(%i1) batch("temp/diffeq.nonlinear2.max")
read and interpret file: /home/dennis/src/mine/omni/temp/diffeq.nonlinear2.max
(%i2) load("stringproc")
(%i3) alias(convfloat,float)
(%i4) alias(int_trunc,truncate)
(%i5) alias(elapsed_time_seconds,elapsed_real_time)
(%i6) alias(ln,log)
(%i7) alias(arcsin,asin)
(%i8) alias(arccos,acos)
(%i9) alias(arctan,atan)
(%i10) alias(float_abs,abs)
(%i11) keepfloat:true
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_ats],
fixnum),convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_att],
fixnum),convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(factorial_2([nnn],fixnum),fixnum)
(%i43) mode_declare(factorial_1([nnn],fixnum),fixnum)
(%i44) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum)
(%i45) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i46) mode_declare(elaped_time_seconds(),convfloat)
(%i47) mode_declare(Si([x],convfloat),convfloat)
(%i48) mode_declare(Ci([x],convfloat),convfloat)
(%i49) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i50) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i51) mode_declare(main_prog(),fixnum)
(%i52) define_variable(MAX_TERMS,20,fixnum)
(%i53) define_variable(glob_iolevel,5,fixnum)
(%i54) define_variable(glob_yes_pole,4,fixnum)
(%i55) define_variable(glob_no_pole,3,fixnum)
(%i56) define_variable(glob_not_given,0,fixnum)
(%i57) define_variable(glob_no_sing_tests,4,fixnum)
(%i58) define_variable(glob_ratio_test,1,fixnum)
(%i59) define_variable(glob_three_term_test,2,fixnum)
(%i60) define_variable(glob_six_term_test,3,fixnum)
(%i61) define_variable(glob_log_10,log(10.0),convfloat)
(%i62) define_variable(ALWAYS,1,fixnum)
(%i63) define_variable(INFO,2,fixnum)
(%i64) define_variable(DEBUGL,3,fixnum)
(%i65) define_variable(DEBUGMASSIVE,4,fixnum)
(%i66) define_variable(MAX_UNCHANGED,10,fixnum)
(%i67) define_variable(glob_prec,1.0E-16,convfloat)
(%i68) define_variable(glob_est_digits,1,fixnum)
(%i69) define_variable(glob_check_sign,1.0,convfloat)
(%i70) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i71) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i72) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i73) define_variable(glob_percent_done,0.0,convfloat)
(%i74) define_variable(glob_subiter_method,3,fixnum)
(%i75) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i76) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i77) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i78) define_variable(glob_html_log,true,boolean)
(%i79) define_variable(glob_good_digits,0,fixnum)
(%i80) define_variable(glob_max_opt_iter,10,fixnum)
(%i81) define_variable(glob_dump,false,boolean)
(%i82) define_variable(glob_djd_debug,true,boolean)
(%i83) define_variable(glob_display_flag,true,boolean)
(%i84) define_variable(glob_djd_debug2,true,boolean)
(%i85) define_variable(glob_h_reason,0,fixnum)
(%i86) define_variable(glob_sec_in_minute,60,fixnum)
(%i87) define_variable(glob_min_in_hour,60.0,convfloat)
(%i88) define_variable(glob_hours_in_day,24.0,convfloat)
(%i89) define_variable(glob_days_in_year,365,fixnum)
(%i90) define_variable(glob_sec_in_hour,3600,fixnum)
(%i91) define_variable(glob_sec_in_day,86400,fixnum)
(%i92) define_variable(glob_sec_in_year,31536000,fixnum)
(%i93) define_variable(glob_almost_1,0.999,convfloat)
(%i94) define_variable(glob_clock_sec,0.0,convfloat)
(%i95) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i96) define_variable(glob_not_yet_finished,true,boolean)
(%i97) define_variable(glob_initial_pass,true,boolean)
(%i98) define_variable(glob_not_yet_start_msg,true,boolean)
(%i99) define_variable(glob_reached_optimal_h,false,boolean)
(%i100) define_variable(glob_optimal_done,false,boolean)
(%i101) define_variable(glob_disp_incr,0.1,convfloat)
(%i102) define_variable(glob_h,0.1,convfloat)
(%i103) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i106) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i109) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i110) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i111) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i112) define_variable(glob_max_h,0.1,convfloat)
(%i113) define_variable(glob_min_h,1.0E-6,convfloat)
(%i114) define_variable(glob_type_given_pole,0,fixnum)
(%i115) define_variable(glob_large_float,1.0E+100,convfloat)
(%i116) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i117) define_variable(glob_least_given_sing,9.9E+100,convfloat)
(%i118) define_variable(glob_least_ratio_sing,9.9E+100,convfloat)
(%i119) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i120) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i121) define_variable(glob_last_good_h,0.1,convfloat)
(%i122) define_variable(glob_look_poles,false,boolean)
(%i123) define_variable(glob_display_interval,0.1,convfloat)
(%i124) define_variable(glob_next_display,0.0,convfloat)
(%i125) define_variable(glob_dump_closed_form,false,boolean)
(%i126) define_variable(glob_abserr,1.0E-11,convfloat)
(%i127) define_variable(glob_relerr,1.0E-11,convfloat)
