#BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 omniout_str := proc(iolevel,str) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 1 printf("%s\n",str); fi;# end if 1; end; # End Function number 2 # Begin Function number 3 omniout_str_noeol := proc(iolevel,str) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 1 printf("%s",str); fi;# end if 1; end; # End Function number 3 # Begin Function number 4 omniout_labstr := proc(iolevel,label,str) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 1 print(label,str); fi;# end if 1; end; # End Function number 4 # Begin Function number 5 omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 1 if vallen = 4 then printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); else printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); fi;# end if 1; fi;# end if 0; end; # End Function number 5 # Begin Function number 6 omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 0 if vallen = 5 then # if number 1 printf("%-30s = %-32d %s\n",prelabel,value, postlabel); else printf("%-30s = %-32d %s \n",prelabel,value, postlabel); fi;# end if 1; fi;# end if 0; end; # End Function number 6 # Begin Function number 7 omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then # if number 0 print(prelabel,"[",elemnt,"]",value, postlabel); fi;# end if 0; end; # End Function number 7 # Begin Function number 8 logitem_time := proc(fd,secs_in) global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; fprintf(fd,""); if (secs_in >= 0) then # if number 0 years_int := int_trunc(secs_in / glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp / glob_sec_in_day) ; sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; hours_int := int_trunc(sec_temp / glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp / glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if (years_int > 0) then # if number 1 fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); elif (days_int > 0) then # if number 2 fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); elif (hours_int > 0) then # if number 3 fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); elif (minutes_int > 0) then # if number 4 fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); else fprintf(fd,"%d Seconds",sec_int); fi;# end if 4 else fprintf(fd," 0.0 Seconds"); fi;# end if 3 fprintf(fd,"\n"); end; # End Function number 8 # Begin Function number 9 omniout_timestr := proc(secs_in) global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; if (secs_in >= 0) then # if number 3 years_int := int_trunc(secs_in / glob_sec_in_year); sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); days_int := int_trunc(sec_temp / glob_sec_in_day) ; sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; hours_int := int_trunc(sec_temp / glob_sec_in_hour); sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); minutes_int := int_trunc(sec_temp / glob_sec_in_minute); sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); if (years_int > 0) then # if number 4 printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); elif (days_int > 0) then # if number 5 printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); elif (hours_int > 0) then # if number 6 printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); elif (minutes_int > 0) then # if number 7 printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); else printf(" = %d Seconds\n",sec_int); fi;# end if 7 else printf(" 0.0 Seconds\n"); fi;# end if 6 end; # End Function number 9 # Begin Function number 10 zero_ats_ar := proc(arr_a) global ATS_MAX_TERMS; local iii; iii := 1; while (iii <= ATS_MAX_TERMS) do # do number 1 arr_a [iii] := glob__0; iii := iii + 1; od;# end do number 1 end; # End Function number 10 # Begin Function number 11 ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) global ATS_MAX_TERMS; local iii_ats, lll_ats,ma_ats, ret_ats; ret_ats := glob__0; if (jjj_ats <= mmm_ats) then # if number 6 ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while (iii_ats <= mmm_ats) do # do number 1 lll_ats := ma_ats - iii_ats; if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); fi;# end if 7; iii_ats := iii_ats + 1; od;# end do number 1 fi;# end if 6; ret_ats; end; # End Function number 11 # Begin Function number 12 att := proc(mmm_att,arr_aa,arr_bb,jjj_att) global ATS_MAX_TERMS; local al_att, iii_att,lll_att, ma_att, ret_att; ret_att := glob__0; if (jjj_att < mmm_att) then # if number 6 ma_att := mmm_att + 2; iii_att := jjj_att; while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 lll_att := ma_att - iii_att; al_att := (lll_att - 1); if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); fi;# end if 7; iii_att := iii_att + 1; od;# end do number 1; ret_att := ret_att / c(mmm_att) ; fi;# end if 6; ret_att; end; # End Function number 12 # Begin Function number 13 logditto := proc(file) fprintf(file,""); fprintf(file,"ditto"); fprintf(file,""); end; # End Function number 13 # Begin Function number 14 logitem_integer := proc(file,n) fprintf(file,""); fprintf(file,"%d",n); fprintf(file,""); end; # End Function number 14 # Begin Function number 15 logitem_str := proc(file,str) fprintf(file,""); fprintf(file,str); fprintf(file,""); end; # End Function number 15 # Begin Function number 16 logitem_good_digits := proc(file,rel_error) global glob_small_float,glob_prec; local good_digits; fprintf(file,""); fprintf(file,"%d",glob_min_good_digits); fprintf(file,""); end; # End Function number 16 # Begin Function number 17 log_revs := proc(file,revs) fprintf(file,revs); end; # End Function number 17 # Begin Function number 18 logitem_float := proc(file,x) fprintf(file,""); fprintf(file,"%g",x); fprintf(file,""); end; # End Function number 18 # Begin Function number 19 logitem_h_reason := proc(file) global glob_h_reason; fprintf(file,""); if (glob_h_reason = 1) then # if number 6 fprintf(file,"Max H"); elif (glob_h_reason = 2) then # if number 7 fprintf(file,"Display Interval"); elif (glob_h_reason = 3) then # if number 8 fprintf(file,"Optimal"); elif (glob_h_reason = 4) then # if number 9 fprintf(file,"Pole Accuracy"); elif (glob_h_reason = 5) then # if number 10 fprintf(file,"Min H (Pole)"); elif (glob_h_reason = 6) then # if number 11 fprintf(file,"Pole"); elif (glob_h_reason = 7) then # if number 12 fprintf(file,"Opt Iter"); else fprintf(file,"Impossible"); fi;# end if 12 fprintf(file,""); end; # End Function number 19 # Begin Function number 20 logstart := proc(file) fprintf(file,""); end; # End Function number 20 # Begin Function number 21 logend := proc(file) fprintf(file,"\n"); end; # End Function number 21 # Begin Function number 22 chk_data := proc() global glob_max_iter,ALWAYS, ATS_MAX_TERMS; local errflag; errflag := false; if (glob_max_iter < 2) then # if number 12 omniout_str(ALWAYS,"Illegal max_iter"); errflag := true; fi;# end if 12; if (errflag) then # if number 12 quit; fi;# end if 12 end; # End Function number 22 # Begin Function number 23 comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) global glob_small_float; local ms2, rrr, sec_left, sub1, sub2; ; ms2 := c(clock_sec2); sub1 := c(t_end2-t_start2); sub2 := c(t2-t_start2); if (sub1 = glob__0) then # if number 12 sec_left := glob__0; else if (sub2 > glob__0) then # if number 13 rrr := (sub1/sub2); sec_left := rrr * c(ms2) - c(ms2); else sec_left := glob__0; fi;# end if 13 fi;# end if 12; sec_left; end; # End Function number 23 # Begin Function number 24 comp_percent := proc(t_end2,t_start2, t2) global glob_small_float; local rrr, sub1, sub2; sub1 := (t_end2-t_start2); sub2 := (t2-t_start2); if (sub2 > glob_small_float) then # if number 12 rrr := (glob__100*sub2)/sub1; else rrr := 0.0; fi;# end if 12; rrr; end; # End Function number 24 # Begin Function number 25 comp_rad_from_ratio := proc(term1,term2,last_no) #TOP TWO TERM RADIUS ANALYSIS global glob_h,glob_larger_float; local ret; if (float_abs(term2) > glob__0) then # if number 12 ret := float_abs(term1 * glob_h / term2); else ret := glob_larger_float; fi;# end if 12; ret; #BOTTOM TWO TERM RADIUS ANALYSIS end; # End Function number 25 # Begin Function number 26 comp_ord_from_ratio := proc(term1,term2,last_no) #TOP TWO TERM ORDER ANALYSIS global glob_h,glob_larger_float; local ret; if (float_abs(term2) > glob__0) then # if number 12 ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); else ret := glob_larger_float; fi;# end if 12; ret; #BOTTOM TWO TERM ORDER ANALYSIS end; # End Function number 26 # Begin Function number 27 c := proc(in_val) #To Force Conversion when needed local ret; ret := evalf(in_val); ret; #End Conversion end; # End Function number 27 # Begin Function number 28 comp_rad_from_three_terms := proc(term1,term2,term3,last_no) #TOP THREE TERM RADIUS ANALYSIS global glob_h,glob_larger_float; local ret,temp; temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); if (float_abs(temp) > glob__0) then # if number 12 ret := float_abs((term2*glob_h*term1)/(temp)); else ret := glob_larger_float; fi;# end if 12; ret; #BOTTOM THREE TERM RADIUS ANALYSIS end; # End Function number 28 # Begin Function number 29 comp_ord_from_three_terms := proc(term1,term2,term3,last_no) #TOP THREE TERM ORDER ANALYSIS local ret; ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); ret; #TOP THREE TERM ORDER ANALYSIS end; # End Function number 29 # Begin Function number 30 comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) #TOP SIX TERM RADIUS ANALYSIS global glob_h,glob_larger_float,glob_six_term_ord_save; local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 rad_c := glob_larger_float; ord_no := glob_larger_float; else if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; if (float_abs(rcs) <> glob__0) then # if number 15 if (rcs > glob__0) then # if number 16 rad_c := sqrt(rcs) * float_abs(glob_h); else rad_c := glob_larger_float; ord_no := glob_larger_float; fi;# end if 16 else rad_c := glob_larger_float; ord_no := glob_larger_float; fi;# end if 15 else rad_c := glob_larger_float; ord_no := glob_larger_float; fi;# end