(%i1) batch("diffeq.max")
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load("stringproc")
(%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac
(%i3) alias(convfloat,float)
(%o3) [convfloat]
(%i4) alias(int_trunc,truncate)
(%o4) [truncate]
(%i5) alias(elapsed_time_seconds,elapsed_real_time)
(%o5) [elapsed_time_seconds]
(%i6) alias(ln,log)
(%o6) [log]
(%i7) alias(arcsin,asin)
(%o7) [asin]
(%i8) alias(arccos,acos)
(%o8) [acos]
(%i9) alias(arctan,atan)
(%o9) [atan]
(%i10) alias(float_abs,abs)
(%o10) [mabs]
(%i11) keepfloat:true
(%o11) true
(%i12) mode_declare(display_poles(),fixnum)
(%o12) [display_poles()]
(%i13) mode_declare(est_size_answer(),convfloat)
(%o13) [est_size_answer()]
(%i14) mode_declare(test_suggested_h(),convfloat)
(%o14) [test_suggested_h()]
(%i15) mode_declare(reached_interval(),boolean)
(%o15) [reached_interval()]
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%o16) [display_alot([iter], fixnum)]
(%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat)
(%o17) [adjust_for_pole([h_param], convfloat)]
(%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%o18) [prog_report([x_start], convfloat, [x_end], convfloat)]
(%i19) mode_declare(check_for_pole(),fixnum)
(%o19) [check_for_pole()]
(%i20) mode_declare(atomall(),fixnum)
(%o20) [atomall()]
(%i21) mode_declare(log10([x],convfloat),convfloat)
(%o21) [log10([x], convfloat)]
(%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%o22) [logitem_timestr([fd], fixnum, [secs_in], number)]
(%i23) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%o23) [omniout_timestr(secs_in, number)]
(%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum)
(%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))]
(%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_ats],
fixnum),convfloat)
(%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)]
(%i26) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_att],
fixnum),convfloat)
(%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)]
(%i27) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%o27) [logitem_ditto([file], fixnum)]
(%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%o28) [logitem_integer([file], fixnum, [n], fixnum)]
(%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)]
(%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%o30) [logitem_number([file], fixnum, [x], number)]
(%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%o31) [logitem_pole([file], fixnum, [pole], fixnum)]
(%i32) mode_declare(logstart([file],fixnum),fixnum)
(%o32) [logstart([file], fixnum)]
(%i33) mode_declare(logend([file],fixnum),fixnum)
(%o33) [logend([file], fixnum)]
(%i34) mode_declare(chk_data(),fixnum)
(%o34) [chk_data()]
(%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2],
convfloat, [clock_sec2], convfloat)]
(%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2],
convfloat)]
(%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i43) mode_declare(factorial_2([nnn],fixnum),fixnum)
(%o43) [factorial_2([nnn], fixnum)]
(%i44) mode_declare(factorial_1([nnn],fixnum),fixnum)
(%o44) [factorial_1([nnn], fixnum)]
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum)
(%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)]
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%o46) [convfloat([mmm], fixnum)]
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%o47) [elaped_time_seconds()]
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%o48) [Si([x], convfloat)]
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%o49) [Ci([x], convfloat)]
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat,
[estimated_h], convfloat, [estimated_answer], convfloat)]
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%o51) [my_check_sign([x0], convfloat, [xf], convfloat)]
(%i52) mode_declare(main_prog(),fixnum)
(%o52) [main_prog()]
(%i53) define_variable(MAX_TERMS,30,fixnum)
(%o53) 30
(%i54) define_variable(glob_iolevel,5,fixnum)
(%o54) 5
(%i55) define_variable(glob_yes_pole,4,fixnum)
(%o55) 4
(%i56) define_variable(glob_no_pole,3,fixnum)
(%o56) 3
(%i57) define_variable(glob_not_given,0,fixnum)
(%o57) 0
(%i58) define_variable(glob_no_sing_tests,4,fixnum)
(%o58) 4
(%i59) define_variable(glob_ratio_test,1,fixnum)
(%o59) 1
(%i60) define_variable(glob_three_term_test,2,fixnum)
(%o60) 2
(%i61) define_variable(glob_six_term_test,3,fixnum)
(%o61) 3
(%i62) define_variable(glob_log_10,log(10.0),convfloat)
(%o62) 2.302585092994046
(%i63) define_variable(ALWAYS,1,fixnum)
(%o63) 1
(%i64) define_variable(INFO,2,fixnum)
(%o64) 2
(%i65) define_variable(DEBUGL,3,fixnum)
(%o65) 3
(%i66) define_variable(DEBUGMASSIVE,4,fixnum)
(%o66) 4
(%i67) define_variable(MAX_UNCHANGED,10,fixnum)
(%o67) 10
(%i68) define_variable(glob_check_sign,1.0,convfloat)
(%o68) 1.0
(%i69) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%o69) 8.0
(%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%o70) 0.0
(%i71) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%o71) 0.1
(%i72) define_variable(glob_percent_done,0.0,convfloat)
(%o72) 0.0
(%i73) define_variable(glob_subiter_method,3,fixnum)
(%o73) 3
(%i74) define_variable(glob_total_exp_sec,0.1,convfloat)
(%o74) 0.1
(%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%o75) 0.1
(%i76) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%o76) 100.0
(%i77) define_variable(glob_html_log,true,boolean)
(%o77) true
(%i78) define_variable(glob_good_digits,0,fixnum)
(%o78) 0
(%i79) define_variable(glob_max_opt_iter,10,fixnum)
(%o79) 10
(%i80) define_variable(glob_dump,false,boolean)
(%o80) false
(%i81) define_variable(glob_djd_debug,true,boolean)
(%o81) true
(%i82) define_variable(glob_display_flag,true,boolean)
(%o82) true
(%i83) define_variable(glob_djd_debug2,true,boolean)
(%o83) true
(%i84) define_variable(glob_sec_in_minute,60,fixnum)
(%o84) 60
(%i85) define_variable(glob_min_in_hour,60.0,convfloat)
(%o85) 60.0
(%i86) define_variable(glob_hours_in_day,24.0,convfloat)
(%o86) 24.0
(%i87) define_variable(glob_days_in_year,365,fixnum)
(%o87) 365
(%i88) define_variable(glob_sec_in_hour,3600,fixnum)
(%o88) 3600
(%i89) define_variable(glob_sec_in_day,86400,fixnum)
(%o89) 86400
(%i90) define_variable(glob_sec_in_year,31536000,fixnum)
(%o90) 31536000
(%i91) define_variable(glob_almost_1,0.999,convfloat)
(%o91) 0.999
(%i92) define_variable(glob_clock_sec,0.0,convfloat)
(%o92) 0.0
(%i93) define_variable(glob_clock_start_sec,0.0,convfloat)
(%o93) 0.0
(%i94) define_variable(glob_not_yet_finished,true,boolean)
(%o94) true
(%i95) define_variable(glob_initial_pass,true,boolean)
(%o95) true
(%i96) define_variable(glob_not_yet_start_msg,true,boolean)
(%o96) true
(%i97) define_variable(glob_reached_optimal_h,false,boolean)
