(%i1) batch("temp/diffeq.sing1_back.max") read and interpret file: /home/dennis/src/mine/omni/temp/diffeq.sing1_back.max (%i2) load("stringproc") (%i3) alias(convfloat,float) (%i4) alias(int_trunc,truncate) (%i5) alias(elapsed_time_seconds,elapsed_real_time) (%i6) alias(ln,log) (%i7) alias(arcsin,asin) (%i8) alias(arccos,acos) (%i9) alias(arctan,atan) (%i10) alias(float_abs,abs) (%i11) keepfloat:true (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_ats], fixnum),convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_att], fixnum),convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(factorial_2([nnn],fixnum),fixnum) (%i43) mode_declare(factorial_1([nnn],fixnum),fixnum) (%i44) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum) (%i45) mode_declare(convfloat([mmm],fixnum),convfloat) (%i46) mode_declare(elaped_time_seconds(),convfloat) (%i47) mode_declare(Si([x],convfloat),convfloat) (%i48) mode_declare(Ci([x],convfloat),convfloat) (%i49) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i50) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i51) mode_declare(main_prog(),fixnum) (%i52) define_variable(MAX_TERMS,20,fixnum) (%i53) define_variable(glob_iolevel,5,fixnum) (%i54) define_variable(glob_yes_pole,4,fixnum) (%i55) define_variable(glob_no_pole,3,fixnum) (%i56) define_variable(glob_not_given,0,fixnum) (%i57) define_variable(glob_no_sing_tests,4,fixnum) (%i58) define_variable(glob_ratio_test,1,fixnum) (%i59) define_variable(glob_three_term_test,2,fixnum) (%i60) define_variable(glob_six_term_test,3,fixnum) (%i61) define_variable(glob_log_10,log(10.0),convfloat) (%i62) define_variable(ALWAYS,1,fixnum) (%i63) define_variable(INFO,2,fixnum) (%i64) define_variable(DEBUGL,3,fixnum) (%i65) define_variable(DEBUGMASSIVE,4,fixnum) (%i66) define_variable(MAX_UNCHANGED,10,fixnum) (%i67) define_variable(glob_prec,1.0E-16,convfloat) (%i68) define_variable(glob_est_digits,1,fixnum) (%i69) define_variable(glob_check_sign,1.0,convfloat) (%i70) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i71) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i72) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i73) define_variable(glob_percent_done,0.0,convfloat) (%i74) define_variable(glob_subiter_method,3,fixnum) (%i75) define_variable(glob_total_exp_sec,0.1,convfloat) (%i76) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i77) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i78) define_variable(glob_html_log,true,boolean) (%i79) define_variable(glob_good_digits,0,fixnum) (%i80) define_variable(glob_max_opt_iter,10,fixnum) (%i81) define_variable(glob_dump,false,boolean) (%i82) define_variable(glob_djd_debug,true,boolean) (%i83) define_variable(glob_display_flag,true,boolean) (%i84) define_variable(glob_djd_debug2,true,boolean) (%i85) define_variable(glob_h_reason,0,fixnum) (%i86) define_variable(glob_sec_in_minute,60,fixnum) (%i87) define_variable(glob_min_in_hour,60.0,convfloat) (%i88) define_variable(glob_hours_in_day,24.0,convfloat) (%i89) define_variable(glob_days_in_year,365,fixnum) (%i90) define_variable(glob_sec_in_hour,3600,fixnum) (%i91) define_variable(glob_sec_in_day,86400,fixnum) (%i92) define_variable(glob_sec_in_year,31536000,fixnum) (%i93) define_variable(glob_almost_1,0.999,convfloat) (%i94) define_variable(glob_clock_sec,0.0,convfloat) (%i95) define_variable(glob_clock_start_sec,0.0,convfloat) (%i96) define_variable(glob_not_yet_finished,true,boolean) (%i97) define_variable(glob_initial_pass,true,boolean) (%i98) define_variable(glob_not_yet_start_msg,true,boolean) (%i99) define_variable(glob_reached_optimal_h,false,boolean) (%i100) define_variable(glob_optimal_done,false,boolean) (%i101) define_variable(glob_disp_incr,0.1,convfloat) (%i102) define_variable(glob_h,0.1,convfloat) (%i103) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i106) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i109) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i110) define_variable(glob_guess_error_rc,0.1,convfloat) (%i111) define_variable(glob_guess_error_ord,0.1,convfloat) (%i112) define_variable(glob_max_h,0.1,convfloat) (%i113) define_variable(glob_min_h,1.0E-6,convfloat) (%i114) define_variable(glob_type_given_pole,0,fixnum) (%i115) define_variable(glob_large_float,1.0E+100,convfloat) (%i116) define_variable(glob_larger_float,1.1E+100,convfloat) (%i117) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%i118) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%i119) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i120) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i121) define_variable(glob_last_good_h,0.1,convfloat) (%i122) define_variable(glob_look_poles,false,boolean) (%i123) define_variable(glob_display_interval,0.1,convfloat) (%i124) define_variable(glob_next_display,0.0,convfloat) (%i125) define_variable(glob_dump_closed_form,false,boolean) (%i126) define_variable(glob_abserr,1.0E-11,convfloat) (%i127) define_variable(glob_relerr,1.0E-11,convfloat) (%i128) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i129) define_variable(glob_max_hours,0.0,convfloat) (%i130) define_variable(glob_max_iter,1000,fixnum) (%i131) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i132) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i133) define_variable(glob_no_eqs,0,fixnum) (%i134) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i135) define_variable(glob_optimal_start,0.0,convfloat) (%i136) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i137) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i138) define_variable(glob_small_float,0.0,convfloat) (%i139) define_variable(glob_smallish_float,0.0,convfloat) (%i140) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i141) define_variable(glob_warned,false,boolean) (%i142) define_variable(glob_warned2,false,boolean) (%i143) define_variable(glob_max_sec,10000.0,convfloat) (%i144) define_variable(glob_orig_start_sec,0.0,convfloat) (%i145) define_variable(glob_start,0,fixnum) (%i146) define_variable(glob_iter,0,fixnum) (%i147) define_variable(glob_normmax,0.0,convfloat) (%i148) define_variable(glob_max_minutes,0.0,convfloat) (%i149) array(array_y_init,MAX_TERMS) (%i150) array(array_norms,MAX_TERMS) (%i151) array(array_fact_1,MAX_TERMS) (%i152) array(array_1st_rel_error,2) (%i153) array(array_last_rel_error,2) (%i154) array(array_est_rel_error,2) (%i155) array(array_max_est_error,2) (%i156) array(array_type_pole,2) (%i157) array(array_type_real_pole,2) (%i158) array(array_type_complex_pole,2) (%i159) array(array_est_digits,2) (%i160) array(array_good_digits,2) (%i161) array(array_y,MAX_TERMS) (%i162) array(array_x,MAX_TERMS) (%i163) array(array_tmp0,MAX_TERMS) (%i164) array(array_tmp1,MAX_TERMS) (%i165) array(array_tmp2,MAX_TERMS) (%i166) array(array_tmp3,MAX_TERMS) (%i167) array(array_tmp4,MAX_TERMS) (%i168) array(array_tmp5,MAX_TERMS) (%i169) array(array_tmp6,MAX_TERMS) (%i170) array(array_tmp7,MAX_TERMS) (%i171) array(array_tmp8,MAX_TERMS) (%i172) array(array_tmp9,MAX_TERMS) (%i173) array(array_m1,MAX_TERMS) (%i174) array(array_y_higher,2,MAX_TERMS) (%i175) array(array_y_higher_work,2,MAX_TERMS) (%i176) array(array_y_higher_work2,2,MAX_TERMS) (%i177) array(array_y_set_initial,2,MAX_TERMS) (%i178) array(array_given_rad_poles,2,3) (%i179) array(array_given_ord_poles,2,3) (%i180) array(array_rad_test_poles,2,4) (%i181) array(array_ord_test_poles,2,4) (%i182) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%i183) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i184) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i185) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i186) 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)) (%i187) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i188) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i189) 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) (%i190) 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) (%i191) 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) (%i192) 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) (%i193) 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) (%i194) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i195) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i196) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i197) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > glob_prec then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%i198) log_revs(file,revs):=printf(file,revs) (%i199) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i200) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i201) logstart(file):=(printf(file,""),0) (%i202) logend(file):=(printf(file,"~%"),0) (%i203) 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) (%i204) 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) (%i205) 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) (%i206) 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) (%i207) 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) (%i208) 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) (%i209) 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) (%i210) 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) (%i211) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i212) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i213) 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) (%i214) 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) (%i215) log10(x):=log(x)/glob_log_10 (%i216) expt(x,y):=if y = 0.0 then 1.0 elseif x < 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i217) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(10.0,-glob_desired_digits_correct) *abs(estimated_answer), omniout_float(ALWAYS,"estimated_h",32, estimated_h,32,""), omniout_float(ALWAYS,"estimated_answer", 