(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) display_alot(iter) := if iter >= 0 then (ind_var : array_t , omniout_float(ALWAYS, 1 "t[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_x1(ind_var), omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_x1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_x2(ind_var), omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_x2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%o3) display_alot(iter) := if iter >= 0 then (ind_var : array_t , omniout_float(ALWAYS, 1 "t[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_x1(ind_var), omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_x1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_x2(ind_var), omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_x2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%i4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_x1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_x2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_t ), hnew : sz2) 1 (%o4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_x1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_x2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_t ), hnew : sz2) 1 (%i5) prog_report(t_start, t_end) := (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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t ), 1 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(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t )), glob_percent_done : percent_done, 1 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 (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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o5) prog_report(t_start, t_end) := (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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t ), 1 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(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(t_end), convfloat(t_start), convfloat(glob_h) + convfloat(array_t )), glob_percent_done : percent_done, 1 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 (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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_x1_higher ! < glob_small_float) ! 1, m! or (!array_x1_higher ! < glob_small_float) ! 1, m - 1! or (!array_x1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_x1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_x1_higher 1, m - 1 array_x1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_x1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 2 + n, 1, 2 while (m >= 10) and ((!array_x2_higher ! < glob_small_float) ! 1, m! or (!array_x2_higher ! < glob_small_float) ! 1, m - 1! or (!array_x2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_x2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_x2_higher 1, m - 1 array_x2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_x2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_x1_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_x1_higher ! >= glob_large_float) ! 1, m! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_x1_higher array_x1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_x1_higher array_x1_higher 1, m - 1 1, m - 2 array_x1_higher array_x1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_x1_higher array_x1_higher 1, m - 3 1, m - 4 array_x1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_x1_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), n : - 1 - 2 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_x2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_x2_higher ! >= glob_large_float) ! 1, m! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_x2_higher array_x2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_x2_higher array_x2_higher 1, m - 1 1, m - 2 array_x2_higher array_x2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_x2_higher array_x2_higher 1, m - 3 1, m - 4 array_x2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_x2_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_x1_higher ! < glob_small_float) ! 1, m! or (!array_x1_higher ! < glob_small_float) ! 1, m - 1! or (!array_x1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_x1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_x1_higher 1, m - 1 array_x1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_x1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 2 + n, 1, 2 while (m >= 10) and ((!array_x2_higher ! < glob_small_float) ! 1, m! or (!array_x2_higher ! < glob_small_float) ! 1, m - 1! or (!array_x2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_x2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_x2_higher 1, m - 1 array_x2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_x2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_x1_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_x1_higher ! >= glob_large_float) ! 1, m! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_x1_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_x1_higher array_x1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_x1_higher array_x1_higher 1, m - 1 1, m - 2 array_x1_higher array_x1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_x1_higher array_x1_higher 1, m - 3 1, m - 4 array_x1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_x1_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), n : - 1 - 2 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_x2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_x2_higher ! >= glob_large_float) ! 1, m! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_x2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_x2_higher array_x2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_x2_higher array_x2_higher 1, m - 1 1, m - 2 array_x2_higher array_x2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_x2_higher array_x2_higher 1, m - 3 1, m - 4 array_x2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_x2_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%i7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_x1 ! > array_norms ! iii! iii then array_norms : !array_x1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_x2 ! > array_norms ! iii! iii then array_norms : !array_x2 !, iii : 1 + iii)) iii ! iii! (%o7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_x1 ! > array_norms ! iii! iii then array_norms : !array_x1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_x2 ! > array_norms ! iii! iii then array_norms : !array_x2 !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : array_const_4D0 array_x2 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_x2_higher , array_tmp4 : array_const_2D0 array_tmp3 , 1 2, 1 1 1 1 array_tmp5 : array_tmp2 - array_tmp4 , 1 1 1 array_tmp6 : array_const_2D0 array_x1 , 1 1 1 array_tmp7 : array_tmp5 - array_tmp6 , 1 1 1 if not array_x1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp7 glob_h factorial_3(0, 1), 1 array_x1 : temporary, array_x1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp9 : array_x2_higher , array_tmp10 : 1 2, 1 1 array_const_3D0 array_tmp9 , array_tmp11 : array_const_2D0 array_x2 , 1 1 1 1 1 array_tmp12 : array_tmp10 - array_tmp11 , 1 1 1 array_tmp13 : array_x1_higher , array_tmp14 : 1 3, 1 1 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 1 1 1 2, 1 array_tmp16 : array_tmp14 - array_tmp15 , 1 1 1 array_tmp17 : array_x1 + array_tmp16 , 1 1 1 if not array_x2_set_initial then (if 1 <= glob_max_terms 2, 3 2 then (temporary : array_tmp17 glob_h factorial_3(0, 2), 1 array_x2 : temporary, array_x2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 2 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 2, glob_h 3, 1 array_tmp1 : ats(2, array_const_4D0, array_x2, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_x2_higher , array_tmp4 : 2 2, 2 2 