/* BEGIN OUTFILE1 */ load("stringproc"); /* Begin Function number 1*/ display_alot(iter) := ( /* TOP DISPLAY ALOT */ if (iter >= 0) then ( /* if number 1*/ ind_var : array_x[1], omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "), term_no : 1, numeric_val : array_y[term_no], abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "), if (abs(analytic_val_y) # 0.0) then ( /* if number 2*/ relerr : abserr*100.0/abs(analytic_val_y) ) else ( relerr : -1.0 )/* end if 2*/ , if glob_iter = 1 then ( /* if number 2*/ array_1st_rel_error[1] : relerr ) else ( array_last_rel_error[1] : relerr )/* end if 2*/ , omniout_float(ALWAYS,"absolute error ",4,abserr,20," "), omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"), omniout_float(ALWAYS,"h ",4,glob_h,20," ") /* BOTTOM DISPLAY ALOT */ )/* end if 1*/ /* End Function number1*/); /* Begin Function number 1*/ adjust_for_pole(h_param) := ( /* TOP ADJUST FOR POLE */ block( hnew : h_param, glob_normmax : glob_small_float, if (abs(array_y_higher[1,1]) > glob_small_float) then ( /* if number 1*/ tmp : abs(array_y_higher[1,1]), if (tmp < glob_normmax) then ( /* if number 2*/ glob_normmax : tmp )/* end if 2*/ )/* end if 1*/ , if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] # glob_large_float)) then ( /* if number 1*/ sz2 : array_pole[1]/10.0, if (sz2 < hnew) then ( /* if number 2*/ omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."), omniout_str(INFO,"Reached Optimal"), newline(), return(hnew) )/* end if 2*/ )/* end if 1*/ , if (not glob_reached_optimal_h) then ( /* if number 1*/ glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x[1] )/* end if 1*/ , hnew : sz2 )/* END block */ /* BOTTOM ADJUST FOR POLE */ /* End Function number1*/); /* Begin Function number 1*/ prog_report(x_start,x_end) := ( /* TOP PROGRESS REPORT */ clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1), expect_sec : comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)), percent_done : comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)), glob_percent_done : percent_done, omniout_str_noeol(INFO,"Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO,"Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then ( /* if number 1*/ omniout_str_noeol(INFO,"Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO,"Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)) )/* end if 1*/ , omniout_str_noeol(INFO,"Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ",33,percent_done,4,"%") /* BOTTOM PROGRESS REPORT */ /* End Function number1*/); /* Begin Function number 1*/ check_for_pole() := ( /* TOP CHECK FOR POLE */ /* IN RADII REAL EQ = 1 */ /* Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 */ /* Applies to pole of arbitrary r_order on the real axis, */ /* Due to Prof. George Corliss. */ n : glob_max_terms, m : n - 1 - 1, while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do ( /* do number 2*/ m : m - 1 )/* end do number 2*/ , if (m > 10) then ( /* if number 1*/ rm0 : array_y_higher[1,m]/array_y_higher[1,m-1], rm1 : array_y_higher[1,m-1]/array_y_higher[1,m-2], hdrc : convfloat(m-1)*rm0-convfloat(m-2)*rm1, if (abs(hdrc) > glob_small_float) then ( /* if number 2*/ rcs : glob_h/hdrc, ord_no : convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0, array_real_pole[1,1] : rcs, array_real_pole[1,2] : ord_no ) else ( array_real_pole[1,1] : glob_large_float, array_real_pole[1,2] : glob_large_float )/* end if 2*/ ) else ( array_real_pole[1,1] : glob_large_float, array_real_pole[1,2] : glob_large_float )/* end if 1*/ , /* BOTTOM RADII REAL EQ = 1 */ /* TOP RADII COMPLEX EQ = 1 */ /* Computes radius of convergence for complex conjugate pair of poles. */ /* from 6 adjacent Taylor series terms */ /* Also computes r_order of poles. */ /* Due to Manuel Prieto. */ /* With a correction by Dennis J. Darland */ n : glob_max_terms - 1 - 1, cnt : 0, while ((cnt < 5) and (n >= 10)) do ( /* do number 2*/ if (abs(array_y_higher[1,n]) > glob_small_float) then ( /* if number 1*/ cnt : cnt + 1 ) else ( cnt : 0 )/* end if 1*/ , n : n - 1 )/* end do number 2*/ , m : n + cnt, if (m <= 10) then ( /* if number 1*/ array_complex_pole[1,1] : glob_large_float, array_complex_pole[1,2] : glob_large_float ) elseif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then ( /* if number 2*/ array_complex_pole[1,1] : glob_large_float, array_complex_pole[1,2] : glob_large_float ) else ( rm0 : (array_y_higher[1,m])/(array_y_higher[1,m-1]), rm1 : (array_y_higher[1,m-1])/(array_y_higher[1,m-2]), rm2 : (array_y_higher[1,m-2])/(array_y_higher[1,m-3]), rm3 : (array_y_higher[1,m-3])/(array_y_higher[1,m-4]), rm4 : (array_y_higher[1,m-4])/(array_y_higher[1,m-5]), nr1 : convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2, nr2 : convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3, dr1 : (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3, dr2 : (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4, ds1 : 3.0/rm1 - 8.0/rm2 + 5.0/rm3, ds2 : 3.0/rm2 - 8.0/rm3 + 5.0/rm4, if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then ( /* if number 3*/ array_complex_pole[1,1] : glob_large_float, array_complex_pole[1,2] : glob_large_float ) else ( if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then ( /* if number 4*/ 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)/(2.0*dr1) -convfloat(m)/2.0, if (abs(rcs) > glob_small_float) then ( /* if number 5*/ if (rcs > 0.0) then ( /* if number 6*/ rad_c : sqrt(rcs) * glob_h ) else ( rad_c : glob_large_float )/* end if 6*/ ) else ( rad_c : glob_large_float, ord_no : glob_large_float )/* end if 5*/ ) else ( rad_c : glob_large_float, ord_no : glob_large_float )/* end if 4*/ )/* end if 3*/ , array_complex_pole[1,1] : rad_c, array_complex_pole[1,2] : ord_no )/* end if 2*/ , /* BOTTOM RADII COMPLEX EQ = 1 */ found : false, /* TOP WHICH RADII EQ = 1 */ if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] # glob_large_float) and (array_complex_pole[1,2] # glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then ( /* if number 2*/ array_poles[1,1] : array_complex_pole[1,1], array_poles[1,2] : array_complex_pole[1,2], found : true, array_type_pole[1] : 2, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"Complex estimate of poles used") )/* end if 3*/ )/* end if 2*/ , if not found and ((array_real_pole[1,1] # glob_large_float) and (array_real_pole[1,2] # glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then ( /* if number 2*/ array_poles[1,1] : array_real_pole[1,1], array_poles[1,2] : array_real_pole[1,2], found : true, array_type_pole[1] : 1, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"Real estimate of pole used") )/* end if 3*/ )/* end if 2*/ , if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then ( /* if number 2*/ array_poles[1,1] : glob_large_float, array_poles[1,2] : glob_large_float, found : true, array_type_pole[1] : 3, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"NO POLE") )/* end if 3*/ )/* end if 2*/ , if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then ( /* if number 2*/ array_poles[1,1] : array_real_pole[1,1], array_poles[1,2] : array_real_pole[1,2], found : true, array_type_pole[1] : 1, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"Real estimate of pole used") )/* end if 3*/ )/* end if 2*/ , if not found and ((array_complex_pole[1,1] # glob_large_float) and (array_complex_pole[1,2] # glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then ( /* if number 2*/ array_poles[1,1] : array_complex_pole[1,1], array_poles[1,2] : array_complex_pole[1,2], array_type_pole[1] : 2, found : true, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"Complex estimate of poles used") )/* end if 3*/ )/* end if 2*/ , if not found then ( /* if number 2*/ array_poles[1,1] : glob_large_float, array_poles[1,2] : glob_large_float, array_type_pole[1] : 3, if (glob_display_flag) then ( /* if number 3*/ omniout_str(ALWAYS,"NO POLE") )/* end if 3*/ )/* end if 2*/ , /* BOTTOM WHICH RADII EQ = 1 */ array_pole[1] : glob_large_float, array_pole[2] : glob_large_float, /* TOP WHICH RADIUS EQ = 1 */ if array_pole[1] > array_poles[1,1] then ( /* if number 2*/ array_pole[1] : array_poles[1,1], array_pole[2] : array_poles[1,2] )/* end if 2*/ , /* BOTTOM WHICH RADIUS EQ = 1 */ /* BOTTOM CHECK FOR POLE */ display_pole() /* End Function number1*/); /* Begin Function number 1*/ get_norms() := ( if (not glob_initial_pass) then ( /* if number 2*/ set_z(array_norms,glob_max_terms+1), /* TOP GET NORMS */ iii : 1, while (iii <= glob_max_terms) do ( /* do number 2*/ if (abs(array_y[iii]) > array_norms[iii]) then ( /* if number 3*/ array_norms[iii] : abs(array_y[iii]) )/* end if 3*/ , iii : iii + 1 )/* end do number 2*/ /* GET NORMS */ )/* end if 2*/ /* End Function number1*/); /* Begin Function number 1*/ atomall() := ( /* TOP ATOMALL */ /* END OUTFILE1 */ /* BEGIN ATOMHDR1 */ /* emit pre cos $eq_no = 1 */ array_tmp1_g[1] : sin(array_x[1]), array_tmp1[1] : cos(array_x[1]), /* emit pre add $eq_no = 1 i = 1 */ array_tmp2[1] : array_const_0D0[1] + array_tmp1[1], /* emit pre sin $eq_no = 1 iii = 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 $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 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1), array_y[2] : temporary, array_y_higher[1,2] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,1] : temporary )/* end if 2*/ )/* end if 1*/ , kkk : 2, /* END ATOMHDR1 */ /* BEGIN ATOMHDR2 */ /* emit pre cos $eq_no = 1 */ array_tmp1_g[2] : (att(1,array_tmp1,array_x,1)), array_tmp1[2] : (-att(1,array_tmp1_g,array_x,1)), /* emit pre add $eq_no = 1 i = 2 */ array_tmp2[2] : array_const_0D0[2] + array_tmp1[2], /* emit pre sin $eq_no = 1 iii = 2 */ /* emit pre sin 2 $eq_no = 1 */ array_tmp3[2] : att(1,array_tmp3_g,array_x,1), array_tmp3_g[2] : -att(1,array_tmp3,array_x,1), /* emit pre add $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 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2), array_y[3] : temporary, array_y_higher[1,3] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,2] : temporary )/* end if 2*/ )/* end if 1*/ , kkk : 3, /* END ATOMHDR2 */ /* BEGIN ATOMHDR3 */ /* emit pre cos $eq_no = 1 */ array_tmp1_g[3] : (att(2,array_tmp1,array_x,1)), array_tmp1[3] : (-att(2,array_tmp1_g,array_x,1)), /* emit pre add $eq_no = 1 i = 3 */ array_tmp2[3] : array_const_0D0[3] + array_tmp1[3], /* emit pre sin $eq_no = 1 iii = 3 */ /* emit pre sin 3 $eq_no = 1 */ array_tmp3[3] : att(2,array_tmp3_g,array_x,1), array_tmp3_g[3] : -att(2,array_tmp3,array_x,1), /* emit pre add $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 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3), array_y[4] : temporary, array_y_higher[1,4] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,3] : temporary )/* end if 2*/ )/* end if 1*/ , kkk : 4, /* END ATOMHDR3 */ /* BEGIN ATOMHDR4 */ /* emit pre cos $eq_no = 1 */ array_tmp1_g[4] : (att(3,array_tmp1,array_x,1)), array_tmp1[4] : (-att(3,array_tmp1_g,array_x,1)), /* emit pre add $eq_no = 1 i = 4 */ array_tmp2[4] : array_const_0D0[4] + array_tmp1[4], /* emit pre sin $eq_no = 1 iii = 4 */ /* emit pre sin 4 $eq_no = 1 */ array_tmp3[4] : att(3,array_tmp3_g,array_x,1), array_tmp3_g[4] : -att(3,array_tmp3,array_x,1), /* emit pre add $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 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4), array_y[5] : temporary, array_y_higher[1,5] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,4] : temporary )/* end if 2*/ )/* end if 1*/ , kkk : 5, /* END ATOMHDR4 */ /* BEGIN ATOMHDR5 */ /* emit pre cos $eq_no = 1 */ array_tmp1_g[5] : (att(4,array_tmp1,array_x,1)), array_tmp1[5] : (-att(4,array_tmp1_g,array_x,1)), /* emit pre add $eq_no = 1 i = 5 */ array_tmp2[5] : array_const_0D0[5] + array_tmp1[5], /* emit pre sin $eq_no = 1 iii = 5 */ /* emit pre sin 5 $eq_no = 1 */ array_tmp3[5] : att(4,array_tmp3_g,array_x,1), array_tmp3_g[5] : -att(4,array_tmp3,array_x,1), /* emit pre add $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 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5), array_y[6] : temporary, array_y_higher[1,6] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,5] : temporary )/* end if 2*/ )/* end if 1*/ , kkk : 6, /* END ATOMHDR5 */ /* BEGIN OUTFILE3 */ /* Top Atomall While Loop-- outfile3 */ while (kkk <= glob_max_terms) do ( /* do number 1*/ /* END OUTFILE3 */ /* BEGIN OUTFILE4 */ /* emit cos $eq_no = 1 */ array_tmp1_g[kkk] : (att(kkk-1,array_tmp1,array_x,1)), array_tmp1[kkk] : (-att(kkk-1,array_tmp1_g,array_x,1)), /* emit add $eq_no = 1 */ array_tmp2[kkk] : array_const_0D0[kkk] + array_tmp1[kkk], /* emit sin $eq_no = 1 */ array_tmp3[kkk] : att(kkk-1,array_tmp3_g,array_x,1), array_tmp3_g[kkk] : -att(kkk-1,array_tmp3,array_x,1), /* emit 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 + 1 <= glob_max_terms) then ( /* if number 1*/ if not array_y_set_initial[1,kkk + order_d] then ( /* if number 2*/ temporary : array_tmp4[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)), array_y[kkk + order_d] : temporary, array_y_higher[1,kkk + order_d] : temporary, term : kkk + order_d - 1, adj2 : 2, while (adj2 <= order_d + 1) and (term >= 1) do ( /* do number 2*/ temporary : temporary / glob_h * convfp(adj2), array_y_higher[adj2,term] : temporary, adj2 : adj2 + 1, term : term - 1 )/* end do number 2*/ )/* end if 2*/ )/* end if 1*/ , kkk : kkk + 1 )/* end do number 1*/ /* BOTTOM ATOMALL */ /* END OUTFILE4 */ /* BEGIN OUTFILE5 */ /* End Function number1*/); /* BEGIN ATS LIBRARY BLOCK */ log10(x) := (log(x)/log(10.0)); omniout_str(iolevel,str) := ( if (glob_iolevel) >= iolevel then ( printf(true,"~a~%",string(str)) ) ); omniout_str_noeol(iolevel,str) := ( if (glob_iolevel >= iolevel) then ( printf(true,"~a",string(str)) ) ); omniout_labstr(iolevel,label,str) := ( if (glob_iolevel >= iolevel) then ( printf(true,"~a = ~a~%",string(label),string(str)) ) ); omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( if vallen = 4 then ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) ) else ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) ) ) ); omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( printf(true,"~a = ~d ~a~%",prelabel,value, postlabel), newline() ) ); omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( sprint(prelabel,"[",elemnt,"]=",value, postlabel), newline() ) ); /*Function Start*/ dump_series(iolevel,dump_label,series_name, array_series,numb ) := ( if (glob_iolevel >= iolevel) then ( i : 1, while (i <= numb) do ( sprint(dump_label,series_name,"i = ",i,"series = ",array_series[i]), newline(), i : i + 1 ) ) ); dump_series_2(iolevel,dump_label,series_name, /*Function Start*/ array_series2,numb,subnum ) := ( if (glob_iolevel >= iolevel) then ( sub : 1, while (sub <= subnum) do ( i : 1, while (i <= num) do ( sprint(dump_label,series_name,"sub = ",sub,"i = ",i,"series2 = ",array_series2[sub,i]), i : i + 1 ), sub : sub + 1 ) ) ); cs_info(iolevel,str ) := ( if (glob_iolevel >= iolevel) then ( sprint(concat("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)) ) ); logitem_time(fd,secs_in) := ( secs : (secs_in), printf(fd,""), if (secs >= (0.0)) then ( /* if number 1*/ sec_in_millinium : ((sec_in_min) * (min_in_hour) * (hours_in_day) * (days_in_year) * (years_in_century) * (centuries_in_millinium)), milliniums : (secs / (sec_in_millinium)), millinium_int : floor(milliniums), centuries : (milliniums - (millinium_int))*(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) * (years_in_century), years_int : floor(years), days : (years - years_int) * (days_in_year), days_int : floor(days), hours : (days - days_int) * (hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) * (min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) * (sec_in_min), sec_int : floor(seconds), if (millinium_int > 0) then ( /* if number 2*/ printf(fd,"~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (cent_int > 0) then ( /* if number 3*/ printf(fd,"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (years_int > 0) then ( /* if number 4*/ printf(fd,"~d Years ~d Days ~d Hours ~d Minutes ~d Seconds",years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (days_int > 0) then ( /* if number 5*/ printf(fd,"~d Days ~d Hours ~d Minutes ~d Seconds",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0) then ( /* if number 6*/ printf(fd,"~d Hours ~d Minutes ~d Seconds",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0) then ( /* if number 7*/ printf(fd,"~d Minutes ~d Seconds",minutes_int,sec_int) ) else ( printf(fd,"~d Seconds",sec_int) )/* end if 7*/ ) else ( printf(fd,"Unknown") )/* end if 6*/ , printf(fd,"") /* End Function number1*/); omniout_timestr(secs_in) := ( secs : convfloat(secs_in), if (secs >= convfloat(0.0)) then ( /* if number 6*/ sec_in_millinium : (convfloat(sec_in_min) * convfloat(min_in_hour) * convfloat(hours_in_day) * convfloat(days_in_year) * convfloat(years_in_century) * convfloat(centuries_in_millinium)), milliniums : (secs / convfloat(sec_in_millinium)), millinium_int : floor(milliniums), centuries : (milliniums - (millinium_int))*convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) * convfloat(years_in_century), years_int : floor(years), days : (years - years_int) * convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) * convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) * convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) * convfloat(sec_in_min), sec_int : floor(seconds), if (millinium_int > 0) then ( /* if number 7*/ printf(true,"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (cent_int > 0) then ( /* if number 8*/ printf(true,"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",cent_int,years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (years_int > 0) then ( /* if number 9*/ printf(true,"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (days_int > 0) then ( /* if number 10*/ printf(true,"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0) then ( /* if number 11*/ printf(true,"= ~d Hours ~d Minutes ~d Seconds~%",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0) then ( /* if number 12*/ printf(true,"= ~d Minutes ~d Seconds~%",minutes_int,sec_int) ) else ( printf(true,"= ~d Seconds~%",sec_int) )/* end if 12*/ ) else ( printf(true," Unknown~%") )/* end if 11*/ /* End Function number1*/); mode_declare(ats,bfloat); /* Begin Function number 1*/ ats( mmm_ats,array_a,array_b,jjj_ats) := ( ret_ats : 0.0, if (jjj_ats <= mmm_ats) then ( /* if number 11*/ ma_ats : mmm_ats + 1, iii_ats : jjj_ats, while (iii_ats <= mmm_ats) do ( /* do number 1*/ lll_ats : ma_ats - iii_ats, ret_ats : ret_ats + array_a[iii_ats]*array_b[lll_ats], iii_ats : iii_ats + 1 )/* end do number 1*/ )/* end if 11*/ , ret_ats /* End Function number1*/); mode_declare(att,bfloat); /* Begin Function number 1*/ att( mmm_att,array_aa,array_bb,jjj_att) := ( ret_att : 0.0, if (jjj_att <= mmm_att) then ( /* if number 11*/ ma_att : mmm_att + 2, iii_att : jjj_att, while (iii_att <= mmm_att) do ( /* do number 1*/ lll_att : ma_att - iii_att, al_att : (lll_att - 1), if (lll_att <= glob_max_terms) then ( /* if number 12*/ ret_att : ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att) )/* end if 12*/ , iii_att : iii_att + 1 )/* end do number 1*/ , ret_att : ret_att / convfp(mmm_att) )/* end if 11*/ , ret_att /* End Function number1*/); /* Begin Function number 1*/ display_pole() := ( if ((array_pole[1] # glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] # glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then ( /* if number 11*/ omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "), omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ") )/* end if 11*/ /* End Function number1*/); /* Begin Function number 1*/ logditto(file) := ( printf(file,""), printf(file,"ditto"), printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ logitem_integer(file,n) := ( printf(file,""), printf(file,"~d",n), printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ logitem_str(file,str) := ( printf(file,""), printf(file,str), printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ log_revs(file,revs) := ( printf(file,revs) /* End Function number1*/); /* Begin Function number 1*/ logitem_float(file,x) := ( printf(file,""), printf(file,"~g",x), printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ logitem_pole(file,pole) := ( printf(file,""), if pole = 0 then ( /* if number 11*/ printf(file,"NA") ) elseif pole = 1 then ( /* if number 12*/ printf(file,"Real") ) elseif pole = 2 then ( /* if number 13*/ printf(file,"Complex") ) else ( printf(file,"No Pole") )/* end if 13*/ , printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ logstart(file) := ( printf(file,"") /* End Function number1*/); /* Begin Function number 1*/ logend(file) := ( printf(file,"~%") /* End Function number1*/); /* Begin Function number 1*/ chk_data() := ( errflag : false, if ((glob_max_terms < 15) or (glob_max_terms > 512)) then ( /* if number 13*/ omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"), glob_max_terms : 30 )/* end if 13*/ , if (glob_max_iter < 2) then ( /* if number 13*/ omniout_str(ALWAYS,"Illegal max_iter"), errflag : true )/* end if 13*/ , if (errflag) then ( /* if number 13*/ quit() )/* end if 13*/ /* End Function number1*/); mode_declare(comp_expect_sec,bfloat); /* Begin Function number 1*/ comp_expect_sec(t_end2,t_start2,t2,clock_sec) := ( ms2 : clock_sec, sub1 : (t_end2-t_start2), sub2 : (t2-t_start2), if (sub1 = 0.0) then ( /* if number 13*/ sec_left : 0.0 ) else ( if (abs(sub2) > 0.0) then ( /* if number 14*/ rrr : (sub1/sub2), sec_left : rrr * ms2 - ms2 ) else ( sec_left : 0.0 )/* end if 14*/ )/* end if 13*/ , sec_left /* End Function number1*/); mode_declare(comp_percent,bfloat); /* Begin Function number 1*/ comp_percent(t_end2,t_start2,t2) := ( sub1 : (t_end2-t_start2), sub2 : (t2-t_start2), if (abs(sub2) > glob_small_float) then ( /* if number 13*/ rrr : (100.0*sub2)/sub1 ) else ( rrr : 0.0 )/* end if 13*/ , rrr /* End Function number1*/); mode_declare(factorial_1,bfloat); /* Begin Function number 1*/ factorial_1(nnn) := ( (nnn!) /* End Function number1*/); mode_declare(factorial_3,bfloat); /* Begin Function number 1*/ factorial_3(mmm2,nnn2) := ( (mmm2!)/(nnn2!) /* End Function number1*/); /* Begin Function number 1*/ convfp(mmm) := ( (mmm) /* End Function number1*/); /* Begin Function number 1*/ convfloat(mmm) := ( (mmm) /* End Function number1*/); elapsed_time_seconds() :=( t: elapsed_real_time(), t); arcsin(x) :=( asin(x) ); arccos(x) :=( acos(x) ); arctan(x) :=( atan(x) ); /* END ATS LIBRARY BLOCK */ /* BEGIN USER DEF BLOCK */ /* BEGIN USER DEF BLOCK */ exact_soln_y (x) := ( 2.0 + sin(x) - cos(x) ); /* END USER DEF BLOCK */ /* END USER DEF BLOCK */ /* END OUTFILE5 */ /* Begin Function number 1*/ mainprog() := ( /* BEGIN OUTFIEMAIN */ define_variable(INFO,2,fixnum), define_variable(glob_iolevel,5,fixnum), define_variable(DEBUGL,3,fixnum), define_variable(DEBUGMASSIVE,4,fixnum), define_variable(ALWAYS,1,fixnum), define_variable(glob_max_terms,30,fixnum), /* Top Generate Globals Definition */ define_variable(glob_iter,0,fixnum), define_variable(glob_hmin,0.00000000001,float), define_variable(hours_in_day,24.0,float), define_variable(glob_dump,false,boolean), define_variable(glob_percent_done,0.0,float), define_variable(glob_start,0,fixnum), define_variable(glob_warned,false,boolean), define_variable(glob_small_float,0.1e-50,float), define_variable(glob_not_yet_finished,true,boolean), define_variable(glob_log10normmin,0.1,float), define_variable(glob_max_sec,10000.0,float), define_variable(glob_log10_relerr,0.1e-10,float), define_variable(glob_clock_start_sec,0.0,float), define_variable(centuries_in_millinium,10.0,float), define_variable(glob_optimal_expect_sec,0.1,float), define_variable(glob_no_eqs,0,fixnum), define_variable(glob_max_rel_trunc_err,0.1e-10,float), define_variable(glob_large_float,9.0e100,float), define_variable(glob_hmax,1.0,float), define_variable(glob_h,0.1,float), define_variable(glob_max_opt_iter,10,fixnum), define_variable(glob_orig_start_sec,0.0,float), define_variable(glob_hmin_init,0.001,float), define_variable(glob_initial_pass,true,boolean), define_variable(glob_clock_sec,0.0,float), define_variable(glob_log10abserr,0.0,float), define_variable(glob_log10_abserr,0.1e-10,float), define_variable(glob_last_good_h,0.1,float), define_variable(glob_disp_incr,0.1,float), define_variable(glob_reached_optimal_h,false,boolean), define_variable(glob_subiter_method,3,fixnum), define_variable(glob_log10relerr,0.0,float), define_variable(glob_abserr,0.1e-10,float), define_variable(glob_look_poles,false,boolean), define_variable(djd_debug2,true,boolean), define_variable(djd_debug,true,boolean), define_variable(glob_max_minutes,0.0,float), define_variable(glob_normmax,0.0,float), define_variable(glob_curr_iter_when_opt,0,fixnum), define_variable(glob_max_trunc_err,0.1e-10,float), define_variable(glob_relerr,0.1e-10,float), define_variable(glob_optimal_done,false,boolean), define_variable(glob_not_yet_start_msg,true,boolean), define_variable(years_in_century,100.0,float), define_variable(glob_optimal_clock_start_sec,0.0,float), define_variable(MAX_UNCHANGED,10,fixnum), define_variable(glob_unchanged_h_cnt,0,fixnum), define_variable(glob_max_hours,0.0,float), define_variable(glob_dump_analytic,false,boolean), define_variable(glob_almost_1,0.9990,float), define_variable(sec_in_min,60.0,float), define_variable(glob_current_iter,0,fixnum), define_variable(glob_warned2,false,boolean), define_variable(glob_smallish_float,0.1e-100,float), define_variable(glob_optimal_start,0.0,float), define_variable(glob_max_iter,1000,fixnum), define_variable(days_in_year,365.0,float), define_variable(min_in_hour,60.0,float), define_variable(glob_display_flag,true,boolean), define_variable(glob_html_log,true,boolean), /* Bottom Generate Globals Deninition */ ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, /* Write Set Defaults */ glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : -1, opt_iter : -1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS,"##############temp/addpostode.ode#################"), omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"max_terms : 30,"), 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 : 0.0,"), omniout_str(ALWAYS,"x_end : 10.0 ,"), omniout_str(ALWAYS,"array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"glob_h : 0.00001 ,"), omniout_str(ALWAYS,"glob_look_poles : true,"), omniout_str(ALWAYS,"glob_max_iter : 100,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_h : 0.0001 ,"), omniout_str(ALWAYS,"glob_look_poles : true,"), omniout_str(ALWAYS,"glob_max_iter : 1000,"), omniout_str(ALWAYS,"glob_max_minutes : 15,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := ("), omniout_str(ALWAYS,"2.0 + sin(x) - 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 : 1.0e-200, glob_smallish_float : 1.0e-64, glob_large_float : 1.0e100, glob_almost_1 : 0.99, glob_log10_abserr : -8.0, glob_log10_relerr : -8.0, glob_hmax : 0.01, /* BEGIN FIRST INPUT BLOCK */ /* BEGIN FIRST INPUT BLOCK */ max_terms : 30, Digits : 32, /* END FIRST INPUT BLOCK */ /* START OF INITS AFTER INPUT BLOCK */ glob_max_terms : max_terms, glob_html_log : true, /* END OF INITS AFTER INPUT BLOCK */ array(array_y,max_terms+ 1), array(array_x,max_terms+ 1), array(array_1st_rel_error,max_terms+ 1), array(array_tmp0,max_terms+ 1), array(array_tmp1,max_terms+ 1), array(array_tmp2,max_terms+ 1), array(array_tmp3,max_terms+ 1), array(array_tmp4,max_terms+ 1), array(array_type_pole,max_terms+ 1), array(array_tmp3_g,max_terms+ 1), array(array_m1,max_terms+ 1), array(array_last_rel_error,max_terms+ 1), array(array_tmp1_g,max_terms+ 1), array(array_pole,max_terms+ 1), array(array_norms,max_terms+ 1), array(array_y_init,max_terms+ 1), array(array_real_pole,1+ 1,3+ 1), array(array_y_higher_work,2+ 1,max_terms+ 1), array(array_y_higher,2+ 1,max_terms+ 1), array(array_complex_pole,1+ 1,3+ 1), array(array_y_higher_work2,2+ 1,max_terms+ 1), array(array_y_set_initial,2+ 1,max_terms+ 1), array(array_poles,1+ 1,3+ 1), term : 1, while term <= max_terms do ( /* do number 2*/ array_y[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_x[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_1st_rel_error[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp0[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp1[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp2[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp3[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp4[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_type_pole[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp3_g[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_m1[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_last_rel_error[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_tmp1_g[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_pole[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_norms[term] : 0.0, term : term + 1 )/* end do number 2*/ , term : 1, while term <= max_terms do ( /* do number 2*/ array_y_init[term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : 1, while ord <=1 do ( /* do number 2*/ term : 1, while term <= 3 do ( /* do number 3*/ array_real_pole[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=2 do ( /* do number 2*/ term : 1, while term <= max_terms do ( /* do number 3*/ array_y_higher_work[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=2 do ( /* do number 2*/ term : 1, while term <= max_terms do ( /* do number 3*/ array_y_higher[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=1 do ( /* do number 2*/ term : 1, while term <= 3 do ( /* do number 3*/ array_complex_pole[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=2 do ( /* do number 2*/ term : 1, while term <= max_terms do ( /* do number 3*/ array_y_higher_work2[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=2 do ( /* do number 2*/ term : 1, while term <= max_terms do ( /* do number 3*/ array_y_set_initial[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , ord : 1, while ord <=1 do ( /* do number 2*/ term : 1, while term <= 3 do ( /* do number 3*/ array_poles[ord,term] : 0.0, term : term + 1 )/* end do number 3*/ , ord : ord + 1 )/* end do number 2*/ , /* BEGIN ARRAYS DEFINED AND INITIALIZATED */ array(array_x,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_x[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_y,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_y[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp4,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp4[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp3,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp3[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp2,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp2[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp1,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp1[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp0,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp0[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp3_g,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp3_g[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_tmp1_g,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_tmp1_g[term] : 0.0, term : term + 1 )/* end do number 2*/ , array(array_const_1,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_const_1[term] : 0.0, term : term + 1 )/* end do number 2*/ , array_const_1[1] : 1, array(array_const_0D0,max_terms+1 + 1), term : 1, while term <= max_terms + 1 do ( /* do number 2*/ array_const_0D0[term] : 0.0, term : term + 1 )/* end do number 2*/ , array_const_0D0[1] : 0.0, array(array_m1,max_terms+1 + 1), term : 1, while term <= max_terms do ( /* do number 2*/ array_m1[term] : 0.0, term : term + 1 )/* end do number 2*/ , array_m1[1] : -1.0, /* END ARRAYS DEFINED AND INITIALIZATED */ /* TOP SECOND INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start : 0.0, x_end : 10.0 , array_y_init[0 + 1] : exact_soln_y(x_start), glob_h : 0.00001 , glob_look_poles : true, glob_max_iter : 100, /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h : 0.0001 , glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15, /* END OVERRIDE BLOCK */ /* END SECOND INPUT BLOCK */ /* BEGIN INITS AFTER SECOND INPUT BLOCK */ glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours), glob_abserr : 10.0 ^ (glob_log10_abserr), glob_relerr : 10.0 ^ (glob_log10_relerr), chk_data(), /* AFTER INITS AFTER SECOND INPUT BLOCK */ 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, if glob_html_log then ( /* if number 2*/ html_log_file : openw("html/entry.html") )/* end if 2*/ , /* BEGIN SOLUTION CODE */ omniout_str(ALWAYS,"START of Soultion"), /* Start Series -- INITIALIZE FOR SOLUTION */ array_x[1] : x_start, array_x[2] : glob_h, 