(%o97) false
(%i98) define_variable(glob_optimal_done,false,boolean)
(%o98) false
(%i99) define_variable(glob_disp_incr,0.1,convfloat)
(%o99) 0.1
(%i100) define_variable(glob_h,0.1,convfloat)
(%o100) 0.1
(%i101) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%o101) 0.1
(%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%o102) 0.1
(%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%o103) 0.1
(%i104) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%o104) 0.1
(%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%o105) 0.1
(%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%o106) 0.1
(%i107) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%o107) 0.1
(%i108) define_variable(glob_guess_error_rc,0.1,convfloat)
(%o108) 0.1
(%i109) define_variable(glob_guess_error_ord,0.1,convfloat)
(%o109) 0.1
(%i110) define_variable(glob_max_h,0.1,convfloat)
(%o110) 0.1
(%i111) define_variable(glob_min_h,1.0E-6,convfloat)
(%o111) 1.0E-6
(%i112) define_variable(glob_type_given_pole,0,fixnum)
(%o112) 0
(%i113) define_variable(glob_large_float,1.0E+100,convfloat)
(%o113) 1.0E+100
(%i114) define_variable(glob_larger_float,1.1E+100,convfloat)
(%o114) 1.1E+100
(%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat)
(%o115) 9.9E+100
(%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat)
(%o116) 9.9E+100
(%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%o117) 9.9E+100
(%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%o118) 9.9E+100
(%i119) define_variable(glob_last_good_h,0.1,convfloat)
(%o119) 0.1
(%i120) define_variable(glob_look_poles,false,boolean)
(%o120) false
(%i121) define_variable(glob_neg_h,false,boolean)
(%o121) false
(%i122) define_variable(glob_display_interval,0.0,convfloat)
(%o122) 0.0
(%i123) define_variable(glob_next_display,0.0,convfloat)
(%o123) 0.0
(%i124) define_variable(glob_dump_analytic,false,boolean)
(%o124) false
(%i125) define_variable(glob_abserr,1.0E-11,convfloat)
(%o125) 1.0E-11
(%i126) define_variable(glob_relerr,1.0E-11,convfloat)
(%o126) 1.0E-11
(%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%o127) 1.0E+9
(%i128) define_variable(glob_max_hours,0.0,convfloat)
(%o128) 0.0
(%i129) define_variable(glob_max_iter,1000,fixnum)
(%o129) 1000
(%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%o130) 1.0E-11
(%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%o131) 1.0E-11
(%i132) define_variable(glob_no_eqs,0,fixnum)
(%o132) 0
(%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%o133) 0.0
(%i134) define_variable(glob_optimal_start,0.0,convfloat)
(%o134) 0.0
(%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%o135) 1.0001
(%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%o136) 0.9999
(%i137) define_variable(glob_small_float,0.0,convfloat)
(%o137) 0.0
(%i138) define_variable(glob_smallish_float,0.0,convfloat)
(%o138) 0.0
(%i139) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%o139) 0
(%i140) define_variable(glob_warned,false,boolean)
(%o140) false
(%i141) define_variable(glob_warned2,false,boolean)
(%o141) false
(%i142) define_variable(glob_max_sec,10000.0,convfloat)
(%o142) 10000.0
(%i143) define_variable(glob_orig_start_sec,0.0,convfloat)
(%o143) 0.0
(%i144) define_variable(glob_start,0,fixnum)
(%o144) 0
(%i145) define_variable(glob_curr_iter_when_opt,0,fixnum)
(%o145) 0
(%i146) define_variable(glob_current_iter,0,fixnum)
(%o146) 0
(%i147) define_variable(glob_iter,0,fixnum)
(%o147) 0
(%i148) define_variable(glob_normmax,0.0,convfloat)
(%o148) 0.0
(%i149) define_variable(glob_max_minutes,0.0,convfloat)
(%o149) 0.0
(%i150) array(array_y_init,MAX_TERMS)
(%o150) array_y_init
(%i151) array(array_norms,MAX_TERMS)
(%o151) array_norms
(%i152) array(array_fact_1,MAX_TERMS)
(%o152) array_fact_1
(%i153) array(array_1st_rel_error,2)
(%o153) array_1st_rel_error
(%i154) array(array_last_rel_error,2)
(%o154) array_last_rel_error
(%i155) array(array_type_pole,2)
(%o155) array_type_pole
(%i156) array(array_type_real_pole,2)
(%o156) array_type_real_pole
(%i157) array(array_type_complex_pole,2)
(%o157) array_type_complex_pole
(%i158) array(array_y,MAX_TERMS)
(%o158) array_y
(%i159) array(array_x,MAX_TERMS)
(%o159) array_x
(%i160) array(array_tmp0,MAX_TERMS)
(%o160) array_tmp0
(%i161) array(array_tmp1,MAX_TERMS)
(%o161) array_tmp1
(%i162) array(array_tmp2,MAX_TERMS)
(%o162) array_tmp2
(%i163) array(array_tmp3,MAX_TERMS)
(%o163) array_tmp3
(%i164) array(array_tmp4_a1,MAX_TERMS)
(%o164) array_tmp4_a1
(%i165) array(array_tmp4_a2,MAX_TERMS)
(%o165) array_tmp4_a2
(%i166) array(array_tmp4,MAX_TERMS)
(%o166) array_tmp4
(%i167) array(array_tmp5,MAX_TERMS)
(%o167) array_tmp5
(%i168) array(array_m1,MAX_TERMS)
(%o168) array_m1
(%i169) array(array_y_higher,2,MAX_TERMS)
(%o169) array_y_higher
(%i170) array(array_y_higher_work,2,MAX_TERMS)
(%o170) array_y_higher_work
(%i171) array(array_y_higher_work2,2,MAX_TERMS)
(%o171) array_y_higher_work2
(%i172) array(array_y_set_initial,2,MAX_TERMS)
(%o172) array_y_set_initial
(%i173) array(array_given_rad_poles,2,3)
(%o173) array_given_rad_poles
(%i174) array(array_given_ord_poles,2,3)
(%o174) array_given_ord_poles
(%i175) array(array_rad_test_poles,2,3)
(%o175) array_rad_test_poles
(%i176) array(array_ord_test_poles,2,3)
(%o176) array_ord_test_poles
(%i177) array(array_fact_2,MAX_TERMS,MAX_TERMS)
(%o177) array_fact_2
(%i178) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%o178) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i179) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%o179) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i180) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%o180) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i181) 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))
(%o181) 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))
(%i182) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%o182) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i183) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%o183) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i184) 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)
(%o184) 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, "~%"),
secs
if secs >= 0 then (years_int : truncate(----------------),
glob_sec_in_year
sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)),
sec_temp
days_int : truncate(---------------), sec_temp :
glob_sec_in_day
mod(sec_temp, truncate(glob_sec_in_day)),
sec_temp
hours_int : truncate(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)),
sec_temp
minutes_int : truncate(------------------),
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)
(%i185) 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)