(%i128) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i129) define_variable(glob_max_hours,0.0,convfloat)
(%i130) define_variable(glob_max_iter,1000,fixnum)
(%i131) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i132) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i133) define_variable(glob_no_eqs,0,fixnum)
(%i134) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i135) define_variable(glob_optimal_start,0.0,convfloat)
(%i136) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i137) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i138) define_variable(glob_small_float,0.0,convfloat)
(%i139) define_variable(glob_smallish_float,0.0,convfloat)
(%i140) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i141) define_variable(glob_warned,false,boolean)
(%i142) define_variable(glob_warned2,false,boolean)
(%i143) define_variable(glob_max_sec,10000.0,convfloat)
(%i144) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i145) define_variable(glob_start,0,fixnum)
(%i146) define_variable(glob_iter,0,fixnum)
(%i147) define_variable(glob_normmax,0.0,convfloat)
(%i148) define_variable(glob_max_minutes,0.0,convfloat)
(%i149) array(array_y_init,MAX_TERMS)
(%i150) array(array_norms,MAX_TERMS)
(%i151) array(array_fact_1,MAX_TERMS)
(%i152) array(array_1st_rel_error,2)
(%i153) array(array_last_rel_error,2)
(%i154) array(array_est_rel_error,2)
(%i155) array(array_max_est_error,2)
(%i156) array(array_type_pole,2)
(%i157) array(array_type_real_pole,2)
(%i158) array(array_type_complex_pole,2)
(%i159) array(array_est_digits,2)
(%i160) array(array_good_digits,2)
(%i161) array(array_y,MAX_TERMS)
(%i162) array(array_x,MAX_TERMS)
(%i163) array(array_tmp0,MAX_TERMS)
(%i164) array(array_tmp1,MAX_TERMS)
(%i165) array(array_tmp2,MAX_TERMS)
(%i166) array(array_m1,MAX_TERMS)
(%i167) array(array_y_higher,2,MAX_TERMS)
(%i168) array(array_y_higher_work,2,MAX_TERMS)
(%i169) array(array_y_higher_work2,2,MAX_TERMS)
(%i170) array(array_y_set_initial,2,MAX_TERMS)
(%i171) array(array_given_rad_poles,2,3)
(%i172) array(array_given_ord_poles,2,3)
(%i173) array(array_rad_test_poles,2,4)
(%i174) array(array_ord_test_poles,2,4)
(%i175) array(array_fact_2,MAX_TERMS,MAX_TERMS)
(%i176) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i177) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i178) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i179) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (if vallen = 4
then printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel)
else printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel))
(%i180) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i181) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i182) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"
~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i183) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i184) zero_ats_ar(arr_a):=(
block(modedcclare([iii],fixnum),iii:1,
while iii <= MAX_TERMS do
(arr_a[iii]:0.0,iii:1+iii)),0)
(%i185) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:0.0,
if jjj_ats <= mmm_ats
then (ma_ats:1+mmm_ats,iii_ats:jjj_ats,
while iii_ats <= mmm_ats do
(lll_ats:ma_ats-iii_ats,
if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS
then ret_ats
:arr_a[iii_ats]*arr_b[lll_ats]+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i186) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:0.0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= MAX_TERMS do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS
then ret_att
:arr_aa[iii_att]*arr_bb[lll_att]*al_att
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/mmm_att),ret_att)
(%i187) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i188) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i189) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i190) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
if rel_error # -1.0
then (if rel_error > glob_prec
then (
good_digits
:3-floor(log10(rel_error)),
printf(file,"~d",good_digits))
else (good_digits:16,
printf(file,"~d",
good_digits)))
else printf(file,"Unknown"),
printf(file," | ")),0)
(%i191) log_revs(file,revs):=printf(file,revs)
(%i192) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i193) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i194) logstart(file):=(printf(file,""),0)
(%i195) logend(file):=(printf(file,"
~%"),0)
(%i196) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(ALWAYS,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i197) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:clock_sec2,
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub1 = 0.0 then sec_left:0.0
else (if sub2 > 0.0
then (rrr:sub1/sub2,
sec_left:rrr*ms2-ms2)
else sec_left:0.0),sec_left)
(%i198) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:100.0*sub2/sub1
else rrr:0.0,rrr)
(%i199) comp_rad_from_ratio(term1,term2,last_no):=(
if term2 > 0.0 then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i200) comp_ord_from_ratio(term1,term2,last_no):=(
if term2 > 0.0
then ret
:abs(term2)*convfloat(last_no)
*log(abs(term1*glob_h/term2))
