=142.55
memory used=13306.9MB, alloc=40.3MB, time=142.98
TOP MAIN SOLVE Loop
x[1] = 1.26
y2[1] (closed_form) = 0.95209034159051576385681622142542
y2[1] (numeric) = 0.95209034159051576385681622142553
absolute error = 1.1e-31
relative error = 1.1553525458124000744228465106062e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.30581690837828932688634248917648
y1[1] (numeric) = 0.30581690837828932688634248917653
absolute error = 5e-32
relative error = 1.6349651909419936926311241884046e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2912
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2912
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 2
memory used=13348.0MB, alloc=40.3MB, time=143.42
memory used=13389.0MB, alloc=40.3MB, time=143.86
TOP MAIN SOLVE Loop
memory used=13430.0MB, alloc=40.3MB, time=144.30
x[1] = 1.27
y2[1] (closed_form) = 0.95510085558469223509018174218289
y2[1] (numeric) = 0.955100855584692235090181742183
absolute error = 1.1e-31
relative error = 1.1517108309222523102971129643005e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.29628087292531873355113701608796
y1[1] (numeric) = 0.296280872925318733551137016088
absolute error = 4e-32
relative error = 1.3500702763921751980119693012842e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.283
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.283
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 2
memory used=13471.0MB, alloc=40.3MB, time=144.75
memory used=13512.0MB, alloc=40.3MB, time=145.19
TOP MAIN SOLVE Loop
x[1] = 1.28
y2[1] (closed_form) = 0.95801586028922496370075385916029
y2[1] (numeric) = 0.95801586028922496370075385916039
absolute error = 1.0e-31
relative error = 1.0438240549567728717927004514947e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.28671520963195551277938689359259
y1[1] (numeric) = 0.28671520963195551277938689359264
absolute error = 5e-32
relative error = 1.7438907431587929162692549603174e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2747
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2747
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 2
memory used=13553.0MB, alloc=40.3MB, time=145.61
memory used=13593.9MB, alloc=40.3MB, time=146.05
memory used=13634.9MB, alloc=40.3MB, time=146.48
TOP MAIN SOLVE Loop
x[1] = 1.29
y2[1] (closed_form) = 0.96083506420607265890556129128537
y2[1] (numeric) = 0.96083506420607265890556129128548
absolute error = 1.1e-31
relative error = 1.1448374866595004854124647987321e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.27712087505655764138660609006118
y1[1] (numeric) = 0.27712087505655764138660609006124
absolute error = 6e-32
relative error = 2.1651201840263600101325262745046e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2663
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2663
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 2
memory used=13676.0MB, alloc=40.3MB, time=146.94
memory used=13717.0MB, alloc=40.3MB, time=147.38
memory used=13757.9MB, alloc=40.3MB, time=147.81
TOP MAIN SOLVE Loop
x[1] = 1.3
y2[1] (closed_form) = 0.96355818541719296470134863003955
y2[1] (numeric) = 0.96355818541719296470134863003969
absolute error = 1.4e-31
relative error = 1.4529480639447220197146856827052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.26749882862458740699798410929287
y1[1] (numeric) = 0.26749882862458740699798410929293
absolute error = 6e-32
relative error = 2.2430004762452647031662010378488e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2578
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2578
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 2
memory used=13799.0MB, alloc=40.3MB, time=148.25
memory used=13839.9MB, alloc=40.3MB, time=148.69
memory used=13880.9MB, alloc=40.3MB, time=149.13
TOP MAIN SOLVE Loop
x[1] = 1.31
y2[1] (closed_form) = 0.9661849516127340291692578059375
y2[1] (numeric) = 0.96618495161273402916925780593762
absolute error = 1.2e-31
relative error = 1.2419982302529005341090772913190e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.2578500325326696613381769786162
y1[1] (numeric) = 0.25785003253266966133817697861625
absolute error = 5e-32
relative error = 1.9391116421001415982201674906100e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2491
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2491
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 2
memory used=13921.9MB, alloc=40.3MB, time=149.56
memory used=13962.8MB, alloc=40.3MB, time=150.00
TOP MAIN SOLVE Loop
memory used=14003.8MB, alloc=40.3MB, time=150.44
x[1] = 1.32
y2[1] (closed_form) = 0.96871510011826526273589984597277
y2[1] (numeric) = 0.9687151001182652627358998459729
absolute error = 1.3e-31