(%o185) omniout_timestr(secs_in) := (block(mode_declare([[days_int, hours_int,
minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]),
secs
secs : secs_in, if secs >= 0 then (years_int : truncate(----------------),
glob_sec_in_year
sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)),
sec_temp
days_int : truncate(---------------), sec_temp :
glob_sec_in_day
mod(sec_temp, truncate(glob_sec_in_day)),
sec_temp
hours_int : truncate(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)),
sec_temp
minutes_int : truncate(------------------),
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)
(%i186) 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)
(%o186) zero_ats_ar(arr_a) := (block(modedcclare([iii], fixnum), iii : 1,
while iii <= MAX_TERMS do (arr_a : 0.0, iii : 1 + iii)), 0)
iii
(%i187) 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)
(%o187) 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 arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i188) 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)
(%o188) 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 arr_bb al_att + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : -------), ret_att)
mmm_att
(%i189) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%o189) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "), 0)
(%i190) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%o190) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "), 0)
(%i191) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%o191) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "), 0)
(%i192) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
if rel_error # -1.0
then (if rel_error > +1.0E-34
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)
(%o192) logitem_good_digits(file, rel_error) :=
(block(mode_declare([[good_digits], fixnum]), printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
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)
(%i193) log_revs(file,revs):=printf(file,revs)
(%o193) log_revs(file, revs) := printf(file, revs)
(%i194) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%o194) logitem_float(file, x) := (printf(file, ""),
printf(file, "~g", x), printf(file, " | "), 0)
(%i195) logitem_pole(file,pole):=(printf(file,""),
if pole = 0 then printf(file,"NA") elseif pole = 1
then printf(file,"Real") elseif pole = 2
then printf(file,"Complex") elseif pole = 4
then printf(file,"Yes") else printf(file,"No"),
printf(file," | "),0)
(%o195) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") elseif pole = 4
then printf(file, "Yes") else printf(file, "No"), printf(file, " | "), 0)
(%i196) logstart(file):=(printf(file,""),0)
(%o196) logstart(file) := (printf(file, "
"), 0)
(%i197) logend(file):=(printf(file,"
~%"),0)
(%o197) logend(file) := (printf(file, "~%"), 0)
(%i198) 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)
(%o198) 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)
(%i199) 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)
(%o199) 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
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i200) 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)
(%o200) comp_percent(t_end2, t_start2, t2) :=
block(mode_declare([[rrr, sub1, sub2], convfloat]), sub1 : t_end2 - t_start2,
100.0 sub2
sub2 : t2 - t_start2, if sub2 > glob_small_float then rrr : ----------
sub1
else rrr : 0.0, rrr)
(%i201) 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)
(%o201) comp_rad_from_ratio(term1, term2, last_no) :=
!term1 glob_h!
(if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret)
! term2 !
(%i202) 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)
(%o202) comp_ord_from_ratio(term1, term2, last_no) :=
!term1 glob_h!
mabs(term2) convfloat(last_no) log(!------------!)
! term2 !
(if term2 > 0.0 then ret : --------------------------------------------------
log(convfloat(last_no))
+ 1.0 else ret : glob_larger_float, ret)
(%i203) 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)
(%o203) comp_rad_from_three_terms(term1, term2, term3, last_no) :=
(temp : mabs(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2
+ term2 term2 convfloat(last_no)), if temp > 0.0
!term2 glob_h term1!
then ret : !------------------! else ret : glob_larger_float, ret)
! temp !
(%i204) 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)
(%o204) comp_ord_from_three_terms(term1, term2, term3, last_no) :=
(ret : mabs((- 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)
(%i205) 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)
(%o205) 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)
term6 term5
and (term2 # 0.0) and (term1 # 0.0) then (rm0 : -----, rm1 : -----,
term5 term4
term4 term3 term2
rm2 : -----, rm3 : -----, rm4 : -----,
term3 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,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (mabs(nr1 dr2 - nr2 dr1) = 0.0) or (mabs(dr1) = 0.0)
rm4 rm3 rm2
then (rad_c : glob_larger_float, ord_no : glob_larger_float)
else (if mabs(nr1 dr2 - nr2 dr1) # 0.0
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(last_no)
ord_no : ------------- - ------------------,
2.0 dr1 2.0
if mabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) mabs(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)
(%i206) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%o206) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6,
last_no) := glob_six_term_ord_save
(%i207) factorial_2(nnn):=nnn!
(%o207) factorial_2(nnn) := nnn!
(%i208) 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)
(%o208) factorial_1(nnn) := block(mode_declare([[ret], convfloat]),
if nnn <= MAX_TERMS then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i209) 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)
(%o209) factorial_3(mmm, nnn) := block(mode_declare([[ret], convfloat]),
if (nnn <= MAX_TERMS) and (mmm <= MAX_TERMS)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i210) log10(x):=log(x)/glob_log_10
log(x)
(%o210) log10(x) := -----------
glob_log_10
(%i211) expt(x,y):=(if x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y),x^y)
(%o211) expt(x, y) := (if (x <= 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i212) 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/estimated_steps),
omniout_float(ALWAYS,"step_error",32,
step_error,32,""),
step_error)
(%o212) 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) mabs(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,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
!desired_abs_gbl_error!
32, estimated_steps, 32, ""), step_error : !---------------------!,
! estimated_steps !