ats(2, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 2 2 2 array_tmp6 : ats(2, array_const_2D0, array_x1, 1), 2 array_tmp7 : array_tmp5 - array_tmp6 , 2 2 2 if not array_x1_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp7 glob_h factorial_3(1, 2), 2 array_x1 : temporary, array_x1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp9 : array_x2_higher , array_tmp10 : 2 2, 2 2 ats(2, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(2, array_const_2D0, array_x2, 1), 2 array_tmp12 : array_tmp10 - array_tmp11 , 2 2 2 array_tmp13 : array_x1_higher , array_tmp14 : 2 3, 2 2 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 2 2 2 2, 2 array_tmp16 : array_tmp14 - array_tmp15 , 2 2 2 array_tmp17 : array_x1 + array_tmp16 , 2 2 2 if not array_x2_set_initial then (if 2 <= glob_max_terms 2, 4 2 then (temporary : array_tmp17 glob_h factorial_3(1, 3), 2 array_x2 : temporary, array_x2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 3 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 3, glob_h 3, 2 array_tmp1 : ats(3, array_const_4D0, array_x2, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_x2_higher , array_tmp4 : 3 2, 3 3 ats(3, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 3 3 3 array_tmp6 : ats(3, array_const_2D0, array_x1, 1), 3 array_tmp7 : array_tmp5 - array_tmp6 , 3 3 3 if not array_x1_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp7 glob_h factorial_3(2, 3), 3 array_x1 : temporary, array_x1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp9 : array_x2_higher , array_tmp10 : 3 2, 3 3 ats(3, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(3, array_const_2D0, array_x2, 1), 3 array_tmp12 : array_tmp10 - array_tmp11 , 3 3 3 array_tmp13 : array_x1_higher , array_tmp14 : 3 3, 3 3 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 3 3 3 2, 3 array_tmp16 : array_tmp14 - array_tmp15 , 3 3 3 array_tmp17 : array_x1 + array_tmp16 , 3 3 3 if not array_x2_set_initial then (if 3 <= glob_max_terms 2, 5 2 then (temporary : array_tmp17 glob_h factorial_3(2, 4), 3 array_x2 : temporary, array_x2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 4, glob_h 3, 3 array_tmp1 : ats(4, array_const_4D0, array_x2, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_x2_higher , array_tmp4 : 4 2, 4 4 ats(4, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 4 4 4 array_tmp6 : ats(4, array_const_2D0, array_x1, 1), 4 array_tmp7 : array_tmp5 - array_tmp6 , 4 4 4 if not array_x1_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp7 glob_h factorial_3(3, 4), 4 array_x1 : temporary, array_x1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp9 : array_x2_higher , array_tmp10 : 4 2, 4 4 ats(4, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(4, array_const_2D0, array_x2, 1), 4 array_tmp12 : array_tmp10 - array_tmp11 , 4 4 4 array_tmp13 : array_x1_higher , array_tmp14 : 4 3, 4 4 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 4 4 4 2, 4 array_tmp16 : array_tmp14 - array_tmp15 , 4 4 4 array_tmp17 : array_x1 + array_tmp16 , 4 4 4 if not array_x2_set_initial then (if 4 <= glob_max_terms 2, 6 2 then (temporary : array_tmp17 glob_h factorial_3(3, 5), 4 array_x2 : temporary, array_x2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 5 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 5, glob_h 3, 4 array_tmp1 : ats(5, array_const_4D0, array_x2, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_x2_higher , array_tmp4 : 5 2, 5 5 ats(5, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 5 5 5 array_tmp6 : ats(5, array_const_2D0, array_x1, 1), 5 array_tmp7 : array_tmp5 - array_tmp6 , 5 5 5 if not array_x1_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp7 glob_h factorial_3(4, 5), 5 array_x1 : temporary, array_x1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 6, glob_h 2, 5 array_tmp9 : array_x2_higher , array_tmp10 : 5 2, 5 5 ats(5, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(5, array_const_2D0, array_x2, 1), 5 array_tmp12 : array_tmp10 - array_tmp11 , 5 5 5 array_tmp13 : array_x1_higher , array_tmp14 : 5 3, 5 5 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 5 5 5 2, 5 array_tmp16 : array_tmp14 - array_tmp15 , 5 5 5 array_tmp17 : array_x1 + array_tmp16 , 5 5 5 if not array_x2_set_initial then (if 5 <= glob_max_terms 2, 7 2 then (temporary : array_tmp17 glob_h factorial_3(4, 6), 5 array_x2 : temporary, array_x2_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 6, glob_h 3, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_const_4D0, array_x2, 1), array_tmp2 : array_tmp1 + array_const_0D0 , kkk kkk kkk array_tmp3 : array_x2_higher , kkk 2, kkk array_tmp4 : ats(kkk, array_const_2D0, array_tmp3, 1), kkk array_tmp5 : array_tmp2 - array_tmp4 , kkk kkk kkk array_tmp6 : ats(kkk, array_const_2D0, array_x1, 1), kkk array_tmp7 : array_tmp5 - array_tmp6 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_x1_set_initial 1, order_d + kkk order_d array_tmp7 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_x1 : temporary, array_x1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_x1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp9 : array_x2_higher , kkk 2, kkk array_tmp10 : ats(kkk, array_const_3D0, array_tmp9, 1), kkk array_tmp11 : ats(kkk, array_const_2D0, array_x2, 1), kkk array_tmp12 : array_tmp10 - array_tmp11 , kkk kkk kkk array_tmp13 : array_x1_higher , kkk 3, kkk array_tmp14 : array_tmp12 - array_tmp13 , kkk kkk kkk array_tmp15 : array_x1_higher , kkk 2, kkk array_tmp16 : array_tmp14 - array_tmp15 , kkk kkk kkk array_tmp17 : array_x1 + array_tmp16 , order_d : 2, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_x2_set_initial 2, order_d + kkk order_d array_tmp17 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_x2 : temporary, array_x2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_x2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_const_4D0 array_x2 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_x2_higher , array_tmp4 : array_const_2D0 array_tmp3 , 1 2, 1 1 1 1 array_tmp5 : array_tmp2 - array_tmp4 , 1 1 1 array_tmp6 : array_const_2D0 array_x1 , 1 1 1 array_tmp7 : array_tmp5 - array_tmp6 , 1 1 1 if not array_x1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp7 glob_h factorial_3(0, 1), 1 array_x1 : temporary, array_x1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp9 : array_x2_higher , array_tmp10 : 1 2, 1 1 array_const_3D0 array_tmp9 , array_tmp11 : array_const_2D0 array_x2 , 1 1 1 1 1 array_tmp12 : array_tmp10 - array_tmp11 , 1 1 1 array_tmp13 : array_x1_higher , array_tmp14 : 1 3, 1 1 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 1 1 1 2, 1 array_tmp16 : array_tmp14 - array_tmp15 , 1 1 1 array_tmp17 : array_x1 + array_tmp16 , 1 1 1 if not array_x2_set_initial then (if 1 <= glob_max_terms 2, 3 2 then (temporary : array_tmp17 glob_h factorial_3(0, 2), 1 array_x2 : temporary, array_x2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 2 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 2, glob_h 3, 1 array_tmp1 : ats(2, array_const_4D0, array_x2, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_x2_higher , array_tmp4 : 2 2, 2 2 ats(2, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 2 2 2 array_tmp6 : ats(2, array_const_2D0, array_x1, 1), 2 array_tmp7 : array_tmp5 - array_tmp6 , 2 2 2 if not array_x1_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp7 glob_h factorial_3(1, 2), 2 array_x1 : temporary, array_x1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp9 : array_x2_higher , array_tmp10 : 2 2, 2 2 ats(2, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(2, array_const_2D0, array_x2, 1), 2 array_tmp12 : array_tmp10 - array_tmp11 , 2 2 2 array_tmp13 : array_x1_higher , array_tmp14 : 2 3, 2 2 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 2 2 2 2, 2 array_tmp16 : array_tmp14 - array_tmp15 , 2 2 2 array_tmp17 : array_x1 + array_tmp16 , 2 2 2 if not