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] * glob_h ^ (term_no - 1) / 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, array_y_higher[r_order,term_no] : array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))), term_no : term_no + 1 )/* end do number 3*/ , r_order : r_order + 1 )/* end do number 2*/ , current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_y(), if (abs(array_y_higher[1,1]) > glob_small_float) then ( /* if number 2*/ tmp : abs(array_y_higher[1,1]), log10norm : (log10(tmp)), if (log10norm < glob_log10normmin) then ( /* if number 3*/ glob_log10normmin : log10norm )/* end if 3*/ )/* end if 2*/ , display_alot(current_iter) , glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL," "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do ( /* do number 2*/ /* left paren 0001C */ omniout_str(INFO," "), omniout_str(INFO,"TOP MAIN SOLVE Loop"), glob_iter : glob_iter + 1, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : glob_current_iter + 1, atomall(), if (glob_look_poles) then ( /* if number 2*/ /* left paren 0004C */ check_for_pole() )/* end if 2*/ ,/* was right paren 0004C */ array_x[1] : array_x[1] + glob_h, array_x[2] : glob_h, /* Jump Series array_y */ order_diff : 1, /* 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 : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ array_y_higher_work[2,iii] : array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 3*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 2, calc_term : 1, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 3*/ , array_y_higher_work2[ord,calc_term] : temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 2, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 3*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 1, calc_term : 2, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 3*/ , array_y_higher_work2[ord,calc_term] : temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 1, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 3*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 1, calc_term : 1, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 3*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 3*/ , array_y_higher_work2[ord,calc_term] : temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(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 : glob_max_terms, while (term_no >= 1) do ( /* do number 3*/ array_y[term_no] : array_y_higher_work2[1,term_no], ord : 1, while ord <= order_diff do ( /* do number 4*/ array_y_higher[ord,term_no] : array_y_higher_work2[ord,term_no], ord : ord + 1 )/* end do number 4*/ , term_no : term_no - 1 )/* end do number 3*/ , /* END PART 2 HEVE MOVED TERMS to REGULAR Array */ display_alot(current_iter) )/* end do number 2*/ ,/* right paren 0001C */ omniout_str(ALWAYS,"Finished!"), if (glob_iter >= glob_max_iter) then ( /* if number 2*/ omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") )/* end if 2*/ , if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then ( /* if number 2*/ omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") )/* end if 2*/ , glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;"), omniout_int(INFO,"Iterations ",32,glob_iter,4," ") , prog_report(x_start,x_end), if glob_html_log then ( /* if number 2*/ logstart(html_log_file), logitem_str(html_log_file,"2012-06-13T11:49:59-05:00") , logitem_str(html_log_file,"Maxima") , logitem_str(html_log_file,"add") , logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( 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_str(html_log_file,"16") , logitem_integer(html_log_file,glob_max_terms) , logitem_float(html_log_file,array_1st_rel_error[1]) , logitem_float(html_log_file,array_last_rel_error[1]) , logitem_integer(html_log_file,glob_iter) , logitem_pole(html_log_file,array_type_pole[1]) , if array_type_pole[1] = 1 or array_type_pole[1] = 2 then ( /* if number 3*/ logitem_float(html_log_file,array_pole[1]) , logitem_float(html_log_file,array_pole[2]) , 0 ) else ( logitem_str(html_log_file,"NA") , logitem_str(html_log_file,"NA") , 0 )/* end if 3*/ , logitem_time(html_log_file,convfloat(glob_clock_sec)) , if glob_percent_done < 100.0 then ( /* if number 3*/ logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) , 0 ) else ( logitem_str(html_log_file,"Done") , 0 )/* end if 3*/ , log_revs(html_log_file," 090 ") , logitem_str(html_log_file,"add diffeq.max") , logitem_str(html_log_file,"add maxima results") , logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") , logend(html_log_file) )/* end if 2*/ , if glob_html_log then ( /* if number 2*/ close(html_log_file) )/* end if 2*/ /* END OUTFILEMAIN */ /* End Function number1*/); mainprog();