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i213) exact_soln_y(x):=block(
10.0*atan(sqrt(0.2+0.1*x))-10.0*sqrt(0.2+0.1*x)
+10.0*(0.2+0.1*x)
*atan(sqrt(0.2+0.1*x)))
(%o213) exact_soln_y(x) := block(10.0 atan(sqrt(0.2 + 0.1 x))
- 10.0 sqrt(0.2 + 0.1 x) + 10.0 (0.2 + 0.1 x) atan(sqrt(0.2 + 0.1 x)))
(%i214) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 4
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])),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given,
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," "))
elseif glob_type_given_pole = 3
then omniout_str(ALWAYS,
"NO 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)
(%o214) display_poles() := (block(mode_declare([[rad_given], convfloat]),
if glob_type_given_pole = 4 then (rad_given :
sqrt(array_given_rad_poles array_given_rad_poles
1, 2 1, 2
+ (array_x - array_given_rad_poles )
1 1, 1
(array_x - array_given_rad_poles )),
1 1, 1
if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given,
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 , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\
1, 1
dius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 1 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 , 4, " ")) else omniout_str(ALWAYS,
1, 1
"NO POLE (ratio test) for Equation 1"),
if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float)
1, 2 1, 2
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 2 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 , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO REAL POLE (three term test) for Equation 1"),
if (array_rad_test_poles > 0.0) and (array_rad_test_poles <
1, 3 1, 3
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 3 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 , 4, " ")) else omniout_str(ALWAYS,
1, 3
"NO COMPLEX POLE (six term test) for Equation 1")), 0)
(%i215) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0
else ret:-1.0,ret)
(%o215) my_check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i216) 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)
(%o216) est_size_answer() := block([min_size],
min_size : glob_estimated_size_answer,
if !array_y ! < min_size then (min_size : !array_y !,
! 1! ! 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)
(%i217) 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)
(%o217) 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 : mabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 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)
(%i218) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
then ret:true else ret:false,return(ret))
(%o218) reached_interval() := block(mode_declare([[ret], boolean]),
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i219) display_alot(iter):=(
block(mode_declare(
[[abserr],convfloat,[analytic_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,
" "),
analytic_val_y
:exact_soln_y(ind_var),
omniout_float(ALWAYS,
"y[1] (analytic) ",
33,
analytic_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val-analytic_val_y),
omniout_float(ALWAYS,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if abs(analytic_val_y) # 0.0
then (
relerr
:abserr*100.0
/abs(analytic_val_y),
if relerr > 1.0E-34
then glob_good_digits
:3-floor(log10(relerr))
else glob_good_digits
:16)
else (relerr:-1.0,
glob_good_digits:-1),
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
omniout_float(ALWAYS,
"absolute error ",
4,abserr,20," "),
omniout_float(ALWAYS,
"relative error ",
4,relerr,20,"%"),
omniout_int(INFO,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(ALWAYS,
"h ",
4,glob_h,20,
" ")))),0)
(%o219) display_alot(iter) := (block(mode_declare([[abserr], convfloat,
[analytic_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 , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : mabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if mabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : --------------------, if relerr > 1.0E-34
mabs(analytic_val_y)
then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16)
else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " ")))), 0)
(%i220) adjust_for_pole(h_param):=(
block(mode_declare(
[[hnew],convfloat,[sz2],convfloat,[tmp],
convfloat]),hnew:h_param,
glob_normmax:glob_small_float,
if abs(array_y_higher[1,1]) > glob_small_float
then (tmp:abs(array_y_higher[1,1]),
if tmp < glob_normmax
then glob_normmax:tmp),
if glob_look_poles
and glob_min_pole_est > glob_small_float
and glob_min_pole_est < glob_large_float
then (sz2:glob_min_pole_est/10.0,
if sz2 < hnew
then (
omniout_float(INFO,
"glob_h adjusted to ",
20,h_param,12,
"due to singularity."),
omniout_str(INFO,
"Reached Optimal"),
return(hnew))),
if not glob_reached_optimal_h
then (glob_reached_optimal_h:true,
glob_curr_iter_when_opt
:glob_current_iter,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
glob_optimal_start:array_x[1]),
hnew:sz2),hnew)
(%o220) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat,
[sz2], convfloat, [tmp], convfloat]), hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (glob_min_pole_est > glob_small_float)
and (glob_min_pole_est < glob_large_float)
glob_min_pole_est
then (sz2 : -----------------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))),
if not glob_reached_optimal_h then (glob_reached_optimal_h : true,
glob_curr_iter_when_opt : glob_current_iter,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), hnew)
1
(%i221) 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)
(%o221) 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)
(%i222) 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),
glob_min_pole_est:glob_larger_float,
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)),
glob_min_pole_est:glob_larger_float,
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)),
glob_min_pole_est:glob_larger_float,
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,
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)
(%o222) 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), glob_min_pole_est : glob_larger_float,
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 : glob_larger_float,
1, 1
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 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 , array_y_higher ,
1, last_no - 1 1, last_no
tmp_rad
last_no), tmp_ratio : ------------, if (cnt > 0)
prev_tmp_rad
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 : rad_c, last_no : last_no - 1,
1, 1
tmp_ord : comp_ord_from_ratio(array_y_higher ,
1, last_no - 1
array_y_higher , last_no), array_rad_test_poles : rad_c,
1, last_no 1, 1
array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float,
1, 1
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 : glob_larger_float,
1, 2
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 2
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 , array_y_higher , last_no),
1, last_no - 1 1, last_no
tmp_rad
tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit)
prev_tmp_rad
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 : rad_c, last_no : last_no - 1,
1, 2
tmp_ord : comp_ord_from_three_terms(array_y_higher ,
1, last_no - 2
array_y_higher , array_y_higher , last_no),
1, last_no - 1 1, last_no
array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est
1, 2
then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)),
1, 2
glob_min_pole_est : glob_larger_float, 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 : glob_larger_float,
1, 3
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 3
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 , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
tmp_rad
array_y_higher , last_no), tmp_ratio : ------------,
1, last_no 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 : rad_c, last_no : last_no - 1,
1, 3
tmp_ord : comp_ord_from_six_terms(array_y_higher ,
1, last_no - 5
array_y_higher , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
array_y_higher , last_no), array_rad_test_poles : rad_c,
1, last_no 1, 3
if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c,
array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est)
1, 3
glob_ratio_of_radius < mabs(glob_h) then (h_new :
glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0,
while term <= MAX_TERMS do (array_y : array_y ratio,
term term
array_y_higher : array_y_higher ratio,
1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ------------, term : 1 + term),
term term mabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles()), 0)
(%i223) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D1[1]*array_x[1],
array_tmp2[1]:array_const_0D2[1]+array_tmp1[1],
array_tmp3[1]:sqrt(array_tmp2[1]),
array_tmp4[1]:atan(array_tmp3[1]),
array_tmp4_a1[1]:sin(array_tmp4[1]),
array_tmp4_a2[1]:cos(array_tmp4[1]),
array_tmp5[1]:array_tmp4[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= MAX_TERMS