if 14 fi;# end if 13 else rad_c := glob_larger_float; ord_no := glob_larger_float; fi;# end if 12; glob_six_term_ord_save := ord_no; rad_c; #BOTTOM SIX TERM RADIUS ANALYSIS end; # End Function number 30 # Begin Function number 31 comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) global glob_six_term_ord_save; #TOP SIX TERM ORDER ANALYSIS #TOP SAVED FROM SIX TERM RADIUS ANALYSIS glob_six_term_ord_save; #BOTTOM SIX TERM ORDER ANALYSIS end; # End Function number 31 # Begin Function number 32 factorial_2 := proc(nnn) ret := nnn!; ret;; end; # End Function number 32 # Begin Function number 33 factorial_1 := proc(nnn) global ATS_MAX_TERMS,array_fact_1; local ret; if (nnn <= ATS_MAX_TERMS) then # if number 12 if (array_fact_1[nnn] = 0) then # if number 13 ret := factorial_2(nnn); array_fact_1[nnn] := ret; else ret := array_fact_1[nnn]; fi;# end if 13; else ret := factorial_2(nnn); fi;# end if 12; ret; end; # End Function number 33 # Begin Function number 34 factorial_3 := proc(mmm,nnn) global ATS_MAX_TERMS,array_fact_2; local ret; if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 if (array_fact_2[mmm,nnn] = 0) then # if number 13 ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm,nnn] := ret; else ret := array_fact_2[mmm,nnn]; fi;# end if 13; else ret := factorial_2(mmm)/factorial_2(nnn); fi;# end if 12; ret; end; # End Function number 34 # Begin Function number 35 convfloat := proc(mmm) (mmm); end; # End Function number 35 # Begin Function number 36 elapsed_time_seconds := proc() time(); end; # End Function number 36 # Begin Function number 37 float_abs := proc(x) abs(x); end; # End Function number 37 # Begin Function number 38 expt := proc(x,y) x^y; end; # End Function number 38 # Begin Function number 39 neg := proc(x) -x; end; # End Function number 39 # Begin Function number 40 int_trunc := proc(x) trunc(x); end; # End Function number 40 # Begin Function number 41 estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) local desired_abs_gbl_error,range,estimated_steps,step_error; global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); range := (x_end - x_start); omniout_float(ALWAYS,"range",32,range,32,""); estimated_steps := range / estimated_h; omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); omniout_float(ALWAYS,"step_error",32,step_error,32,""); (step_error);; end; # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(2.0) - cos(c(x))); end; #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 display_poles := proc() local rad_given; global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); if (rad_given < glob_least_given_sing) then # if number 2 glob_least_given_sing := rad_given; fi;# end if 2; elif (glob_type_given_pole = 3) then # if number 2 omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); elif (glob_type_given_pole = 5) then # if number 3 omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); else omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); fi;# end if 3; if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 glob_least_ratio_sing := array_rad_test_poles[1,1]; fi;# end if 4; omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); else omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); fi;# end if 3; if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 glob_least_3_sing := array_rad_test_poles[1,2]; fi;# end if 4; omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); else omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); fi;# end if 3; if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 glob_least_6_sing := array_rad_test_poles[1,3]; fi;# end if 4; omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); else omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); fi;# end if 3 ; end; # End Function number 2 # Begin Function number 3 my_check_sign := proc( x0 ,xf) local ret; if (xf > x0) then # if number 3 ret := glob__1; else ret := glob__m1; fi;# end if 3; ret;; end; # End Function number 3 # Begin Function number 4 est_size_answer := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local min_size; min_size := glob_estimated_size_answer; if (float_abs(array_y[1]) < min_size) then # if number 3 min_size := float_abs(array_y[1]); omniout_float(ALWAYS,"min_size",32,min_size,32,""); fi;# 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,""); fi;# end if 3; min_size; end; # End Function number 4 # Begin Function number 5 test_suggested_h := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); est_tmp := float_abs(array_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; fi;# end if 3; omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); max_estimated_step_error; end; # End Function number 5 # Begin Function number 6 track_estimated_error := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_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])); fi;# 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); fi;# end if 3 ; end; # End Function number 6 # Begin Function number 