/log(convfloat(last_no))
+1.0 else ret:glob_larger_float,ret)
(%i201) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3
-term1*term3*convfloat(last_no)
-2.0*term2*term2
+term2*term2*convfloat(last_no)),
if temp > 0.0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i202) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*convfloat(last_no*last_no)
+term2*term2*convfloat(last_no*last_no)
+4.0*term2*term2
-4.0*term2*term2*convfloat(last_no)
-3.0*term1*term3
+4.0*term1*term3*convfloat(last_no))
/(term1*term3
-term1*term3*convfloat(last_no)
-2.0*term2*term2
+term2*term2*convfloat(last_no))),ret)
(%i203) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # 0.0 and term4 # 0.0 and term3 # 0.0
and term2 # 0.0 and term1 # 0.0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:convfloat(last_no-3)*rm2
-2.0*convfloat(last_no-2)*rm1
+convfloat(last_no-1)*rm0,
nr2
:convfloat(last_no-4)*rm3
-2.0*convfloat(last_no-3)*rm2
+convfloat(last_no-2)*rm1,
dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1,
dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2,
ds1:5.0/rm3-8.0/rm2+3.0/rm1,
ds2:5.0/rm4-8.0/rm3+3.0/rm2,
if
abs(nr1*dr2-nr2*dr1) = 0.0
or abs(dr1) = 0.0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) # 0.0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(2.0*dr1)
-convfloat(last_no)/2.0,
if abs(rcs) # 0.0
then (if rcs > 0.0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i204) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i205) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i206) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= 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])
else ret:factorial_2(nnn),ret)
(%i207) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= MAX_TERMS and mmm <= 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])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i208) log10(x):=log(x)/glob_log_10
(%i209) expt(x,y):=if y = 0.0 then 1.0 elseif x < 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i210) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(ALWAYS,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(10.0,-glob_desired_digits_correct)
*abs(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
:abs(
desired_abs_gbl_error
/sqrt(estimated_steps)
/MAX_TERMS),
omniout_float(ALWAYS,"step_error",32,
step_error,32,""),
step_error)
(%i211) exact_soln_y(x):=block(2.0/(1.0-2.0*x))
2.0
(%o211) exact_soln_y(x) := block(-----------)
1.0 - 2.0 x
(%i212) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
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)
elseif glob_type_given_pole = 3
then omniout_str(ALWAYS,
"NO POLE (given) for Equation 1")
elseif 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"),
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],
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"),
if array_rad_test_poles[1,2] > 0.0
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],
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"),
if array_rad_test_poles[1,3] > 0.0
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],
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")),
0)
(%i213) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0
else ret:-1.0,ret)
(%i214) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),
if min_size < 1.0
then (min_size:1.0,
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),min_size)
(%i215) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:0.0,no_terms:MAX_TERMS,
hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125,
omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(ALWAYS,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i216) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:MAX_TERMS,hn_div_ho:0.5,
hn_div_ho_2:0.25,hn_div_ho_3:0.125,
est_tmp:abs(array_y[no_terms])*hn_div_ho_3
+abs(array_y[no_terms-1])*hn_div_ho_2
+abs(array_y[no_terms-2])*hn_div_ho
+abs(array_y[no_terms-3]),
if glob_prec*abs(array_y[1]) > est_tmp
then est_tmp:glob_prec*abs(array_y[1]),
if est_tmp >= array_max_est_error[1]
then array_max_est_error[1]:est_tmp)
(%i217) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display-glob_h/10.0
then ret:true else ret:false,return(ret))
(%i218) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(ALWAYS,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(ALWAYS,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(ALWAYS,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
abs(closed_form_val_y)
> glob_prec
then (
relerr
:abserr*100.0
/abs(closed_form_val_y),
if relerr > glob_prec
then glob_good_digits
:3-floor(log10(relerr))
else glob_good_digits:16)
else (relerr:-1.0,
glob_good_digits:-16),
if abs(numeric_val) > glob_prec
then (
est_rel_err
:array_max_est_error[1]
*100.0*sqrt(glob_iter)*16
*MAX_TERMS
/abs(numeric_val),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits
:16)
else (relerr:-1.0,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
array_good_digits[1]
:glob_good_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