then (
temporary
:array_tmp5[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]:array_const_0D1[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp2[2]/array_tmp3[1]/2.0,
array_tmp4[2]:(-att(1,array_tmp4_a2,array_tmp4,2)
-array_tmp3[1]
*att(1,array_tmp4_a1,array_tmp4,2)
+ats(2,array_tmp3,array_tmp4_a2,2))
/(array_tmp3[1]*array_tmp4_a1[1]
+array_tmp4_a2[1]),
array_tmp4_a1[2]:att(1,array_tmp4_a2,array_tmp4,1),
array_tmp4_a2[2]:-att(1,array_tmp4_a1,array_tmp4,1),
array_tmp5[2]:array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= MAX_TERMS
then (
temporary
:array_tmp5[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_tmp3[3]:0.0,
array_tmp3[3]:(-ats(3,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/2.0,
array_tmp4[3]:(-att(2,array_tmp4_a2,array_tmp4,2)
-array_tmp3[1]
*att(2,array_tmp4_a1,array_tmp4,2)
+ats(3,array_tmp3,array_tmp4_a2,2))
/(array_tmp3[1]*array_tmp4_a1[1]
+array_tmp4_a2[1]),
array_tmp4_a1[3]:att(2,array_tmp4_a2,array_tmp4,1),
array_tmp4_a2[3]:-att(2,array_tmp4_a1,array_tmp4,1),
array_tmp5[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= MAX_TERMS
then (
temporary
:array_tmp5[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_tmp3[4]:0.0,
array_tmp3[4]:(-ats(4,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/2.0,
array_tmp4[4]:(-att(3,array_tmp4_a2,array_tmp4,2)
-array_tmp3[1]
*att(3,array_tmp4_a1,array_tmp4,2)
+ats(4,array_tmp3,array_tmp4_a2,2))
/(array_tmp3[1]*array_tmp4_a1[1]
+array_tmp4_a2[1]),
array_tmp4_a1[4]:att(3,array_tmp4_a2,array_tmp4,1),
array_tmp4_a2[4]:-att(3,array_tmp4_a1,array_tmp4,1),
array_tmp5[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= MAX_TERMS
then (
temporary
:array_tmp5[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_tmp3[5]:0.0,
array_tmp3[5]:(-ats(5,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/2.0,
array_tmp4[5]:(-att(4,array_tmp4_a2,array_tmp4,2)
-array_tmp3[1]
*att(4,array_tmp4_a1,array_tmp4,2)
+ats(5,array_tmp3,array_tmp4_a2,2))
/(array_tmp3[1]*array_tmp4_a1[1]
+array_tmp4_a2[1]),
array_tmp4_a1[5]:att(4,array_tmp4_a2,array_tmp4,1),
array_tmp4_a2[5]:-att(4,array_tmp4_a1,array_tmp4,1),
array_tmp5[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= MAX_TERMS
then (
temporary
:array_tmp5[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_tmp3[kkk]:0.0,
array_tmp3[kkk]
:(-ats(kkk,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/2.0,
array_tmp4[kkk]
:(-att(kkk-1,array_tmp4_a2,array_tmp4,2)
-array_tmp3[1]
*att(kkk-1,array_tmp4_a1,array_tmp4,2)
+ats(kkk,array_tmp3,array_tmp4_a2,2))
/(array_tmp3[1]*array_tmp4_a1[1]
+array_tmp4_a2[1]),
array_tmp4_a1[kkk]
:att(kkk-1,array_tmp4_a2,array_tmp4,1),
array_tmp4_a2[kkk]
:-att(kkk-1,array_tmp4_a1,array_tmp4,1),
array_tmp5[kkk]:array_tmp4[kkk],order_d:1,
if order_d+kkk <= MAX_TERMS
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:array_tmp5[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)
(%o223) atomall() := (block(mode_declare([[kkk, order_d], fixnum,
[adj2, adj3, temporary, term, temp, temp2], convfloat]),
array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ),
1 1 1 1 1
array_tmp4 : atan(array_tmp3 ), array_tmp4_a1 : sin(array_tmp4 ),
1 1 1 1
array_tmp4_a2 : cos(array_tmp4 ), array_tmp5 :
1 1 1
array_tmp4 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= MAX_TERMS then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
-----------
array_tmp3
1
array_tmp3 : -----------, array_tmp4 :
2 2.0 2
(- att(1, array_tmp4_a2, array_tmp4, 2)
- array_tmp3 att(1, array_tmp4_a1, array_tmp4, 2)
1
+ ats(2, array_tmp3, array_tmp4_a2, 2))
/(array_tmp3 array_tmp4_a1 + array_tmp4_a2 ),
1 1 1
array_tmp4_a1 : att(1, array_tmp4_a2, array_tmp4, 1),
2
array_tmp4_a2 : - att(1, array_tmp4_a1, array_tmp4, 1),
2
array_tmp5 : array_tmp4 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= MAX_TERMS then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
- ats(3, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : 0.0, array_tmp3 : -----------------------------------,
3 3 2.0
array_tmp4 : (- att(2, array_tmp4_a2, array_tmp4, 2)
3
- array_tmp3 att(2, array_tmp4_a1, array_tmp4, 2)
1
+ ats(3, array_tmp3, array_tmp4_a2, 2))
/(array_tmp3 array_tmp4_a1 + array_tmp4_a2 ),
1 1 1
array_tmp4_a1 : att(2, array_tmp4_a2, array_tmp4, 1),
3
array_tmp4_a2 : - att(2, array_tmp4_a1, array_tmp4, 1),
3
array_tmp5 : array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= MAX_TERMS then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
- ats(4, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : 0.0, array_tmp3 : -----------------------------------,
4 4 2.0
array_tmp4 : (- att(3, array_tmp4_a2, array_tmp4, 2)
4
- array_tmp3 att(3, array_tmp4_a1, array_tmp4, 2)
1
+ ats(4, array_tmp3, array_tmp4_a2, 2))
/(array_tmp3 array_tmp4_a1 + array_tmp4_a2 ),
1 1 1
array_tmp4_a1 : att(3, array_tmp4_a2, array_tmp4, 1),
4
array_tmp4_a2 : - att(3, array_tmp4_a1, array_tmp4, 1),
4
array_tmp5 : array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= MAX_TERMS then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
- ats(5, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : 0.0, array_tmp3 : -----------------------------------,
5 5 2.0
array_tmp4 : (- att(4, array_tmp4_a2, array_tmp4, 2)
5
- array_tmp3 att(4, array_tmp4_a1, array_tmp4, 2)
1
+ ats(5, array_tmp3, array_tmp4_a2, 2))
/(array_tmp3 array_tmp4_a1 + array_tmp4_a2 ),
1 1 1
array_tmp4_a1 : att(4, array_tmp4_a2, array_tmp4, 1),
5
array_tmp4_a2 : - att(4, array_tmp4_a1, array_tmp4, 1),
5
array_tmp5 : array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= MAX_TERMS then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= MAX_TERMS do (array_tmp3 : 0.0,
kkk
- ats(kkk, array_tmp3, array_tmp3, 2)
-------------------------------------
array_tmp3
1
array_tmp3 : -------------------------------------,
kkk 2.0
array_tmp4 : (- att(kkk - 1, array_tmp4_a2, array_tmp4, 2)
kkk
- array_tmp3 att(kkk - 1, array_tmp4_a1, array_tmp4, 2)
1
+ ats(kkk, array_tmp3, array_tmp4_a2, 2))
/(array_tmp3 array_tmp4_a1 + array_tmp4_a2 ),
1 1 1
array_tmp4_a1 : att(kkk - 1, array_tmp4_a2, array_tmp4, 1),
kkk
array_tmp4_a2 : - att(kkk - 1, array_tmp4_a1, array_tmp4, 1),
kkk
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
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
temporary adj2
then (if adj2 > 0 then temporary : -------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk)), 0)
(%i224) exact_soln_y(x):=block(
10.0*atan(sqrt(0.2+0.1*x))-10.0*sqrt(0.2+0.1*x)
+10.0*(0.2+0.1*x)
*atan(sqrt(0.2+0.1*x)))
(%o224) exact_soln_y(x) := block(10.0 atan(sqrt(0.2 + 0.1 x))
- 10.0 sqrt(0.2 + 0.1 x) + 10.0 (0.2 + 0.1 x) atan(sqrt(0.2 + 0.1 x)))
(%i225) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2],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,best_h,found_h],
convfloat,[repeat_it],fixnum]),Digits:32,
max_terms:30,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_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 <= 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_tmp3[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4_a1[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4_a2[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp5[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 <= 3 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 <= 3 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_tmp3),
zero_ats_ar(array_tmp4_a1),zero_ats_ar(array_tmp4_a2),
zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5),
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_const_0D1),
array_const_0D1[1]:0.1,zero_ats_ar(array_const_0D2),
array_const_0D2[1]:0.2,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,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,ALWAYS:1,INFO:2,DEBUGL:3,
DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO,
glob_orig_start_sec:elapsed_time_seconds(),
glob_curr_iter_when_opt:0,glob_display_flag:true,
glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000,
glob_max_hours:0.0,glob_max_minutes:15.0,
omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/arctan_sqrtpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"Digits:32,"),
omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"x_start:-1.0,"),
omniout_str(ALWAYS,"x_end:0.5,"),
omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:1000000,"),
omniout_str(ALWAYS,"glob_display_interval:0.1,"),
omniout_str(ALWAYS,"glob_max_minutes:10,"),
omniout_str(ALWAYS,"glob_max_h:0.0001,"),
omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"glob_desired_digits_correct:10,"),
omniout_str(ALWAYS,"glob_display_interval:0.01,"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:1000000000,"),
omniout_str(ALWAYS,"glob_max_minutes:10.0,"),
omniout_str(ALWAYS,"glob_subiter_method:3,"),
omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS,"exact_soln_y (x) := (block("),