7 reached_interval := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local ret; if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 ret := true; else ret := false; fi;# end if 3; return(ret); end; # End Function number 7 # Begin Function number 8 display_alot := proc(iter) global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; #TOP DISPLAY ALOT if (reached_interval()) then # if number 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 := evalf(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 := -int_trunc(log10(c(relerr))) + 3; else glob_good_digits := Digits; fi;# end if 6; else relerr := glob__m1 ; glob_good_digits := -16; fi;# end if 5; if (glob_good_digits < glob_min_good_digits) then # if number 5 glob_min_good_digits := glob_good_digits; fi;# 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; fi;# end if 5; if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val)); if (evalf(est_rel_err) > glob_prec) then # if number 6 glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; else glob_est_digits := Digits; fi;# end if 6; else relerr := glob__m1 ; glob_est_digits := -16; fi;# 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; fi;# 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," "); fi;# end if 4; #BOTTOM DISPLAY ALOT fi;# end if 3; end; # End Function number 8 # Begin Function number 9 prog_report := proc(x_start,x_end) global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; #TOP PROGRESS REPORT clock_sec1 := elapsed_time_seconds(); total_clock_sec := (clock_sec1) - (glob_orig_start_sec); glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO,"Total Elapsed Time "); omniout_timestr((total_clock_sec)); omniout_str_noeol(INFO,"Elapsed Time(since restart) "); omniout_timestr((glob_clock_sec)); if (c(percent_done) < glob__100) then # if number 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)); fi;# 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 end; # End Function number 9 # Begin Function number 10 check_for_pole := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; #TOP CHECK FOR POLE tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1,1] := glob_larger_float; array_ord_test_poles[1,1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 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; fi;# 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; elif (cnt = 0) then # if number 4 rad_c := tmp_rad; elif (cnt > 0) then # if number 5 found_sing := 0; fi;# end if 5; prev_tmp_rad := tmp_rad;; cnt := cnt + 1; last_no := last_no + 1; od;# end do number 1; if (found_sing = 1) then # if number 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; fi;# end if 6; fi;# 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; fi;# end if 5; if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 rad_c := tmp_rad; elif (cnt = 0) then # if number 6 rad_c := tmp_rad; elif (cnt > 0) then # if number 7 found_sing := 0; fi;# end if 7; prev_tmp_rad := tmp_rad;; cnt := cnt + 1; last_no := last_no + 1; od;# end do number 1; if (found_sing = 1) then # if number 7 if (rad_c < array_rad_test_poles[1,2]) 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; fi;# end if 9; array_ord_test_poles[1,2] := tmp_ord; fi;# end if 8; fi;# end if 7; #BOTTOM general radius test1 tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[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; fi;# end if 7; if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 rad_c := tmp_rad; elif (cnt = 0) then # if number 8 rad_c := tmp_rad; elif (cnt > 0) then # if number 9 found_sing := 0; fi;# end if 9; prev_tmp_rad := tmp_rad;; cnt := cnt + 1; last_no := last_no + 1; od;# end do number 1; if (found_sing = 1) then # if number 9 if (rad_c < array_rad_test_poles[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; fi;# end if 11; array_ord_test_poles[1,3] := tmp_ord; fi;# end if 10; fi;# 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; fi;# 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; od;# end do number 1; glob_h := h_new; fi;# end if 9; #BOTTOM ADJUST ALL SERIES ; if (reached_interval()) then # if number 9 display_poles(); fi;# end if 9 end; # End Function number 10 # Begin Function number 11 atomall := proc() global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; local kkk, order_d, adj2, adj3 , temporary, term; #TOP ATOMALL # before write maple main top matter # before generate constants assign # before generate globals assign #END OUTFILE1 #BEGIN OUTFILE2 #END OUTFILE2 #BEGIN ATOMHDR1 #emit pre 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 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_tmp2[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; fi;# end if 3; temporary := c(temporary) / c(glob_h) * c(1); array_y_higher[2,1] := c(temporary); fi;# end if 2; fi;# 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 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_tmp2[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; fi;# end if 