array_x2_set_initial then (if 2 <= glob_max_terms 2, 4 2 then (temporary : array_tmp17 glob_h factorial_3(1, 3), 2 array_x2 : temporary, array_x2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 3 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 3, glob_h 3, 2 array_tmp1 : ats(3, array_const_4D0, array_x2, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_x2_higher , array_tmp4 : 3 2, 3 3 ats(3, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 3 3 3 array_tmp6 : ats(3, array_const_2D0, array_x1, 1), 3 array_tmp7 : array_tmp5 - array_tmp6 , 3 3 3 if not array_x1_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp7 glob_h factorial_3(2, 3), 3 array_x1 : temporary, array_x1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp9 : array_x2_higher , array_tmp10 : 3 2, 3 3 ats(3, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(3, array_const_2D0, array_x2, 1), 3 array_tmp12 : array_tmp10 - array_tmp11 , 3 3 3 array_tmp13 : array_x1_higher , array_tmp14 : 3 3, 3 3 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 3 3 3 2, 3 array_tmp16 : array_tmp14 - array_tmp15 , 3 3 3 array_tmp17 : array_x1 + array_tmp16 , 3 3 3 if not array_x2_set_initial then (if 3 <= glob_max_terms 2, 5 2 then (temporary : array_tmp17 glob_h factorial_3(2, 4), 3 array_x2 : temporary, array_x2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 4, glob_h 3, 3 array_tmp1 : ats(4, array_const_4D0, array_x2, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_x2_higher , array_tmp4 : 4 2, 4 4 ats(4, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 4 4 4 array_tmp6 : ats(4, array_const_2D0, array_x1, 1), 4 array_tmp7 : array_tmp5 - array_tmp6 , 4 4 4 if not array_x1_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp7 glob_h factorial_3(3, 4), 4 array_x1 : temporary, array_x1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp9 : array_x2_higher , array_tmp10 : 4 2, 4 4 ats(4, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(4, array_const_2D0, array_x2, 1), 4 array_tmp12 : array_tmp10 - array_tmp11 , 4 4 4 array_tmp13 : array_x1_higher , array_tmp14 : 4 3, 4 4 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 4 4 4 2, 4 array_tmp16 : array_tmp14 - array_tmp15 , 4 4 4 array_tmp17 : array_x1 + array_tmp16 , 4 4 4 if not array_x2_set_initial then (if 4 <= glob_max_terms 2, 6 2 then (temporary : array_tmp17 glob_h factorial_3(3, 5), 4 array_x2 : temporary, array_x2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 5 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 5, glob_h 3, 4 array_tmp1 : ats(5, array_const_4D0, array_x2, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_x2_higher , array_tmp4 : 5 2, 5 5 ats(5, array_const_2D0, array_tmp3, 1), array_tmp5 : array_tmp2 - array_tmp4 , 5 5 5 array_tmp6 : ats(5, array_const_2D0, array_x1, 1), 5 array_tmp7 : array_tmp5 - array_tmp6 , 5 5 5 if not array_x1_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp7 glob_h factorial_3(4, 5), 5 array_x1 : temporary, array_x1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_x1_higher : temporary)), kkk : 6, glob_h 2, 5 array_tmp9 : array_x2_higher , array_tmp10 : 5 2, 5 5 ats(5, array_const_3D0, array_tmp9, 1), array_tmp11 : ats(5, array_const_2D0, array_x2, 1), 5 array_tmp12 : array_tmp10 - array_tmp11 , 5 5 5 array_tmp13 : array_x1_higher , array_tmp14 : 5 3, 5 5 array_tmp12 - array_tmp13 , array_tmp15 : array_x1_higher , 5 5 5 2, 5 array_tmp16 : array_tmp14 - array_tmp15 , 5 5 5 array_tmp17 : array_x1 + array_tmp16 , 5 5 5 if not array_x2_set_initial then (if 5 <= glob_max_terms 2, 7 2 then (temporary : array_tmp17 glob_h factorial_3(4, 6), 5 array_x2 : temporary, array_x2_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_x2_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_x2_higher : temporary)), kkk : 6, glob_h 3, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_const_4D0, array_x2, 1), array_tmp2 : array_tmp1 + array_const_0D0 , kkk kkk kkk array_tmp3 : array_x2_higher , kkk 2, kkk array_tmp4 : ats(kkk, array_const_2D0, array_tmp3, 1), kkk array_tmp5 : array_tmp2 - array_tmp4 , kkk kkk kkk array_tmp6 : ats(kkk, array_const_2D0, array_x1, 1), kkk array_tmp7 : array_tmp5 - array_tmp6 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_x1_set_initial 1, order_d + kkk order_d array_tmp7 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_x1 : temporary, array_x1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_x1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp9 : array_x2_higher , kkk 2, kkk array_tmp10 : ats(kkk, array_const_3D0, array_tmp9, 1), kkk array_tmp11 : ats(kkk, array_const_2D0, array_x2, 1), kkk array_tmp12 : array_tmp10 - array_tmp11 , kkk kkk kkk array_tmp13 : array_x1_higher , kkk 3, kkk array_tmp14 : array_tmp12 - array_tmp13 , kkk kkk kkk array_tmp15 : array_x1_higher , kkk 2, kkk array_tmp16 : array_tmp14 - array_tmp15 , kkk kkk kkk array_tmp17 : array_x1 + array_tmp16 , order_d : 2, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_x2_set_initial 2, order_d + kkk order_d array_tmp17 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_x2 : temporary, array_x2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_x2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) 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)) (%o13) 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)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) 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 ), newline(), i : 1 + i)) i (%o16) 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 ), newline(), i : 1 + i)) i (%i17) dump_series_2(iolevel, dump_label, series_name, 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 ), i : 1 + i), sub : 1 + sub)) sub, i (%o17) dump_series_2(iolevel, dump_label, series_name, 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 ), i : 1 + i), sub : 1 + sub)) sub, i (%i18) 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)) (%o18) 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)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, 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 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 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 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 printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, 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 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 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 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 printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, 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 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 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 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 printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, 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 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 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 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 printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) 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 sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o36) 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 sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_x1(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, 6.0 c3 exp(- t) + 2.0 c1) (%o49) exact_soln_x1(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, 6.0 c3 exp(- t) + 2.0 c1) (%i50) exact_soln_x1p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, - 6.0 c3 exp(- t)) (%o50) exact_soln_x1p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, - 6.0 c3 exp(- t)) (%i51) exact_soln_x2(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, c3 