omniout_str(ALWAYS,
" (10.0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x +"),
omniout_str(ALWAYS,
"0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))) "),
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:-1.0,x_end:0.5,
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_max_iter:1000000,
glob_display_interval:0.1,glob_max_minutes:10,
glob_max_h:1.0E-4,glob_desired_digits_correct:10,
glob_display_interval:0.01,glob_look_poles:true,
glob_max_iter:1000000000,glob_max_minutes:10.0,
glob_subiter_method:3,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_h:glob_min_h*glob_check_sign,
if abs(glob_max_h) < abs(glob_h)
then glob_h:abs(glob_max_h)*glob_check_sign,
if abs(glob_display_interval) < abs(glob_h)
then glob_h:abs(glob_display_interval),
if glob_h > 0.0
then (glob_neg_h:false,
glob_display_interval:abs(glob_display_interval))
else (glob_neg_h:true,
glob_display_interval
:-abs(glob_display_interval)),chk_data(),
best_h:glob_h,min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(ALWAYS,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:0.0,
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(),estimated_step_error:test_suggested_h(),
omniout_float(ALWAYS,"estimated_step_error",32,
estimated_step_error,32,""),
if estimated_step_error > est_needed_step_err
and opt_iter = 1
or glob_check_sign*glob_h
>= glob_check_sign*glob_max_h
then (found_h:true,
glob_h:glob_check_sign*glob_max_h,
best_h:glob_h)
elseif estimated_step_error > est_needed_step_err
and not found_h
then (glob_h:glob_h/2.0,best_h:glob_h,
found_h:true)
else (glob_h:glob_h*2.0,best_h:glob_h),
omniout_float(ALWAYS,"best_h",32,best_h,32,""),
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 opt_iter > 100
then (glob_h:glob_check_sign*glob_max_h,found_h:false),
if glob_check_sign*glob_display_interval
< glob_check_sign*glob_h
then glob_h:glob_check_sign*glob_display_interval,
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,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_current_iter:0,glob_iter:0,
omniout_str(DEBUGL," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_current_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and 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(),
glob_current_iter:1+glob_current_iter,
atomall(),display_alot(current_iter),
if glob_look_poles then 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 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
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,
"2014-01-08T19:56:45-06:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"arctan_sqrt"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
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_str(html_log_file,"16"),
logitem_good_digits(html_log_file,
array_last_rel_error[
1]),
logitem_integer(html_log_file,
MAX_TERMS),
if
glob_least_given_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_given_sing),
0)
else (
logitem_str(html_log_file,
"NOT GIVEN"),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,
" 225 | "),
logitem_str(html_log_file,
"arctan_sqrt diffeq.max"),
logitem_str(html_log_file,
"arctan_sqrt maxima results"),
logitem_str(html_log_file,
"All Tests - Maxima only - to save time"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%o225) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2],
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, best_h,
found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30,
glob_html_log : true, term : 1, while term <=
MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_complex_pole : 0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <=
MAX_TERMS do (array_tmp4_a1 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp4_a2 : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1,
while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term),
ord, 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_tmp3), zero_ats_ar(array_tmp4_a1),
zero_ats_ar(array_tmp4_a2), zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),
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 : 0.0,
1
zero_ats_ar(array_const_0D1), array_const_0D1 : 0.1,
1
zero_ats_ar(array_const_0D2), array_const_0D2 : 0.2, zero_ats_ar(array_m1),
1
array_m1 : - 1.0, iiif : 0, while iiif <= MAX_TERMS do (jjjf : 0,
1
while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0,
iiif iiif, jjjf
jjjf : 1 + jjjf), iiif : 1 + iiif), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3,
1, 30
DEBUGMASSIVE : 4, MAX_TERMS : 30, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), glob_curr_iter_when_opt : 0,
glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1,
glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0,
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/arctan_sqrtpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:0.5,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "glob_max_h:0.0001,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.01,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000000,"),
omniout_str(ALWAYS, "glob_max_minutes:10.0,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\
0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x +"
), omniout_str(ALWAYS, "0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))) "),
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 : - 1.0, x_end : 0.5,
array_y_init : exact_soln_y(x_start), glob_look_poles : true,
1 + 0
glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10,
glob_max_h : 1.0E-4, glob_desired_digits_correct : 10,
glob_display_interval : 0.01, glob_look_poles : true,
glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3,
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_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h)
then glob_h : mabs(glob_max_h) glob_check_sign,
if mabs(glob_display_interval) < mabs(glob_h)
then glob_h : mabs(glob_display_interval),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : mabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- mabs(glob_display_interval)), chk_data(), best_h : glob_h,
min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1,
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), estimated_step_error : 0.0,
while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter",
32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
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 expt(glob_h, term_no - 1)
it
----------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(),
omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32,
""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1))
or (glob_check_sign glob_h >= glob_check_sign glob_max_h)
then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h)
elseif (estimated_step_error > est_needed_step_err) and (not found_h)
glob_h
then (glob_h : ------, best_h : glob_h, found_h : true)
2.0
else (glob_h : glob_h 2.0, best_h : glob_h),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), 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 opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false),
if glob_check_sign glob_display_interval < glob_check_sign glob_h
then glob_h : glob_check_sign glob_display_interval,
if glob_html_log then html_log_file : openw("entry.html"),
if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
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 expt(glob_h, term_no - 1)
it
----------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
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(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS,
2
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2, iii : MAX_TERMS,
factorial_1(calc_term - 1)
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1, iii : MAX_TERMS,
factorial_1(calc_term - 1)
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : MAX_TERMS,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
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 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
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,
"2014-01-08T19:56:45-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "arctan_sqrt"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, MAX_TERMS),
1
if glob_least_given_sing < glob_large_float
then (logitem_float(html_log_file, glob_least_given_sing), 0)
else (logitem_str(html_log_file, "NOT GIVEN"), 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, " 225 | "), logitem_str(html_log_file, "arctan_sqrt diffeq.max"),
logitem_str(html_log_file,
"arctan_sqrt maxima results"),
logitem_str(html_log_file, "All Tests - Maxima only - to save time"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i226) main():=(alias(convfloat,convfloat),compile(all),main_prog())
(%o226) main() := (alias(convfloat, convfloat), compile(all), main_prog())
(%i227) 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.