32,estimated_answer,32,""), omniout_float(ALWAYS, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(ALWAYS,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(ALWAYS,"estimated_steps",32, estimated_steps,32,""), step_error :abs( desired_abs_gbl_error /sqrt(estimated_steps) /MAX_TERMS), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%i218) exact_soln_y(x):=block(1.0/(1.0E-6+x*x)) 1.0 (%o218) exact_soln_y(x) := block(------------) 1.0E-6 + x x (%i219) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > 0.0 and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > 0.0 and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i220) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%i221) 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) (%i222) 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) (%i223) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:MAX_TERMS,hn_div_ho:0.5, hn_div_ho_2:0.25,hn_div_ho_3:0.125, est_tmp:abs(array_y[no_terms])*hn_div_ho_3 +abs(array_y[no_terms-1])*hn_div_ho_2 +abs(array_y[no_terms-2])*hn_div_ho +abs(array_y[no_terms-3]), if glob_prec*abs(array_y[1]) > est_tmp then est_tmp:glob_prec*abs(array_y[1]), if est_tmp >= array_max_est_error[1] then array_max_est_error[1]:est_tmp) (%i224) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display-glob_h/10.0 then ret:true else ret:false,return(ret)) (%i225) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33,numeric_val, 20," "), if abs(closed_form_val_y) > glob_prec then ( relerr :abserr*100.0 /abs(closed_form_val_y), if relerr > glob_prec then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits:16) else (relerr:-1.0, glob_good_digits:-16), if abs(numeric_val) > glob_prec then ( est_rel_err :array_max_est_error[1] *100.0*sqrt(glob_iter)*34 *MAX_TERMS /abs(numeric_val), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits :16) else (relerr:-1.0, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, array_good_digits[1] :glob_good_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(INFO, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%i226) 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) (%i227) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, omniout_str(ALWAYS, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(ALWAYS, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:1.0, while term <= MAX_TERMS do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%i228) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_m1[1]*array_const_2D0[1], array_tmp2[1]:array_x[1]*array_tmp1[1], array_tmp3[1]:array_x[1]*array_x[1], array_tmp4[1]:array_const_0D000001[1]+array_tmp3[1], array_tmp5[1]:array_tmp2[1]/array_tmp4[1], array_tmp6[1]:array_x[1]*array_x[1], array_tmp7[1]:array_const_0D000001[1]+array_tmp6[1], array_tmp8[1]:array_tmp5[1]/array_tmp7[1], array_tmp9[1]:array_tmp8[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp9[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_m1[2]*array_const_2D0[1], array_tmp2[2]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp3[2]:array_x[2]*array_x[1] +array_x[1]*array_x[2], array_tmp4[2]:array_tmp3[2], array_tmp5[2]:(array_tmp2[2] -ats(2,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp6[2]:array_x[2]*array_x[1] +array_x[1]*array_x[2], array_tmp7[2]:array_tmp6[2], array_tmp8[2]:(array_tmp5[2] -ats(2,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[2]:array_tmp8[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp9[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y_higher[2,2]:temporary,0)),kkk:3, array_tmp1[3]:array_m1[3]*array_const_2D0[1], array_tmp2[3]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp3[3]:array_x[2]*array_x[2], array_tmp4[3]:array_tmp3[3], array_tmp5[3]:(array_tmp2[3] -ats(3,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp6[3]:array_x[2]*array_x[2], array_tmp7[3]:array_tmp6[3], array_tmp8[3]:(array_tmp5[3] -ats(3,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[3]:array_tmp8[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp9[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y_higher[2,3]:temporary,0)),kkk:4, array_tmp1[4]:array_m1[4]*array_const_2D0[1], array_tmp2[4]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp4[4]:array_tmp3[4], array_tmp5[4]:(array_tmp2[4] -ats(4,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp7[4]:array_tmp6[4], array_tmp8[4]:(array_tmp5[4] -ats(4,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[4]:array_tmp8[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp9[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y_higher[2,4]:temporary,0)),kkk:5, array_tmp1[5]:array_m1[5]*array_const_2D0[1], array_tmp2[5]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp4[5]:array_tmp3[5], array_tmp5[5]:(array_tmp2[5] -ats(5,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp7[5]:array_tmp6[5], array_tmp8[5]:(array_tmp5[5] -ats(5,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[5]:array_tmp8[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp9[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp1[kkk]:array_m1[kkk]*array_const_2D0[1], array_tmp2[kkk] :array_tmp1[kkk]*array_x[1] +array_tmp1[kkk-1]*array_x[2], array_tmp4[kkk]:array_tmp3[kkk], array_tmp5[kkk] :(array_tmp2[kkk] -ats(kkk,array_tmp4,array_tmp5,2)) /array_tmp4[1],array_tmp7[kkk]:array_tmp6[kkk], array_tmp8[kkk] :(array_tmp5[kkk] -ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1],array_tmp9[kkk]:array_tmp8[kkk], order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp9[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) (%i229) exact_soln_y(x):=block(1.0/(1.0E-6+x*x)) 