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,
" ")))),0)
(%i219) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
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:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
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,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:total_clock_sec+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
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 percent_done < 100.0
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)),
omniout_str_noeol(INFO,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(INFO,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i220) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[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],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),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:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-3 and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
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:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-4 and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
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:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-7 and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< 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*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(ALWAYS,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:1.0,
while term <= MAX_TERMS do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i221) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_y[1]*array_y[1],
array_tmp2[1]:array_tmp1[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= MAX_TERMS
then (
temporary
:array_tmp2[1]*expt(glob_h,1)
*factorial_3(0,1),
if 2 <= MAX_TERMS
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:temporary*1.0/glob_h,
array_y_higher[2,1]:temporary,0)),kkk:2,
array_tmp1[2]:ats(2,array_y,array_y,1),
array_tmp2[2]:array_tmp1[2],
if not array_y_set_initial[1,3]
then (if 2 <= MAX_TERMS
then (
temporary
:array_tmp2[2]*expt(glob_h,1)
*factorial_3(1,2),
if 3 <= MAX_TERMS
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:temporary*2.0/glob_h,
array_y_higher[2,2]:temporary,0)),kkk:3,
array_tmp1[3]:ats(3,array_y,array_y,1),
array_tmp2[3]:array_tmp1[3],
if not array_y_set_initial[1,4]
then (if 3 <= MAX_TERMS
then (
temporary
:array_tmp2[3]*expt(glob_h,1)
*factorial_3(2,3),
if 4 <= MAX_TERMS
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:temporary*3.0/glob_h,
array_y_higher[2,3]:temporary,0)),kkk:4,
array_tmp1[4]:ats(4,array_y,array_y,1),
array_tmp2[4]:array_tmp1[4],
if not array_y_set_initial[1,5]
then (if 4 <= MAX_TERMS
then (
temporary
:array_tmp2[4]*expt(glob_h,1)
*factorial_3(3,4),
if 5 <= MAX_TERMS
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:temporary*4.0/glob_h,
array_y_higher[2,4]:temporary,0)),kkk:5,
array_tmp1[5]:ats(5,array_y,array_y,1),
array_tmp2[5]:array_tmp1[5],
if not array_y_set_initial[1,6]
then (if 5 <= MAX_TERMS
then (
temporary
:array_tmp2[5]*expt(glob_h,1)
*factorial_3(4,5),
if 6 <= MAX_TERMS
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:temporary*5.0/glob_h,
array_y_higher[2,5]:temporary,0)),kkk:6,
while kkk <= MAX_TERMS do
(array_tmp1[kkk]:ats(kkk,array_y,array_y,1),
array_tmp2[kkk]:array_tmp1[kkk],order_d:1,
if order_d+kkk <= MAX_TERMS
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:array_tmp2[kkk]*expt(glob_h,order_d)
*factorial_3(kkk-1,
-1+order_d
+kkk),
array_y[order_d+kkk]:temporary,
array_y_higher[1,order_d+kkk]:temporary,
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= MAX_TERMS
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:temporary*adj2/glob_h
else temporary:temporary,
array_y_higher[adj3,term]
:temporary),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i222) exact_soln_y(x):=block(2.0/(1.0-2.0*x))
2.0
(%o222) exact_soln_y(x) := block(-----------)
1.0 - 2.0 x
(%i223) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:20,
glob_html_log:true,term:1,
while term <= MAX_TERMS do
(array_y_init[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_norms[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_fact_1[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_1st_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_est_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:0.0,term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 2 do (array_good_digits[term]:0,term:1+term),
term:1,
while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do
(array_tmp0[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp2[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher[ord,term]:0.0,term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work2[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_set_initial[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= MAX_TERMS do
(term:1,
while term <= MAX_TERMS do
(array_fact_2[ord,term]:0.0,term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:1,