3; temporary := c(temporary) / c(glob_h) * c(2); array_y_higher[2,2] := c(temporary); fi;# end if 2; fi;# 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 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_tmp2[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; fi;# end if 3; temporary := c(temporary) / c(glob_h) * c(3); array_y_higher[2,3] := c(temporary); fi;# end if 2; fi;# 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 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_tmp2[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; fi;# end if 3; temporary := c(temporary) / c(glob_h) * c(4); array_y_higher[2,4] := c(temporary); fi;# end if 2; fi;# 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 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_tmp2[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; fi;# end if 3; temporary := c(temporary) / c(glob_h) * c(5); array_y_higher[2,5] := c(temporary); fi;# end if 2; fi;# end if 1; kkk := 6; #END ATOMHDR5 #BEGIN OUTFILE3 #Top Atomall While Loop-- outfile3 while (kkk <= ATS_MAX_TERMS) do # do number 1 #END OUTFILE3 #BEGIN OUTFILE4 #emit 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 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_tmp2[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); fi;# end if 4; array_y_higher[adj3,term] := c(temporary); fi;# end if 3; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1; od;# end do number 1 fi;# end if 2 fi;# end if 1; kkk := kkk + 1; od;# end do number 1; #BOTTOM ATOMALL #END OUTFILE4 #BEGIN OUTFILE5 #BOTTOM ATOMALL ??? end; # End Function number 12 #END OUTFILE5 # Begin Function number 12 main := proc() #BEGIN OUTFIEMAIN local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, term,ord,order_diff,term_no,html_log_file,iiif,jjjf, rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, x_start,x_end ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, #Top Generate Globals Decl MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, #Bottom Generate Globals Decl #BEGIN CONST array_const_1, array_const_0D0, #END CONST array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 20; # before first input block #BEGIN FIRST INPUT BLOCK #BEGIN BLOCK 1 #BEGIN FIRST INPUT BLOCK Digits:=50; max_terms:=20; #END BLOCK 1 #END FIRST INPUT BLOCK #START OF INITS AFTER INPUT BLOCK glob_html_log := true; #END OF INITS AFTER INPUT BLOCK # before generate arrays array_y_init:= Array(0..(20),[]); array_norms:= Array(0..(20),[]); array_fact_1:= Array(0..(20),[]); array_1st_rel_error:= Array(0..(2),[]); array_last_rel_error:= Array(0..(2),[]); array_est_rel_error:= Array(0..(2),[]); array_max_est_error:= Array(0..(2),[]); array_type_pole:= Array(0..(2),[]); array_type_real_pole:= Array(0..(2),[]); array_type_complex_pole:= Array(0..(2),[]); array_est_digits:= Array(0..(2),[]); array_y:= Array(0..(20),[]); array_x:= Array(0..(20),[]); array_tmp0:= Array(0..(20),[]); array_tmp1_g:= Array(0..(20),[]); array_tmp1:= Array(0..(20),[]); array_tmp2:= Array(0..(20),[]); array_m1:= Array(0..(20),[]); array_y_higher := Array(0..(2) ,(0..20+ 1),[]); array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]); array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); array_fact_2 := Array(0..(20) ,(0..20+ 1),[]); # before generate constants # before generate globals definition #Top Generate Globals Definition #Bottom Generate Globals Deninition # before generate const definition # before arrays initialized term := 1; while (term <= 20) do # do number 1 array_y_init[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_norms[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_fact_1[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_1st_rel_error[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_last_rel_error[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_est_rel_error[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_max_est_error[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_pole[term] := 0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_real_pole[term] := 0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_type_complex_pole[term] := 0; term := term + 1; od;# end do number 1; term := 1; while (term <= 2) do # do number 1 array_est_digits[term] := 0; term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_y[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_x[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_tmp0[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_tmp1_g[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_tmp1[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_tmp2[term] := c(0.0); term := term + 1; od;# end do number 1; term := 1; while (term <= 20) do # do number 1 array_m1[term] := c(0.0); term := term + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 20) do # do number 2 array_y_higher[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 20) do # do number 2 array_y_higher_work[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 