exp(- t) + c2 exp(2.0 t) + c1) (%o51) exact_soln_x2(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, c3 exp(- t) + c2 exp(2.0 t) + c1) (%i52) exact_soln_x2p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, 2.0 c2 exp(2.0 t) - c3 exp(- t)) (%o52) exact_soln_x2p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4, 2.0 c2 exp(2.0 t) - c3 exp(- t)) (%i53) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_almost_1, 0.999, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_html_log, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_dump_analytic, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_dump, false, boolean), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, 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/mtest6postode.ode#################"), omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t\ ,2) - diff (x1,t,1) + x1;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* # */"), omniout_str(ALWAYS, "/* # was complicated.ode */"), omniout_str(ALWAYS, "/* # */"), omniout_str(ALWAYS, "t_start : 0.5,"), omniout_str(ALWAYS, "t_end : 5.0,"), omniout_str(ALWAYS, "array_x1_init[0 + 1] : exact_soln_x1(t_start),"), omniout_str(ALWAYS, "array_x1_init[1 + 1] : exact_soln_x1p(t_start),"), omniout_str(ALWAYS, "array_x2_init[0 + 1] : exact_soln_x2(t_start),"), omniout_str(ALWAYS, "array_x2_init[1 + 1] : exact_soln_x2p(t_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), 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_x1 (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x1p (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "- 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x2 (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x2p (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) "), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_m1, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_x1_init, 1 + max_terms), array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms), array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms), array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_x2_init, 1 + max_terms), array(array_x1, 1 + max_terms), array(array_x2, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_t, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_x2_set_initial, 1 + 3, 1 + max_terms), array(array_x1_set_initial, 1 + 3, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_x2_higher, 1 + 3, 1 + max_terms), array(array_x1_higher_work2, 1 + 3, 1 + max_terms), array(array_x1_higher, 1 + 3, 1 + max_terms), array(array_x2_higher_work2, 1 + 3, 1 + max_terms), array(array_x2_higher_work, 1 + 3, 1 + max_terms), array(array_x1_higher_work, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x1_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp11 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp12 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp14 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp15 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp17 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x2_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_t : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term array(array_tmp17, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term), term array(array_tmp16, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term), term array(array_tmp15, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term), term array(array_tmp14, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term), term array(array_tmp13, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term), term array(array_tmp12, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term), term array(array_tmp11, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term), term array(array_tmp10, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term), term array(array_x2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x2 : 0.0, term : 1 + term), term array(array_x1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x1 : 0.0, term : 1 + term), term array(array_t, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_t : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_4D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_4D0 : 0.0, term : 1 + term), term array_const_4D0 : 4.0, array(array_const_2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term), term array_const_2 : 2, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, t_start : 0.5, t_end : 5.0, 1 array_x1_init : exact_soln_x1(t_start), 1 + 0 array_x1_init : exact_soln_x1p(t_start), 1 + 1 array_x2_init : exact_soln_x2(t_start), 1 + 0 array_x2_init : exact_soln_x2p(t_start), glob_h : 1.0E-5, 1 + 1 glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_x1_set_initial : true, array_x1_set_initial : true, 1, 1 1, 2 array_x1_set_initial : false, array_x1_set_initial : false, 1, 3 1, 4 array_x1_set_initial : false, array_x1_set_initial : false, 1, 5 1, 6 array_x1_set_initial : false, array_x1_set_initial : false, 1, 7 1, 8 array_x1_set_initial : false, array_x1_set_initial : false, 1, 9 1, 10 array_x1_set_initial : false, array_x1_set_initial : false, 1, 11 1, 12 array_x1_set_initial : false, array_x1_set_initial : false, 1, 13 1, 14 array_x1_set_initial : false, array_x1_set_initial : false, 1, 15 1, 16 array_x1_set_initial : false, array_x1_set_initial : false, 1, 17 1, 18 array_x1_set_initial : false, array_x1_set_initial : false, 1, 19 1, 20 array_x1_set_initial : false, array_x1_set_initial : false, 1, 21 1, 22 array_x1_set_initial : false, array_x1_set_initial : false, 1, 23 1, 24 array_x1_set_initial : false, array_x1_set_initial : false, 1, 25 1, 26 array_x1_set_initial : false, array_x1_set_initial : false, 1, 27 1, 28 array_x1_set_initial : false, array_x1_set_initial : false, 1, 29 1, 30 array_x2_set_initial : true, array_x2_set_initial : true, 2, 1 2, 2 array_x2_set_initial : false, array_x2_set_initial : false, 2, 3 2, 4 array_x2_set_initial : false, array_x2_set_initial : false, 2, 5 2, 6 array_x2_set_initial : false, array_x2_set_initial : false, 2, 7 2, 8 array_x2_set_initial : false, array_x2_set_initial : false, 2, 9 2, 10 array_x2_set_initial : false, array_x2_set_initial : false, 2, 11 2, 12 array_x2_set_initial : false, array_x2_set_initial : false, 2, 13 2, 14 array_x2_set_initial : false, array_x2_set_initial : false, 2, 15 2, 16 array_x2_set_initial : false, array_x2_set_initial : false, 2, 17 2, 18 array_x2_set_initial : false, array_x2_set_initial : false, 2, 19 2, 20 array_x2_set_initial : false, array_x2_set_initial : false, 2, 21 2, 22 array_x2_set_initial : false, array_x2_set_initial : false, 2, 23 2, 24 array_x2_set_initial : false, array_x2_set_initial : false, 2, 25 2, 26 array_x2_set_initial : false, array_x2_set_initial : false, 2, 27 2, 28 array_x2_set_initial : false, array_x2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_t : t_start, 1 array_t : glob_h, order_diff : 2, term_no : 1, 2 while term_no <= order_diff do (array_x1 : term_no term_no - 1 array_x1_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_x1_init glob_h it array_x1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 2, term_no : 1, while term_no <= order_diff do (array_x2 : term_no term_no - 1 array_x2_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_x2_init glob_h it array_x2_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_x1(), if !array_x1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_x2(), if !array_x2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x2_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), 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_t <= t_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 3 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 3 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_t : glob_h + array_t , array_t : glob_h, order_diff : 2, ord : 3, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 3, iii array_x1_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 2, iii array_x1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 2, iii array_x1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_x1 : array_x1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_x1_higher : ord, term_no array_x1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 2, ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 3, iii array_x2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 2, iii array_x2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 2, iii array_x2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_x2 : array_x2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_x2_higher : ord, term_no array_x2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff (x1,t,1) = 4.