zero_ats_ar(array_const_0D0),array_const_0D0[1]:0.0,
zero_ats_ar(array_m1),array_m1[1]:-1.0,iiif:0,
while iiif <= MAX_TERMS do
(jjjf:0,
while jjjf <= MAX_TERMS do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,ALWAYS:1,INFO:2,DEBUGL:3,
DEBUGMASSIVE:4,MAX_TERMS:20,glob_iolevel:INFO,
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/nonlinear2postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = y * y ; "),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"Digits:32,"),
omniout_str(ALWAYS,"max_terms:20,"),omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,"x_start:0.0,"),
omniout_str(ALWAYS,"x_end:0.2,"),
omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,""),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:1,"),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"array_given_rad_poles[1,1]:0.5,"),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"array_given_rad_poles[1,2]:0.0,"),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"array_given_ord_poles[1,1]:0.0,"),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"array_given_ord_poles[1,2]:0.0,"),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"glob_desired_digits_correct:16,"),
omniout_str(ALWAYS,"glob_max_minutes:3.0,"),
omniout_str(ALWAYS,"glob_subiter_method:3,"),
omniout_str(ALWAYS,"glob_max_iter:100000000,"),
omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS,"exact_soln_y (x) := (block("),
omniout_str(ALWAYS," (2.0/(1.0 - 2.0*x)) "),
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:0.0,glob_smallish_float:0.0,
glob_large_float:1.0E+100,glob_larger_float:1.1E+100,
glob_almost_1:0.99,x_start:0.0,x_end:0.2,
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:1,
array_given_rad_poles[1,1]:0.5,
array_given_rad_poles[1,2]:0.0,
array_given_ord_poles[1,1]:0.0,
array_given_ord_poles[1,2]:0.0,
glob_desired_digits_correct:16,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000000,
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
omniout_str(ALWAYS,"START of Optimize"),
glob_check_sign:my_check_sign(x_start,x_end),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:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval:abs(glob_display_interval)
*glob_check_sign,
display_max:(x_end-x_start)/10.0,
if glob_display_interval > display_max
then glob_display_interval:display_max,chk_data(),
min_value:glob_larger_float,est_answer:est_size_answer(),
opt_iter:1,glob_prec:expt(10.0,-16),
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]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,order_diff:1,term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]*expt(glob_h,term_no-1)
/factorial_1(term_no-1),term_no:1+term_no),
rows:order_diff,r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),r_order:1+r_order),
atomall(),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(ALWAYS,"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true),
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),
if glob_look_poles
then (check_for_pole(),
if opt_iter > 2 and not found_h
and (glob_min_pole_est
< 0.999*last_min_pole_est
or glob_min_pole_est
> 1.111
*last_min_pole_est)
then (
omniout_str(ALWAYS,
"SETTING H FOR POLE ACCURACY"),
glob_h_reason:4,found_h:true,
glob_h:glob_h/2.0,
last_min_pole_est:glob_min_pole_est)
else last_min_pole_est
:glob_min_pole_est),
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*2.0)
else (
omniout_str(ALWAYS,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/2.0)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(ALWAYS,"Beginning glob_h too large."),
found_h:false),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(ALWAYS,"START of Soultion"),
array_x[1]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),
r_order:1+r_order),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")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),
term_no:MAX_TERMS,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(ALWAYS,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(INFO,
"diff ( y , x , 1 ) = y * y ; "),
omniout_int(INFO,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2014-09-23T02:00:55-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"nonlinear2"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = y * y ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
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]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if array_good_digits[1] # -16
then (
logitem_integer(html_log_file,
array_good_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_integer(html_log_file,
MAX_TERMS),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if glob_percent_done < 100.0
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 269 | "),
logitem_str(html_log_file,
"nonlinear2 diffeq.max"),
logitem_str(html_log_file,
"nonlinear2 maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i224) main():=(alias(convfloat,convfloat),compile(all),main_prog())