1.0 (%o229) exact_soln_y(x) := block(------------) 1.0E-6 + x x (%i230) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:20, glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_est_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 2 do (array_good_digits[term]:0,term:1+term), term:1, while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[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_tmp6[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp7[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp8[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp9[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term), ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher[ord,term]:0.0,term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= MAX_TERMS do (term:1, while term <= MAX_TERMS do (array_fact_2[ord,term]:0.0,term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_m1),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), zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6), zero_ats_ar(array_tmp7),zero_ats_ar(array_tmp8), zero_ats_ar(array_tmp9),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_2D0), array_const_2D0[1]:2.0,zero_ats_ar(array_const_0D000001), array_const_0D000001[1]:1.0E-6,zero_ats_ar(array_m1), array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:20,glob_iolevel:INFO, glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing1_backpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:20,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:-1.5,"), omniout_str(ALWAYS,"x_end:-2.0,"), 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_h:0.1,"), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"glob_type_given_pole:2,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,2]:0.001,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,1]:1.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,2]:0.0,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:16,"), omniout_str(ALWAYS,"glob_max_minutes:3.0,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"glob_max_iter:100000000,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := (block("), omniout_str(ALWAYS," (1.0 / (x * x + 0.000001)) "), omniout_str(ALWAYS,"));"),omniout_str(ALWAYS,""), 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:-1.5,x_end:-2.0, array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_h:0.1,glob_type_given_pole:2, array_given_rad_poles[1,1]:0.0, array_given_rad_poles[1,2]:0.001, array_given_ord_poles[1,1]:1.0, array_given_ord_poles[1,2]:0.0, glob_desired_digits_correct:16,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000000, glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, omniout_str(ALWAYS,"START of Optimize"), glob_check_sign:my_check_sign(x_start,x_end),found_h:false, glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval:abs(glob_display_interval) *glob_check_sign, display_max:(x_end-x_start)/10.0, if glob_display_interval > display_max then glob_display_interval:display_max,chk_data(), min_value:glob_larger_float,est_answer:est_size_answer(), opt_iter:1,glob_prec:expt(10.0,-16), est_needed_step_err:estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no]*expt(glob_h,term_no-1) /factorial_1(term_no-1),term_no:1+term_no), rows:order_diff,r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), atomall(), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(ALWAYS,"SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then (omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval,found_h:true), if glob_look_poles then (check_for_pole(), if opt_iter > 2 and not found_h and (glob_min_pole_est < 0.999*last_min_pole_est or glob_min_pole_est > 1.111 *last_min_pole_est) then ( omniout_str(ALWAYS, "SETTING H FOR POLE ACCURACY"), glob_h_reason:4,found_h:true, glob_h:glob_h/2.0, last_min_pole_est:glob_min_pole_est) else last_min_pole_est :glob_min_pole_est), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err", 32,est_needed_step_err,16, ""), estimated_step_error:test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(ALWAYS, "Double H and LOOP"), glob_h:glob_h*2.0) else ( omniout_str(ALWAYS, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/2.0)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(ALWAYS,"Beginning