relative error = 1.3419838297568500065565996071124e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.24817545165237295957398272942735
y1[1] (numeric) = 0.24817545165237295957398272942741
absolute error = 6e-32
relative error = 2.4176444366481443149116142792461e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2404
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2404
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 2
memory used=14044.8MB, alloc=40.3MB, time=150.88
memory used=14085.8MB, alloc=40.3MB, time=151.31
TOP MAIN SOLVE Loop
x[1] = 1.33
y2[1] (closed_form) = 0.9711483779210445623376830377638
y2[1] (numeric) = 0.97114837792104456233768303776392
absolute error = 1.2e-31
relative error = 1.2356505218789144986376325445111e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.23847605343372320751578498601058
y1[1] (numeric) = 0.23847605343372320751578498601063
absolute error = 5e-32
relative error = 2.0966465722687708339780876237170e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2316
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2316
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 2
memory used=14126.8MB, alloc=40.3MB, time=151.75
memory used=14167.8MB, alloc=40.3MB, time=152.19
memory used=14208.8MB, alloc=40.3MB, time=152.63
TOP MAIN SOLVE Loop
x[1] = 1.34
y2[1] (closed_form) = 0.97348454169531937478787034808955
y2[1] (numeric) = 0.97348454169531937478787034808966
absolute error = 1.1e-31
relative error = 1.1299614455966136539947011034401e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.22875280780845946523263949230014
y1[1] (numeric) = 0.22875280780845946523263949230019
absolute error = 5e-32
relative error = 2.1857655203894270738370516051356e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2227
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2227
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 2
memory used=14249.8MB, alloc=40.3MB, time=153.06
memory used=14290.8MB, alloc=40.3MB, time=153.50
memory used=14331.7MB, alloc=40.3MB, time=153.94
TOP MAIN SOLVE Loop
x[1] = 1.35
y2[1] (closed_form) = 0.97572335782665906926111353926522
y2[1] (numeric) = 0.97572335782665906926111353926532
absolute error = 1.0e-31
relative error = 1.0248806610794017372368662156356e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.21900668709304158142002217301063
y1[1] (numeric) = 0.21900668709304158142002217301067
absolute error = 4e-32
relative error = 1.8264282488783834594701364724300e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2137
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2137
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 2
memory used=14372.7MB, alloc=40.3MB, time=154.38
memory used=14413.6MB, alloc=40.3MB, time=154.81
memory used=14454.6MB, alloc=40.3MB, time=155.25
TOP MAIN SOLVE Loop
x[1] = 1.36
y2[1] (closed_form) = 0.97786460243531618567849243942663
y2[1] (numeric) = 0.97786460243531618567849243942673
absolute error = 1.0e-31
relative error = 1.0226364647105098859550318372739e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.20923866589141935767597525239186
y1[1] (numeric) = 0.20923866589141935767597525239189
absolute error = 3e-32
relative error = 1.4337694169569959131632634099302e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2046
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2046
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 2
memory used=14495.7MB, alloc=40.3MB, time=155.69
memory used=14536.6MB, alloc=40.3MB, time=156.12
TOP MAIN SOLVE Loop
memory used=14577.6MB, alloc=40.3MB, time=156.56
x[1] = 1.37
y2[1] (closed_form) = 0.97990806139861422288768850489193
y2[1] (numeric) = 0.97990806139861422288768850489204
absolute error = 1.1e-31
relative error = 1.1225542919097732509429232058675e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.19944972099757296568819838964531
y1[1] (numeric) = 0.19944972099757296568819838964535
absolute error = 4e-32
relative error = 2.0055179721453080444837095002736e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1954
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1954
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 2
memory used=14618.7MB, alloc=40.3MB, time=157.01
memory used=14659.6MB, alloc=40.3MB, time=157.45
TOP MAIN SOLVE Loop
x[1] = 1.38
y2[1] (closed_form) = 0.98185353037235972787813108520605
y2[1] (numeric) = 0.98185353037235972787813108520617
absolute error = 1.2e-31
relative error = 1.2221782199478470588190898782452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.1896408312978343632091500735982
y1[1] (numeric) = 0.18964083129783436320915007359825
absolute error = 5e-32
