/* BEGIN OUTFILE1 */ load("stringproc")$ /* before maxima top matter */ keepfloat : true$ alias(convfloat,float)$ alias(int_trunc,truncate)$ alias(elapsed_time_seconds,elapsed_real_time)$ alias(ln,log)$ alias(arcsin,asin)$ alias(arccos,acos)$ alias(arctan,atan)$ alias(float_abs,abs)$ mode_declare(display_poles(),fixnum)$ mode_declare(est_size_answer(),float)$ mode_declare(test_suggested_h(),float)$ mode_declare(reached_interval(),boolean)$ mode_declare(display_alot([iter],fixnum),fixnum)$ mode_declare(prog_report([x_start],float,[x_end],float),fixnum)$ mode_declare(check_for_pole(),fixnum)$ mode_declare(atomall(),fixnum)$ mode_declare(log10([x],float),float)$ mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)$ mode_declare(omniout_timestr(secs_in,number),fixnum)$ mode_declare(zero_ats_ar(ar,array([40],float)),fixnum)$ mode_declare(ats([mmm_ats],fixnum,[arr_a],completearray([40],float),[arr_b],completearray([40],float),[jjj_ats],fixnum),float)$ mode_declare(att([mmm_att],fixnum,[arr_a],completearray([40],float),[arr_b],completearray([40],float),[jjj_att],fixnum),float)$ mode_declare(logitem_ditto([file],fixnum),fixnum)$ mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)$ mode_declare(logitem_good_digits([file],fixnum,[relerror],float),fixnum)$ mode_declare(logitem_number([file],fixnum,[x],number),fixnum)$ mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)$ mode_declare(logstart([file],fixnum),fixnum)$ mode_declare(logend([file],fixnum),fixnum)$ mode_declare(chk_data(),fixnum)$ mode_declare(comp_expect_sec([t_end2],float,[t_start2],float,[t2],float,[clock_sec2],float),float)$ mode_declare(comp_percent([t_end2],float,[start2],float,[t2],float),float)$ mode_declare(comp_rad_from_ratio([term1],float,[term2],float,[last_no],fixnum),float)$ mode_declare(comp_ord_from_ratio([term1],float,[term2],float,[last_no],fixnum),float)$ mode_declare(comp_rad_from_three_terms([term1],float,[term2],float,[term3],float,[last_no],fixnum),float)$ mode_declare(comp_ord_from_three_terms([term1],float,[term2],float,[term3],float,[last_no],fixnum),float)$ mode_declare(comp_rad_from_six_terms([term1],float,[term2],float,[term3],float,[term4],float,[term5],float,[term6],float,[last_no],fixnum),float)$ mode_declare(comp_ord_from_six_terms([term1],float,[term2],float,[term3],float,[term4],float,[term5],float,[term6],float,[last_no],fixnum),float)$ mode_declare(neg([nnn],float),float)$ mode_declare(factorial_2([nnn],fixnum),float)$ mode_declare(factorial_1([nnn],fixnum),float)$ mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),float)$ mode_declare(float([mmm],fixnum),float)$ mode_declare(elaped_time_seconds(),float)$ mode_declare(Si([x],float),float)$ mode_declare(Ci([x],float),float)$ mode_declare(estimated_needed_step_error([x_start],float,[x_end],float,[estimated_h],float,[estimated_answer],float),float)$ mode_declare(my_check_sign([x0],float,[xf],float),float)$ mode_declare(main_prog(),fixnum)$ define_variable(always,1,fixnum )$ define_variable(info,2,fixnum )$ define_variable(debugl,3,fixnum )$ define_variable(debugmassive,4,fixnum )$ define_variable(glob_iolevel,5,fixnum )$ define_variable(glob_yes_pole,4,fixnum )$ define_variable(glob_no_pole,3,fixnum )$ define_variable(glob_not_given,0,fixnum )$ define_variable(glob_no_sing_tests,4,fixnum )$ define_variable(glob_ratio_test,1,fixnum )$ define_variable(glob_three_term_test,2,fixnum )$ define_variable(glob_six_term_test,3,fixnum )$ define_variable(ats_max_terms,40,fixnum )$ define_variable(glob_log_10,0.0,float )$ /* Top Generate Globals Definition */ define_variable(max_unchanged,10,fixnum )$ define_variable(glob__small,0.1e-50,float )$ define_variable(glob_small_float,0.1e-50,float )$ define_variable(glob_smallish_float,0.1e-60,float )$ define_variable(glob_large_float,1.0e100,float )$ define_variable(glob_larger_float,1.1e100,float )$ define_variable(glob__m2,-2.0,float )$ define_variable(glob__m1,-1.0,float )$ define_variable(glob__0,0.0,float )$ define_variable(glob__1,1.0,float )$ define_variable(glob__2,2.0,float )$ define_variable(glob__3,3.0,float )$ define_variable(glob__4,4.0,float )$ define_variable(glob__5,5.0,float )$ define_variable(glob__8,8.0,float )$ define_variable(glob__10,10.0,float )$ define_variable(glob__100,100.0,float )$ define_variable(glob__pi,0.0,float )$ define_variable(glob__0_5,0.5,float )$ define_variable(glob__0_8,0.8,float )$ define_variable(glob__m0_8,-0.8,float )$ define_variable(glob__0_25,0.25,float )$ define_variable(glob__0_125,0.125,float )$ define_variable(glob_prec,1.0e-16,float )$ define_variable(glob_check_sign,1.0,float )$ define_variable(glob_desired_digits_correct,8.0,float )$ define_variable(glob_max_estimated_step_error,0.0,float )$ define_variable(glob_ratio_of_radius,0.1,float )$ define_variable(glob_percent_done,0.0,float )$ define_variable(glob_total_exp_sec,0.1,float )$ define_variable(glob_optimal_expect_sec,0.1,float )$ define_variable(glob_estimated_size_answer,100.0,float )$ define_variable(glob_almost_1,0.9990,float )$ define_variable(glob_clock_sec,0.0,float )$ define_variable(glob_clock_start_sec,0.0,float )$ define_variable(glob_disp_incr,0.1,float )$ define_variable(glob_h,0.1,float )$ define_variable(glob_diff_rc_fm,0.1,float )$ define_variable(glob_diff_rc_fmm1,0.1,float )$ define_variable(glob_diff_rc_fmm2,0.1,float )$ define_variable(glob_diff_ord_fm,0.1,float )$ define_variable(glob_diff_ord_fmm1,0.1,float )$ define_variable(glob_diff_ord_fmm2,0.1,float )$ define_variable(glob_six_term_ord_save,0.1,float )$ define_variable(glob_guess_error_rc,0.1,float )$ define_variable(glob_guess_error_ord,0.1,float )$ define_variable(glob_least_given_sing,9.9e200,float )$ define_variable(glob_least_ratio_sing,9.9e200,float )$ define_variable(glob_least_3_sing,9.9e100,float )$ define_variable(glob_least_6_sing,9.9e100,float )$ define_variable(glob_last_good_h,0.1,float )$ define_variable(glob_max_h,0.1,float )$ define_variable(glob_min_h,0.000001,float )$ define_variable(glob_display_interval,0.1,float )$ define_variable(glob_abserr,0.1e-10,float )$ define_variable(glob_relerr,0.1e-10,float )$ define_variable(glob_min_pole_est,0.1e+10,float )$ define_variable(glob_max_rel_trunc_err,0.1e-10,float )$ define_variable(glob_max_trunc_err,0.1e-10,float )$ define_variable(glob_max_hours,0.0,float )$ define_variable(glob_optimal_clock_start_sec,0.0,float )$ define_variable(glob_optimal_start,0.0,float )$ define_variable(glob_upper_ratio_limit,1.0001,float )$ define_variable(glob_lower_ratio_limit,0.9999,float )$ define_variable(glob_max_sec,10000.0,float )$ define_variable(glob_orig_start_sec,0.0,float )$ define_variable(glob_normmax,0.0,float )$ define_variable(glob_max_minutes,0.0,float )$ define_variable(glob_next_display,0.0,float )$ define_variable(glob_est_digits,1,fixnum )$ define_variable(glob_subiter_method,3,fixnum )$ define_variable(glob_html_log,true,boolean )$ define_variable(glob_min_good_digits,99999,fixnum )$ define_variable(glob_good_digits,0,fixnum )$ define_variable(glob_min_apfp_est_good_digits,99999,fixnum )$ define_variable(glob_apfp_est_good_digits,0,fixnum )$ define_variable(glob_max_opt_iter,10,fixnum )$ define_variable(glob_dump,false,boolean )$ define_variable(glob_djd_debug,true,boolean )$ define_variable(glob_display_flag,true,boolean )$ define_variable(glob_djd_debug2,true,boolean )$ define_variable(glob_h_reason,0,fixnum )$ define_variable(glob_sec_in_minute,60 ,fixnum )$ define_variable(glob_min_in_hour,60,fixnum )$ define_variable(glob_hours_in_day,24,fixnum )$ define_variable(glob_days_in_year,365,fixnum )$ define_variable(glob_sec_in_hour,3600,fixnum )$ define_variable(glob_sec_in_day,86400,fixnum )$ define_variable(glob_sec_in_year,31536000,fixnum )$ define_variable(glob_not_yet_finished,true,boolean )$ define_variable(glob_initial_pass,true,boolean )$ define_variable(glob_not_yet_start_msg,true,boolean )$ define_variable(glob_reached_optimal_h,false,boolean )$ define_variable(glob_optimal_done,false,boolean )$ define_variable(glob_type_given_pole,0,fixnum )$ define_variable(glob_optimize,false,boolean )$ define_variable(glob_look_poles,false,boolean )$ define_variable(glob_dump_closed_form,false,boolean )$ define_variable(glob_max_iter,1000,fixnum )$ define_variable(glob_no_eqs,0,fixnum )$ define_variable(glob_unchanged_h_cnt,0,fixnum )$ define_variable(glob_warned,false,boolean )$ define_variable(glob_warned2,false,boolean )$ define_variable(glob_start,0,fixnum )$ define_variable(glob_iter,0,fixnum )$ /* Bottom Generate Globals Deninition */ completearray(array_y_init,[40],float)$ completearray(array_norms,[40],float)$ completearray(array_fact_1,[40],float)$ completearray(array_1st_rel_error,[2],float)$ completearray(array_last_rel_error,[2],float)$ completearray(array_est_rel_error,[2],float)$ completearray(array_max_est_error,[2],float)$ completearray(array_type_pole,[2],float)$ completearray(array_type_real_pole,[2],float)$ completearray(array_type_complex_pole,[2],float)$ completearray(array_est_digits,[2],float)$ completearray(array_y,[40],float)$ completearray(array_x,[40],float)$ completearray(array_tmp0,[40],float)$ completearray(array_tmp1_g,[40],float)$ completearray(array_tmp1,[40],float)$ completearray(array_tmp2,[40],float)$ completearray(array_tmp3_g,[40],float)$ completearray(array_tmp3,[40],float)$ completearray(array_tmp4,[40],float)$ completearray(array_m1,[40],float)$ completearray(array_y_higher,[2,40],float)$ completearray(array_y_higher_work,[2,40],float)$ completearray(array_y_higher_work2,[2,40],float)$ completearray(array_y_set_initial,[2,40],float)$ completearray(array_given_rad_poles,[2,3],float)$ completearray(array_given_ord_poles,[2,3],float)$ completearray(array_rad_test_poles,[2,4],float)$ completearray(array_ord_test_poles,[2,4],float)$ completearray(array_fact_2,[40,40],float)$ /* before library and user */ /* BEGIN ATS LIBRARY BLOCK */ /* Begin Function number 2*/ omniout_str(iolevel,str) := ( if (glob_iolevel) >= iolevel then ( /* if number 1*/ printf(true,"~a~%",string(str)) )/* end if 1*/ )$ /* End Function number2 */ /* Begin Function number 3*/ omniout_str_noeol(iolevel,str) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ printf(true,"~a",string(str)) )/* end if 1*/ )$ /* End Function number3 */ /* Begin Function number 4*/ omniout_labstr(iolevel,label,str) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ printf(true,"~a = ~a~%",string(label),string(str)) )/* end if 1*/ )$ /* End Function number4 */ /* Begin Function number 5*/ omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ if vallen = 4 then ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) ) else ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) )/* end if 1*/ )/* end if 0*/ )$ /* End Function number5 */ omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 0*/ printf(true,"~a = ~d ~a~%",prelabel,value, postlabel), newline() )/* end if 0*/ )$ /* End Function number5 */ /* Begin Function number 6*/ omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 0*/ sprint(prelabel,"[",elemnt,"]=",value, postlabel), newline() )/* end if 0*/ )$ /* End Function number6 */ logitem_time(fd,secs_in) := ( block(modedeclare([[days_int,hours_int, minutes_int, sec_int, years_int],fixnum,[secs,secs_temp],float ]), secs : (secs_in), printf(fd,"~%"), if (secs >= 0) then ( /* if number 0*/ years_int : int_trunc(secs / glob_sec_in_year), sec_temp : mod(int_trunc(secs) , int_trunc(glob_sec_in_year)), days_int : int_trunc(sec_temp / glob_sec_in_day) , sec_temp : mod(sec_temp , int_trunc(glob_sec_in_day)) , hours_int : int_trunc(sec_temp / glob_sec_in_hour), sec_temp : mod(sec_temp , int_trunc(glob_sec_in_hour)), minutes_int : int_trunc(sec_temp / glob_sec_in_minute), sec_int : mod(sec_temp , int_trunc(glob_sec_in_minute)), if ((int_trunc(years_int)) > 0.1) then ( /* if number 1*/ 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 ( /* if number 2*/ printf(fd,"~d Days ~d Hours ~d Minutes ~d Seconds~%",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0.1) then ( /* if number 3*/ printf(fd,"~d Hours ~d Minutes ~d Seconds~%",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0.1) then ( /* if number 4*/ printf(fd,"~d Minutes ~d Seconds~%",minutes_int,sec_int) ) else ( printf(fd,"~d Seconds~%",sec_int) )/* end if 4*/ ) else ( printf(fd," 0.0 Seconds~%") )/* end if 3*/ , printf(fd,"~%") ),0 )$ /* End Function number6 */ /* Begin Function number 7*/ omniout_timestr(secs_in) := ( block(modedeclare([[days_int,hours_int, minutes_int, sec_int, years_int],fixnum,[secs,secs_temp],float ]), secs : (secs_in), if (secs >= 0) then ( /* if number 3*/ years_int : int_trunc(secs / glob_sec_in_year), sec_temp : mod(int_trunc(secs) , int_trunc(glob_sec_in_year)), days_int : int_trunc(sec_temp / glob_sec_in_day) , sec_temp : mod(sec_temp , int_trunc(glob_sec_in_day)) , hours_int : int_trunc(sec_temp / glob_sec_in_hour), sec_temp : mod(sec_temp , int_trunc(glob_sec_in_hour)), minutes_int : int_trunc(sec_temp / glob_sec_in_minute), sec_int : mod(sec_temp , int_trunc(glob_sec_in_minute)), if (years_int > 0) then ( /* if number 4*/ 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 ( /* if number 5*/ printf(true,"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0.1) then ( /* if number 6*/ printf(true,"= ~d Hours ~d Minutes ~d Seconds~%",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0.1) then ( /* if number 7*/ printf(true,"= ~d Minutes ~d Seconds~%",minutes_int,sec_int) ) else ( printf(true,"= ~d Seconds~%",sec_int) )/* end if 7*/ ) else ( printf(true,"= 0.0 Seconds~%") )/* end if 6*/ ),0 )$ /* End Function number7 */ /* Begin Function number 8*/ zero_ats_ar(arr_a) := ( block(modedeclare([ iii],fixnum), iii : 1, while (iii <= ats_max_terms) do ( /* do number 1*/ arr_a [iii] : glob__0, iii : iii + 1 )/* end do number 1*/ ),0 )$ /* End Function number8 */ /* Begin Function number 9*/ ats(mmm_ats,arr_a,arr_b,jjj_ats) := ( block(modedeclare([ [iii_ats, lll_ats,ma_ats],fixnum, [ret_ats],float]), ret_ats : glob__0, if (jjj_ats <= mmm_ats) then ( /* if number 6*/ ma_ats : mmm_ats + 1, iii_ats : jjj_ats, while (iii_ats <= mmm_ats) do ( /* do number 1*/ lll_ats : ma_ats - iii_ats, if ((lll_ats <= ats_max_terms and (iii_ats <= ats_max_terms) )) then ( /* if number 7*/ ret_ats : ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) )/* end if 7*/ , iii_ats : iii_ats + 1 )/* end do number 1*/ )/* end if 6*/ , ret_ats ) )$ /* End Function number9 */ /* Begin Function number 10*/ att(mmm_att,arr_aa,arr_bb,jjj_att) := ( block(modedeclare([ [al_att, iii_att,lll_att, ma_att],float , [ret_att],fixnum]), ret_att : glob__0, if (jjj_att < mmm_att) then ( /* if number 6*/ ma_att : mmm_att + 2, iii_att : jjj_att, while ((iii_att < mmm_att) and (iii_att <= ats_max_terms) ) do ( /* do number 1*/ lll_att : ma_att - iii_att, al_att : (lll_att - 1), if ((lll_att <= ats_max_terms and (iii_att <= ats_max_terms) )) then ( /* if number 7*/ ret_att : ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att) )/* end if 7*/ , iii_att : iii_att + 1 )/* end do number 1*/ , ret_att : ret_att / c(mmm_att) )/* end if 6*/ , ret_att ) )$ /* End Function number10 */ /* Begin Function number 11*/ logditto(file) := ( printf(file,""), printf(file,"ditto"), printf(file,""),0 )$ /* End Function number11 */ /* Begin Function number 12*/ logitem_integer(file,n) := ( printf(file,""), printf(file,"~d",n), printf(file,""),0 )$ /* End Function number12 */ /* Begin Function number 13*/ logitem_str(file,str) := ( printf(file,""), printf(file,str), printf(file,""),0 )$ /* End Function number13 */ /* Begin Function number 14*/ logitem_good_digits(file,rel_error) := ( block(modedeclare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"") ),0 )$ /* End Function number14 */ /* Begin Function number 15*/ log_revs(file,revs) := ( printf(file,revs) )$ /* End Function number15 */ /* Begin Function number 16*/ logitem_float(file,x) := ( printf(file,""), printf(file,"~g",x), printf(file,""),0 )$ /* End Function number16 */ /* Begin Function number 17*/ logitem_h_reason(file) := ( printf(file,""), if (glob_h_reason = 1) then ( /* if number 6*/ printf(file,"Max H") ) elseif (glob_h_reason = 2) then ( /* if number 7*/ printf(file,"Display_interval") ) elseif (glob_h_reason = 3) then ( /* if number 8*/ printf(file,"Optimal") ) elseif (glob_h_reason = 4) then ( /* if number 9*/ printf(file,"Pole Accuracy") ) elseif (glob_h_reason = 5) then ( /* if number 10*/ printf(file,"Min H (Pole)") ) elseif (glob_h_reason = 6) then ( /* if number 11*/ printf(file,"Pole") ) elseif (glob_h_reason = 7) then ( /* if number 12*/ printf(file,"Opt Iter") ) else ( printf(file,"Impossible") )/* end if 12*/ , printf(file,""),0 )$ /* End Function number17 */ /* Begin Function number 18*/ logstart(file) := ( printf(file,""),0 )$ /* End Function number18 */ /* Begin Function number 19*/ logend(file) := ( printf(file,"~%"),0 )$ /* End Function number19 */ /* Begin Function number 20*/ chk_data() := ( block(modedeclare([ [errflag],boolean]), errflag : false, if (glob_max_iter < 2) then ( /* if number 12*/ omniout_str(always,"Illegal max_iter"), errflag : true )/* end if 12*/ , if (errflag) then ( /* if number 12*/ quit() )/* end if 12*/ ),0 )$ /* End Function number20 */ /* Begin Function number 21*/ comp_expect_sec(t_end2,t_start2,t2,clock_sec2) := ( block(modedeclare([[ ms2, rrr, sec_left, sub1, sub2], float]), ms2 : c(clock_sec2), sub1 : c(t_end2-t_start2), sub2 : c(t2-t_start2), if (sub1 = glob__0) then ( /* if number 12*/ sec_left : glob__0 ) else ( if (sub2 > glob__0) then ( /* if number 13*/ rrr : (sub1/sub2), sec_left : rrr * c(ms2) - c(ms2) ) else ( sec_left : glob__0 )/* end if 13*/ )/* end if 12*/ , sec_left ) )$ /* End Function number21 */ /* Begin Function number 22*/ comp_percent(t_end2,t_start2, t2) := ( block(modedeclare([ [rrr, sub1, sub2],float]), sub1 : (t_end2-t_start2), sub2 : (t2-t_start2), if (sub2 > glob_small_float) then ( /* if number 12*/ rrr : (glob__100*sub2)/sub1 ) else ( rrr : 0.0 )/* end if 12*/ , rrr ) )$ /* End Function number22 */ /* Begin Function number 23*/ comp_rad_from_ratio(term1,term2,last_no) := ( /* TOP TWO TERM RADIUS ANALYSIS */ if (float_abs(term2) > glob__0) then ( /* if number 12*/ ret : float_abs(term1 * glob_h / term2) ) else ( ret : glob_larger_float )/* end if 12*/ , ret /* BOTTOM TWO TERM RADIUS ANALYSIS */ )$ /* End Function number23 */ /* Begin Function number 24*/ comp_ord_from_ratio(term1,term2,last_no) := ( /* TOP TWO TERM ORDER ANALYSIS */ if (float_abs(term2) > glob__0) then ( /* if number 12*/ ret : glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)) ) else ( ret : glob_larger_float )/* end if 12*/ , ret /* BOTTOM TWO TERM ORDER ANALYSIS */ )$ /* End Function number24 */ /* Begin Function number 25*/ c(in_val) := ( /* To Force Conversion when needed */ ret : in_val, ret /* End Conversion */ )$ /* End Function number25 */ /* Begin Function number 26*/ comp_rad_from_three_terms(term1,term2,term3,last_no) := ( /* TOP THREE TERM RADIUS ANALYSIS */ temp : float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3), if (float_abs(temp) > glob__0) then ( /* if number 12*/ ret : float_abs((term2*glob_h*term1)/(temp)) ) else ( ret : glob_larger_float )/* end if 12*/ , ret /* BOTTOM THREE TERM RADIUS ANALYSIS */ )$ /* End Function number26 */ /* Begin Function number 27*/ comp_ord_from_three_terms(term1,term2,term3,last_no) := ( /* TOP THREE TERM ORDER ANALYSIS */ ret : float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)), ret /* TOP THREE TERM ORDER ANALYSIS */ )$ /* End Function number27 */ /* Begin Function number 28*/ comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no) := ( /* TOP SIX TERM RADIUS ANALYSIS */ if ((term5 # glob__0) and (term4 # glob__0) and (term3 # glob__0) and (term2 # glob__0) and (term1 # glob__0)) then ( /* if number 12*/ rm0 : term6/term5, rm1 : term5/term4, rm2 : term4/term3, rm3 : term3/term2, rm4 : term2/term1, nr1 : c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2, nr2 : c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3, dr1 : glob__m1/rm1 + glob__2/rm2 - glob__1/rm3, dr2 : glob__m1/rm2 + glob__2/rm3 - glob__1/rm4, ds1 : glob__3/rm1 - glob__8/rm2 + glob__5/rm3, ds2 : glob__3/rm2 - glob__8/rm3 + glob__5/rm4, if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then ( /* if number 13*/ rad_c : glob_larger_float, ord_no : glob_larger_float ) else ( if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then ( /* if number 14*/ rcs : ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)), /* (Manuels) rcs : (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) */ ord_no : (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2, if (float_abs(rcs) # glob__0) then ( /* if number 15*/ if (rcs > glob__0) then ( /* if number 16*/ rad_c : sqrt(rcs) * float_abs(glob_h) ) else ( rad_c : glob_larger_float, ord_no : glob_larger_float )/* end if 16*/ ) else ( rad_c : glob_larger_float, ord_no : glob_larger_float )/* end if 15*/ ) else ( rad_c : glob_larger_float, ord_no : glob_larger_float )/* end if 14*/ )/* end if 13*/ ) else ( rad_c : glob_larger_float, ord_no : glob_larger_float )/* end if 12*/ , glob_six_term_ord_save : ord_no, rad_c /* BOTTOM SIX TERM RADIUS ANALYSIS */ )$ /* End Function number28 */ /* Begin Function number 29*/ comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no) := ( /* TOP SIX TERM ORDER ANALYSIS */ /* TOP SAVED FROM SIX TERM RADIUS ANALYSIS */ glob_six_term_ord_save /* BOTTOM SIX TERM ORDER ANALYSIS */ )$ /* End Function number29 */ /* Begin Function number 30*/ factorial_2(nnn) := ( block(modedeclare([[ ret],float]), ret : nnn!, ret ) )$ /* End Function number30 */ /* Begin Function number 31*/ factorial_1(nnn) := ( block(modedeclare([[ ret],float]), if (nnn <= ats_max_terms) then ( /* if number 12*/ if (array_fact_1[nnn] = 0) then ( /* if number 13*/ ret : factorial_2(nnn), array_fact_1[nnn] : ret ) else ( ret : array_fact_1[nnn] )/* end if 13*/ ) else ( ret : factorial_2(nnn) )/* end if 12*/ , ret ) )$ /* End Function number31 */ /* Begin Function number 32*/ factorial_1(in) := ( block(modedeclare([[ ret],float]), ret : (in!), ret ) )$ /* End Function number32 */ /* Begin Function number 33*/ neg(in) := ( block(modedeclare([[ ret],float]), ret : (-in), ret ) )$ /* End Function number33 */ /* Begin Function number 34*/ factorial_3(mmm,nnn) := ( block(modedeclare([ [ret],float]), if ((nnn <= ats_max_terms) and (mmm <= ats_max_terms)) then ( /* if number 12*/ if (array_fact_2[mmm,nnn] = 0) then ( /* if number 13*/ ret : factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn] : ret ) else ( ret : array_fact_2[mmm,nnn] )/* end if 13*/ ) else ( ret : factorial_2(mmm)/factorial_2(nnn) )/* end if 12*/ , ret ) )$ /* End Function number34 */ /* Begin Function number 35*/ log10(x) := ( (log(x)/glob_log_10) )$ /* End Function number35 */ /* Begin Function number 36*/ c(x) := ( x )$ /* End Function number36 */ /* Begin Function number 37*/ expt(x,y) := ( if (y = 0.0) then ( /* if number 12*/ 1.0 ) elseif ((x <= 0.0) and (y < 0.0)) then ( /* if number 13*/ print("expt error x = ",x,"y = ",y) ) else ( (x^y) )/* end if 13*/ )$ /* End Function number37 */ /* Begin Function number 38*/ 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(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))), omniout_float(always,"estimated_h",32,estimated_h,32,""), omniout_float(always,"estimated_answer",32,estimated_answer,32,""), omniout_float(always,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""), range : (x_end - x_start), omniout_float(always,"range",32,range,32,""), estimated_steps : range / estimated_h, omniout_float(always,"estimated_steps",32,estimated_steps,32,""), step_error : (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ats_max_terms))), omniout_float(always,"step_error",32,step_error,32,""), (step_error) ) )$ /* End Function number38 */ /* END ATS LIBRARY BLOCK */ /* BEGIN USER FUNCTION BLOCK */ /* BEGIN BLOCK 3 */ /* BEGIN USER DEF BLOCK */ exact_soln_y (x) := (block( (c(2.0) - c(cos(x)) - c(cos(x))) )); /* END USER DEF BLOCK */ /* END BLOCK 3 */ /* END USER FUNCTION BLOCK */ /* before write_aux functions */ /* Begin Function number 2*/ display_poles() := ( block(modedeclare([[rad_given],float]), if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then ( /* if number 1*/ rad_given : sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]), omniout_float(always,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "), omniout_float(always,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "), if (rad_given < glob_least_given_sing) then ( /* if number 2*/ glob_least_given_sing : rad_given )/* end if 2*/ ) elseif (glob_type_given_pole = 3) then ( /* if number 2*/ omniout_str(always,"NO POLE (given) for Equation 1") ) elseif (glob_type_given_pole = 5) then ( /* if number 3*/ omniout_str(always,"SOME POLE (given) for Equation 1") ) else ( omniout_str(always,"NO info (given) for Equation 1") )/* end if 3*/ , if (array_rad_test_poles[1,1] < glob_large_float) then ( /* if number 3*/ omniout_float(always,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "), if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then ( /* if number 4*/ glob_least_ratio_sing : array_rad_test_poles[1,1] )/* end if 4*/ , omniout_float(always,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ") ) else ( omniout_str(always,"NO POLE (ratio test) for Equation 1") )/* end if 3*/ , if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then ( /* if number 3*/ omniout_float(always,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "), if (array_rad_test_poles[1,2]< glob_least_3_sing) then ( /* if number 4*/ glob_least_3_sing : array_rad_test_poles[1,2] )/* end if 4*/ , omniout_float(always,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ") ) else ( omniout_str(always,"NO REAL POLE (three term test) for Equation 1") )/* end if 3*/ , if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then ( /* if number 3*/ omniout_float(always,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "), if (array_rad_test_poles[1,3]< glob_least_6_sing) then ( /* if number 4*/ glob_least_6_sing : array_rad_test_poles[1,3] )/* end if 4*/ , omniout_float(always,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ") ) else ( omniout_str(always,"NO COMPLEX POLE (six term test) for Equation 1") )/* end if 3*/ ),0 )$ /* End Function number2 */ /* Begin Function number 3*/ my_check_sign( x0 ,xf) := ( block( [ret], if (xf > x0) then ( /* if number 3*/ ret : glob__1 ) else ( ret : glob__m1 )/* end if 3*/ , ret ) )$ /* End Function number3 */ /* Begin Function number 4*/ est_size_answer() := ( block( [ min_size], min_size : glob_estimated_size_answer, if (float_abs(array_y[1]) < min_size) then ( /* if number 3*/ min_size : float_abs(array_y[1]), omniout_float(always,"min_size",32,min_size,32,"") )/* end if 3*/ , if (min_size < glob__1) then ( /* if number 3*/ min_size : glob__1, omniout_float(always,"min_size",32,min_size,32,"") )/* end if 3*/ , min_size ) )$ /* End Function number4 */ /* Begin Function number 5*/ 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 : glob__small, no_terms : ats_max_terms, hn_div_ho : glob__0_5, hn_div_ho_2 : glob__0_25, hn_div_ho_3 : glob__0_125, omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,""), omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,""), est_tmp : float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3), if (est_tmp >= max_estimated_step_error) then ( /* if number 3*/ max_estimated_step_error : est_tmp )/* end if 3*/ , omniout_float(always,"max_estimated_step_error",32,max_estimated_step_error,32,""), max_estimated_step_error ) )$ /* End Function number5 */ /* Begin Function number 6*/ track_estimated_error() := ( block ([hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp], no_terms : ats_max_terms, hn_div_ho : glob__0_5, hn_div_ho_2 : glob__0_25, hn_div_ho_3 : glob__0_125, est_tmp : c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3), if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then ( /* if number 3*/ est_tmp : c(glob_prec) * c(float_abs(array_y[1])) )/* end if 3*/ , if (c(est_tmp) >= c(array_max_est_error[1])) then ( /* if number 3*/ array_max_est_error[1] : c(est_tmp) )/* end if 3*/ ) )$ /* End Function number6 */ /* Begin Function number 7*/ reached_interval() := ( block(modedeclare([[ret],boolean]), if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then ( /* if number 3*/ ret : true ) else ( ret : false )/* end if 3*/ , return(ret) ) )$ /* End Function number7 */ /* Begin Function number 8*/ display_alot(iter) := ( block(modedeclare([[abserr,est_rel_err],float, [closed_form_val_y],float, [ind_var],float, [numeric_val],float, [relerr],float, [term_no],fixnum]), /* TOP DISPLAY ALOT */ if (reached_interval()) then ( /* if number 3*/ if (iter >= 0) then ( /* if number 4*/ ind_var : array_x[1], omniout_float(always,"x[1] ",33,ind_var,20," "), closed_form_val_y : exact_soln_y(ind_var), omniout_float(always,"y[1] (closed_form) ",33,closed_form_val_y,20," "), term_no : 1, numeric_val : array_y[term_no], abserr : float_abs(numeric_val - closed_form_val_y), omniout_float(always,"y[1] (numeric) ",33,numeric_val,20," "), if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then ( /* if number 5*/ relerr : abserr*glob__100/float_abs(closed_form_val_y), if (c(relerr) > c(glob_prec)) then ( /* if number 6*/ glob_good_digits : -floor(log10(c(relerr))) + 3 ) else ( glob_good_digits : 16 )/* end if 6*/ ) else ( relerr : glob__m1 , glob_good_digits : -16 )/* end if 5*/ , if (glob_good_digits < glob_min_good_digits) then ( /* if number 5*/ glob_min_good_digits : glob_good_digits )/* end if 5*/ , if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then ( /* if number 5*/ glob_min_apfp_est_good_digits : glob_apfp_est_good_digits )/* end if 5*/ , if (c(float_abs(numeric_val)) > c(glob_prec)) then ( /* if number 5*/ est_rel_err : c(array_max_est_error[1])*glob__100 * c(sqrt(glob_iter))*c(22)*c(ats_max_terms)/c(float_abs(numeric_val)), if (est_rel_err > glob_prec) then ( /* if number 6*/ glob_est_digits : -floor(log10(est_rel_err)) + 3 ) else ( glob_est_digits : 16 )/* end if 6*/ ) else ( relerr : glob__m1 , glob_est_digits : -16 )/* end if 5*/ , array_est_digits[1] : glob_est_digits, if (glob_iter = 1) then ( /* if number 5*/ array_1st_rel_error[1] : relerr ) else ( array_last_rel_error[1] : relerr )/* end if 5*/ , array_est_rel_error[1] : est_rel_err, omniout_float(always,"absolute error ",4,abserr,20," "), omniout_float(always,"relative error ",4,relerr,20,"%"), omniout_int(info,"Desired digits ",32,glob_desired_digits_correct,4," "), omniout_int(info,"Estimated correct digits ",32,glob_est_digits,4," "), omniout_int(info,"Correct digits ",32,glob_good_digits,4," ") , omniout_float(always,"h ",4,glob_h,20," ") )/* end if 4*/ /* BOTTOM DISPLAY ALOT */ )/* end if 3*/ ),0 )$ /* End Function number8 */ /* Begin Function number 9*/ prog_report(x_start,x_end) := ( block(modedeclare([ [clock_sec],float, [opt_clock_sec],float, [clock_sec1],float, [expect_sec],float, [left_sec],float, [percent_done],float, [total_clock_sec],float]), /* TOP PROGRESS REPORT */ clock_sec1 : elapsed_time_seconds(), total_clock_sec : (clock_sec1) - (glob_orig_start_sec), glob_clock_sec : (clock_sec1) - (glob_clock_start_sec), left_sec : (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1), expect_sec : comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)), opt_clock_sec : ( clock_sec1) - (glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)), glob_total_exp_sec : glob_optimal_expect_sec + c(total_clock_sec), percent_done : comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)), glob_percent_done : percent_done, omniout_str_noeol(info,"Total Elapsed Time "), omniout_timestr((total_clock_sec)), omniout_str_noeol(info,"Elapsed Time(since restart) "), omniout_timestr((glob_clock_sec)), if (c(percent_done) < glob__100) then ( /* if number 3*/ omniout_str_noeol(info,"Expected Time Remaining "), omniout_timestr((expect_sec)), omniout_str_noeol(info,"Optimized Time Remaining "), omniout_timestr((glob_optimal_expect_sec)), omniout_str_noeol(info,"Expected Total Time "), omniout_timestr((glob_total_exp_sec)) )/* end if 3*/ , omniout_str_noeol(info,"Time to Timeout "), omniout_timestr((left_sec)), omniout_float(info, "Percent Done ",33,percent_done,4,"%") /* BOTTOM PROGRESS REPORT */ ),0 )$ /* End Function number9 */ /* Begin Function number 10*/ check_for_pole() := ( block(modedeclare([cnt],fixnum,[ dr1, dr2, ds1, ds2, hdrc],float ,[ m, n],fixnum,[ nr1, nr2],float,[ 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],float ,[ found_sing],fixnum ,[ h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad],float, [last_no],fixnum), /* TOP CHECK FOR POLE */ tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles[1,1] : glob_larger_float, array_ord_test_poles[1,1] : glob_larger_float, found_sing : 1, last_no : ats_max_terms - 1 - 10, cnt : 0, while (last_no < ats_max_terms-3 and found_sing = 1) do ( /* do number 1*/ tmp_rad : comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), if (float_abs(prev_tmp_rad) > glob__0) then ( /* if number 3*/ tmp_ratio : tmp_rad / prev_tmp_rad ) else ( tmp_ratio : glob_large_float )/* end if 3*/ , if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then ( /* if number 3*/ rad_c : tmp_rad ) elseif (cnt = 0) then ( /* if number 4*/ rad_c : tmp_rad ) elseif (cnt > 0) then ( /* if number 5*/ found_sing : 0 )/* end if 5*/ , prev_tmp_rad : tmp_rad, cnt : cnt + 1, last_no : last_no + 1 )/* end do number 1*/ , if (found_sing = 1) then ( /* if number 5*/ if (rad_c < array_rad_test_poles[1,1]) then ( /* if number 6*/ array_rad_test_poles[1,1] : rad_c, last_no : last_no - 1, tmp_ord : comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), array_rad_test_poles[1,1] : rad_c, array_ord_test_poles[1,1] : tmp_ord )/* end if 6*/ )/* end if 5*/ , /* BOTTOM general radius test1 */ tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles[1,2] : glob_larger_float, array_ord_test_poles[1,2] : glob_larger_float, found_sing : 1, last_no : ats_max_terms - 1 - 10, cnt : 0, while (last_no < ats_max_terms-4 and found_sing = 1) do ( /* do number 1*/ tmp_rad : comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), if (float_abs(prev_tmp_rad) > glob__0) then ( /* if number 5*/ tmp_ratio : tmp_rad / prev_tmp_rad ) else ( tmp_ratio : glob_large_float )/* end if 5*/ , if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then ( /* if number 5*/ rad_c : tmp_rad ) elseif (cnt = 0) then ( /* if number 6*/ rad_c : tmp_rad ) elseif (cnt > 0) then ( /* if number 7*/ found_sing : 0 )/* end if 7*/ , prev_tmp_rad : tmp_rad, cnt : cnt + 1, last_no : last_no + 1 )/* end do number 1*/ , if (found_sing = 1) then ( /* if number 7*/ if (rad_c < array_rad_test_poles[1,2]) then ( /* if number 8*/ array_rad_test_poles[1,2] : rad_c, last_no : last_no - 1, tmp_ord : comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), array_rad_test_poles[1,2] : rad_c, if (rad_c < glob_min_pole_est) then ( /* if number 9*/ glob_min_pole_est : rad_c )/* end if 9*/ , array_ord_test_poles[1,2] : tmp_ord )/* end if 8*/ )/* end if 7*/ , /* BOTTOM general radius test1 */ tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles[1,3] : glob_larger_float, array_ord_test_poles[1,3] : glob_larger_float, found_sing : 1, last_no : ats_max_terms - 1 - 10, cnt : 0, while (last_no < ats_max_terms-7 and found_sing = 1) do ( /* do number 1*/ tmp_rad : comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), if (float_abs(prev_tmp_rad) > glob__0) then ( /* if number 7*/ tmp_ratio : tmp_rad / prev_tmp_rad ) else ( tmp_ratio : glob_large_float )/* end if 7*/ , if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then ( /* if number 7*/ rad_c : tmp_rad ) elseif (cnt = 0) then ( /* if number 8*/ rad_c : tmp_rad ) elseif (cnt > 0) then ( /* if number 9*/ found_sing : 0 )/* end if 9*/ , prev_tmp_rad : tmp_rad, cnt : cnt + 1, last_no : last_no + 1 )/* end do number 1*/ , if (found_sing = 1) then ( /* if number 9*/ if (rad_c < array_rad_test_poles[1,3]) then ( /* if number 10*/ array_rad_test_poles[1,3] : rad_c, last_no : last_no - 1, tmp_ord : comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no), array_rad_test_poles[1,3] : rad_c, if (rad_c < glob_min_pole_est) then ( /* if number 11*/ glob_min_pole_est : rad_c )/* end if 11*/ , array_ord_test_poles[1,3] : tmp_ord )/* end if 10*/ )/* end if 9*/ , /* BOTTOM general radius test1 */ /* START ADJUST ALL SERIES */ if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then ( /* if number 9*/ h_new : glob_check_sign * glob_min_pole_est * glob_ratio_of_radius, omniout_str(always,"SETTING H FOR POLE"), glob_h_reason : 6, if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then ( /* if number 10*/ omniout_str(always,"SETTING H FOR MIN H"), h_new : glob_min_h, glob_h_reason : 5 )/* end if 10*/ , term : 1, ratio : c(1.0), while (term <= ats_max_terms) do ( /* do number 1*/ array_y[term] : array_y[term]* ratio, array_y_higher[1,term] : array_y_higher[1,term]* ratio, array_x[term] : array_x[term]* ratio, ratio : ratio * h_new / float_abs(glob_h), term : term + 1 )/* end do number 1*/ , glob_h : h_new )/* end if 9*/ /* BOTTOM ADJUST ALL SERIES */ , if (reached_interval()) then ( /* if number 9*/ display_poles() )/* end if 9*/ ),0 )$ /* End Function number10 */ /* Begin Function number 11*/ atomall() := ( block(modedeclare([ [kkk, order_d],fixnum,[ adj2, adj3, temporary, term,temp,temp2],float]), /* TOP ATOMALL */ /* END OUTFILE1 */ /* BEGIN OUTFILE2 */ /* END OUTFILE2 */ /* BEGIN ATOMHDR1 */ /* emit pre sin 1 $eq_no = 1 */ array_tmp1[1] : sin(array_x[1]), array_tmp1_g[1] : cos(array_x[1]), /* emit pre add CONST FULL $eq_no = 1 i = 1 */ array_tmp2[1] : array_const_0D0[1] + array_tmp1[1], /* emit pre sin 1 $eq_no = 1 */ array_tmp3[1] : sin(array_x[1]), array_tmp3_g[1] : cos(array_x[1]), /* emit pre add FULL FULL $eq_no = 1 i = 1 */ array_tmp4[1] : array_tmp2[1] + array_tmp3[1], /* emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 */ if ( not array_y_set_initial[1,2]) then ( /* if number 1*/ if (1 <= ats_max_terms) then ( /* if number 2*/ temporary : c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)), if (2 <= ats_max_terms) then ( /* if number 3*/ array_y[2] : temporary, array_y_higher[1,2] : temporary )/* end if 3*/ , temporary : c(temporary) / c(glob_h) * c(1), array_y_higher[2,1] : c(temporary), 0 )/* end if 2*/ )/* end if 1*/ , kkk : 2, /* END ATOMHDR1 */ /* BEGIN ATOMHDR2 */ /* emit pre sin ID_LINEAR iii = 2 $eq_no = 1 */ array_tmp1[2] : array_tmp1_g[1] * array_x[2] / c(1), array_tmp1_g[2] : neg(array_tmp1[1]) * array_x[2] / c(1), /* emit pre add CONST FULL $eq_no = 1 i = 2 */ array_tmp2[2] : array_tmp1[2], /* emit pre sin ID_LINEAR iii = 2 $eq_no = 1 */ array_tmp3[2] : array_tmp3_g[1] * array_x[2] / c(1), array_tmp3_g[2] : neg(array_tmp3[1]) * array_x[2] / c(1), /* emit pre add FULL FULL $eq_no = 1 i = 2 */ array_tmp4[2] : array_tmp2[2] + array_tmp3[2], /* emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 */ if ( not array_y_set_initial[1,3]) then ( /* if number 1*/ if (2 <= ats_max_terms) then ( /* if number 2*/ temporary : c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)), if (3 <= ats_max_terms) then ( /* if number 3*/ array_y[3] : temporary, array_y_higher[1,3] : temporary )/* end if 3*/ , temporary : c(temporary) / c(glob_h) * c(2), array_y_higher[2,2] : c(temporary), 0 )/* end if 2*/ )/* end if 1*/ , kkk : 3, /* END ATOMHDR2 */ /* BEGIN ATOMHDR3 */ /* emit pre sin ID_LINEAR iii = 3 $eq_no = 1 */ array_tmp1[3] : array_tmp1_g[2] * array_x[2] / c(2), array_tmp1_g[3] : neg(array_tmp1[2]) * array_x[2] / c(2), /* emit pre add CONST FULL $eq_no = 1 i = 3 */ array_tmp2[3] : array_tmp1[3], /* emit pre sin ID_LINEAR iii = 3 $eq_no = 1 */ array_tmp3[3] : array_tmp3_g[2] * array_x[2] / c(2), array_tmp3_g[3] : neg(array_tmp3[2]) * array_x[2] / c(2), /* emit pre add FULL FULL $eq_no = 1 i = 3 */ array_tmp4[3] : array_tmp2[3] + array_tmp3[3], /* emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 */ if ( not array_y_set_initial[1,4]) then ( /* if number 1*/ if (3 <= ats_max_terms) then ( /* if number 2*/ temporary : c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)), if (4 <= ats_max_terms) then ( /* if number 3*/ array_y[4] : temporary, array_y_higher[1,4] : temporary )/* end if 3*/ , temporary : c(temporary) / c(glob_h) * c(3), array_y_higher[2,3] : c(temporary), 0 )/* end if 2*/ )/* end if 1*/ , kkk : 4, /* END ATOMHDR3 */ /* BEGIN ATOMHDR4 */ /* emit pre sin ID_LINEAR iii = 4 $eq_no = 1 */ array_tmp1[4] : array_tmp1_g[3] * array_x[2] / c(3), array_tmp1_g[4] : neg(array_tmp1[3]) * array_x[2] / c(3), /* emit pre add CONST FULL $eq_no = 1 i = 4 */ array_tmp2[4] : array_tmp1[4], /* emit pre sin ID_LINEAR iii = 4 $eq_no = 1 */ array_tmp3[4] : array_tmp3_g[3] * array_x[2] / c(3), array_tmp3_g[4] : neg(array_tmp3[3]) * array_x[2] / c(3), /* emit pre add FULL FULL $eq_no = 1 i = 4 */ array_tmp4[4] : array_tmp2[4] + array_tmp3[4], /* emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 */ if ( not array_y_set_initial[1,5]) then ( /* if number 1*/ if (4 <= ats_max_terms) then ( /* if number 2*/ temporary : c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)), if (5 <= ats_max_terms) then ( /* if number 3*/ array_y[5] : temporary, array_y_higher[1,5] : temporary )/* end if 3*/ , temporary : c(temporary) / c(glob_h) * c(4), array_y_higher[2,4] : c(temporary), 0 )/* end if 2*/ )/* end if 1*/ , kkk : 5, /* END ATOMHDR4 */ /* BEGIN ATOMHDR5 */ /* emit pre sin ID_LINEAR iii = 5 $eq_no = 1 */ array_tmp1[5] : array_tmp1_g[4] * array_x[2] / c(4), array_tmp1_g[5] : neg(array_tmp1[4]) * array_x[2] / c(4), /* emit pre add CONST FULL $eq_no = 1 i = 5 */ array_tmp2[5] : array_tmp1[5], /* emit pre sin ID_LINEAR iii = 5 $eq_no = 1 */ array_tmp3[5] : array_tmp3_g[4] * array_x[2] / c(4), array_tmp3_g[5] : neg(array_tmp3[4]) * array_x[2] / c(4), /* emit pre add FULL FULL $eq_no = 1 i = 5 */ array_tmp4[5] : array_tmp2[5] + array_tmp3[5], /* emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 */ if ( not array_y_set_initial[1,6]) then ( /* if number 1*/ if (5 <= ats_max_terms) then ( /* if number 2*/ temporary : c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)), if (6 <= ats_max_terms) then ( /* if number 3*/ array_y[6] : temporary, array_y_higher[1,6] : temporary )/* end if 3*/ , temporary : c(temporary) / c(glob_h) * c(5), array_y_higher[2,5] : c(temporary), 0 )/* end if 2*/ )/* end if 1*/ , kkk : 6, /* END ATOMHDR5 */ /* BEGIN OUTFILE3 */ /* Top Atomall While Loop-- outfile3 */ while (kkk <= ats_max_terms) do ( /* do number 1*/ /* END OUTFILE3 */ /* BEGIN OUTFILE4 */ /* emit sin LINEAR $eq_no = 1 */ array_tmp1[kkk] : array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1), array_tmp1_g[kkk] : neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1), /* emit NOT FULL - FULL add $eq_no = 1 */ array_tmp2[kkk] : array_tmp1[kkk], /* emit sin LINEAR $eq_no = 1 */ array_tmp3[kkk] : array_tmp3_g[kkk - 1] * array_x[2] / c(kkk - 1), array_tmp3_g[kkk] : neg(array_tmp3[kkk - 1]) * array_x[2] / c(kkk - 1), /* emit FULL - FULL add $eq_no = 1 */ array_tmp4[kkk] : array_tmp2[kkk] + array_tmp3[kkk], /* emit assign $eq_no = 1 */ order_d : 1, if (kkk + order_d <= ats_max_terms) then ( /* if number 1*/ if ( not array_y_set_initial[1,kkk + order_d]) then ( /* if number 2*/ temporary : c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))), array_y[kkk + order_d] : c(temporary), array_y_higher[1,kkk + order_d] : c(temporary), term : kkk + order_d - 1, adj2 : kkk + order_d - 1, adj3 : 2, while ((term >= 1) and (term <= ats_max_terms) and (adj3 < order_d + 1)) do ( /* do number 1*/ if (adj3 <= order_d + 1) then ( /* if number 3*/ if (adj2 > 0) then ( /* if number 4*/ temporary : c(temporary) / c(glob_h) * c(adj2) ) else ( temporary : c(temporary) )/* end if 4*/ , array_y_higher[adj3,term] : c(temporary) )/* end if 3*/ , term : term - 1, adj2 : adj2 - 1, adj3 : adj3 + 1 )/* end do number 1*/ )/* end if 2*/ )/* end if 1*/ , kkk : kkk + 1 )/* end do number 1*/ /* BOTTOM ATOMALL */ /* END OUTFILE4 */ /* BEGIN OUTFILE5 */ ),0 /* BOTTOM ATOMALL ??? */ )$ /* End Function number13 */ /* END OUTFILE5 */ /* before write ccc cpp library user def */ /* BEGIN ATS LIBRARY BLOCK */ /* END ATS LIBRARY BLOCK */ /* BEGIN USER FUNCTION BLOCK */ /* BEGIN BLOCK 3 */ /* BEGIN USER DEF BLOCK */ exact_soln_y (x) := (block( (c(2.0) - c(cos(x)) - c(cos(x))) )); /* END USER DEF BLOCK */ /* END BLOCK 3 */ /* END USER FUNCTION BLOCK */ /* Begin Function number 12*/ main_prog() := ( /* BEGIN OUTFIEMAIN */ block(modedeclare([[ d1,d2,d3,d4,est_err_2,display_max],float,[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],float,[current_iter],fixnum,[ x_start,x_end ],float,[it, opt_iter],fixnum, [tmp],float,[subiter],fixnum,[ est_needed_step_err,estimated_step_error,min_value,est_answer,last_min_pole_est],float,[repeat_it],fixnum],[found_h],boolean), /* before first input block */ /* BEGIN FIRST INPUT BLOCK */ /* BEGIN BLOCK 1 */ /* BEGIN FIRST INPUT BLOCK */ max_terms:40, Digits:32, /* END BLOCK 1 */ /* END FIRST INPUT BLOCK */ /* START OF INITS AFTER INPUT BLOCK */ glob_html_log : true, /* END OF INITS AFTER INPUT BLOCK */ /* before generate arrays */ /*before arrays initialized */ term : 1, while (term <= 40) do ( /* do number 1*/ array_y_init[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_norms[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_fact_1[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_1st_rel_error[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_last_rel_error[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_est_rel_error[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_max_est_error[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_pole[term] : 0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_real_pole[term] : 0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_complex_pole[term] : 0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_est_digits[term] : 0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_y[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_x[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp0[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp1_g[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp1[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp2[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp3_g[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp3[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_tmp4[term] : c(0.0), term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 40) do ( /* do number 1*/ array_m1[term] : c(0.0), term : term + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 40) do ( /* do number 2*/ array_y_higher[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 