glob_h too large."), found_h:false), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(ALWAYS,"START of Soultion"), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start, glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(DEBUGL," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(INFO," "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1), term_no:MAX_TERMS, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(ALWAYS,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "), omniout_int(INFO, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-09-23T02:43:49-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sing1_back"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if array_good_digits[1] # -16 then ( logitem_integer(html_log_file, array_good_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_integer(html_log_file, MAX_TERMS), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 269 "), logitem_str(html_log_file, "sing1_back diffeq.max"), logitem_str(html_log_file, "sing1_back maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i231) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%i232) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable fixnum in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable good_digits in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable array_good_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable array_const_2D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D000001 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_tmp6 in translation. warning: encountered undefined variable array_tmp7 in translation. warning: encountered undefined variable array_tmp8 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp9 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ALWAYS in translation. warning: variable x_start (declared type [found_h]) assigned type convfloat. warning: variable x_end (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable glob_display_interval (declared type convfloat) assigned type [found_h]. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: variable glob_prec (declared type convfloat) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type [found_h]. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable last_min_pole_est in translation. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable DEBUGL in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. Warning: modedcclare has a function or macro call which has not been translated properly. The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################" "##############temp/sing1_backpostode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:20," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.5," "x_end:-2.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_h:0.1," "" "" "" "" "" "" "" "glob_type_given_pole:2," "" "array_given_rad_poles[1,1]:0.0," "" "array_given_rad_poles[1,2]:0.001," "" "array_given_ord_poles[1,1]:1.0," "" "array_given_ord_poles[1,2]:0.0," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:16," "glob_max_minutes:3.0," "glob_subiter_method:3," "glob_max_iter:100000000," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0 / (x * x + 0.000001)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 500000. "" step_error = 7.071067811865475000000000000000000000E-21 "" est_needed_step_err = 7.071067811865475000000000000000000000E-21 "" opt_iter = 1 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 500000. "" step_error = 7.071067811865475000000000000000000000E-21 "" est_needed_step_err = 7.071067811865475000000000000000000000E-21 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.150257577510789600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" estimated_step_error = 1.150257577510789600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" "Double H and LOOP" opt_iter = 2 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -2.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 250000. "" step_error = 1.000000000000000000000000000000000000E-20 "" est_needed_step_err = 1.000000000000000000000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.5383253993976960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-94 "" estimated_step_error = 7.5383253993976960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-94 "" "Double H and LOOP" opt_iter = 3 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -4.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 125000. "" step_error = 1.41421356237309500000000000000000000E-20 "" est_needed_step_err = 1.41421356237309500000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.940313446481448500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 4.940313446481448500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" "Double H and LOOP" opt_iter = 4 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -8.