relative error = 2.6365630048032268768302730981699e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1862
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1862
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 2
memory used=14700.6MB, alloc=40.3MB, time=157.89
memory used=14741.6MB, alloc=40.3MB, time=158.33
memory used=14782.5MB, alloc=40.3MB, time=158.76
TOP MAIN SOLVE Loop
x[1] = 1.39
y2[1] (closed_form) = 0.98370081481127654484003822444291
y2[1] (numeric) = 0.98370081481127654484003822444302
absolute error = 1.1e-31
relative error = 1.1182261755176399924950747116541e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.17981297767299947659616321780405
y1[1] (numeric) = 0.17981297767299947659616321780409
absolute error = 4e-32
relative error = 2.2245335413299457859169812246486e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1769
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1769
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 2
memory used=14823.5MB, alloc=40.3MB, time=159.20
memory used=14864.4MB, alloc=40.3MB, time=159.64
memory used=14905.3MB, alloc=40.3MB, time=160.08
TOP MAIN SOLVE Loop
x[1] = 1.4
y2[1] (closed_form) = 0.9854497299884601806594745788061
y2[1] (numeric) = 0.98544972998846018065947457880621
absolute error = 1.1e-31
relative error = 1.1162416169243673409902737327472e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.16996714290024093861674803520365
y1[1] (numeric) = 0.16996714290024093861674803520367
absolute error = 2e-32
relative error = 1.1766980169654689653988540619690e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1675
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1675
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 2
memory used=14946.3MB, alloc=40.3MB, time=160.51
memory used=14987.2MB, alloc=40.3MB, time=160.95
memory used=15028.2MB, alloc=40.3MB, time=161.39
TOP MAIN SOLVE Loop
x[1] = 1.41
y2[1] (closed_form) = 0.98710010101385034142908886194224
y2[1] (numeric) = 0.98710010101385034142908886194236
absolute error = 1.2e-31
relative error = 1.2156821772862551725899653507496e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.16010431155483119016356254936092
y1[1] (numeric) = 0.16010431155483119016356254936095
absolute error = 3e-32
relative error = 1.8737783953885495486989139863589e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.158
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.158
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 2
memory used=15069.2MB, alloc=40.3MB, time=161.83
memory used=15110.1MB, alloc=40.3MB, time=162.27
TOP MAIN SOLVE Loop
memory used=15151.0MB, alloc=40.3MB, time=162.70
x[1] = 1.42
y2[1] (closed_form) = 0.9886517628517197927362734733357
y2[1] (numeric) = 0.98865176285171979273627347333582
absolute error = 1.2e-31
relative error = 1.2137741974369783120159352477734e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.15022546991168577348698210297591
y1[1] (numeric) = 0.15022546991168577348698210297594
absolute error = 3e-32
relative error = 1.9969982465447660472718376492287e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1485
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1485
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 2
memory used=15192.0MB, alloc=40.3MB, time=163.14
memory used=15233.0MB, alloc=40.3MB, time=163.59
TOP MAIN SOLVE Loop
x[1] = 1.43
y2[1] (closed_form) = 0.99010456033717779485729149548183
y2[1] (numeric) = 0.99010456033717779485729149548195
absolute error = 1.2e-31
relative error = 1.2119932056381427064035653085188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.14033160584673666253389762457492
y1[1] (numeric) = 0.14033160584673666253389762457495
absolute error = 3e-32
relative error = 2.1377935368860908801729634797422e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1389
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1389
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 2
memory used=15274.0MB, alloc=40.3MB, time=164.02
memory used=15315.0MB, alloc=40.3MB, time=164.47
memory used=15355.9MB, alloc=40.3MB, time=164.89
TOP MAIN SOLVE Loop
x[1] = 1.44
y2[1] (closed_form) = 0.99145834819168646252760446395798
y2[1] (numeric) = 0.9914583481916864625276044639581
absolute error = 1.2e-31
relative error = 1.2103382882283165112527731482405e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.13042370873814549297752015612917
y1[1] (numeric) = 0.1304237087381454929775201561292
absolute error = 3e-32
relative error = 2.3001952858304045212098108052567e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1293
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1293
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 2
memory used=15396.9MB, alloc=40.3MB, time=165.33