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.
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.
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 rad_given 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 ALWAYS in translation.
warning: encountered undefined variable array_given_ord_poles 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.
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.
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 analytic_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 array_1st_rel_error in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_good_digits 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 glob_small_float in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: encountered undefined variable tmp in translation.
warning: variable glob_normmax (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_normmax in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable hnew in translation.
warning: encountered undefined variable sz2 in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_current_iter in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_optimal_start (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_reached_optimal_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: 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 term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable h_new 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_const_0D1 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp4_a1 in translation.
warning: encountered undefined variable array_tmp4_a2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp5 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: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable array_y_init in translation.
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: encountered undefined variable ord in translation.
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: encountered undefined variable iiif in translation.
warning: encountered undefined variable jjjf in translation.
warning: encountered undefined variable INFO in translation.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable ALWAYS in translation.
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_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: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable est_answer in translation.
warning: encountered undefined variable est_needed_step_err in translation.
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 any.
warning: encountered undefined variable order_diff in translation.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: encountered undefined variable it in translation.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable best_h in translation.
warning: encountered undefined variable glob_html_log in translation.
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_current_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 glob_iter in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable calc_term in translation.
warning: encountered undefined variable temp_sum in translation.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_ratio_sing 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 $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared
nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
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_CURR_ITER_WHEN_OPT 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 : $GLOB_NEG_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NEG_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: 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/arctan_sqrtpostode.ode#################"
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-1.0,"
"x_end:0.5,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes:10,"
"glob_max_h:0.0001,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.01,"
"glob_look_poles:true,"
"glob_max_iter:1000000000,"
"glob_max_minutes:10.0,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (10.0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x +"
"0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1.5 ""
estimated_steps = 1500000. ""
step_error = 6.66666666666666700000000000000000E-17 ""
est_needed_step_err = 6.66666666666666700000000000000000E-17 ""
opt_iter = 1
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.792822763189857000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 ""
estimated_step_error = 2.792822763189857000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 ""
best_h = 2.000000E-6 ""
opt_iter = 2
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.8742307796397562000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 ""
estimated_step_error = 1.8742307796397562000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 ""
best_h = 4.000000E-6 ""
opt_iter = 3
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.25777384374257340000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 ""
estimated_step_error = 1.25777384374257340000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 ""
best_h = 8.000000E-6 ""
opt_iter = 4
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 8.440762065201292000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-138 ""
estimated_step_error = 8.440762065201292000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-138 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.6644789768200810000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
estimated_step_error = 5.6644789768200810000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
best_h = 3.200000E-5 ""
opt_iter = 6
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.80133990057714700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 ""
estimated_step_error = 3.80133990057714700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 ""
best_h = 6.400000E-5 ""
opt_iter = 7
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.5509989911265360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 ""
estimated_step_error = 2.5509989911265360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 ""
best_h = 1.280000E-4 ""
opt_iter = 8
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.71189674101237560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
estimated_step_error = 1.71189674101237560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
best_h = 1.0000E-4 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1. " "
y[1] (analytic) = 0.20677340069798467 " "
y[1] (numeric) = 0.20677340069798467 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.9998713929753494 " "
Order of pole (three term test) = 1.5052359882119808 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9899000000000011 " "
y[1] (analytic) = 0.2098741190478992 " "
y[1] (numeric) = 0.20987411904811876 " "
absolute error = 2.1954660311962470000000000000E-13 " "
relative error = 1.04608707407852410000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0099687443967562 " "
Order of pole (three term test) = 1.5052900043506128 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9799000000000022 " "
y[1] (analytic) = 0.21295849786866317 " "
y[1] (numeric) = 0.2129584978690984 " "
absolute error = 4.352351812286770000000000000E-13 " "
relative error = 2.04375587536824860000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0199660946770384 " "
Order of pole (three term test) = 1.5053435086759648 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9699000000000033 " "
y[1] (analytic) = 0.2160570825021524 " "
y[1] (numeric) = 0.21605708250280325 " "
absolute error = 6.508682481864980000000000000E-13 " "
relative error = 3.0124828154152920000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0299634177052994 " "
Order of pole (three term test) = 1.505397035906843 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9599000000000044 " "
y[1] (analytic) = 0.21916979100842449 " "
y[1] (numeric) = 0.21916979100928755 " "
absolute error = 8.6305962376798110000000000000E-13 " "
relative error = 3.9378584968163177000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0399607134580797 " "
Order of pole (three term test) = 1.505450586064122 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9499000000000055 " "
y[1] (analytic) = 0.22229654259348974 " "
y[1] (numeric) = 0.2222965425945653 " "
absolute error = 1.075556310681236000000000000E-12 " "
relative error = 4.8383852404222470000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0499579819118339 " "
Order of pole (three term test) = 1.5055041591691949 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9399000000000066 " "
y[1] (analytic) = 0.22543725758242994 " "
y[1] (numeric) = 0.22543725758371438 " "
absolute error = 1.2844447727644592000000000000E-12 " "
relative error = 5.6975709629310430000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0599552230430431 " "
Order of pole (three term test) = 1.5055577552427615 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299000000000077 " "
y[1] (analytic) = 0.2285918573933694 " "
y[1] (numeric) = 0.22859185739486348 " "
absolute error = 1.4940826353893044000000000000E-12 " "
relative error = 6.5360273652190130000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0699524368281303 " "
Order of pole (three term test) = 1.5056113743058779 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199000000000088 " "
y[1] (analytic) = 0.2317602645123258 " "
y[1] (numeric) = 0.23176026451402723 " "
absolute error = 1.701444540813668000000000000E-12 " "
relative error = 7.3413988562443140000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0799496232434969 " "