\ 0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), omniout_str(INFO, "diff (x2,t,2)\ = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(t_start, t_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T15:53:47-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest6"), logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), logitem_float(html_log_file, t_start), logitem_float(html_log_file, t_end), logitem_float(html_log_file, array_t ), logitem_float(html_log_file, glob_h), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest6 diffeq.max"), logitem_str(html_log_file, "\ mtest6 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * dif\ f(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o53) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_almost_1, 0.999, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_html_log, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_dump_analytic, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_dump, false, boolean), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, 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/mtest6postode.ode#################"), omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t\ ,2) - diff (x1,t,1) + x1;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* # */"), omniout_str(ALWAYS, "/* # was complicated.ode */"), omniout_str(ALWAYS, "/* # */"), omniout_str(ALWAYS, "t_start : 0.5,"), omniout_str(ALWAYS, "t_end : 5.0,"), omniout_str(ALWAYS, "array_x1_init[0 + 1] : exact_soln_x1(t_start),"), omniout_str(ALWAYS, "array_x1_init[1 + 1] : exact_soln_x1p(t_start),"), omniout_str(ALWAYS, "array_x2_init[0 + 1] : exact_soln_x2(t_start),"), omniout_str(ALWAYS, "array_x2_init[1 + 1] : exact_soln_x2p(t_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), 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_x1 (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x1p (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "- 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x2 (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_x2p (t) := ("), omniout_str(ALWAYS, " "), omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"), omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) "), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_m1, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_x1_init, 1 + max_terms), array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms), array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms), array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_x2_init, 1 + max_terms), array(array_x1, 1 + max_terms), array(array_x2, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_t, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_x2_set_initial, 1 + 3, 1 + max_terms), array(array_x1_set_initial, 1 + 3, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_x2_higher, 1 + 3, 1 + max_terms), array(array_x1_higher_work2, 1 + 3, 1 + max_terms), array(array_x1_higher, 1 + 3, 1 + max_terms), array(array_x2_higher_work2, 1 + 3, 1 + max_terms), array(array_x2_higher_work, 1 + 3, 1 + max_terms), array(array_x1_higher_work, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x1_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp11 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp12 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp14 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp15 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp17 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x2_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_t : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_x1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term array(array_tmp17, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term), term array(array_tmp16, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term), term array(array_tmp15, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term), term array(array_tmp14, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term), term array(array_tmp13, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term), term array(array_tmp12, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term), term array(array_tmp11, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term), term array(array_tmp10, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term), term array(array_x2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x2 : 0.0, term : 1 + term), term array(array_x1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x1 : 0.0, term : 1 + term), term array(array_t, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_t : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_4D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_4D0 : 0.0, term : 1 + term), term array_const_4D0 : 4.0, array(array_const_2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term), term array_const_2 : 2, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, t_start : 0.5, t_end : 5.0, 1 array_x1_init : exact_soln_x1(t_start), 1 + 0 array_x1_init : exact_soln_x1p(t_start), 1 + 1 array_x2_init : exact_soln_x2(t_start), 1 + 0 array_x2_init : exact_soln_x2p(t_start), glob_h : 1.0E-5, 1 + 1 glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_x1_set_initial : true, array_x1_set_initial : true, 1, 1 1, 2 array_x1_set_initial : false, array_x1_set_initial : false, 1, 3 1, 4 array_x1_set_initial : false, array_x1_set_initial : false, 1, 5 1, 6 array_x1_set_initial : false, array_x1_set_initial : false, 1, 7 1, 8 array_x1_set_initial : false, array_x1_set_initial : false, 1, 9 1, 10 array_x1_set_initial : false, array_x1_set_initial : false, 1, 11 1, 12 array_x1_set_initial : false, array_x1_set_initial : false, 1, 13 1, 14 array_x1_set_initial : false, array_x1_set_initial : false, 1, 15 1, 16 array_x1_set_initial : false, array_x1_set_initial : false, 1, 17 1, 18 array_x1_set_initial : false, array_x1_set_initial : false, 1, 19 1, 20 array_x1_set_initial : false, array_x1_set_initial : false, 1, 21 1, 22 array_x1_set_initial : false, array_x1_set_initial : false, 1, 23 1, 24 array_x1_set_initial : false, array_x1_set_initial : false, 1, 25 1, 26 array_x1_set_initial : false, array_x1_set_initial : false, 1, 27 1, 28 array_x1_set_initial : false, array_x1_set_initial : false, 1, 29 1, 30 array_x2_set_initial : true, array_x2_set_initial : true, 2, 1 2, 2 array_x2_set_initial : false, array_x2_set_initial : false, 2, 3 2, 4 array_x2_set_initial : false, array_x2_set_initial : false, 2, 5 2, 6 array_x2_set_initial : false, array_x2_set_initial : false, 2, 7 2, 8 array_x2_set_initial : false, array_x2_set_initial : false, 2, 9 2, 10 array_x2_set_initial : false, array_x2_set_initial : false, 2, 11 2, 12 array_x2_set_initial : false, array_x2_set_initial : false, 2, 13 2, 14 array_x2_set_initial : false, array_x2_set_initial : false, 2, 15 2, 16 array_x2_set_initial : false, array_x2_set_initial : false, 2, 17 