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 62500. "" step_error = 2.000000000000000000000000000000000000E-20 "" est_needed_step_err = 2.000000000000000000000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.237679249464048000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-84 "" estimated_step_error = 3.237679249464048000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-84 "" "Double H and LOOP" opt_iter = 5 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.600000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 31250. "" step_error = 2.8284271247461900000000000000000000E-20 "" est_needed_step_err = 2.8284271247461900000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.12183948188619770000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 "" estimated_step_error = 2.12183948188619770000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 "" "Double H and LOOP" opt_iter = 6 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -3.200000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 15625. "" step_error = 4.000000000000000000000000000000000000E-20 "" est_needed_step_err = 4.000000000000000000000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.390560870335942600000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 1.390560870335942600000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" "Double H and LOOP" opt_iter = 7 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -6.400000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 7812.5 "" step_error = 5.6568542494923800000000000000000000E-20 "" est_needed_step_err = 5.6568542494923800000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.1130767971135280000000000000000000000000000000000000000000000000000000000000000000000E-70 "" estimated_step_error = 9.1130767971135280000000000000000000000000000000000000000000000000000000000000000000000E-70 "" "Double H and LOOP" opt_iter = 8 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.280000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 3906.25 "" step_error = 8.00000000000000000000000000000000000E-20 "" est_needed_step_err = 8.00000000000000000000000000000000000E-20 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.97221111144512800000000000000000000000000000000000000000000000000000000000000000E-65 "" estimated_step_error = 5.97221111144512800000000000000000000000000000000000000000000000000000000000000000E-65 "" "Double H and LOOP" opt_iter = 9 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -2.560000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 1953.125 "" step_error = 1.1313708498984760000000000000000000E-19 "" est_needed_step_err = 1.1313708498984760000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.913771472025887000000000000000000000000000000000000000000000000000000000000E-60 "" estimated_step_error = 3.913771472025887000000000000000000000000000000000000000000000000000000000000E-60 "" "Double H and LOOP" opt_iter = 10 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -5.120000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 976.5625 "" step_error = 1.60000000000000000000000000000000000E-19 "" est_needed_step_err = 1.60000000000000000000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.56469756533238450000000000000000000000000000000000000000000000000000000E-55 "" estimated_step_error = 2.56469756533238450000000000000000000000000000000000000000000000000000000E-55 "" "Double H and LOOP" opt_iter = 11 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.024000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 488.28125 "" step_error = 2.2627416997969520000000000000000000E-19 "" est_needed_step_err = 2.2627416997969520000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.680496576012369000000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 1.680496576012369000000000000000000000000000000000000000000000000000E-50 "" "Double H and LOOP" opt_iter = 12 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -2.048000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 244.140625 "" step_error = 3.20000000000000000000000000000000000E-19 "" est_needed_step_err = 3.20000000000000000000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.1009324896407095000000000000000000000000000000000000000000000E-45 "" estimated_step_error = 1.1009324896407095000000000000000000000000000000000000000000000E-45 "" "Double H and LOOP" opt_iter = 13 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -4.096000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 122.0703125 "" step_error = 4.5254833995939040000000000000000000E-19 "" est_needed_step_err = 4.5254833995939040000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.20986344923282100000000000000000000000000000000000000000E-41 "" estimated_step_error = 7.20986344923282100000000000000000000000000000000000000000E-41 "" "Double H and LOOP" opt_iter = 14 