memory used=15437.9MB, alloc=40.3MB, time=165.78
memory used=15478.9MB, alloc=40.3MB, time=166.22
TOP MAIN SOLVE Loop
x[1] = 1.45
y2[1] (closed_form) = 0.99271299103758849766535413432301
y2[1] (numeric) = 0.99271299103758849766535413432312
absolute error = 1.1e-31
relative error = 1.1080745491708279078977561201952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.12050276936736657053286662724802
y1[1] (numeric) = 0.12050276936736657053286662724804
absolute error = 2e-32
relative error = 1.6597128933217872056632451020372e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1196
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1196
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=15519.9MB, alloc=40.3MB, time=166.66
memory used=15560.9MB, alloc=40.3MB, time=167.09
memory used=15601.9MB, alloc=40.3MB, time=167.53
TOP MAIN SOLVE Loop
x[1] = 1.46
y2[1] (closed_form) = 0.99386836341164484228683230125003
y2[1] (numeric) = 0.99386836341164484228683230125014
absolute error = 1.1e-31
relative error = 1.1067864120596794587398333969033e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.11056977982006955117464810912337
y1[1] (numeric) = 0.11056977982006955117464810912339
absolute error = 2e-32
relative error = 1.8088125012590279658008208398940e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1099
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1099
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=15642.9MB, alloc=40.3MB, time=167.97
memory used=15683.8MB, alloc=40.3MB, time=168.41
TOP MAIN SOLVE Loop
memory used=15724.8MB, alloc=40.3MB, time=168.86
x[1] = 1.47
y2[1] (closed_form) = 0.99492434977758089785992846273557
y2[1] (numeric) = 0.99492434977758089785992846273566
absolute error = 9e-32
relative error = 9.0459138948724936187700476929769e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.10062573338693170090697460146241
y1[1] (numeric) = 0.10062573338693170090697460146243
absolute error = 2e-32
relative error = 1.9875631537605674709012349381457e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1001
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1001
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=15765.8MB, alloc=40.3MB, time=169.30
memory used=15806.8MB, alloc=40.3MB, time=169.72
TOP MAIN SOLVE Loop
x[1] = 1.48
y2[1] (closed_form) = 0.99588084453764005648407513256269
y2[1] (numeric) = 0.99588084453764005648407513256278
absolute error = 9e-32
relative error = 9.0372257377622833800487766002822e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.090671624464309655776226540647838
y1[1] (numeric) = 0.090671624464309655776226540647863
absolute error = 2.5e-32
relative error = 2.7572021729731498816142627996907e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0903
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0903
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=15847.9MB, alloc=40.3MB, time=170.17
memory used=15888.9MB, alloc=40.3MB, time=170.61
memory used=15929.8MB, alloc=40.3MB, time=171.03
TOP MAIN SOLVE Loop
x[1] = 1.49
y2[1] (closed_form) = 0.9967377520431433885532007170437
y2[1] (numeric) = 0.99673775204314338855320071704379
absolute error = 9e-32
relative error = 9.0294563254492227332902187450867e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.080708448454800614868318484563714
y1[1] (numeric) = 0.080708448454800614868318484563738
absolute error = 2.4e-32
relative error = 2.9736663830727447585817409075188e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08045
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08045
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=15970.8MB, alloc=40.3MB, time=171.48
memory used=16011.8MB, alloc=40.3MB, time=171.92
memory used=16052.7MB, alloc=40.3MB, time=172.36
TOP MAIN SOLVE Loop
x[1] = 1.5
y2[1] (closed_form) = 0.99749498660405443094172337114149
y2[1] (numeric) = 0.99749498660405443094172337114156
absolute error = 7e-32
relative error = 7.0175791297270743696792855465612e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.070737201667702910088189851434269
y1[1] (numeric) = 0.070737201667702910088189851434292
absolute error = 2.3e-32
relative error = 3.2514715676830777088423425398626e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07056
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07056
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 2
memory used=16093.8MB, alloc=40.3MB, time=172.80
memory used=16134.7MB, alloc=40.3MB, time=173.23
memory used=16175.6MB, alloc=40.3MB, time=173.67
TOP MAIN SOLVE Loop
x[1] = 1.51
y2[1] (closed_form) = 0.99815247249754811924273786483671
y2[1] (numeric) = 0.99815247249754811924273786483679
absolute error = 8e-32