2, 18 array_x2_set_initial : false, array_x2_set_initial : false, 2, 19 2, 20 array_x2_set_initial : false, array_x2_set_initial : false, 2, 21 2, 22 array_x2_set_initial : false, array_x2_set_initial : false, 2, 23 2, 24 array_x2_set_initial : false, array_x2_set_initial : false, 2, 25 2, 26 array_x2_set_initial : false, array_x2_set_initial : false, 2, 27 2, 28 array_x2_set_initial : false, array_x2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_t : t_start, 1 array_t : glob_h, order_diff : 2, term_no : 1, 2 while term_no <= order_diff do (array_x1 : term_no term_no - 1 array_x1_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_x1_init glob_h it array_x1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 2, term_no : 1, while term_no <= order_diff do (array_x2 : term_no term_no - 1 array_x2_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_x2_init glob_h it array_x2_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_x1(), if !array_x1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_x2(), if !array_x2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_x2_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), 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_t <= t_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 3 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 3 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_t : glob_h + array_t , array_t : glob_h, order_diff : 2, ord : 3, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 3, iii array_x1_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 2, iii array_x1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 2, iii array_x1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x1_higher_work : 1, iii array_x1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_x1 : array_x1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_x1_higher : ord, term_no array_x1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 2, ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 3, iii array_x2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 2, iii array_x2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 2, iii array_x2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_x2_higher_work : 1, iii array_x2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_x2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_x2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_x2 : array_x2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_x2_higher : ord, term_no array_x2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff (x1,t,1) = 4.\ 0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), omniout_str(INFO, "diff (x2,t,2)\ = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(t_start, t_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T15:53:47-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest6"), logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"), logitem_float(html_log_file, t_start), logitem_float(html_log_file, t_end), logitem_float(html_log_file, array_t ), logitem_float(html_log_file, glob_h), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest6 diffeq.max"), logitem_str(html_log_file, "\ mtest6 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * dif\ f(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i54) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest6postode.ode#################" "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;" "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "/* # */" "/* # was complicated.ode */" "/* # */" "t_start : 0.5," "t_end : 5.0," "array_x1_init[0 + 1] : exact_soln_x1(t_start)," "array_x1_init[1 + 1] : exact_soln_x1p(t_start)," "array_x2_init[0 + 1] : exact_soln_x2(t_start)," "array_x2_init[1 + 1] : exact_soln_x2p(t_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 10," "/* 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 */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_x1 (t) := (" " " "c1 : 1.0," "c2 : 0.0002," "c3 : 0.0003," "2.0 * c1 + 6.0 * c3 * exp(-t) " ");" "exact_soln_x1p (t) := (" " " "c1 : 1.0," "c2 : 0.0002," "c3 : 0.0003," "- 6.0 * c3 * exp(-t) " ");" "exact_soln_x2 (t) := (" " " "c1 : 1.0," "c2 : 0.0002," "c3 : 0.0003," "c1 + c2 * exp(2.0 * t) + c3 * exp(-t) " ");" "exact_soln_x2p (t) := (" " " "c1 : 1.0," "c2 : 0.0002," "c3 : 0.0003," "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) " ");" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" t[1] = 0.5 " " x1[1] (analytic) = 2.001091755187483 " " x1[1] (numeric) = 2.001091755187483 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007256155636055 " " x2[1] (numeric) = 1.0007256155636055 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " t[1] = 0.5 " " x1[1] (analytic) = 2.001091755187483 " " x1[1] (numeric) = 2.001091755187483 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007256155636055 " " x2[1] (numeric) = 1.0007256155636055 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5001 " " x1[1] (analytic) = 2.0010916460174224 " " x1[1] (numeric) = 2.0010916460065054 " " absolute error = 1.09170450457440890000000000E-11 " " relative error = 5.4555447610164280000000000E-10 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007257061107426 " " x2[1] (numeric) = 1.000725706116202 " " absolute error = 5.459410701291745000000000000E-12 " " relative error = 5.4554516466948770000000000E-10 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5002 " " x1[1] (analytic) = 2.001091536858279 " " x1[1] (numeric) = 2.0010915368145916 " " absolute error = 4.36872760189999100000000000E-11 " " relative error = 2.1831722944363202000000000E-9 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007257966814496 " " x2[1] (numeric) = 1.0007257967032905 " " absolute error = 2.184097347424085500000000000E-11 " " relative error = 2.1825132865235072000000000E-9 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5003 " " x1[1] (analytic) = 2.0010914277100507 " " x1[1] (numeric) = 2.001091427611741 " " absolute error = 9.83098047413477600000000000E-11 " " relative error = 4.912809248993116300000000E-9 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007258872757308 " " x2[1] (numeric) = 1.0007258873248799 " " absolute error = 4.91491292109458300000000000E-11 " " relative error = 4.911347836193602000000000E-9 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5004 " " x1[1] (analytic) = 2.0010913185727364 " " x1[1] (numeric) = 2.0010913183979517 " " absolute error = 1.74784631212787640000000000E-10 " " relative error = 8.734465518417796000000000E-9 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007259778935902 " " x2[1] (numeric) = 1.0007259779809783 " " absolute error = 8.73880967589002500000000000E-11 " " relative error = 8.732470095644149000000000E-9 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5005 " " x1[1] (analytic) = 2.0010912094463356 " " x1[1] (numeric) = 2.0010912091732234 " " absolute error = 2.7311219952252940000000000E-10 " " relative error = 1.36481634736726700000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007260685350323 " " x2[1] (numeric) = 1.0007260686715944 " " absolute error = 1.36562094965597680000000000E-10 " " relative error = 1.364630134653248300000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5005999999999999 " " x1[1] (analytic) = 2.001091100330847 " " x1[1] (numeric) = 2.0010910999375544 " " absolute error = 3.93292509670573050000000000E-10 " " relative error = 1.965390329333575600000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000726159200061 " " x2[1] (numeric) = 1.000726159396737 " " absolute error = 1.96676008812346480000000000E-10 " " relative error = 1.965332943525341000000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5006999999999999 " " x1[1] (analytic) = 2.001090991226269 " " x1[1] (numeric) = 2.001090990690944 " " absolute