20) do # do number 2 array_y_higher_work2[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 20) do # do number 2 array_y_set_initial[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 3) do # do number 2 array_given_rad_poles[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=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; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=2) do # do number 1 term := 1; while (term <= 4) do # do number 2 array_rad_test_poles[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=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; od;# end do number 2; ord := ord + 1; od;# end do number 1; ord := 1; while (ord <=20) do # do number 1 term := 1; while (term <= 20) do # do number 2 array_fact_2[ord,term] := c(0.0); term := term + 1; od;# end do number 2; ord := ord + 1; od;# end do number 1; # before symbols initialized #BEGIN SYMBOLS INITIALIZATED zero_ats_ar(array_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_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; od;# end do number 2; iiif := iiif + 1; od;# end do number 1; #Done Initing Factorial Table ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1e-50); glob_small_float := c(0.1e-50); glob_smallish_float := c(0.1e-60); glob_large_float := c(1.0e100); glob_larger_float := c(1.1e100); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.0); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(1.0e-16); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.0); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.0); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.0); glob_clock_start_sec := c(0.0); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(9.9e200); glob_least_ratio_sing := c(9.9e200); glob_least_3_sing := c(9.9e100); glob_least_6_sing := c(9.9e100); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.000001); glob_display_interval := c(0.1); glob_abserr := c(0.1e-10); glob_relerr := c(0.1e-10); glob_min_pole_est := c(0.1e+10); glob_max_rel_trunc_err := c(0.1e-10); glob_max_trunc_err := c(0.1e-10); glob_max_hours := c(0.0); glob_optimal_clock_start_sec := c(0.0); glob_optimal_start := c(0.0); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.0); glob_normmax := c(0.0); glob_max_minutes := c(0.0); glob_next_display := c(0.0); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60 ; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; # before generate set diff initial array_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; # before generate init omniout const ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; glob_iolevel := INFO; # set default block #Write Set Defaults 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/sinpostode.ode#################"); omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) ; "); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"Digits:=50;"); omniout_str(ALWAYS,"max_terms:=20;"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"x_start := c(0.0);"); omniout_str(ALWAYS,"x_end := c(1.0);"); omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS,"glob_look_poles := false;"); omniout_str(ALWAYS,""); 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,""); 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(1.0000001);"); omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);"); omniout_str(ALWAYS,"glob_look_poles:=true;"); omniout_str(ALWAYS,"glob_h:=c(0.01);"); 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,""); omniout_str(ALWAYS,"exact_soln_y := proc(x)"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)));"); omniout_str(ALWAYS,""); omniout_str(ALWAYS,"end;"); omniout_str(ALWAYS,"#END USER DEF BLOCK"); omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(1.0e100); glob_larger_float := c( 1.1e100); glob_almost_1 := c( 0.99); # before second block #TOP SECOND INPUT BLOCK #BEGIN SECOND INPUT BLOCK #BEGIN BLOCK 2 #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.0); x_end := c(1.0); array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := false; 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(1.0000001); glob_lower_ratio_limit:=c(0.9999999); glob_look_poles:=true; glob_h:=c(0.01); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK #END BLOCK 2 #END SECOND INPUT BLOCK #BEGIN INITS AFTER SECOND INPUT BLOCK glob_last_good_h := glob_h; glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); # after second input block glob_check_sign := c(my_check_sign(x_start,x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0,c(-Digits)); if (glob_optimize) then # if number 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); fi;# 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; od;# end do number 2; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 2 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 3 it := term_no + r_order - 1; if (term_no < ATS_MAX_TERMS) then # if number 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))); fi;# end if 10; term_no := term_no + 1; od;# end