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -8.192000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 61.03515625 "" step_error = 6.4000000000000000000000000000000000E-19 "" est_needed_step_err = 6.4000000000000000000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.718244967515526400000000000000000000000000000000000E-36 "" estimated_step_error = 4.718244967515526400000000000000000000000000000000000E-36 "" "Double H and LOOP" opt_iter = 15 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -1.638400E-2 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 30.517578125 "" step_error = 9.0509667991878080000000000000000000E-19 "" est_needed_step_err = 9.0509667991878080000000000000000000E-19 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.08325989659715000000000000000000000000000000000E-31 "" estimated_step_error = 3.08325989659715000000000000000000000000000000000E-31 "" "Double H and LOOP" opt_iter = 16 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -3.276800E-2 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 15.2587890625 "" step_error = 1.2800000000000000000000000000000000E-18 "" est_needed_step_err = 1.2800000000000000000000000000000000E-18 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.00909362817844500000000000000000000000000E-26 "" estimated_step_error = 2.00909362817844500000000000000000000000000E-26 "" "Double H and LOOP" opt_iter = 17 min_size = 0.444444246913668 "" min_size = 1. "" glob_desired_digits_correct = 16. "" estimated_h = -6.553600E-2 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000000000E-16 "" range = -0.5 "" estimated_steps = 7.62939453125 "" step_error = 1.8101933598375616000000000000000000E-18 "" est_needed_step_err = 1.8101933598375616000000000000000000E-18 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.3017943905559765000000000000000000000E-21 "" estimated_step_error = 1.3017943905559765000000000000000000000E-21 "" "Double H and LOOP" opt_iter = 18 "SETTING H FOR MAX H" "SETTING H FOR DISPLAY INTERVAL" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -1.6 " " y[1] (closed_form) = 0.3906248474121689 " " y[1] (numeric) = 0.39062484741216896 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.421086026631713200000000000000E-14 "%" Desired digits = 16 Estimated correct digits = 14 Correct digits = 17 h = -0.1 " " Radius of convergence (given) for eq 1 = 1.6000003124999698 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6000062500747148 " " Order of pole (three term test) = 2.000027344213617 " " Radius of convergence (six term test) for eq 1 = 1.6000002655588987 " " Order of pole (six term test) = 1.0000000000034444 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7000000000000002 " " y[1] (closed_form) = 0.3460206415153489 " " y[1] (numeric) = 0.34602064151534895 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.60427282569486400000000000000E-14 "%" Desired digits = 16 Estimated correct digits = 14 Correct digits = 17 h = -0.1 " " Radius of convergence (given) for eq 1 = 1.7000002941176218 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.700005882415234 " " Order of pole (three term test) = 2.0000242218171516 " " Radius of convergence (six term test) for eq 1 = 1.700000176717956 " " Order of pole (six term test) = 1.0000000000069855 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8000000000000003 " " y[1] (closed_form) = 0.30864188004880233 " " y[1] (numeric) = 0.30864188004880244 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.597123710008533500000000000000E-14 "%" Desired digits = 16 Estimated correct digits = 14 Correct digits = 17 h = -0.1 " " Radius of convergence (given) for eq 1 = 1.8000002777777566 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8000055556080243 " " Order of pole (three term test) = 2.000021605227659 " " Radius of convergence (six term test) for eq 1 = 1.8000006216367792 " " Order of pole (six term test) = 0.9999999999837428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9000000000000004 " " y[1] (closed_form) = 0.2770082335157247 " " y[1] (numeric) = 0.2770082335157248 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.007906229119841400000000000000E-14 "%" Desired digits = 16 Estimated correct digits = 14 Correct digits = 17 h = -0.1 " " Radius of convergence (given) for eq 1 = 1.900000263157877 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9000052632025208 " " Order of pole (three term test) = 2.0000193908148893 " " Radius of convergence (six term test) for eq 1 = 1.9000001468340786 " " Order of pole (six term test) = 1.0000000000055147 " " "Finished!" "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; " Iterations = 5 "Total Elapsed Time "= 0 Seconds "Elapsed Time(since restart) "= 0 Seconds "Expected Time Remaining "= 0 Seconds "Optimized Time Remaining "= 0 Seconds "Expected Total Time "= 0 Seconds "Time to Timeout "= 2 Minutes 59 Seconds Percent Done = 0.0 "%" (%o232) temp/diffeq.sing1_back.max