relative error = 8.0148075774261545522267390254129e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.060758881219385906581595514916193
y1[1] (numeric) = 0.060758881219385906581595514916216
absolute error = 2.3e-32
relative error = 3.7854548237898680467664619680148e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06065
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06065
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
memory used=16216.7MB, alloc=40.3MB, time=174.11
memory used=16257.6MB, alloc=40.3MB, time=174.55
TOP MAIN SOLVE Loop
memory used=16298.6MB, alloc=40.3MB, time=174.98
x[1] = 1.52
y2[1] (closed_form) = 0.99871014397558300717231239411685
y2[1] (numeric) = 0.99871014397558300717231239411693
absolute error = 8e-32
relative error = 8.0103321752137807696780439868792e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.050774484933579196726129270152727
y1[1] (numeric) = 0.050774484933579196726129270152749
absolute error = 2.2e-32
relative error = 4.3328849182378451846945838457867e-29 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05071
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05071
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
memory used=16339.6MB, alloc=40.3MB, time=175.42
memory used=16380.6MB, alloc=40.3MB, time=175.88
TOP MAIN SOLVE Loop
x[1] = 1.53
y2[1] (closed_form) = 0.99916794527147601592426506870898
y2[1] (numeric) = 0.99916794527147601592426506870906
absolute error = 8e-32
relative error = 8.0066619809609517692808259147125e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.040785011241591058688989007076121
y1[1] (numeric) = 0.040785011241591058688989007076141
absolute error = 2.0e-32
relative error = 4.9037622869660345937564607594618e-29 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04075
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04075
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
memory used=16421.6MB, alloc=40.3MB, time=176.31
memory used=16462.7MB, alloc=40.3MB, time=176.75
memory used=16503.6MB, alloc=40.3MB, time=177.19
TOP MAIN SOLVE Loop
x[1] = 1.54
y2[1] (closed_form) = 0.99952583060547905600596353844003
y2[1] (numeric) = 0.99952583060547905600596353844011
absolute error = 8e-32
relative error = 8.0037951547023748903674666920324e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.030791459082466157622476807076397
y1[1] (numeric) = 0.030791459082466157622476807076416
absolute error = 1.9e-32
relative error = 6.1705422757375377396982542539992e-29 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03078
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03078
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
memory used=16544.6MB, alloc=40.3MB, time=177.62
memory used=16585.6MB, alloc=40.3MB, time=178.06
memory used=16626.6MB, alloc=40.3MB, time=178.50
TOP MAIN SOLVE Loop
x[1] = 1.55
y2[1] (closed_form) = 0.99978376418935696389761134763447
y2[1] (numeric) = 0.99978376418935696389761134763453
absolute error = 6e-32
relative error = 6.0012976954720905919209077716776e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.020794827803092473643912774695556
y1[1] (numeric) = 0.020794827803092473643912774695575
absolute error = 1.9e-32
relative error = 9.1368873933038491691096837140113e-29 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02079
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02079
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
memory used=16667.6MB, alloc=40.3MB, time=178.94
memory used=16708.5MB, alloc=40.3MB, time=179.38
memory used=16749.4MB, alloc=40.3MB, time=179.81
TOP MAIN SOLVE Loop
x[1] = 1.56
y2[1] (closed_form) = 0.99994172022996629574517002341348
y2[1] (numeric) = 0.99994172022996629574517002341355
absolute error = 7e-32
relative error = 7.0004079821673428203756274131935e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y1[1] (closed_form) = 0.010796117058267445823920663760906
y1[1] (numeric) = 0.010796117058267445823920663760924
absolute error = 1.8e-32
relative error = 1.6672661015856592469124032239810e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0108
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0108
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE
SETTING H FOR POLE
memory used=16791.1MB, alloc=40.3MB, time=180.26
SETTING H FOR POLE
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ;
diff ( y1 , x , 1 ) = neg ( y2 ) ;
Iterations = 1464
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 7 Minutes 2 Seconds
Optimized Time Remaining = 7 Minutes 2 Seconds
Expected Total Time = 10 Minutes 2 Seconds
Time to Timeout 0.0 Seconds
Percent Done = 29.89 %
> quit
memory used=16801.1MB, alloc=40.3MB, time=180.36