Order of pole (three term test) = 1.5056650163791196 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099000000000099 " "
y[1] (analytic) = 0.23494240246884468 " "
y[1] (numeric) = 0.23494240247075163 " "
absolute error = 1.9069468226717845000000000000E-12 " "
relative error = 8.1166566896099630000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0899467822654942 " "
Order of pole (three term test) = 1.5057186814840968 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.899900000000011 " "
y[1] (analytic) = 0.23813819581242512 " "
y[1] (numeric) = 0.23813819581453738 " "
absolute error = 2.1122548155005916000000000000E-12 " "
relative error = 8.8698699017790350000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.0999439138704767 " "
Order of pole (three term test) = 1.5057723696412646 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899000000000121 " "
y[1] (analytic) = 0.24134757008969565 " "
y[1] (numeric) = 0.24134757009201013 " "
absolute error = 2.314481939436063800000000000E-12 " "
relative error = 9.5898290526641640000000000E-10 "%"
Correct digits = 13
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.109941018034724 " "
Order of pole (three term test) = 1.505826080872237 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799000000000132 " "
y[1] (analytic) = 0.24457045182228754 " "
y[1] (numeric) = 0.24457045182480625 " "
absolute error = 2.5187074648158614000000000000E-12 " "
relative error = 1.0298494548499391000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1199380947344884 " "
Order of pole (three term test) = 1.5058798151978396 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699000000000143 " "
y[1] (analytic) = 0.24780676848542615 " "
y[1] (numeric) = 0.24780676848814584 " "
absolute error = 2.7196855878486303000000000000E-12 " "
relative error = 1.0975025438050448000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1299351439460432 " "
Order of pole (three term test) = 1.5059335726391083 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599000000000154 " "
y[1] (analytic) = 0.2510564484871467 " "
y[1] (numeric) = 0.2510564484900661 " "
absolute error = 2.9193869544030804000000000000E-12 " "
relative error = 1.1628408559091617000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1399321656455472 " "
Order of pole (three term test) = 1.5059873532177759 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499000000000165 " "
y[1] (analytic) = 0.2543194211481694 " "
y[1] (numeric) = 0.2543194211512878 " "
absolute error = 3.1183944315671397000000000000E-12 " "
relative error = 1.2261723534477248000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1499291598091996 " "
Order of pole (three term test) = 1.5060411569542695 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399000000000176 " "
y[1] (analytic) = 0.2575956166823765 " "
y[1] (numeric) = 0.25759561668569225 " "
absolute error = 3.3157365741942610000000000000E-12 " "
relative error = 1.2871867219241812000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1599261264131373 " "
Order of pole (three term test) = 1.5060949838699114 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299000000000187 " "
y[1] (analytic) = 0.2608849661778727 " "
y[1] (numeric) = 0.26088496618138235 " "
absolute error = 3.509637025445045000000000000E-12 " "
relative error = 1.3452814383532383000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1699230654334098 " "
Order of pole (three term test) = 1.506148833987089 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199000000000198 " "
y[1] (analytic) = 0.264187401578603 " "
y[1] (numeric) = 0.26418740158230924 " "
absolute error = 3.70625752310616000000000000E-12 " "
relative error = 1.4028895779889970000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1799199768461388 " "
Order of pole (three term test) = 1.5062027073257764 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099000000000209 " "
y[1] (analytic) = 0.26750285566653487 " "
y[1] (numeric) = 0.2675028556704362 " "
absolute error = 3.9013237085328000000000000E-12 " "
relative error = 1.4584232003101055000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1899168606273243 " "
Order of pole (three term test) = 1.5062566039081149 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.799900000000022 " "
y[1] (analytic) = 0.27083126204433716 " "
y[1] (numeric) = 0.27083126204842906 " "
absolute error = 4.091893490709708000000000000E-12 " "
relative error = 1.5108645360297565000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.1999137167529879 " "
Order of pole (three term test) = 1.5063105237551118 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7899000000000231 " "
y[1] (analytic) = 0.27417255511856053 " "
y[1] (numeric) = 0.2741725551228449 " "
absolute error = 4.284350652028479000000000000E-12 " "
relative error = 1.5626475269108522000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2099105451990655 " "
Order of pole (three term test) = 1.5063644668886214 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7799000000000242 " "
y[1] (analytic) = 0.2775266700833292 " "
y[1] (numeric) = 0.2775266700878041 " "
absolute error = 4.474864923054156000000000000E-12 " "
relative error = 1.6124089701759290000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2199073459415237 " "
Order of pole (three term test) = 1.506418433329756 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7699000000000253 " "
y[1] (analytic) = 0.28089354290446433 " "
y[1] (numeric) = 0.2808935429091299 " "
absolute error = 4.6655457275335266000000000000E-12 " "
relative error = 1.6609658161919164000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2299041189562905 " "
Order of pole (three term test) = 1.5064724230994584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7599000000000264 " "
y[1] (analytic) = 0.2842731103040821 " "
y[1] (numeric) = 0.2842731103089353 " "
absolute error = 4.853228929846409300000000000E-12 " "
relative error = 1.7072416468286408000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2399008642191691 " "
Order of pole (three term test) = 1.5065264362201969 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7499000000000275 " "
y[1] (analytic) = 0.287665309745599 " "
y[1] (numeric) = 0.28766530975063936 " "
absolute error = 5.0403570206469790000000000000E-12 " "
relative error = 1.7521601840362650000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2498975817059903 " "
Order of pole (three term test) = 1.506580472713583 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7399000000000286 " "
y[1] (analytic) = 0.2910700794191774 " "
y[1] (numeric) = 0.29107007942440427 " "
absolute error = 5.226874488784006000000000000E-12 " "
relative error = 1.7957443441847730000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2598942713926014 " "
Order of pole (three term test) = 1.5066345326005794 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7299000000000297 " "
y[1] (analytic) = 0.2944873582275611 " "
y[1] (numeric) = 0.294487358232973 " "
absolute error = 5.411893155837788000000000000E-12 " "
relative error = 1.8377336088076898000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2698909332547677 " "
Order of pole (three term test) = 1.5066886159025326 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7199000000000308 " "
y[1] (analytic) = 0.2979170857722977 " "
y[1] (numeric) = 0.297917085777892 " "
absolute error = 5.594302798783701000000000000E-12 " "
relative error = 1.8778052907846673000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.279887567268195 " "
Order of pole (three term test) = 1.5067427226418089 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.709900000000032 " "
y[1] (analytic) = 0.30135920234033486 " "
y[1] (numeric) = 0.30135920234611197 " "
absolute error = 5.777101019788233000000000000E-12 " "
relative error = 1.917014969154306000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2898841734085613 " "
Order of pole (three term test) = 1.5067968528400262 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.699900000000033 " "
y[1] (analytic) = 0.30481364889098606 " "
y[1] (numeric) = 0.3048136488969459 " "
absolute error = 5.959843729641534000000000000E-12 " "
relative error = 1.955241752239586000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.2998807516515554 " "
Order of pole (three term test) = 1.506851006518911 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6899000000000342 " "
y[1] (analytic) = 0.30828036704323525 " "
y[1] (numeric) = 0.3082803670493778 " "
absolute error = 6.1425309283436040000000000000E-12 " "
relative error = 1.9925144722181204000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.3098773019727823 " "
Order of pole (three term test) = 1.5069051837004512 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6799000000000353 " "
y[1] (analytic) = 0.31175929906338684 " "
y[1] (numeric) = 0.3117592990697072 " "
absolute error = 6.3203331457373220000000000000E-12 " "
relative error = 2.0273118283000352000000000E-9 "%"
Correct digits = 12
h = 1.0000E-4 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.3198738243479253 " "
Order of pole (three term test) = 1.506959384405076 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; "
Iterations = 3219
"Total Elapsed Time "= 10 Minutes 0 Seconds
"Elapsed Time(since restart) "= 9 Minutes 59 Seconds
"Expected Time Remaining "= 36 Minutes 35 Seconds
"Optimized Time Remaining "= 36 Minutes 31 Seconds
"Expected Total Time "= 46 Minutes 32 Seconds
"Time to Timeout "= 0.0 Seconds
Percent Done = 21.4666666666643 "%"
(%o227) true
(%o227) diffeq.max