(%i225) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable fixnum in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable good_digits in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable array_good_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: encountered undefined variable INFO in translation.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ALWAYS in translation.
warning: variable x_start (declared type [found_h]) assigned type convfloat.
warning: variable x_end (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable x_start in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable glob_display_interval (declared type convfloat) assigned type [found_h].
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: variable glob_prec (declared type convfloat) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type [found_h].
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable last_min_pole_est in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable DEBUGL in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
Warning: modedcclare has a function or macro call which has not been translated properly.
The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################"
"##############temp/nonlinear2postode.ode#################"
"diff ( y , x , 1 ) = y * y ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:20,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
""
""
""
""
""
"x_start:0.0,"
"x_end:0.2,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:1,"
""
"array_given_rad_poles[1,1]:0.5,"
""
"array_given_rad_poles[1,2]:0.0,"
""
"array_given_ord_poles[1,1]:0.0,"
""
"array_given_ord_poles[1,2]:0.0,"
""
""
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:16,"
"glob_max_minutes:3.0,"
"glob_subiter_method:3,"
"glob_max_iter:100000000,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (2.0/(1.0 - 2.0*x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000000000E-16 ""
range = 0.2 ""
estimated_steps = 200000. ""
step_error = 1.11803398874989510000000000000000000E-20 ""
est_needed_step_err = 1.11803398874989510000000000000000000E-20 ""
opt_iter = 1
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 200000. ""
step_error = 2.2360679774997902000000000000000000E-20 ""
est_needed_step_err = 2.2360679774997902000000000000000000E-20 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.31072131072131100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-91 ""
estimated_step_error = 1.31072131072131100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-91 ""
"Double H and LOOP"
opt_iter = 2
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 2.000000E-6 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 100000. ""
step_error = 3.16227766016837940000000000000000000E-20 ""
est_needed_step_err = 3.16227766016837940000000000000000000E-20 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 8.589951771903542000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 ""
estimated_step_error = 8.589951771903542000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 ""
"Double H and LOOP"
opt_iter = 3
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 4.000000E-6 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 50000. ""
step_error = 4.4721359549995804000000000000000000E-20 ""
est_needed_step_err = 4.4721359549995804000000000000000000E-20 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.6295220523013280000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
estimated_step_error = 5.6295220523013280000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
"Double H and LOOP"
opt_iter = 4
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 8.000000E-6 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 25000. ""
step_error = 6.32455532033675900000000000000000000E-20 ""
est_needed_step_err = 6.32455532033675900000000000000000000E-20 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.689378329768547300000000000000000000000000000000000000000000000000000000000000000000000000000E-77 ""
estimated_step_error = 3.689378329768547300000000000000000000000000000000000000000000000000000000000000000000000000000E-77 ""
"Double H and LOOP"
opt_iter = 5
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.600000E-5 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 12500. ""
step_error = 8.9442719099991610000000000000000000E-20 ""
est_needed_step_err = 8.9442719099991610000000000000000000E-20 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.417890325474465800000000000000000000000000000000000000000000000000000000000000000000000E-72 ""
estimated_step_error = 2.417890325474465800000000000000000000000000000000000000000000000000000000000000000000000E-72 ""
"Double H and LOOP"
opt_iter = 6
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 3.200000E-5 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 6250. ""
step_error = 1.26491106406735170000000000000000000E-19 ""
est_needed_step_err = 1.26491106406735170000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.58461395793194070000000000000000000000000000000000000000000000000000000000000000000E-67 ""