do number 3; r_order := r_order + 1; od;# 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; fi;# 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; fi;# end if 10; if (glob_look_poles) then # if number 10 check_for_pole(); fi;# 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; fi;# end if 11; fi;# end if 10; opt_iter := opt_iter + 1; od;# 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; fi;# 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; fi;# end if 10; else found_h := true; glob_h := glob_h * glob_check_sign; fi;# end if 9; #END OPTIMIZE CODE if (glob_html_log) then # if number 9 html_log_file := fopen("entry.html",WRITE,TEXT); fi;# 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; od;# end do number 1; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 1 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 2 it := term_no + r_order - 1; if (term_no < ATS_MAX_TERMS) then # if number 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))); fi;# end if 10; term_no := term_no + 1; od;# end do number 2; r_order := r_order + 1; od;# end do number 1 ; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL," "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 #left paren 0001C if (reached_interval()) then # if number 10 omniout_str(INFO," "); omniout_str(INFO,"TOP MAIN SOLVE Loop"); fi;# 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(); fi;# end if 10; if (reached_interval()) then # if number 10 glob_next_display := glob_next_display + glob_display_interval; fi;# 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; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := glob__0; ord := 2; calc_term := 1; #sum_subseriesarray_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; od;# 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; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := glob__0; ord := 1; calc_term := 2; #sum_subseriesarray_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; od;# 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; od;# end do number 2; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 temp_sum := glob__0; ord := 1; calc_term := 1; #sum_subseriesarray_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; od;# 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; od;# end do number 3; term_no := term_no - 1; od;# end do number 2; #END PART 2 HEVE MOVED TERMS to REGULAR Array ; od;# end do number 1;#right paren 0001C omniout_str(ALWAYS,"Finished!"); if (glob_iter >= glob_max_iter) then # if number 10 omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); fi;# 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!"); fi;# end if 10; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO,"diff ( y , x , 1 ) = 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,"2015-05-19T20:43:54-05:00") ; logitem_str(html_log_file,"Maple") ; logitem_str(html_log_file,"sin") ; logitem_str(html_log_file,"diff ( y , x , 1 ) = 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_integer(html_log_file,Digits) ; ; 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]) ; else logitem_str(html_log_file,"Unknown") ; fi;# end if 11; if (glob_min_good_digits <> -16) then # if number 11 logitem_integer(html_log_file,glob_min_good_digits) ; else logitem_str(html_log_file,"Unknown") ; fi;# end if 11; if (glob_good_digits <> -16) then # if number 11 logitem_integer(html_log_file,glob_good_digits) ; else logitem_str(html_log_file,"Unknown") ; fi;# 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") ; elif (glob_type_given_pole = 4) then # if number 12 logitem_str(html_log_file,"No Solution") ; logitem_str(html_log_file,"NA") ; elif (glob_type_given_pole = 5) then # if number 13 logitem_str(html_log_file,"Some Pole") ; logitem_str(html_log_file,"????") ; elif (glob_type_given_pole = 3) then # if number 14 logitem_str(html_log_file,"No Pole") ; logitem_str(html_log_file,"NA") ; elif (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) ; elif (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) ; fi;# end if 16; if (glob_least_ratio_sing < glob_large_float) then # if number 16 logitem_float(html_log_file,glob_least_ratio_sing) ; else logitem_str(html_log_file,"NONE") ; fi;# end if 16; if (glob_least_3_sing < glob_large_float) then # if number 16 logitem_float(html_log_file,glob_least_3_sing) ; else logitem_str(html_log_file,"NONE") ; fi;# end if 16; if (glob_least_6_sing < glob_large_float) then # if number 16 logitem_float(html_log_file,glob_least_6_sing) ; else logitem_str(html_log_file,"NONE") ; fi;# 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; fi;# end if 16; log_revs(html_log_file," 308.maple.seems.ok ") ; logitem_str(html_log_file,"sin diffeq.mxt") ; logitem_str(html_log_file,"sin maple results") ; logitem_str(html_log_file,"OK") ; logend(html_log_file) ; ; fi;# end if 15; if (glob_html_log) then # if number 15 fclose(html_log_file); fi;# end if 15 ; ;; fi;# end if 14 #END OUTFILEMAIN end; # End Function number 12 main();