error = 5.3532511756770870000000000E-10 " " relative error = 2.67516629635947400000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007262498886806 " " x2[1] (numeric) = 1.0007262501564143 " " absolute error = 2.6773361305743040000000000E-10 " " relative error = 2.675393126613923600000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5007999999999999 " " x1[1] (analytic) = 2.0010908821326012 " " x1[1] (numeric) = 2.0010908814333908 " " absolute error = 6.9921046730314630000000000E-10 " " relative error = 3.49414648553085300000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000726340600895 " " x2[1] (numeric) = 1.0007263409506348 " " absolute error = 3.4973979268215770000000000E-10 " " relative error = 3.49485946849518600000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5008999999999999 " " x1[1] (analytic) = 2.0010907730498424 " " x1[1] (numeric) = 2.001090772164894 " " absolute error = 8.8494855887688570000000000E-10 " " relative error = 4.422330914694811400000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000726431336709 " " x2[1] (numeric) = 1.0007264317794073 " " absolute error = 4.4269832244481220000000000E-10 " " relative error = 4.42376965954104900000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5009999999999999 " " x1[1] (analytic) = 2.001090663977991 " " x1[1] (numeric) = 2.0010906628854523 " " absolute error = 1.0925385041105073000000000E-9 " " relative error = 5.459715163223228000000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007265220961263 " " x2[1] (numeric) = 1.0007265226427404 " " absolute error = 5.4661408732670220000000000E-10 " " relative error = 5.46217248426435200000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5010999999999999 " " x1[1] (analytic) = 2.001090554917046 " " x1[1] (numeric) = 2.001090553595065 " " absolute error = 1.3219811911824308000000000E-9 " " relative error = 6.60630368742724300000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000726612879151 " " x2[1] (numeric) = 1.0007266135406425 " " absolute error = 6.6149152821992630000000000E-10 " " relative error = 6.61011228947709400000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5011999999999999 " " x1[1] (analytic) = 2.0010904458670074 " " x1[1] (numeric) = 2.0010904442937303 " " absolute error = 1.573277064181866000000000E-9 " " relative error = 7.86209872437932900000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007267036857879 " " x2[1] (numeric) = 1.000726704473122 " " absolute error = 7.8733419783816320000000000E-10 " " relative error = 7.86762454662520400000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5012999999999999 " " x1[1] (analytic) = 2.0010903368278723 " " x1[1] (numeric) = 2.0010903349814475 " " absolute error = 1.8464247908411835000000000E-9 " " relative error = 9.22709363420411800000000E-8 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.00072679451604 " " x2[1] (numeric) = 1.0007267954401877 " " absolute error = 9.241476472965360000000000E-10 " " relative error = 9.23476469662693100000000E-8 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5013999999999998 " " x1[1] (analytic) = 2.0010902277996414 " " x1[1] (numeric) = 2.0010902256582157 " " absolute error = 2.1414257034280126000000000E-9 " " relative error = 1.07012950924390920000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007268853699127 " " x2[1] (numeric) = 1.0007268864418482 " " absolute error = 1.0719354293087235000000000E-9 " " relative error = 1.07115682108659350000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5014999999999998 " " x1[1] (analytic) = 2.001090118782312 " " x1[1] (numeric) = 2.0010901163240336 " " absolute error = 2.458278469674724000000000E-9 " " relative error = 1.22846964592010320000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007269762474096 " " x2[1] (numeric) = 1.0007269774781118 " " absolute error = 1.2307022068114293000000000E-9 " " relative error = 1.22980816548625040000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5015999999999998 " " x1[1] (analytic) = 2.0010900097758846 " " x1[1] (numeric) = 2.0010900069788997 " " absolute error = 2.796984865938157000000000E-9 " " relative error = 1.3977306629257572000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007270671485349 " " x2[1] (numeric) = 1.0007270685489873 " " absolute error = 1.4004524206967517000000000E-9 " " relative error = 1.39943493752716360000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5016999999999998 " " x1[1] (analytic) = 2.001089900780357 " " x1[1] (numeric) = 2.0010898976228138 " " absolute error = 3.157543115861472000000000E-9 " " relative error = 1.57791167434813280000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007271580732928 " " x2[1] (numeric) = 1.0007271596544831 " " absolute error = 1.5811902898121843000000000E-9 " " relative error = 1.5800413499884040000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5017999999999998 " " x1[1] (analytic) = 2.001089791795728 " " x1[1] (numeric) = 2.001089788255774 " " absolute error = 3.539954107623089000000000E-9 " " relative error = 1.769013125816020000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007272490216874 " " x2[1] (numeric) = 1.000727250794608 " " absolute error = 1.7729204770944307000000000E-9 " " relative error = 1.7716320594124330000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5018999999999998 " " x1[1] (analytic) = 2.001089682821997 " " x1[1] (numeric) = 2.0010896788777797 " " absolute error = 3.944217397133798000000000E-9 " " relative error = 1.97103479718687250000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000727339993723 " " x2[1] (numeric) = 1.00072734196937 " " absolute error = 1.9756469793463793000000000E-9 " " relative error = 1.97421105668879940000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5019999999999998 " " x1[1] (analytic) = 2.001089573859163 " " x1[1] (numeric) = 2.0010895694888298 " " absolute error = 4.370333428482809000000000E-9 " " relative error = 2.1839769121651490000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000727430989404 " " x2[1] (numeric) = 1.0007274331787783 " " absolute error = 2.189374237460128800000000E-9 " " relative error = 2.18778277647043970000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5020999999999998 " " x1[1] (analytic) = 2.001089464907225 " " x1[1] (numeric) = 2.001089460088923 " " absolute error = 4.8183022016701216000000000E-9 " " relative error = 2.40783947253128380000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007275220087344 " " x2[1] (numeric) = 1.0007275244228413 " " absolute error = 2.4141069143723826000000000E-9 " " relative error = 2.41235187529029750000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5021999999999998 " " x1[1] (analytic) = 2.0010893559661813 " " x1[1] (numeric) = 2.001089350678058 " " absolute error = 5.288123272606526000000000E-9 " " relative error = 2.6426222581416280000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007276130517182 " " x2[1] (numeric) = 1.0007276157015674 " " absolute error = 2.649849228930634000000000E-9 " " relative error = 2.64792256591173700000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5022999999999997 " " x1[1] (analytic) = 2.0010892470360315 " " x1[1] (numeric) = 2.001089241256234 " " absolute error = 5.779797529470443000000000E-9 " " relative error = 2.8883257146233480000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.00072770411836 " " x2[1] (numeric) = 1.0007277070149654 " " absolute error = 2.896605399982377000000000E-9 " " relative error = 2.8944990610950290000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5023999999999997 " " x1[1] (analytic) = 2.001089138116774 " " x1[1] (numeric) = 2.00108913182345 " " absolute error = 6.2933240840834510000000000E-9 " " relative error = 3.1449493999083430000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007277952086635 " " x2[1] (numeric) = 1.0007277983630436 " " absolute error = 3.154380090464315000000000E-9 " " relative error = 3.15208601736358230000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5024999999999997 " " x1[1] (analytic) = 2.0010890292084076 " " x1[1] (numeric) = 2.0010890223797047 " " absolute error = 6.828702936445552000000000E-9 " " relative error = 3.41249331577558900000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007278863226332 " " x2[1] (numeric) = 1.0007278897458107 " " absolute error = 3.423177519223941000000000E-9 " " relative error = 3.42068764747134660000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5025999999999997 " " x1[1] (analytic) = 2.0010889203109317 " " x1[1] (numeric) = 2.001088912924997 " " absolute error = 7.3859345306459550000000000E-9 " " relative error = 3.69095768592747950000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000727977460273 " " x2[1] (numeric) = 1.0007279811632754 " " absolute error = 3.703002349197959000000000E-9 " " relative error = 3.7003086079353280000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5026999999999997 " " x1[1] (analytic) = 2.0010888114243452 " " x1[1] (numeric) = 2.001088803459326 " " absolute error = 7.965019310773869000000000E-9 " " relative error = 3.9803427340661040000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007280686215876 " " x2[1] (numeric) = 1.0007280726154462 " " absolute error = 3.993858577189257600000000E-9 " " relative error = 3.99095288962009100000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5027999999999997 " " x1[1] (analytic) = 2.0010887025486466 " " x1[1] (numeric) = 2.00108869398269 " " absolute error = 8.565956388650875000000000E-9 " " relative error = 4.28064801812184370000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007281598065807 " " x2[1] (numeric) = 1.0007281641023316 " " absolute error = 4.29575086613454000000000E-9 " " relative error = 4.29262514903629430000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5028999999999997 " " x1[1] (analytic) = 2.001088593683835 " " x1[1] (numeric) = 2.001088584495089 " " absolute error = 9.188746208366183000000000E-9 " " relative error = 4.59187376179606140000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007282510152569 " " x2[1] (numeric) = 1.0007282556239403 " " absolute error = 4.6086834348813000000000E-9 " " relative error = 4.605329598925290000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5029999999999997 " " x1[1] (analytic) = 2.0010884848299093 " " x1[1] (numeric) = 2.001088474996521 " " absolute error = 9.833388325830583000000000E-9 " " relative error = 4.914019744942169600000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007283422476199 " " x2[1] (numeric) = 1.0007283471802808 " " absolute error = 4.932660946366241000000000E-9 " " relative error = 4.9290708957913226000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5030999999999997 " " x1[1] (analytic) = 2.0010883759868685 " " x1[1] (numeric) = 2.0010883654869853 " " absolute error = 1.049988318513328500000000E-8 " " relative error = 5.2470861912608450000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007284335036741 " " x2[1] (numeric) = 1.0007284387713618 " " absolute error = 5.267687619436856000000000E-9 " " relative error = 5.2638532523694060000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5031999999999996 " " x1[1] (analytic) = 2.001088267154712 " " x1[1] (numeric) = 2.0010882559664807 " " absolute error = 1.118823123036349900000000E-8 " " relative error = 5.5910733244524560000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007285247834241 " " x2[1] (numeric) = 1.0007285303971918 " " absolute error = 5.613767672940639000000000E-9 " " relative error = 5.6096808813914460000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5032999999999996 " " x1[1] (analytic) = 2.0010881583334372 " " x1[1] (numeric) = 2.001088146435006 " " absolute error = 1.189843112925359500000000E-8 " " relative error = 5.945980480521631000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007286160868734 " " x2[1] (numeric) = 1.0007286220577793 " " absolute error = 5.970905991858899000000000E-9 " " relative error = 5.966558661235050000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5033999999999996 " " x1[1] (analytic) = 2.0010880495230445 " " x1[1] (numeric) = 2.0010880368925608 " " absolute error = 1.263048376998199300000000E-8 " " relative error = 6.3118081050918500000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007287074140268 " " x2[1] (numeric) = 1.000728713753133 " " absolute error = 6.339106350949919000000000E-9 " " relative error = 6.334490360859880000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5034999999999996 " " x1[1] (analytic) = 2.0010879407235325 " " x1[1] (numeric) = 2.001087927339143 " " absolute error = 1.338438959663790200000000E-8 " " relative error = 6.6885564218624570000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000728798764888 " " x2[1] (numeric) = 1.0007288054832617 " " absolute error = 6.718373635195007000000000E-9 " " relative error = 6.7134808586371330000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5035999999999996 " " x1[1] (analytic) = 2.0010878319348997 " " x1[1] (numeric) = 2.001087817774752 " " absolute error = 1.416014772104290400000000E-8 " " relative error = 7.0762249887607980000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007288901394618 " " x2[1] (numeric) = 1.0007288972481738 " " absolute error = 7.108712063441658000000000E-9 " " relative error = 7.1035343672860150000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5036999999999996 " " x1[1] (analytic) = 2.001087723157145 " " x1[1] (numeric) = 2.0010877081993867 " " absolute error = 1.495775814319699700000000E-8 " " relative error = 7.4748138075615830000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007289815377518 " " x2[1] (numeric) = 1.0007289890478779 " " absolute error = 7.510126076581969000000000E-9 " " relative error = 7.5046553214054730000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5037999999999996 " " x1[1] (analytic) = 2.0010876143902676 " " x1[1] (numeric) = 2.001087598613046 " " absolute error = 1.577722175127860300000000E-8 " " relative error = 7.884323323887010000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007290729597627 " " x2[1] (numeric) = 1.0007290808823825 " " absolute error = 7.922619893463434000000000E-9 " " relative error = 7.9168479337084150000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5038999999999996 " " x1[1] (analytic) = 2.0010875056342665 " " x1[1] (numeric) = 2.0010874890157284 " " absolute error = 1.66185381011985100000000E-8 " " relative error = 8.304753317587220000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.000729164405498 " " x2[1] (numeric) = 1.0007291727516965 " " absolute error = 8.346198399067362000000000E-9 " " relative error = 8.3401170825530770000000E-7 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" t[1] = 0.5039999999999996 " " x1[1] (analytic) = 2.0010873968891407 " " x1[1] (numeric) = 2.0010873794074335 " " absolute error = 1.74817071929567200000000E-8 " " relative error = 8.7361037904358940000000E-7 "%" h = 1.0000E-4 " " x2[1] (analytic) = 1.0007292558749628 " " x2[1] (numeric) = 1.0007292646558283 " " absolute error = 8.78086559019664000000000E-9 " " relative error = 8.7744667587631480000000E-7 "%" h = 1.0000E-4 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;" "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;" Iterations = 40 "Total Elapsed Time "= 15 Minutes 26 Seconds "Elapsed Time(since restart) "= 15 Minutes 26 Seconds "Expected Time Remaining "= 11 Days 18 Hours 16 Minutes 49 Seconds "Optimized Time Remaining "= 11 Days 18 Hours 9 Minutes 53 Seconds "Time to Timeout " Unknown Percent Done = 9.11111111111010800E-2 "%" (%o54) true (%o54) diffeq.max