estimated_step_error = 1.58461395793194070000000000000000000000000000000000000000000000000000000000000000000E-67 ""
"Double H and LOOP"
opt_iter = 7
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 6.400000E-5 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 3125. ""
step_error = 1.7888543819998320000000000000000000E-19 ""
est_needed_step_err = 1.7888543819998320000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.038525837360556500000000000000000000000000000000000000000000000000000000000000E-62 ""
estimated_step_error = 1.038525837360556500000000000000000000000000000000000000000000000000000000000000E-62 ""
"Double H and LOOP"
opt_iter = 8
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.280000E-4 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 1562.5 ""
step_error = 2.52982212813470330000000000000000000E-19 ""
est_needed_step_err = 2.52982212813470330000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.8065185727960850000000000000000000000000000000000000000000000000000000000E-58 ""
estimated_step_error = 6.8065185727960850000000000000000000000000000000000000000000000000000000000E-58 ""
"Double H and LOOP"
opt_iter = 9
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 2.560000E-4 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 781.25 ""
step_error = 3.5777087639996640000000000000000000E-19 ""
est_needed_step_err = 3.5777087639996640000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.46129113023544500000000000000000000000000000000000000000000000000000E-53 ""
estimated_step_error = 4.46129113023544500000000000000000000000000000000000000000000000000000E-53 ""
"Double H and LOOP"
opt_iter = 10
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 5.120000E-4 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 390.625 ""
step_error = 5.0596442562694070000000000000000000E-19 ""
est_needed_step_err = 5.0596442562694070000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.9245006189785216000000000000000000000000000000000000000000000000E-48 ""
estimated_step_error = 2.9245006189785216000000000000000000000000000000000000000000000000E-48 ""
"Double H and LOOP"
opt_iter = 11
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.024000E-3 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 195.3125 ""
step_error = 7.1554175279993280000000000000000000E-19 ""
est_needed_step_err = 7.1554175279993280000000000000000000E-19 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.9175830311041050000000000000000000000000000000000000000000E-43 ""
estimated_step_error = 1.9175830311041050000000000000000000000000000000000000000000E-43 ""
"Double H and LOOP"
opt_iter = 12
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 2.048000E-3 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 97.65625 ""
step_error = 1.0119288512538814000000000000000000E-18 ""
est_needed_step_err = 1.0119288512538814000000000000000000E-18 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.257996724346712700000000000000000000000000000000000000E-38 ""
estimated_step_error = 1.257996724346712700000000000000000000000000000000000000E-38 ""
"Double H and LOOP"
opt_iter = 13
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 4.096000E-3 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 48.828125 ""
step_error = 1.4310835055998658000000000000000000E-18 ""
est_needed_step_err = 1.4310835055998658000000000000000000E-18 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 8.2613613202579630000000000000000000000000000000000E-34 ""
estimated_step_error = 8.2613613202579630000000000000000000000000000000000E-34 ""
"Double H and LOOP"
opt_iter = 14
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 8.192000E-3 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 24.4140625 ""
step_error = 2.0238577025077628000000000000000000E-18 ""
est_needed_step_err = 2.0238577025077628000000000000000000E-18 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.43652532460593800000000000000000000000000000E-29 ""
estimated_step_error = 5.43652532460593800000000000000000000000000000E-29 ""
"Double H and LOOP"
opt_iter = 15
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4999999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000043 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 2. ""
glob_desired_digits_correct = 16. ""
estimated_h = 1.638400E-2 ""
estimated_answer = 2. ""
desired_abs_gbl_error = 1.9999999999999998E-16 ""
range = 0.2 ""
estimated_steps = 12.20703125 ""
step_error = 2.8621670111997316000000000000000000E-18 ""
est_needed_step_err = 2.8621670111997316000000000000000000E-18 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.592554284321596000000000000000000000000E-24 ""
estimated_step_error = 3.592554284321596000000000000000000000000E-24 ""
"Double H and LOOP"
opt_iter = 16
"SETTING H FOR DISPLAY INTERVAL"
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.30517578125 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.3051757812500028 " "
Order of pole (three term test) = 1.0000000000001306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (closed_form) = 2. " "