40) do ( /* do number 2*/ array_y_higher_work[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 40) do ( /* do number 2*/ array_y_higher_work2[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 40) do ( /* do number 2*/ array_y_set_initial[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_given_rad_poles[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_given_ord_poles[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 4) do ( /* do number 2*/ array_rad_test_poles[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 4) do ( /* do number 2*/ array_ord_test_poles[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=40) do ( /* do number 1*/ term : 1, while (term <= 40) do ( /* do number 2*/ array_fact_2[ord,term] : c(0.0), term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , /*before symbols initialized */ /* BEGIN SYMBOLS INITIALIZATED */ zero_ats_ar(array_y), zero_ats_ar(array_x), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3_g), zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4), zero_ats_ar(array_m1), zero_ats_ar(array_const_1), array_const_1[1] : c(1), zero_ats_ar(array_const_0D0), array_const_0D0[1] : c(0.0), zero_ats_ar(array_m1), array_m1[1] : glob__m1, /* END SYMBOLS INITIALIZATED */ /*before generate factorials init */ /* Initing Factorial Tables */ iiif : 0, while (iiif <= ats_max_terms) do ( /* do number 1*/ jjjf : 0, while (jjjf <= ats_max_terms) do ( /* do number 2*/ array_fact_1[iiif] : 0, array_fact_2[iiif,jjjf] : 0, jjjf : jjjf + 1 )/* end do number 2*/ , iiif : iiif + 1 )/* end do number 1*/ , /* Done Initing Factorial Table */ /*before generate set diff initial */ array_y_set_initial[1,1] : true, array_y_set_initial[1,2] : false, array_y_set_initial[1,3] : false, array_y_set_initial[1,4] : false, array_y_set_initial[1,5] : false, array_y_set_initial[1,6] : false, array_y_set_initial[1,7] : false, array_y_set_initial[1,8] : false, array_y_set_initial[1,9] : false, array_y_set_initial[1,10] : false, array_y_set_initial[1,11] : false, array_y_set_initial[1,12] : false, array_y_set_initial[1,13] : false, array_y_set_initial[1,14] : false, array_y_set_initial[1,15] : false, array_y_set_initial[1,16] : false, array_y_set_initial[1,17] : false, array_y_set_initial[1,18] : false, array_y_set_initial[1,19] : false, array_y_set_initial[1,20] : false, array_y_set_initial[1,21] : false, array_y_set_initial[1,22] : false, array_y_set_initial[1,23] : false, array_y_set_initial[1,24] : false, array_y_set_initial[1,25] : false, array_y_set_initial[1,26] : false, array_y_set_initial[1,27] : false, array_y_set_initial[1,28] : false, array_y_set_initial[1,29] : false, array_y_set_initial[1,30] : false, array_y_set_initial[1,31] : false, array_y_set_initial[1,32] : false, array_y_set_initial[1,33] : false, array_y_set_initial[1,34] : false, array_y_set_initial[1,35] : false, array_y_set_initial[1,36] : false, array_y_set_initial[1,37] : false, array_y_set_initial[1,38] : false, array_y_set_initial[1,39] : false, array_y_set_initial[1,40] : false, /*before generate init omniout const */ /* set default block */ /* Write Set Defaults */ glob_log_10 : log(10.0), 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/addpostode.ode#################"), omniout_str(always,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"max_terms:40,"), omniout_str(always,"Digits:32,"), omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(-5.0),"), omniout_str(always,"x_end:c(5.0),"), omniout_str(always,"array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,""), omniout_str(always,""), omniout_str(always,""), omniout_str(always,""), omniout_str(always,""), omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:3,"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always," (c(2.0) - c(cos(x)) - c(cos(x))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always,"#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : glob__0, glob_smallish_float : glob__0, glob_large_float : c(1.0e100), glob_larger_float : c( 1.1e100), glob_almost_1 : c( 0.99), /* before second block */ /* TOP SECOND INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* BEGIN BLOCK 2 */ /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start:c(-5.0), x_end:c(5.0), array_y_init[0 + 1] : exact_soln_y(x_start), glob_look_poles:true, glob_type_given_pole:3, /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct:8, glob_max_minutes:(3.0), glob_subiter_method:3, glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999), glob_look_poles:false, glob_h:c(0.001), glob_display_interval:c(0.01), /* END OVERRIDE BLOCK */ /* END BLOCK 2 */ /* END SECOND INPUT BLOCK */ /* BEGIN INITS AFTER SECOND INPUT BLOCK */ glob_last_good_h : glob_h, glob_max_sec : (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours), glob_check_sign : c(my_check_sign(x_start,x_end)), glob__pi : 3.141592654, glob_prec : 1.0e-16, if (glob_optimize) then ( /* if number 9*/ /* BEGIN OPTIMIZE CODE */ omniout_str(always,"START of Optimize"), /* Start Series -- INITIALIZE FOR OPTIMIZE */ found_h : false, glob_min_pole_est : glob_larger_float, last_min_pole_est : glob_larger_float, glob_least_given_sing : glob_larger_float, glob_least_ratio_sing : glob_larger_float, glob_least_3_sing : glob_larger_float, glob_least_6_sing : glob_larger_float, glob_min_h : float_abs(glob_min_h) * glob_check_sign, glob_max_h : float_abs(glob_max_h) * glob_check_sign, glob_h : float_abs(glob_min_h) * glob_check_sign, glob_display_interval : c((float_abs(c(glob_display_interval))) * (glob_check_sign)), display_max : c(x_end) - c(x_start)/glob__10, if ((glob_display_interval) > (display_max)) then ( /* if number 10*/ glob_display_interval : c(display_max) )/* end if 10*/ , chk_data(), min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32,est_needed_step_err,16,""), estimated_step_error : glob_small_float, while ((opt_iter <= 100) and ( not found_h)) do ( /* do number 1*/ omniout_int(always,"opt_iter",32,opt_iter,4,""), array_x[1] : c(x_start), array_x[2] : c(glob_h), glob_next_display : c(x_start), order_diff : 1, /* Start Series array_y */ term_no : 1, while (term_no <= order_diff) do ( /* do number 2*/ array_y[term_no] : array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)), term_no : term_no + 1 )/* end do number 2*/ , rows : order_diff, r_order : 1, while (r_order <= rows) do ( /* do number 2*/ term_no : 1, while (term_no <= (rows - r_order + 1)) do ( /* do number 3*/ it : term_no + r_order - 1, if (term_no < ats_max_terms) then ( /* if number 10*/ array_y_higher[r_order,term_no] : array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))) )/* end if 10*/ , term_no : term_no + 1 )/* end do number 3*/ , r_order : r_order + 1 )/* end do number 2*/ , atomall(), if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then ( /* if number 10*/ omniout_str(always,"SETTING H FOR MIN H"), glob_h : glob_check_sign * float_abs(glob_min_h), glob_h_reason : 1, found_h : true )/* end if 10*/ , if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then ( /* if number 10*/ omniout_str(always,"SETTING H FOR DISPLAY INTERVAL"), glob_h_reason : 2, glob_h : glob_display_interval, found_h : true )/* end if 10*/ , if (glob_look_poles) then ( /* if number 10*/ check_for_pole() )/* end if 10*/ , if ( not found_h) then ( /* if number 10*/ est_answer : est_size_answer(), est_needed_step_err : estimated_needed_step_error(x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32,est_needed_step_err,16,""), estimated_step_error : test_suggested_h(), omniout_float(always,"estimated_step_error",32,estimated_step_error,32,""), if (estimated_step_error < est_needed_step_err) then ( /* if number 11*/ omniout_str(always,"Double H and LOOP"), glob_h : glob_h*glob__2 ) else ( omniout_str(always,"Found H for OPTIMAL"), found_h : true, glob_h_reason : 3, glob_h : glob_h/glob__2 )/* end if 11*/ )/* end if 10*/ , opt_iter : opt_iter + 1 )/* end do number 1*/ , if (( not found_h) and (opt_iter = 1)) then ( /* if number 10*/ omniout_str(always,"Beginning glob_h too large."), found_h : false )/* end if 10*/ , if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then ( /* if number 10*/ omniout_str(always,"SETTING H FOR MAX H"), glob_h : glob_check_sign * float_abs(glob_max_h), glob_h_reason : 1, found_h : true )/* end if 10*/ ) else ( found_h : true, glob_h : glob_h * glob_check_sign )/* end if 9*/ , /* END OPTIMIZE CODE */ if (glob_html_log) then ( /* if number 9*/ html_log_file : openw("entry.html") )/* end if 9*/ , /* BEGIN SOLUTION CODE */ if (found_h) then ( /* if number 9*/ omniout_str(always,"START of Soultion"), /* Start Series -- INITIALIZE FOR SOLUTION */ array_x[1] : c(x_start), array_x[2] : c(glob_h), glob_next_display : c(x_start), glob_min_pole_est : glob_larger_float, glob_least_given_sing : glob_larger_float, glob_least_ratio_sing : glob_larger_float, glob_least_3_sing : glob_larger_float, glob_least_6_sing : glob_larger_float, order_diff : 1, /* Start Series array_y */ term_no : 1, while (term_no <= order_diff) do ( /* do number 1*/ array_y[term_no] : array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)), term_no : term_no + 1 )/* end do number 1*/ , rows : order_diff, r_order : 1, while (r_order <= rows) do ( /* do number 1*/ term_no : 1, while (term_no <= (rows - r_order + 1)) do ( /* do number 2*/ it : term_no + r_order - 1, if (term_no < ats_max_terms) then ( /* if number 10*/ array_y_higher[r_order,term_no] : array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))) )/* end if 10*/ , term_no : term_no + 1 )/* end do number 2*/ , r_order : r_order + 1 )/* end do number 1*/ , current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_iter : 0, omniout_str(debugl," "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do ( /* do number 1*/ /* left paren 0001C */ if (reached_interval()) then ( /* if number 10*/ omniout_str(info," "), omniout_str(info,"TOP MAIN SOLVE Loop") )/* end if 10*/ , glob_iter : glob_iter + 1, glob_clock_sec : elapsed_time_seconds(), track_estimated_error(), atomall(), track_estimated_error(), display_alot(current_iter), if (glob_look_poles) then ( /* if number 10*/ check_for_pole() )/* end if 10*/ , if (reached_interval()) then ( /* if number 10*/ glob_next_display : glob_next_display + glob_display_interval )/* end if 10*/ , array_x[1] : array_x[1] + glob_h, array_x[2] : glob_h /* Jump Series array_y */, order_diff : 2, /* START PART 1 SUM AND ADJUST */ /* START SUM AND ADJUST EQ =1 */ /* sum_and_adjust array_y */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 2, calc_term : 1, /* adjust_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[2,iii] : array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : glob__0, ord : 2, calc_term : 1, /* sum_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 2, /* adjust_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : glob__0, ord : 1, calc_term : 2, /* sum_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 1, /* adjust_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : glob__0, ord : 1, calc_term : 1, /* sum_subseriesarray_y */ iii : ats_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* END SUM AND ADJUST EQ =1 */ /* END PART 1 */ /* START PART 2 MOVE TERMS to REGULAR Array */ term_no : ats_max_terms, while (term_no >= 1) do ( /* do number 2*/ array_y[term_no] : array_y_higher_work2[1,term_no], ord : 1, while (ord <= order_diff) do ( /* do number 3*/ array_y_higher[ord,term_no] : array_y_higher_work2[ord,term_no], ord : ord + 1 )/* end do number 3*/ , term_no : term_no - 1 )/* end do number 2*/ /* END PART 2 HEVE MOVED TERMS to REGULAR Array */ )/* end do number 1*/ ,/* right paren 0001C */ omniout_str(always,"Finished!"), if (glob_iter >= glob_max_iter) then ( /* if number 10*/ omniout_str(always,"Maximum Iterations Reached before Solution Completed!") )/* end if 10*/ , if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then ( /* if number 10*/ omniout_str(always,"Maximum Time Reached before Solution Completed!") )/* end if 10*/ , glob_clock_sec : elapsed_time_seconds(), omniout_str(info,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; "), omniout_int(info,"Iterations ",32,glob_iter,4," ") , prog_report(x_start,x_end), if (glob_html_log) then ( /* if number 10*/ logstart(html_log_file), logitem_str(html_log_file,"2015-04-24T20:19:27-05:00") , logitem_str(html_log_file,"Maxima") , logitem_str(html_log_file,"add") , logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ") , logitem_float(html_log_file,x_start) , logitem_float(html_log_file,x_end) , logitem_float(html_log_file,array_x[1]) , logitem_float(html_log_file,glob_h) , logitem_h_reason(html_log_file) , logitem_str(html_log_file,"16") , logitem_float(html_log_file,glob_desired_digits_correct) , if (array_est_digits[1] # -16) then ( /* if number 11*/ logitem_integer(html_log_file,array_est_digits[1]) , 0 ) else ( logitem_str(html_log_file,"Unknown") , 0 )/* end if 11*/ , if (glob_min_good_digits # -16) then ( /* if number 11*/ logitem_integer(html_log_file,glob_min_good_digits) , 0 ) else ( logitem_str(html_log_file,"Unknown") , 0 )/* end if 11*/ , if (glob_good_digits # -16) then ( /* if number 11*/ logitem_integer(html_log_file,glob_good_digits) , 0 ) else ( logitem_str(html_log_file,"Unknown") , 0 )/* end if 11*/ , logitem_str(html_log_file,"NA") , logitem_str(html_log_file,"NA") , logitem_integer(html_log_file,ats_max_terms) , if (glob_type_given_pole = 0) then ( /* if number 11*/ logitem_str(html_log_file,"Not Given") , logitem_str(html_log_file,"NA") , 0 ) elseif (glob_type_given_pole = 4) then ( /* if number 12*/ logitem_str(html_log_file,"No Solution") , logitem_str(html_log_file,"NA") , 0 ) elseif (glob_type_given_pole = 5) then ( /* if number 13*/ logitem_str(html_log_file,"Some Pole") , logitem_str(html_log_file,"????") , 0 ) elseif (glob_type_given_pole = 3) then ( /* if number 14*/ logitem_str(html_log_file,"No Pole") , logitem_str(html_log_file,"NA") , 0 ) elseif (glob_type_given_pole = 1) then ( /* if number 15*/ logitem_str(html_log_file,"Real Sing") , logitem_float(html_log_file,glob_least_given_sing) , 0 ) elseif (glob_type_given_pole = 2) then ( /* if number 16*/ logitem_str(html_log_file,"Complex Sing") , logitem_float(html_log_file,glob_least_given_sing) , 0 )/* end if 16*/ , if (glob_least_ratio_sing < glob_large_float) then ( /* if number 16*/ logitem_float(html_log_file,glob_least_ratio_sing) , 0 ) else ( logitem_str(html_log_file,"NONE") , 0 )/* end if 16*/ , if (glob_least_3_sing < glob_large_float) then ( /* if number 16*/ logitem_float(html_log_file,glob_least_3_sing) , 0 ) else ( logitem_str(html_log_file,"NONE") , 0 )/* end if 16*/ , if (glob_least_6_sing < glob_large_float) then ( /* if number 16*/ logitem_float(html_log_file,glob_least_6_sing) , 0 ) else ( logitem_str(html_log_file,"NONE") , 0 )/* end if 16*/ , logitem_integer(html_log_file,glob_iter) , logitem_time(html_log_file,(glob_clock_sec)) , if (c(glob_percent_done) < glob__100) then ( /* if number 16*/ logitem_time(html_log_file,(glob_total_exp_sec)) , 0 ) else ( logitem_str(html_log_file,"Done") , 0 )/* end if 16*/ , log_revs(html_log_file," 308.maple.seems.ok ") , logitem_str(html_log_file,"add diffeq.max") , logitem_str(html_log_file,"add maxima results") , logitem_str(html_log_file,"OK") , logend(html_log_file) )/* end if 15*/ , if (glob_html_log) then ( /* if number 15*/ close(html_log_file) )/* end if 15*/ )/* end if 14*/ /* END OUTFILEMAIN */ ) )$ /* End Function number12 */ /* Begin Function number 13*/ main() := ( glob_iolevel : 2, compile(all), main_prog() )$ /* End Function number13 */ main()$