y[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 16
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.5 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.5 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.5000000000000026 " "
Order of pole (three term test) = 1.0000000000000737 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000000000000000400E-2 " "
y[1] (closed_form) = 2.0833333333333335 " "
y[1] (numeric) = 2.0833333333333335 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 16
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.48 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.48 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.48000000000000065 " "
Order of pole (three term test) = 1.0000000000000215 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000000100E-2 " "
y[1] (closed_form) = 2.173913043478261 " "
y[1] (numeric) = 2.173913043478261 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 16
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.45999999999999996 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.45999999999999985 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.46000000000000507 " "
Order of pole (three term test) = 1.000000000000103 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.00000000000000100E-2 " "
y[1] (closed_form) = 2.272727272727273 " "
y[1] (numeric) = 2.272727272727273 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 16
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.44 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4399999999999997 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.44000000000000367 " "
Order of pole (three term test) = 1.0000000000001337 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000000200E-2 " "
y[1] (closed_form) = 2.380952380952381 " "
y[1] (numeric) = 2.3809523809523814 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.86517468137026300000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.42 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.4199999999999998 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.42000000000000065 " "
Order of pole (three term test) = 1.0000000000000426 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000002 " "
y[1] (closed_form) = 2.5 " "
y[1] (numeric) = 2.5000000000000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.776356839400250500000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.39999999999999997 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.39999999999999986 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.4000000000000021 " "
Order of pole (three term test) = 1.0000000000001055 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = 2.6315789473684212 " "
y[1] (numeric) = 2.6315789473684217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.687538997430237700000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.38 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.37999999999999984 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.3800000000000006 " "
Order of pole (three term test) = 0.999999999999991 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (closed_form) = 2.7777777777777777 " "
y[1] (numeric) = 2.7777777777777786 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.19744231092045100000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.36 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.36 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.3600000000000016 " "
Order of pole (three term test) = 1.0000000000000884 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (closed_form) = 2.9411764705882355 " "
y[1] (numeric) = 2.9411764705882364 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.01980662698042600000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 15
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.33999999999999997 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.3399999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.3399999999999981 " "
Order of pole (three term test) = 0.9999999999998942 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (closed_form) = 3.1250000000000004 " "
y[1] (numeric) = 3.1250000000000013 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.842170943040400000000000000000E-14 "%"
Desired digits = 16
Estimated correct digits = 14
Correct digits = 17
h = 2.000000000000000400E-2 " "
Radius of convergence (given) for eq 1 = 0.31999999999999995 " "
Order of pole (given) = 0.0 " "
Radius of convergence (ratio test) for eq 1 = 0.3199999999999999 " "
Order of pole (ratio test) = 1. " "
Radius of convergence (three term test) for eq 1 = 0.31999999999999645 " "
Order of pole (three term test) = 0.9999999999998778 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 1 ) = y * y ; "
Iterations = 10
"Total Elapsed Time "= 0 Seconds
"Elapsed Time(since restart) "= 0 Seconds
"Time to Timeout "= 2 Minutes 59 Seconds
Percent Done = 110.00000000000003 "%"
(%o225) temp/diffeq.nonlinear2.max